Representation as a Bottleneck for Mechanistic Interpretability: The Manifestation Unit Protocol

# Representation as a Bottleneck for Mechanistic Interpretability: The Manifestation Unit Protocol
Source: [https://arxiv.org/html/2607.00089](https://arxiv.org/html/2607.00089)
###### Abstract

Mechanistic interpretability has produced a rich inventory of component\-level analyses that characterise what neural\-network components encode and how they interact\. Their outputs, however, are not easily reusable: selectivity tables, circuit diagrams, and feature lists remain locked in per\-study notebooks—non\-composable, not queryable in natural language, and not directly actionable for downstream audit or intervention\. We study the*representation layer*that sits between these analyses and downstream use as a bottleneck that can be evaluated independently and introduceManifestation Units, a typed tuple protocol\(E,S,R,D,G\)\(E,S,R,D,G\)extended with attention\-head primitives\(T\)\(T\)for transformer architectures organising per\-component statistics into structured fields populated automatically and queried through hybrid retrieval\. Instantiated across generative vision \(β\\beta\-VAE\), discriminative vision \(CNN\), and language \(GPT\-2\), the protocol supports two findings: typed structure substantially outperforms unstructured baselines on retrieval, and CNN filters retrieved by the schema satisfy causal sufficiency and necessity criteria under matched\-budget controls\. The schema absorbs attention\-head primitives without modification, set\-recovers known IOI circuit members under retrieval\-budget\-matched controls, and reveals an irreducible two\-field core \(S\+RS\{\+\}R\) with remaining fields either redundant or actively interfering\. We present this as schema infrastructure for mechanistic interpretability rather than frontier\-scale validation\.111Transformer and CNN demos are available at[https://manifestation\-xai\.github\.io/manifestation\-transformers/](https://manifestation-xai.github.io/manifestation-transformers/) and[https://manifestation\-xai\.github\.io/manifestation\-cnn/](https://manifestation-xai.github.io/manifestation-cnn/)\.

Machine Learning, ICML

## 1Introduction

Mechanistic interpretability has produced a rich inventory of analysis techniques for characterising what neural\-network components encode and how they interact: Network Dissection, probing classifiers, sparse\-autoencoder decompositions, and circuit analyses\(Bauet al\.,[2017](https://arxiv.org/html/2607.00089#bib.bib25); Belinkov,[2022](https://arxiv.org/html/2607.00089#bib.bib28); Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67); Elhageet al\.,[2021](https://arxiv.org/html/2607.00089#bib.bib76); Wanget al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib70); Olssonet al\.,[2022](https://arxiv.org/html/2607.00089#bib.bib75); Conmyet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib73)\)\. Their outputs, however, are not easily reusable\. Selectivity tables, circuit diagrams, and SAE feature lists remain in per\-study notebooks and scripts: not composable, not queryable in natural language, and not directly actionable for downstream audit or intervention\.

A practitioner asks of a trained CNN:*“which filters encode ‘dog’, and what happens if I amplify them?”*The needed statistics—selectivity, activation correlations, ablation effects—already exist, but there is no grounded interface to ask\. Semantic search fails on numerical identifiers\(Liet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib55)\), exact\-match fails on conceptual queries, and free\-form prose loses the typing that separates “which filters detect dog” from “what does filter 81 detect\.”

We study the representation layer that sits between component\-level analyses and downstream use, holding the analyses themselves fixed\. We introduce*Manifestation Units*, a typed tuple protocol\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)that organises per\-component statistics into six fields aligned with distinct query primitives: entity identity \(EE\), semantic associations \(SS\), cross\-component relations \(RR\), quantified dynamics \(DD\), intervention guidance \(GG\), and attention\-head primitives \(TT\)\. Each field is extracted automatically from activations and validation\-set statistics; no human annotation is involved\. A hybrid retriever combines exact\-matching onEEwith dense semantic search over the remaining fields\.

We evaluate two hypotheses about this representation layer\.H1 \(structural accessibility\)\.Natural\-language retrieval over component\-level analyses requires typed*structure*, not just the underlying content—random partitions of the same content fail to match the ESRDGT decomposition\. H2 \(causal mediation, minimality, and optimality\)\.On the CNN, components retrieved through the structured representation are causal mediators of the targeted behaviour in the MIB sense\(Muelleret al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib68)\), established by sufficiency and necessity under matched\-budget controls\. On the GPT\-2 schema, a weaker analogue replaces strict causal mediation: the decomposition admits a*minimal\-optimal*core \(S\+RS\{\+\}R\) confirmed via random\-partition controls, with remaining fields either redundant or actively interfering; see §[5\.4](https://arxiv.org/html/2607.00089#S5.SS4)and App\.[G](https://arxiv.org/html/2607.00089#A7)\.

##### Empirical findings\.

We instantiate the protocol across three architectures spanning generative vision \(β\\beta\-VAE on CelebA\), discriminative vision \(CNN on CIFAR\-10\), and language \(GPT\-2 attention heads\)\. On the GPT\-2 schema, theS\+RS\{\+\}Rsubset reaches oracle recall@30 of0\.4110\.411, beating random partitions of identical content atp<0\.01p<0\.01\(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)D; H1\); per\-field ablation isolatesSS\(p<10−10p<10^\{\-10\}\) andRR\(p=\.019p\{=\}\.019\) as the*minimal\-optimal core*,GGas redundant within that subset, andEE/DDas actively interfering when added to the full schema \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)A–C\), with the two necessary fields retrieving weakly anti\-correlated head rankings \(ρ=−0\.20\\rho\{=\}\{\-\}0\.20; Fig\.[5](https://arxiv.org/html/2607.00089#S5.F5)B\) and thereby complementing one another \(H2, minimality and mechanism\)\. On the CNN, retrieved filters flip predictions in76\.3%76\.3\\%of trials under amplification \(vs\.6\.7%6\.7\\%random matched\-budget\) and zeroing them drops natural target\-class accuracy by38\.338\.3pp \(vs\.3\.63\.6pp\); a four\-way decomposition attributes\+17\.4\+17\.4pp of sufficiency to the typed primary\-class rule \(H2, mediation\)\. On theβ\\beta\-VAE and CNN, structured units reach Precision@5 of89\.6%89\.6\\%and96\.8%96\.8\\%respectively, versus18\.0%18\.0\\%and20\.4%20\.4\\%for a BM25\-hybrid baseline over the same per\-component statistics \(H1, original evaluation\)\. On GPT\-2, retrieved heads beat matched\-budget random retrieval by2\.02\.0–4\.5×4\.5\\timesacross four behaviours and recover5/75/7of the known IOI L7–9 name\-mover heads atk=30k\{=\}30\.

##### Contributions\.

1. 1\.Manifestation Units \(ESRDG\[T\]\), a typed tuple protocol for organising component\-level analyses, with automatic extraction, deterministic template grounding, and hybrid retrieval\. The base schema is\(E,S,R,D,G\)\(E,S,R,D,G\); theTTfield extends it for transformer architectures\.
2. 2\.Matched\-budget protocols establishing structural accessibility \(H1, random\-partition controls\) and the H2 cluster of causal mediation, minimality, and optimality \(CNN sufficiency/necessity; GPT\-2 per\-field ablation\)—identifying the*minimal\-optimal*core \(S\+RS\{\+\}R\) and characterising redundancy \(GGwithin the core\) and interference \(EE,DDon the full schema\)\.
3. 3\.A GPT\-2 attention\-head instantiation that supplies the deepest structural evidence—random\-partition H1 confirmation, theS\+RS\{\+\}Rminimal\-optimal core, and complementarySS/RRrankings \(ρ=−0\.20\\rho\{=\}\{\-\}0\.20\)—and recovers known IOI circuit members via set\-overlap retrieval, with a principledSS\-primitive selection procedure validated by reference\-set recovery\.

## 2Related Work

##### Mechanistic interpretability and faithfulness\.

The MI toolkit characterises neural\-component behaviour through complementary lenses: circuit analyses describe how components compose into algorithms\(Elhageet al\.,[2021](https://arxiv.org/html/2607.00089#bib.bib76); Wanget al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib70); Olssonet al\.,[2022](https://arxiv.org/html/2607.00089#bib.bib75); Elhageet al\.,[2022](https://arxiv.org/html/2607.00089#bib.bib71)\); activation and path patching trace causal pathways through transformers\(Menget al\.,[2022](https://arxiv.org/html/2607.00089#bib.bib72); Conmyet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib73); Goldowsky\-Dillet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib77)\); sparse autoencoders decompose polysemantic activations into monosemantic features at scale\(Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67); Cunninghamet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib74)\); Network Dissection and probing classifiers characterise what individual components encode\(Bauet al\.,[2017](https://arxiv.org/html/2607.00089#bib.bib25); Belinkov,[2022](https://arxiv.org/html/2607.00089#bib.bib28)\)\. The MIB benchmark\(Muelleret al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib68)\)formalises the two faithfulness notions our evaluation adopts \(Sec\.[5](https://arxiv.org/html/2607.00089#S5)\):*response faithfulness*—does the output reflect the evidence?—and*causal faithfulness*—do the identified components causally mediate the behaviour, established by sufficiency and necessity under matched intervention?

##### Representation and retrieval over MI outputs\.

Given any of these analyses—SAE feature activations, circuit identifications, attribution\-graph neighbourhoods, probing scores, correlational selectivity—how should the outputs be packaged so they can be queried, grounded, composed, and acted on? Existing community tooling targets*programmatic access*\(TransformerLens, nnsight\) and*visualisation*\(Neuronpedia, Docent\), leaving the typed\-representation layer for natural\-language querying largely unaddressed\.Orgad and others \([2024](https://arxiv.org/html/2607.00089#bib.bib69)\)document that interpretability findings are frequently not acted on downstream; representation is part of the gap\. Standard semantic search fails on neural\-component queries because embedding models cannot reliably represent arbitrary numerical identifiers like “dimension 63”\(Liet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib55)\), and exact match alone cannot handle conceptual queries\. Structured and entity\-aware retrieval\(Edge and others,[2024](https://arxiv.org/html/2607.00089#bib.bib56); Févryet al\.,[2020](https://arxiv.org/html/2607.00089#bib.bib36); Yasunagaet al\.,[2022](https://arxiv.org/html/2607.00089#bib.bib37)\)shows that typed representations outperform unstructured prose for knowledge\-intensive tasks, but targets general\-domain knowledge rather than neural internals indexed by arbitrary identifiers\. Manifestation Units are designed to compose with the MI toolkit above:SScan store SAE feature labels,RRcan encode head–head or attribution\-graph neighbourhoods, andGGcan encode activation\-patching or steering primitives\. The Transformer instantiation \(Sec\.[6](https://arxiv.org/html/2607.00089#S6.SS0.SSS0.Px2)\) demonstrates this composition on attention\-head primitives drawn fromElhageet al\.\([2021](https://arxiv.org/html/2607.00089#bib.bib76)\); Olssonet al\.\([2022](https://arxiv.org/html/2607.00089#bib.bib75)\); Wanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\); Goldowsky\-Dillet al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib77)\); Heimersheim and Nanda \([2024](https://arxiv.org/html/2607.00089#bib.bib78)\)\.

## 3The MANIFESTATION Framework

![Refer to caption](https://arxiv.org/html/2607.00089v1/x1.png)Figure 1:Overview of MANIFESTATION\. The pipeline extracts Manifestation Units\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)encoding entity identity \(EE\), semantic associations \(SS\), cross\-component relationships \(RR\), quantified dynamics \(DD\), manipulation guidance \(GG\), and \(for transformers\) attention\-head primitives \(TT\)\. Hybrid retrieval combines exact matching onEEwith semantic search over the remaining fields; the SLM generates responses grounded in retrieved statistics fromDD\.MANIFESTATION \(Fig\.[1](https://arxiv.org/html/2607.00089#S3.F1)\) populates Manifestation Units automatically from model activations and exposes them through a hybrid retriever for natural\-language access\.

### 3\.1Manifestation Units

Letℐ=\{1,…,n\}\\mathcal\{I\}=\\\{1,\\dots,n\\\}denote the set of neural network components to be analysed \(latent dimensions in a VAE, filters in a CNN, attention heads in GPT\-2\)\. Each componentk∈ℐk\\in\\mathcal\{I\}is represented as a structured tuple:

Mk=\(Ek,Sk,Rk,Dk,Gk,Tk\)\.M\_\{k\}=\(E\_\{k\},S\_\{k\},R\_\{k\},D\_\{k\},G\_\{k\},T\_\{k\}\)\.\(1\)The decomposition is functional: each field corresponds to a recurring class of user query—EEfor entity queries \(“what does dimension 63 do?”\),SSfor concept queries \(“which units encode smiling?”\),RRfor relational queries \(“what correlates with dimension 47?”\),DDfor grounded numeric citation,GGfor intervention queries, andTTfor attention\-head primitives in transformer architectures\. The six fields group queries by the retrieval primitive each requires \(typed identifier matching, ranked semantic similarity, neighbourhood walks, scalar lookup, parameterised intervention, attention\-pattern features\)\. The decomposition is empirically minimal\-optimal \(Sec\.[5\.3](https://arxiv.org/html/2607.00089#S5.SS3)\):S\+RS\{\+\}Ris the highest\-recall combination across query types with both fields necessary within that subset;GGis redundant, andEE/DDactively interfere on the full schema\.

##### Entity \(E\)\.

EkE\_\{k\}is a unique, human\-readable identifier \(e\.g\., “Dimension 63” or “Filter Conv2\.15”\) that enables entity\-aware exact matching\. When a query contains an explicit component reference, pattern extraction onEEguarantees retrieval of the correct unit—something embedding\-only semantic search cannot reliably achieve for arbitrary identifiers\.

##### Semantics \(S\)\.

SkS\_\{k\}stores concept associations with quantified strengths over a predefined concept vocabulary𝒞\\mathcal\{C\}\(facial attributes for CelebA, class labels for CIFAR\-10, functional features for GPT\-2\)\. Templates expose only the top\-mmassociations, ranked by magnitude:

S~k=\{\(cj,sk​j\)\}j=1m​ranked by​\|sk​j\|\.\\tilde\{S\}\_\{k\}=\\\{\(c\_\{j\},s\_\{kj\}\)\\\}\_\{j=1\}^\{m\}\\ \\text\{ranked by\}\\ \|s\_\{kj\}\|\.\(2\)The primary concept identity is the top\-1 concept among the exposed set:

ck∗=arg⁡maxj∈\[m\]⁡\|sk​j\|,sk∗=sk,ck∗\.c\_\{k\}^\{\*\}=\\arg\\max\_\{j\\in\[m\]\}\|s\_\{kj\}\|,\\quad s\_\{k\}^\{\*\}=s\_\{k,c\_\{k\}^\{\*\}\}\.\(3\)The signed scoresk∗s\_\{k\}^\{\*\}is retained for faithful generation; the absolute value is used only for ranking\.SkS\_\{k\}is populated by Pearson correlation for VAE dimensions, entropy\-based class selectivity for CNN filters, and attention\-pattern primitives for GPT\-2 heads \(App\.[B](https://arxiv.org/html/2607.00089#A2)\)\.

##### Relationships \(R\)\.

RkR\_\{k\}encodes cross\-component dependencies derived from model activations\. Letρk​i\\rho\_\{ki\}denote a dependency score between componentskkandii, and lettk​i∈\{synergistic,antagonistic,independent\}t\_\{ki\}\\in\\\{\\text\{synergistic\},\\text\{antagonistic\},\\text\{independent\}\\\}indicate relationship polarity\. Templates expose a top\-rrneighbourhood\. We use these labels to describe statistical co\-activation, not causal mechanisms\. Thresholds and tie\-breaking detailed in App\.[B](https://arxiv.org/html/2607.00089#A2)\.

##### Dynamics \(D\)\.

DkD\_\{k\}is a typed dictionary of quantitative statistics \(variance contributions, selectivity summaries, cluster/family memberships, cross\-layer dependency scores\)\. These values are rendered into the LLM’s context by deterministic templates \(Sec\.[3\.2](https://arxiv.org/html/2607.00089#S3.SS2)\), and a post\-hoc check verifies cited values against stored statistics\.

##### Guidance \(G\)\.

GkG\_\{k\}stores manipulation parameters \(step sizes for VAE latent edits in units ofσ\\sigma, amplification factors for CNN filter activations\)\. These parameters are pre\-computed and retrieved, grounding interventions in measured mappings rather than model priors\.

##### Attention\-head primitives \(T\)\.

For transformer architectures,TkT\_\{k\}stores attention\-pattern features—induction scores, copying scores, QK and OV circuit norms, and previous/first\-token attention ratios—computed from the head’s attention matrices over a reference corpus\. Population details in Sec\.[5\.4](https://arxiv.org/html/2607.00089#S5.SS4)and App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\.

##### Template\-based grounding\.

Deterministic templates substitute field values directly, exposing top\-mm/top\-rrsubsets; every rendered statement traces to a stored field value \(App\.[C\.1](https://arxiv.org/html/2607.00089#A3.SS1)\)\.

### 3\.2Hybrid Retrieval and Generation

The retriever combines exact\-matching onEE\(for entity\-bearing queries\) with dense semantic search over templatedSS/RR/GG/TTdocuments \(for conceptual queries\); hits are aggregated at the unit level before generation \(App\.[C](https://arxiv.org/html/2607.00089#A3)\)\.

##### Grounded generation\.

Generation is next\-token prediction; faithfulness is enforced upstream \(deterministic retrieval and templating\) and verified downstream \(post\-hoc Factual Accuracy check,\>\>94% across 96 configs; App\.[M](https://arxiv.org/html/2607.00089#A13)\)\.

### 3\.3Natural Language Control as a Causal Probe

Beyond querying, the framework supports natural\-language commands that translate into targeted interventions\. Given a command like “make the face smile,” the system identifies the target concept, retrieves components with high association strength, and applies modification parameters drawn fromGG\. Retrieval here uses a typed*primary\-class retrieval rule*: for target conceptcc, the system selects only components whose top\-1 entry inS~\\tilde\{S\}iscc, not those whereccmerely appears in the top\-mm\. This rule is the central element of our H2 protocol \(Sec\.[5\.2](https://arxiv.org/html/2607.00089#S5.SS2)\); it is only definable becauseSSis a typed ranking, and it converts a correlational ranking into a precise intervention target\.

We use this capability as a causal probe in the MIB sense\(Muelleret al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib68)\): causal mediation requires both*sufficiency*\(intervening on the components reproduces the targeted behavior\) and*necessity*\(ablating them disrupts the behavior under natural inputs\)\. We test both directions on the CNN under matched\-budget comparisons against random selection \(Sec\.[5\.2](https://arxiv.org/html/2607.00089#S5.SS2)\)\.

## 4Applications

We instantiate the protocol across three architectures: aβ\\beta\-VAE on CelebA \(512512latent dimensions,4040binary attributes\), a CNN on CIFAR\-10 \(224224filters,1010classes\), and GPT\-2 small \(144144attention heads\)\. This triple tests whether\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)survives across generative vs\. discriminative vs\. language models\. Measurement: Pearson correlation \(VAE\), entropy\-based selectivity \(CNN\), attention\-pattern primitives \(GPT\-2: induction/copying scores, QK/OV norms, position ratios\), with pairwise activation correlations forRRthroughout\. Manipulation:zd←zd\+sign​\(sd,c\)⋅2​σdz\_\{d\}\\leftarrow z\_\{d\}\+\\mathrm\{sign\}\(s\_\{d,c\}\)\\cdot 2\\sigma\_\{d\}for VAE,af′=α⋅afa^\{\\prime\}\_\{f\}=\\alpha\\cdot a\_\{f\}for CNN, zero/mean/path\-patching ablation for GPT\-2 \(no amplitude semantics\)\. Concept vocabularies: CelebA attributes, CIFAR\-10 classes, MI\-derived functional features \(Sec\.[6](https://arxiv.org/html/2607.00089#S6.SS0.SSS0.Px2)\)\. Full instantiation matrix in App\.[F](https://arxiv.org/html/2607.00089#A6), Table[26](https://arxiv.org/html/2607.00089#A6.T26)\.

## 5Evaluation

We organise the evaluation around the two falsifiable hypotheses of Sec\.[1](https://arxiv.org/html/2607.00089#S1), with a brief response\-faithfulness check\.

##### Setup\.

Architectures and instantiation details are in Sec\.[4](https://arxiv.org/html/2607.00089#S4)\. Qwen3\-8B is the conversational interface; hybrid retrieval combines exact match onEEwith semantic search overS/R/G/TS/R/G/Ttemplates\. Metrics span retrieval \(Precision/Recall/NDCG\), generation \(BLEU, ROUGE\), semantic similarity \(BERTScore\), and faithfulness \(Factual Accuracy = cited statistics matching stored MU fields; Attribution = claims supported by retrieved context\); definitions in App\.[J](https://arxiv.org/html/2607.00089#A10)\. VAE/CNN automatic metrics use5050single\-turn queries per architecture \(App\.[F\.3](https://arxiv.org/html/2607.00089#A6.SS3)\); GPT\-2 schema\-level evaluation uses88query paraphrases per IOI\-style behaviour \(App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\)\. Gold sets are pre\-extracted offline and held fixed across all methods\.

### 5\.1H1 — structure beats content

H1 predicts that natural\-language retrieval over component\-level analyses requires typed structure, not just the underlying content\. We test this in two complementary ways: against standard sparse/dense baselines on VAE and CNN with the statistics held fixed \(Table[1](https://arxiv.org/html/2607.00089#S5.T1)\), and against random partitions of the same per\-component text on the GPT\-2 schema \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)D\)\.

##### Baseline comparison \(VAE/CNN\)\.

The structured system reaches Precision@5 of89\.6%89\.6\\%/96\.8%96\.8\\%\(VAE/CNN\); a BM25\-hybrid baseline with full access to the same per\-component statistics reaches only18\.0%18\.0\\%/20\.4%20\.4\\%, and prose serialisation collapses to3\.7%3\.7\\%/2\.8%2\.8\\%\(Table[1](https://arxiv.org/html/2607.00089#S5.T1),[42](https://arxiv.org/html/2607.00089#A14.T42)\)\. Neither exact\-match nor semantic\-search alone suffices; the typedEEvsS/RS/Rseparation is what the hybrid retriever exploits\.

Table 1:Precision and Factual Accuracy atk=5k\{=\}5, macro\-averaged over a2020/1515/1010/55entity/concept/relational/manipulation mix\. The structured system reaches 89\.6%/96\.8%; BM25 hybrid over the same per\-component statistics reaches 18\.0%/20\.4%, identifying the central H1 gap\. Prose serialisation collapses to 3\.7%/2\.8%, controlling for serialisation choice\. Full table \(14 configurations\): App\.[N](https://arxiv.org/html/2607.00089#A14)\.
##### Structure\-versus\-content isolation \(GPT\-2\)\.

A stronger test isolates structure from content\. On the GPT\-2 schema, theS\+RS\{\+\}Rsubset reaches oracle recall@30 of0\.4110\.411, while random partitions of the*same per\-component text*into two groups—identical content, structured arbitrarily—reach mean oracle recall of0\.200\.20–0\.220\.22\(p<0\.01p<0\.01across three baseline configurations; Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)D\)\. Embedding model and content are held fixed; only the field\-level structure varies\. Together with the BM25 baselines \(VAE/CNN Precision@5: 18\.0%/20\.4%; GPT\-2 oracle recall@30: 0\.143, below random at 0\.304; Table[42](https://arxiv.org/html/2607.00089#A14.T42), App\. N\),

### 5\.2H2 — causal mediation on the CNN

H2 concerns the stricter MIB notion: not whether the response reflects retrieved evidence, but whether retrieved components*causally mediate*the behaviour, established by both*sufficiency*\(intervening on the components reproduces the targeted behaviour\) and*necessity*\(ablating them disrupts behaviour under natural inputs\)\. We test both directions on the CNN under matched\-budget comparisons against random selection\.

Table 2:CNN sufficiency and necessity vs\. matched\-budget random selection\. Sufficiency:k=8k\{=\}8filters,α∈\{30,50,70\}\\alpha\\in\\\{30,50,70\\\},n=270n\{=\}270trials, success==target flip withΔ​ptarget\>0\.1\\Delta p\_\{\\text\{target\}\}\>0\.1\. Necessity:k=8k\{=\}8,1,0001\{,\}000correctly classified images per class, ablation==zero post\-ReLU\. Random matched\-budget uses33seeds\.![Refer to caption](https://arxiv.org/html/2607.00089v1/icml2026/fig/fig_necessity_v2.png)Figure 2:Necessity\-direction validation\. \(a\) Primary filters are necessary \(larger drop\); \(b\) necessity increases withkk\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x2.png)Figure 3:Per\-pair success rate, averaged across the full amplification sweepα∈\{10,…,100\}\\alpha\\in\\\{10,\\dots,100\\\}\(vs\. Table[2](https://arxiv.org/html/2607.00089#S5.T2)’s protocol\{30,50,70\}\\\{30,50,70\\\}for the H2 headline\)\. Failures cluster within\-category, tracing filter\-selectivity overlap\. Full breakdown: App\.[E](https://arxiv.org/html/2607.00089#A5)\.##### Sufficiency: targeted amplification flips predictions\.

For each of9090source\-to\-target class pairs, we retrieve target\-associated filters via RAG over the MUs, amplify their post\-ReLU activations byα\\alpha, and requireΔ​ptarget\>0\.1\\Delta p\_\{\\text\{target\}\}\>0\.1with the prediction switching to the target\. Atk=8k\{=\}8filters,α∈\{30,50,70\}\\alpha\\\!\\in\\\!\\\{30,50,70\\\},n=270n\{=\}270trials, RAG\-retrieved filters flip the prediction in76\.3%of trials, against6\.7%for matched\-budget random filters under identical conditions \(\+69\.6\+69\.6pp; Table[2](https://arxiv.org/html/2607.00089#S5.T2), row A vs R\)\.

##### Decomposing sufficiency\.

The matched\-budget gap decomposes \(Table[2](https://arxiv.org/html/2607.00089#S5.T2)\): the typed primary\-class rule contributes\+17\.4\+17\.4pp on top of selectivity\-only ranking \(A vs C3\) operating over a faithfully\-storedSS\(C3=\\,\{=\}\\,C4 at58\.9%58\.9\\%\); the\+52\.2\+52\.2pp gap from random to selectivity\-only confirms amplification does not mechanically dominate this CNN\.

##### Necessity: ablating retrieved filters disrupts natural classification\.

For each classcc, we identify100100natural CIFAR\-10 test images that the unmodified model classifies correctly ascc, then zero the post\-ReLU activations of the top\-k=8k\{=\}8primary\-class filters retrieved by Eq\.[3](https://arxiv.org/html/2607.00089#S3.E3)and re\-evaluate\. Across all1010classes, retrieved\-filter ablation drops top\-11accuracy from100%100\\%to61\.7%61\.7\\%\(a38\.338\.3pp drop\), while random\-filter ablation drops accuracy by only3\.63\.6pp \(Table[2](https://arxiv.org/html/2607.00089#S5.T2), B vs Rnec\{\}\_\{\\text\{nec\}\}\)\. The34\.734\.7pp aggregate gap holds for9/109/10classes \(Fig\.[2](https://arxiv.org/html/2607.00089#S5.F2)a\)\. The remaining class, deer, exhibits a4\.74\.7pp gap; deer’s stored selectivity is distributed across a smaller pool of2424selective filters \(vs\.2929–5757for other classes\), and the MU correctly surfaces this as a flatter top\-mmdistribution inSS\. The necessity gap scales monotonically withkk\(\+11\.2\+11\.2pp atk=3k\{=\}3,\+25\.3\+25\.3pp atk=5k\{=\}5,\+34\.7\+34\.7pp atk=8k\{=\}8; Fig\.[2](https://arxiv.org/html/2607.00089#S5.F2)b\), indicating distributed mediation by populations of filters rather than single units, with the typed primary\-class rule ordering the population by mediation strength\.

##### Joint reading\.

Sufficiency \(\+69\.6\+69\.6pp\) and necessity \(\+34\.7\+34\.7pp\) jointly establish MIB causal faithfulness for the CNN; the per\-pair heatmap \(Fig\.[3](https://arxiv.org/html/2607.00089#S5.F3)\) shows failures cluster within\-category, tracing filter\-selectivity overlap\. Per\-α\\alphamarginalisation and the extended\-search result \(88/9088/90pairs after post\-hocα\\alphatuning over resistant pairs; the primary H2 figure remains76\.3%76\.3\\%\) in App\.[E\.3](https://arxiv.org/html/2607.00089#A5.SS3)\.

### 5\.3Decomposition mechanics on the GPT\-2 schema

![Refer to caption](https://arxiv.org/html/2607.00089v1/icml2026/fig/fig1_ablation_validation.png)Figure 4:Per\-field ablation on the GPT\-2 ESRDGT schema identifiesS\+RS\{\+\}Ras the minimal\-optimal core\.\(A\)Leave\-one\-out on the full six\-field schema:EE\(p<10−8p<10^\{\-8\}\) andDD\(p=\.028p\{=\}\.028\) actively interfere when present;SS\(p=\.028p\{=\}\.028\) is necessary;RR,GG,TTnon\-significant individually\.\(B\)Progressive field addition: recall@30 reaches0\.3750\.375atG\+S\+RG\{\+\}S\{\+\}R, drops in the interference zone whenDD,EE, orTTare added to that subset, and is highest atS\+RS\{\+\}Ralone \(0\.4110\.411\)\.\(C\)Leave\-one\-out within theG\+S\+RG\{\+\}S\{\+\}Rsubset:SS\(p<10−10p<10^\{\-10\}\) andRR\(p=\.019p\{=\}\.019\) are both necessary;GGis redundant within the subset\.\(D\)S\+RS\{\+\}Rversus random partitions of the same per\-component text:S\+RS\{\+\}Rrecall@30=0\.411=0\.411beats three random\-partition baselines \(μ∈\[0\.20,0\.22\]\\mu\\in\[0\.20,0\.22\]\) atp<0\.01p<0\.01across1010seeds, isolating the structural contribution from content\.![Refer to caption](https://arxiv.org/html/2607.00089v1/icml2026/fig/fig2_redundancy_heatmaps.png)Figure 5:Field redundancy analysis on the GPT\-2 ESRDGT schema\.\(A\)Pairwise embedding cosine similarity\.\(B\)Head\-ranking Spearman correlation:SSandRRshow the strongest negative correlation \(ρ=−0\.20\\rho=\-0\.20\), indicating weakly anti\-correlated head rankings\.\(C\)Top\-kkhead\-set Jaccard overlap\. No field pair exceeds redundancy thresholds, confirming functional distinctness\. TheS↔RS\\leftrightarrow Rweak anti\-correlation explains their complementarity, as they retrieve largely\-disjoint head sets and jointly cover a larger functional space\.WithTTpopulated automatically from attention\-pattern features \(induction/copying scores, QK and OV circuit norms, attention\-position ratios\), we use the GPT\-2 instantiation to ask whether the six\-field decomposition itself has identifiable internal structure\. Three findings emerge\.

##### Minimal\-optimal core\.

Leave\-one\-out ablation on the full six\-field schema \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)A\) identifiesSSas necessary \(p=\.028p\{=\}\.028\);EEis removed without loss and—when re\-added on top of theG\+S\+RG\{\+\}S\{\+\}Rsubset—actively interferes with retrieval \(p<10−8p<10^\{\-8\}\), as doesDD\(p=\.028p\{=\}\.028\)\. Within theG\+S\+RG\{\+\}S\{\+\}Rsubset \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)C\),SS\(p<10−10p<10^\{\-10\}\) andRR\(p=\.019p\{=\}\.019\) are both necessary whileGGis redundant \(p=\.102p\{=\}\.102\)\. The progressive curve \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)B\) peaks atG\+S\+RG\{\+\}S\{\+\}R\(recall@30=0\.375=0\.375\) and degrades whenDD,EE, orTTare added to that subset, before rebounding atS\+RS\{\+\}Ralone to0\.4110\.411—while the*full*ESRDGT schema reaches only0\.1960\.196, confirming that interference fromEE,DD,TTis substantial \(App\.[N](https://arxiv.org/html/2607.00089#A14)\)\. The*minimal\-optimal core*of the decomposition is thereforeS\+RS\{\+\}R\.

##### Non\-redundancy and weak anti\-correlation\.

Three measures of pairwise field overlap—description embedding similarity, head\-ranking correlation, and top\-kkJaccard—all agree that no field pair exceeds the redundancy threshold \(Fig\.[5](https://arxiv.org/html/2607.00089#S5.F5)A,C\)\. The two necessary fields,SSandRR, retrieve*weakly anti\-correlated*head rankings: their head\-ranking correlation isρ=−0\.20\\rho\{=\}\{\-\}0\.20\(Fig\.[5](https://arxiv.org/html/2607.00089#S5.F5)B\), the strongest negative correlation in the matrix\. This explains why their union is maximally informative:SSandRRpull in different directions, so combining them spans more of the relevant space than either alone\. Per\-field singleton retrieval and the field–function dissociation between set\-recall and first\-rank MRR are in App\.[I](https://arxiv.org/html/2607.00089#A9); field\-level oracle discriminability is in App\.[H](https://arxiv.org/html/2607.00089#A8)\.

### 5\.4Schema transfer to attention heads

The protocol absorbs attention\-head primitives without modification: theTTfield encodes induction scores, copying scores, QK/OV circuit norms, and attention\-position ratios extracted from each head’s attention matrices over a reference corpus \(App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\)\. Across four IOI\-style behaviours, retrieved heads beat matched\-budget random retrieval by2\.02\.0–4\.5×4\.5\\timeson oracle recall metrics\. Atk=30k\{=\}30,S\+RS\{\+\}Rretrieval recovers5/75/7of the canonical IOI L7–9 name\-mover heads ofWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)—an oracle recall@30 of0\.4110\.411222Averaged over88query paraphrases\. This is set membership with the canonical oracle, not causal restoration; see the path\-patching scope paragraph below\.and a1\.75×1\.75\\timeslift over random matched\-budget retrieval\. The required pivot from surface features \(POS tags, syntactic dependencies\) to functional features \(induction, copying, IOI primitives\) when populatingSSdefines a principledSS\-primitive selection procedure: the schema is invariant across architectures whileSS\-content is chosen functionally, validated by reference\-set recovery \(3/16→13/163/16\\to 13/16heads; App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\)\.

##### Path\-patching scope\.

Framework\-retrieved heads atk=30k\{=\}30collectively restore a non\-trivial fraction of the IOI logit\-difference \(frac\_restored=0\.41\\,\{=\}\\,0\.41vs random0\.230\.23\), consistent with the distributed nature of GPT\-2’s IOI circuit \(the77oracle heads themselves restore only0\.120\.12\)\. Per\-field causal enrichment under path\-patching is not significant after Bonferroni correction \(App\.[G](https://arxiv.org/html/2607.00089#A7)\); the framework’s contribution on GPT\-2 is at the retrieval layer, not strict per\-head causal mediation\.

##### Response\-faithfulness sanity check\.

A grounding\-pipeline check \(n=15n\{=\}15raters,612612ratings, scores\>4\.0/5\.0\>4\.0/5\.0; Qwen3\-8B, Claude\-Opus, and GPT\-5\.1 all reach\>\>94% factual accuracy on identical retrieved context\) is in App\.[K](https://arxiv.org/html/2607.00089#A11)\.

## 6Discussion and Limitations

##### Two kinds of faithfulness\.

We separate*response faithfulness*\(does the generated response reflect retrieved evidence?\) from*causal faithfulness*\(Muelleret al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib68)\)\(do identified components causally mediate the behaviour under both directions of intervention?\)\. Sec\.[5\.2](https://arxiv.org/html/2607.00089#S5.SS2)targets the latter and is the stronger claim; Sec\.[5\.4](https://arxiv.org/html/2607.00089#S5.SS4)’s response\-faithfulness check addresses the former\. The four\-way decomposition \(Table[2](https://arxiv.org/html/2607.00089#S5.T2)\) localises the framework’s H2 contribution to the typed primary\-class rule \(Eq\.[3](https://arxiv.org/html/2607.00089#S3.E3)\) operating over a faithfully\-storedSS; it does not trace causal paths, identify confounding interactions, or rule out multiple\-mediator effects\. Integrating MU\-level evidence with circuit and SAE analyses\(Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67); Conmyet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib73)\)—so retrieved units carry attribution\-graph neighbourhoods or sparse\-feature labels inSS/RR—tightens the claim without changing the interface\.

##### Transformer instantiation \(GPT\-2\)\.

The GPT\-2 instantiation does three kinds of work simultaneously: structural\-isolation test for H1 via random\-partition controls \(Sec\.[5\.1](https://arxiv.org/html/2607.00089#S5.SS1)\), per\-field minimality and optimality withS\+RS\{\+\}Ras the irreducible core \(Sec\.[5\.3](https://arxiv.org/html/2607.00089#S5.SS3)\), and schema transfer to attention heads beating matched\-budget random by2\.02\.0–4\.5×4\.5\\timesacross four behaviours \(Sec\.[5\.4](https://arxiv.org/html/2607.00089#S5.SS4), App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\)\. Each depends on automatic population ofTTwith attention\-pattern primitives—no architecture\-specific retrieval logic\. Two qualifications: the concept vocabulary populatingSShad to pivot from surface linguistic features \(3/163/16reference heads recovered\) to MI\-derived functional features \(attention\-to\-induction\-target, IO\-position, previous\-token, self;13/1613/16recovered\), validating a principledSS\-primitive selection procedure for transformers; and on the strict path\-patching causal\-mediation test, framework retrieval atk=30k\{=\}30collectively restores0\.4090\.409of the IOI logit\-difference but does not show per\-head causal enrichment \(App\.[G](https://arxiv.org/html/2607.00089#A7)\)\. The framework demonstrates set\-overlap retrieval with the canonical IOI circuit, not strict per\-head causal mediation; the latter would require retrieval criteria optimised directly for path\-patching scores, which the currentTTfield does not provide\. All five GPT\-2 experiments were pre\-registered with SHA\-256\-hashed predictions before outcomes were computed\.

##### Limitations\.

Scale\.No frontier\-scale Transformer validation; SAE\-basedSS\(Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67)\)is the natural next step\.Polysemanticity\.Top\-conceptSSis inadequate for polysemantic units; SAE primitives would address this\.Concept vocabulary\.Resolution is conditional on𝒞\\mathcal\{C\}matched to the architecture; label\-free domains need auto\-labelling\(Oikarinen and Weng,[2023](https://arxiv.org/html/2607.00089#bib.bib27)\)or SAE features asSSreplacements\.Per\-head causal mediation on GPT\-2\.Set\-overlap with the canonical IOI circuit, not strict per\-head path\-patching enrichment \(App\.[G](https://arxiv.org/html/2607.00089#A7)\); the IOI circuit is distributed \(the77\-head oracle itself restores only11\.7%11\.7\\%of the logit\-diff\) andTTencodes attention\-pattern features correlated with but not equal to path\-patching scores\.VAE causal\.Manipulation is qualitative; quantitative metrics for generative edits are future work\.Queries\.Programmatic, not user\-elicited\(Orgad and others,[2024](https://arxiv.org/html/2607.00089#bib.bib69)\)\.

## 7Conclusion

We proposed Manifestation Units, a typed schema\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)that organises component\-level interpretability analyses into structured, automatically populated tuples exposed through hybrid retrieval — creating a composable representation layer between per\-component statistics and downstream use\. Two hypotheses were confirmed under matched\-budget controls\.H1: typed structure drives retrieval independently of content — structured retrieval reaches Precision@5 of89\.6%89\.6\\%/96\.8%96\.8\\%\(VAE/CNN\) versus18\.0%18\.0\\%/20\.4%20\.4\\%for BM25 over identical statistics, andS\+RS\{\+\}Rbeats random partitions of the same GPT\-2 text atp<0\.01p\{<\}0\.01\.H2: on the CNN, retrieved components causally mediate the targeted behaviour \(76\.3%76\.3\\%sufficiency under amplification,−38\.3\-38\.3pp accuracy under ablation, both well above matched\-random\); on the GPT\-2 schema the analogue is the minimal\-optimal core \(S\+RS\{\+\}R\), with per\-head causal enrichment under path\-patching not significant after Bonferroni correction \(App\.[G](https://arxiv.org/html/2607.00089#A7)\)\. On the GPT\-2 schema, ablation reveals thatSSandRRform an irreducible core,GGis redundant within it, andEE/DDactively interfere when added; the schema further recovers known IOI circuit members and beats matched\-budget random retrieval by2\.02\.0–4\.5×4\.5\{\\times\}across four behaviours\. The immediate next steps are SAE\-featureSSfor polysemantic components, frontier\-scale validation, and label\-free concept vocabularies, none of which require changing the\(E,S,R,D,G\)\(E,S,R,D,G\)interface or its extension\(T\)\(T\)\.

## Impact Statement

Manifestation Units are interpretability*infrastructure*, not new analyses or new capabilities: a typed representation layer over outputs that already exist in the field’s toolkit\. We expect three groups to benefit\.*Interpretability researchers*gain a composable substrate for organising per\-component statistics across studies; the schema is designed to accept SAE\-feature labels\(Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67); Cunninghamet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib74)\), attribution\-graph neighbourhoods\(Conmyet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib73)\), and steering or activation\-patching primitives as futureSS/RR/GGcontent without changing the interface\.*Educators and students*gain a natural\-language interface to model internals that does not require scripting around per\-paper notebooks, lowering the entry cost for engaging with mechanistic findings\.*Practitioners doing model audit and debugging*gain retrieval\-grounded evidence—every cited statistic traces to a stored field value—which reduces the cost of working with neural\-network internals and supports reproducibility\. We see lowering these access costs as broadly aligned with safer interpretability practice\.

Three scope caveats are worth stating explicitly\.*\(i\) Domain\.*Theβ\\beta\-VAE manipulation experiments edit facial attributes \(smiling, eyeglasses\) on CelebA\. Reconstruction quality is far below current generative baselines, but the same retrieval\-and\-intervention pattern, applied to higher\-quality face models, would warrant separate consideration as face\-attribute manipulation tooling; we do not develop or release such tooling\.*\(ii\) Inherited limits\.*The framework inherits the resolution of its underlying analyses; extending to frontier models requires SAE\-based or similarly scaledSS\-primitives that this paper does not provide\.*\(iii\) Settings\.*All reported results are post\-hoc analyses on small\-scale models—our ownβ\\beta\-VAE on CelebA and CNN on CIFAR\-10, together with the publicly available GPT\-2 small; we make no claim of readiness for safety\-critical deployment, and recommend domain\-specific evaluation, access controls, and auditing for any real\-world use\.

We adopt and recommend two methodological practices for interpretability infrastructure work: pre\-registration of experiments via cryptographically hashed predictions before outcomes are computed \(all five GPT\-2 experiments here\), and explicit reporting of negative results \(the per\-field path\-patching null, App\.[G](https://arxiv.org/html/2607.00089#A7)\)\. Both reduce the risk that interpretability tooling overclaims relative to its evidence—a property of the field worth normalising\.

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## Appendix Navigation

Table 3:Navigation map: each main\-paper section to its supporting appendix\. Section and appendix references are clickable\.
## Appendix AEvaluation\-to\-Contribution Mapping

Table 4:Evaluation\-to\-contribution mapping\.EvaluationWhat we didWhat we wanted to seeSupportsCross\-architecture consistencyApplied the same pipeline to aβ\\beta\-VAE \(512 dims\) and a CNN \(224 filters\)\.Whether the representation\+retrieval interface generalizes across architectures\.C1Hypothesis validation \(main paper\)\.Structural isolation \(H1, GPT\-2\)ComparedS\+RS\{\+\}Rretrieval against random partitions of identical per\-component text on GPT\-2 attention heads \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)D;p<0\.01p<0\.01across 10 seeds and 3 baseline configurations\)\.Whether typed structure beats arbitrary partitioning of the same content\.C1, C3Causal mediation \(H2, CNN\)Targeted amplification \(k=8k\{=\}8,α∈\{30,50,70\}\\alpha\\in\\\{30,50,70\\\},n=270n\{=\}270\) and natural\-image ablation, vs\. matched\-budget random \(Table[2](https://arxiv.org/html/2607.00089#S5.T2)\)\.Whether retrieved components causally mediate the targeted behaviour \(MIB sense: sufficiency\+\+necessity\)\.C1, C3Per\-field ablation \(H2, GPT\-2\)Leave\-one\-out and progressive field addition on the ESRDGT schema, plus field\-merging falsification under coarser groupings \(Fig\.[4](https://arxiv.org/html/2607.00089#S5.F4)A–C, Fig\.[25](https://arxiv.org/html/2607.00089#A6.F25)\)\.Identify the minimal\-optimal field combination; falsify the granularity choice\.C1IOI circuit recovery \(GPT\-2\)Set\-overlap between framework\-retrieved heads atk∈\{7,15,30\}k\\in\\\{7,15,30\\\}and the canonical IOI L7–9 name\-mover heads ofWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)\.Cross\-architecture schema transfer to attention heads\.C1Path\-patching scope \(GPT\-2\)Per\-field causal enrichment under path\-patching, Bonferroni\-corrected across fields and retrieval strategies \(App\.[G](https://arxiv.org/html/2607.00089#A7)\)\.Honest disclosure of where retrieval enrichment does*not*translate to per\-head causal enrichment\.C1 \(scope\)Automatic evaluation \(single\-turn\)Evaluated retrieval, generation, semantic similarity, and faithfulness metrics acrossk∈\{5,10,20\}k\\in\\\{5,10,20\\\}on dims/filters queries\.Correct retrieval of relevant units and grounded generation\.C2LLM\-as\-judge evaluationClaude\-Opus and GPT\-5\.1 rated multi\-turn conversations \(5 turns\) on 7 metrics \(Comprehensibility, Faithfulness, Correctness, Usefulness, Specificity, Trustworthiness, Coherence\)\.Conversational quality under automated judging\.C2Human evaluation15 evaluators across 3 expertise levels \(Beginner, Intermediate, Expert\), 612 assessments total \(315 VAE \+ 297 CNN\), multi\-turn \(5 turns\), same 7 metrics\.Usefulness and faithfulness across user expertise\.C2SLM parameter studiesVaried temperature \(0\.0–1\.0\), max tokens \(256–2000\), and prompting strategy \(Basic, Detailed, Chain\-of\-Thought\) while holding retrieval fixed\.Robustness of grounded generation to decoding/prompt choices\.C2Ablation: retrieval componentsAblated query reformulation, reranking, boosting, over\-retrieval, exact matching, and index composition \(dims\-only, Q&A\-only, interactions\-only\)\.Which retrieval components materially affect performance\.C2Ablation: structured vs\. unstructuredReplaced Manifestation Units with unstructured prose containing identical statistics\.Whether structured\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)representation is essential\.C3Ablation: entity\-aware retrievalDisabled exact matching \(semantic\-only\) and compared against exact\-only retrieval\.Whether hybrid retrieval is necessary for mixed identifier/concept queries\.C3SLM vs\. frontier LLMsCompared Qwen3\-8B against Claude\-Opus and GPT\-5\.1 on identical automatic metrics with same retrieved context\.Whether smaller models suffice when properly grounded\.C3This appendix maps each evaluation to the core contributions stated in the main paper \(C1–C3\)\. We also report manipulation experiments as additional validation evidence \(Table[5](https://arxiv.org/html/2607.00089#A1.T5)\), consistent with our framing in Sec\. 3\.4 that manipulation is used primarily as a validation mechanism\.

Table 5:Additional behavioral validation \(not claimed as a separate contribution\)\. The97\.8%97\.8\\%figure reflects post\-hocα\\alpha\-tuning optimisation over resistant pairs; the primary H2 evaluation uses the fixed\-protocol result of76\.3%76\.3\\%\(Table[2](https://arxiv.org/html/2607.00089#S5.T2), main paper\)\.##### Contributions summary\.

- •C1:Manifestation Units, a structured representation protocol\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)that transforms statistical patterns from neural network analysis into retrievable, groundable knowledge units\.
- •C2:A template\-grounded hybrid retrieval architecture combining entity\-aware exact matching with semantic search, enabling faithful natural language access to component\-level knowledge\.
- •C3:Empirical evidence that structured representation and hybrid retrieval each materially contribute in the studied settings: ablations show retrieval precision drops to near\-zero when either component is removed; the response\-faithfulness check is consistent across user expertise levels\.

## Appendix BKnowledge Extraction Details

This appendix provides implementation details for the three\-level analysis described in Sec\. 3\.3\.

### B\.1Parameter Settings

Table[6](https://arxiv.org/html/2607.00089#A2.T6)summarizes the key parameters used in our experiments\.

Table 6:Parameter settings for knowledge extraction\.
### B\.2Level 1: Individual Semantics

Activation extraction\.For each component, we compute a scalar activation per sample by spatially averaging its post\-ReLU feature map \(CNN\) or spatially averaging the latent activation \(VAE\)\. All correlations and statistics are computed overNNtest samples \(N=1,000N=1\{,\}000for VAE,N=10,000N=10\{,\}000for CNN\)\.

VAE \(CelebA\)\.For each latent dimensiond∈\{1,…,512\}d\\in\\\{1,\\ldots,512\\\}and attributea∈\{1,…,40\}a\\in\\\{1,\\ldots,40\\\}, we compute Pearson correlation:

sd,a=corr​\(z¯⋅,d,𝐚\)s\_\{d,a\}=\\text\{corr\}\(\\bar\{z\}\_\{\\cdot,d\},\\mathbf\{a\}\)\(4\)wherez¯⋅,d∈ℝN\\bar\{z\}\_\{\\cdot,d\}\\in\\mathbb\{R\}^\{N\}is the spatially\-averaged activation of dimensionddacrossNNtest samples, and𝐚∈\{0,1\}N\\mathbf\{a\}\\in\\\{0,1\\\}^\{N\}is the binary attribute vector\. We retain the top\-mmattributes by\|sd,a\|\|s\_\{d,a\}\|for each dimension\.

CNN \(CIFAR\-10\)\.For each filterffand classc∈\{1,…,10\}c\\in\\\{1,\\ldots,10\\\}, we first compute class\-wise mean activationsμf,c\\mu\_\{f,c\}over the validation set and normalize to obtain the distribution:

pf​\(c\)=μf,c∑c′μf,c′\.p\_\{f\}\(c\)=\\frac\{\\mu\_\{f,c\}\}\{\\sum\_\{c^\{\\prime\}\}\\mu\_\{f,c^\{\\prime\}\}\}\.\(5\)We then compute class selectivity as:

sf,c=1−H​\(pf\)log⁡\(10\)s\_\{f,c\}=1\-\\frac\{H\(p\_\{f\}\)\}\{\\log\(10\)\}\(6\)whereH​\(⋅\)H\(\\cdot\)is entropy\. This entropy\-based selectivity is 0 when activations are uniform across classes and approaches 1 when concentrated on a single class\. We retain the top\-mmclasses by selectivity for each filter\.

### B\.3Level 2: Pairwise Relationships

Formal definition ofNr​\(k\)N\_\{r\}\(k\)\.Letρk​i\\rho\_\{ki\}denote the Pearson correlation between the activations of componentskkandiiacross the dataset:

ρk​i=corr​\(𝐚k,𝐚i\)\\rho\_\{ki\}=\\text\{corr\}\(\\mathbf\{a\}\_\{k\},\\mathbf\{a\}\_\{i\}\)\(7\)where𝐚k,𝐚i∈ℝN\\mathbf\{a\}\_\{k\},\\mathbf\{a\}\_\{i\}\\in\\mathbb\{R\}^\{N\}are activation vectors acrossNNsamples\.

The neighbor setNr​\(k\)N\_\{r\}\(k\)is defined as:

𝒩r​\(k\)=\{i1,…,ir\}⊂I∖\{k\}\\mathcal\{N\}\_\{r\}\(k\)=\\\{i\_\{1\},\\ldots,i\_\{r\}\\\}\\subset I\\setminus\\\{k\\\}\(8\)where\|ρk,i1\|≥\|ρk,i2\|≥⋯≥\|ρk,ir\|\|\\rho\_\{k,i\_\{1\}\}\|\\geq\|\\rho\_\{k,i\_\{2\}\}\|\\geq\\cdots\\geq\|\\rho\_\{k,i\_\{r\}\}\|and\|ρk,ir\|≥\|ρk,j\|\|\\rho\_\{k,i\_\{r\}\}\|\\geq\|\\rho\_\{k,j\}\|for allj∉𝒩r​\(k\)j\\notin\\mathcal\{N\}\_\{r\}\(k\)\. Ties are broken by component index \(smaller index preferred\)\.

Relationship classification\.We label relationships as*synergistic*,*antagonistic*, or*independent*using thresholdsτsyn\\tau\_\{\\text\{syn\}\}andτant\\tau\_\{\\text\{ant\}\}:

tk​i=\{synergisticif​ρk​i\>τsynantagonisticif​ρk​i<τantindependentotherwiset\_\{ki\}=\\begin\{cases\}\\text\{synergistic\}&\\text\{if \}\\rho\_\{ki\}\>\\tau\_\{\\text\{syn\}\}\\\\ \\text\{antagonistic\}&\\text\{if \}\\rho\_\{ki\}<\\tau\_\{\\text\{ant\}\}\\\\ \\text\{independent\}&\\text\{otherwise\}\\end\{cases\}\(9\)
Computation and storage\.We compute correlations using minibatch accumulation and store only the top\-rrneighbors per component\. Full pairwise matrices are retained only for analysis layers with≤512\\leq 512components\. For VAEs, this yields a512×512512\\times 512correlation matrix\. For CNNs, we compute both within\-layer matrices \(e\.g\.,32×3232\\times 32for Conv1\) and cross\-layer matrices \(e\.g\.,32×6432\\times 64for Conv1→\\toConv2\)\.

### B\.4Level 3: Collective Organization

VAE: Semantic families\.We cluster using Ward’s linkage on the distancedi​j=1−\|ρi​j\|d\_\{ij\}=1\-\|\\rho\_\{ij\}\|\. The number of clusters \(20\) was determined by dendrogram inspection and silhouette analysis\. Each dimension is assigned a cluster ID stored inDD\.

VAE: Effective dimensionality\.We compute the effective dimensionality as:

dimeff​\(α\)=min⁡\{k:∑i=1kλi∑i=1nλi\>α\}\\text\{dim\}\_\{\\text\{eff\}\}\(\\alpha\)=\\min\\left\\\{k:\\frac\{\\sum\_\{i=1\}^\{k\}\\lambda\_\{i\}\}\{\\sum\_\{i=1\}^\{n\}\\lambda\_\{i\}\}\>\\alpha\\right\\\}\(10\)whereλi\\lambda\_\{i\}are eigenvalues of the covariance matrix of latent activations across the dataset, sorted in descending order, andα=0\.95\\alpha=0\.95\. This measures how many dimensions capture 95% of the variance\.

CNN: Cross\-layer dependencies\.For consecutive layersllandl′l^\{\\prime\}, we compute the cross\-layer correlation matrix:

C\(l→l′\)=\[ρi​j\]i∈Il,j∈Il′C^\{\(l\\to l^\{\\prime\}\)\}=\[\\rho\_\{ij\}\]\_\{i\\in I\_\{l\},j\\in I\_\{l^\{\\prime\}\}\}\(11\)whereIlI\_\{l\}andIl′I\_\{l^\{\\prime\}\}are the filter sets for layersllandl′l^\{\\prime\}\. Strong correlations indicate feature dependencies across the hierarchy\. These dependency scores are stored inDD\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x3.png)Figure 6:Comparison of structured Manifestation Unit representation \(left\) versus unstructured natural language \(right\) for the same dimension\. The structured format\(E,S,R,D,G\)\(E,S,R,D,G\)provides typed fields enabling exact\-match retrieval on entity identifiers and faithful numeric grounding\. The unstructured format buries the same information in prose, causing retrieval failures on entity\-specific queries \(e\.g\., “dimension 0” appears throughout the text but cannot be reliably matched\)\.

## Appendix CRetrieval Implementation Details

Figure[7](https://arxiv.org/html/2607.00089#A3.F7)illustrates the complete RAG conversational architecture for the VAE system\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x4.png)Figure 7:RAG conversational architecture for the VAE system Conversational System\. A user query \(“What does dimension 63 encode?”\) flows through: \(1\) query reformulation with state\-based context tracking, \(2\) entity extraction detecting query type \(dimension, family, correlation\), \(3\) hybrid retrieval combining exact match, semantic search, and family\-aware retrieval across four FAISS indices, \(4\) conversation state management tracking entities and focus, and \(5\) grounded response generation via Qwen3\-8B\. The output cites specific statistics from retrieved Manifestation Units \(correlationρ=0\.303\\rho=0\.303, variance 0\.0174, relationship counts\)\.### C\.1Template Structure

Each Manifestation UnitMk=\(Ek,Sk,Rk,Dk,Gk\)M\_\{k\}=\(E\_\{k\},S\_\{k\},R\_\{k\},D\_\{k\},G\_\{k\}\)is converted to natural language via deterministic templates\. These templates provide*grounded views*of structured fields: each rendered statement is a direct instantiation of values stored in the unit\.

#### C\.1\.1Structured vs\. Unstructured Representations

A key design decision in MANIFESTATION is the use of*structured*templated documents derived from the five\-tuple representation\(E,S,R,D,G\)\(E,S,R,D,G\), rather than unstructured narrative text\. Figure[8](https://arxiv.org/html/2607.00089#A3.F8)illustrates this distinction for the CNN system\.

##### Structured representation \(MANIFESTATION\)\.

Each Manifestation Unit generates multiple specialized documents, with each document corresponding to a specific component of the five\-tuple:

- •EuE\_\{u\}\(Entity\): Unique identifier enabling exact\-match retrieval \(e\.g\., “Filter 0 in conv1”\)
- •SuS\_\{u\}\(Summary\): Primary semantic role and statistical properties
- •DuD\_\{u\}\(Technical Properties\): Activation statistics, sparsity, class\-specific responses
- •RuR\_\{u\}\(Relationships\): Synergistic partnerships and correlation strengths
- •GuG\_\{u\}\(Manipulation Guide\): Actionable instructions for enhancing or suppressing filter behavior

This decomposition enables*field\-specific retrieval*: queries about relationships retrieve relationship documents, while queries about manipulation retrieve guidance documents, improving precision and reducing irrelevant context\.

##### Unstructured representation \(Baseline\)\.

In contrast, unstructured baselines concatenate all information about an entity into free\-form narrative text\. As shown in the right panel of Figure[8](https://arxiv.org/html/2607.00089#A3.F8), this approach loses the explicit field boundaries that enable targeted retrieval\. Queries must rely entirely on semantic similarity, which struggles to distinguish between conceptually related but functionally distinct information \(e\.g\., confusing “what class does filter X detect?” with “what filters detect class Y?”\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x5.png)Figure 8:Comparison of structured Manifestation Units \(left\) versus unstructured baseline \(right\) for CNN filter analysis\. The structured representation decomposes knowledge into five specialized document types\(Eu,Su,Ru,Du,Gu\)\(E\_\{u\},S\_\{u\},R\_\{u\},D\_\{u\},G\_\{u\}\), enabling field\-specific retrieval\. The unstructured baseline concatenates all information into narrative paragraphs, losing explicit structure\.

#### C\.1\.2Templated Documents

Rather than indexing a single concatenated text per unit, we generate*multiple templated documents per unit*, each specializing in a distinct access pattern\. This enables fine\-grained retrieval where queries about encoding retrieve summary documents while queries about redundancy retrieve redundancy\-specific documents\.

##### VAE template fields\.

For the VAE system \(512 latent dimensions\), each Manifestation Unit generates 4 templated documents:

- •summary: Primary attribute \(c∗c^\{\*\}\), correlation strength, semantic family membership, variance characteristics\. > “Dimension 63 primarily encodes ‘Wearing\_Lipstick’ with correlation 0\.303\. Family: Wearing\_Lipstick\. Variance: 0\.0174\. Strong correlations: 368\.”
- •generation\_role: Role during generation, number of strong correlations, hub/peripheral classification\. > “During face generation, this dimension primarily controls ‘Wearing\_Lipstick’\. Hub dimension with 368 strong correlations across latent space\.”
- •redundancy\_notes: Very high correlations \(r\>0\.9r\>0\.9\), redundant dimension IDs, pruning recommendations\. > “This dimension has 156 very high correlations \(\>\>0\.9\)\. Redundant with dimensions 320, 241, 310\. Consider pruning for efficiency\.”
- •manipulation\_guide: How to manipulate the primary attribute, recommended co\-manipulations\. > “To manipulate ‘Wearing\_Lipstick’: adjust dimension 63\. Co\-manipulate correlated dimensions for stronger effect\.”

This yields512×4=2,048512\\times 4=2\{,\}048dimension\-level template entries in the primary Dimension Index\.

##### CNN template fields\.

For the CNN system \(224 filters: 32 in conv1, 64 in conv2, 128 in conv3\), each unit generates up to 5 templated documents:

- •summary: Selectivity score, mean activation, top responding classes, layer role\. > “Filter 0 in conv1 is a general\-purpose low\-level feature detector\. Selectivity: 0\.16\. Mean activation: 0\.128\.”
- •technical\_properties: Sparsity coefficient, activation statistics \(mean, std, range\)\. > “Sparsity: 0\.00 \(dense activation\)\. Std: 0\.048\. Activation range: \[0\.0, 0\.31\]\.”
- •class\_responses: Per\-class activation statistics for CIFAR\-10 classes\. > “Top responding classes: automobile \(μ\\mu=0\.154,σ\\sigma=0\.045\), frog \(μ\\mu=0\.142\), truck \(μ\\mu=0\.138\)\.”
- •relationships: Synergistic filter partnerships and correlation strengths \(when present\)\. > “4 synergistic partners\. Strongest: filter 16 \(rr=0\.75\), filter 17 \(rr=0\.74\), filter 3 \(rr=0\.71\)\.”
- •manipulation\_guide: How to enhance/suppress filter response, partner filters for amplification\. > “To enhance automobile/frog detection: amplify filter 0\. Co\-amplify filters 16, 17 for stronger effect\.”

This yields 943 indexed template entries \(not all filters have documented relationships\)\.

##### Document metadata\.

Each templated document stores metadata for retrieval and traceability:

- •Entity identifier:dimension\_id\(VAE\) orlayer\+filterpair \(CNN\)
- •Field type: Which template family this document instantiates
- •Text: Natural language description derived from structured fields
- •Numeric values: Original statistics for verbatim citation in responses

Table[7](https://arxiv.org/html/2607.00089#A3.T7)shows variable instantiation by architecture\.

Table 7:Template variable instantiation by architecture\.

### C\.2RAG Architecture Details

The MANIFESTATION framework employs distinct RAG architectures for single\-turn retrieval queries and multi\-turn conversational interactions\. This section details the architectural components illustrated in Figure[9](https://arxiv.org/html/2607.00089#A3.F9)–[11](https://arxiv.org/html/2607.00089#A3.F11)\.

#### C\.2\.1Single\-Turn Retrieval Architecture

Figure[9](https://arxiv.org/html/2607.00089#A3.F9)illustrates the RAG architecture for single\-turn queries in the VAE system\. Given a query such as “What does dimension 63 encode?”, the system proceeds through the following stages:

##### Query processing\.

The*Query Reformulation*module normalizes abbreviations and informal references \(e\.g\., “dims”→\\rightarrow“dimension 63”\)\. The*Entity Extraction*module then identifies explicit dimension IDs using pattern matching, classifying the query type \(single dimension, multi\-dimension comparison, attribute exploration, etc\.\)\.

##### Hybrid retrieval\.

Three complementary retrieval strategies operate in parallel:

1. 1\.Exact Match: Direct lookup of extracted entity IDs in the dimension index, guaranteeing retrieval of the target Manifestation Unit when explicitly referenced\.
2. 2\.Semantic Search: FAISS\-based similarity search using sentence embeddings, enabling discovery of related dimensions even without explicit IDs\.
3. 3\.Dynamic Allocation: Query\-adaptivekkselection based on query complexity—simple lookups retrieve fewer documents while comparative queries retrieve more\.

##### Multi\-index search\.

The system maintains three specialized FAISS indices:

- •Dimensions: Primary index containing templated documents for all 512 VAE dimensions
- •Q&A: Pre\-computed question\-answer pairs for common query patterns
- •Interactions: Pairwise correlation and relationship documents

##### Filtering and ranking\.

Retrieved documents undergo similarity thresholding \(0\.3\), exact\-match boosting \(1\.5×\\times\), and over\-retrieval with reranking \(5×\\timesinitial retrieval, then filter to finalkk\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x6.png)Figure 9:VAE single\-turn RAG architecture\. The system processes queries through reformulation and entity extraction, then applies hybrid retrieval \(exact match, semantic search, dynamic allocation\) across multiple FAISS indices before filtering and ranking results for generation\.

#### C\.2\.2Conversational RAG Architecture

For multi\-turn conversations, the architecture extends the single\-turn system with state management and additional retrieval capabilities\. Figure[10](https://arxiv.org/html/2607.00089#A3.F10)and[11](https://arxiv.org/html/2607.00089#A3.F11)illustrate these conversational architectures for VAE and CNN systems respectively\.

##### Extended VAE conversational architecture\.

As shown in Figure[10](https://arxiv.org/html/2607.00089#A3.F10), the conversational system adds three key components:

1. 1\.Family Retrieval: Pre\-computed mapping from semantic families \(e\.g\., “Male”, “Wearing\_Lipstick”\) to member dimensions, enabling efficient lookup for family\-level queries\.
2. 2\.Narratives Database: A fourth FAISS index containing pre\-generated narrative summaries that provide high\-level overviews of dimension families and interaction patterns\.
3. 3\.Conversation State Management: Tracking of discussed entities, correlation pairs, and focus shifts to enable context\-aware retrieval in follow\-up turns\.

The state management component maintains:

- •current\_dimensions: Set of dimension IDs mentioned in conversation \(e\.g\., \{63, 501\}\)
- •current\_families: Semantic families under discussion \(e\.g\., \{Male\}\)
- •last\_focus\_entity: Most recently discussed entity for pronoun resolution
- •discussed\_correlations: Pairs of dimensions whose relationships have been explored

##### CNN conversational architecture\.

Figure[11](https://arxiv.org/html/2607.00089#A3.F11)shows the analogous architecture for CNN filter analysis\. The CNN system operates over a single database \(Conv\-Filter DB\) organized by layer and filter, with 5 field types per filter\. The conversation state tracks filter references across the three convolutional layers \(conv1, conv2, conv3\), maintaining focus for multi\-turn exploration of filter hierarchies and cross\-layer relationships\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x7.png)Figure 10:VAE conversational RAG architecture\. Extends the single\-turn system with family retrieval, a narratives database, and conversation state management for multi\-turn context tracking\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x8.png)Figure 11:CNN conversational RAG architecture\. Processes filter queries through query reformulation and entity extraction, retrieves from a unified Conv\-Filter database with 5 fields per filter, and maintains conversation state for multi\-turn interactions\.

### C\.3Query Structures and Evaluation Protocol

We evaluate the system using two complementary query types: single\-turn retrieval queries and multi\-turn conversational queries\. Figure[12](https://arxiv.org/html/2607.00089#A3.F12)and[13](https://arxiv.org/html/2607.00089#A3.F13)illustrate the JSON structures for both query types\.

#### C\.3\.1Single\-Turn Retrieval Queries

Single\-turn queries test the system’s ability to retrieve and synthesize information from Manifestation Units in response to standalone questions\. As shown in the left panels of Figure[12](https://arxiv.org/html/2607.00089#A3.F12)and[13](https://arxiv.org/html/2607.00089#A3.F13), each retrieval query specifies:

- •id: Unique query identifier \(e\.g\., “T1\_Q1” for CNN tier\-1, “Q001” for VAE\)
- •tier: Complexity level \(1 = simple lookup, 2 = multi\-entity, 3 = reasoning\)
- •question: Natural language query text
- •target\_layer/target\_filter\(CNN\) ordimensions\(VAE\): Ground truth entities
- •target\_field: Expected template field \(e\.g\., “technical\_properties”, “relationships”\)
- •answer\_type: Expected format \(float, integer, string, list\)
- •expected\_format: Granularity of expected answer \(exact\_value, exact\_count, description\)

Example CNN retrieval queries include:

> “What is the mean activation value for Filter 0 in conv1?”→\\rightarrowtechnical\_properties, float “How many synergistic relationships does Filter 1 in conv1 have?”→\\rightarrowrelationships, integer

Example VAE retrieval queries include:

> “What does dimension 63 encode?”→\\rightarrowpairwise\_interaction, dimensions \[373, 255\] “What does dimensions 299 and 335 encode?”→\\rightarrowpairwise\_interaction, multi\-dimension

#### C\.3\.2Multi\-Turn Conversational Queries

Conversational queries test the system’s ability to maintain context across multiple turns and resolve references to previously discussed entities\. As shown in the right panels of Figure[12](https://arxiv.org/html/2607.00089#A3.F12)and[13](https://arxiv.org/html/2607.00089#A3.F13), each conversation specifies:

- •conversation\_id: Unique conversation identifier
- •category: Conversation type \(e\.g\., “Dimension\_Exploration\_Multi\_Turn”\)
- •turns: Ordered list of turn objects, each containing: - –turn: Turn number \(1\-indexed\) - –question: Natural language query for this turn - –filters\(CNN\) ordimensions\(VAE\): Entities relevant to this turn - –target\_field: Expected template field for retrieval - –requires\_context\_from: List of previous turn numbers needed to answer - –context\_only: Whether answer should come only from conversation context

Example CNN conversational sequence:

> Turn 1: “What is the mean activation value for Filter 0 in conv1?” Turn 2: “What is the sparsity value for it?” \(requires context from turn 1\) Turn 3: “Which class does it respond to most strongly?” \(requires context from turns 1, 2\)

Example VAE conversational sequence:

> Turn 1: “What does dimension 63 encode?” Turn 2: “What about its correlation with dimension 501?” \(requires context from turn 1\) Turn 3: “Are there other dimensions in the same family?” \(context\_only: true\) Turn 4: “Are the dimensions related to dimension 542?” \(requires context from turns 1, 2, 3\)

Therequires\_context\_fromfield enables automatic evaluation of context\-dependent retrieval by specifying which previous turns must be considered to correctly answer the current turn\. Thecontext\_onlyflag indicates queries that should be answerable purely from accumulated conversation context without additional retrieval\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x9.png)Figure 12:CNN query structures\. Left: Single\-turn retrieval queries with explicit target specifications\. Right: Multi\-turn conversational queries with context dependencies indicated byrequires\_context\_from\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x10.png)Figure 13:VAE query structures\. Left: Single\-turn dimension queries categorized by relationship discovery type\. Right: Multi\-turn conversational queries demonstrating progressive exploration with context accumulation\.

### C\.4Entity Extraction Patterns

For hybrid retrieval, we use regular expressions to detect explicit component references in user queries\.

##### VAE patterns\.

- •dimension\[s\]?\\s\*\(\\d\+\)matches “dimension 63” or “dimensions 63”
- •dim\[s\]?\\s\*\(\\d\+\)matches “dim 63”
- •\\b\(\\d\{1,3\}\)\\bstandalone numbers in dimension context

##### CNN patterns\.

- •filter\\s\*\(\\d\+\)\\s\*in\\s\*\(conv\[123\]\)matches “filter 5 in conv1”
- •\(conv\[123\]\)\\s\*filter\\s\*\(\\d\+\)matches “conv1 filter 5”
- •filters?\\s\*\(\\d\+\(?:,\\s\*\\d\+\)\*\)\\s\*in\\s\*\(conv\[123\]\)matches filter lists

When a pattern matches, the system performs exact lookup by iterating through documents and matching on the entity identifier field \(dimension\_idfor VAE,layer\+filterfor CNN\)\. Exact matches receive a similarity boost \(×1\.5\\times 1\.5\) during retrieval ranking, ensuring that explicitly referenced components appear at the top of retrieved results\. When no pattern matches, the system falls back to pure semantic search\.

### C\.5Embedding, Indexing, and Retrieval

##### Embedding model\.

We use Sentence\-BERT \(all\-MiniLM\-L6\-v2, 384 dimensions\) to embed templated documents\. We chose this lightweight sentence encoder for efficiency; preliminary experiments with larger encoders \(e\.g\.,all\-mpnet\-base\-v2\) yielded similar retrieval performance\.

##### Index structure\.

We use FAISSIndexFlatIPfor similarity search\. Document and query embeddings are L2\-normalized, so inner product corresponds to cosine similarity\.

The VAE and CNN systems use different index architectures reflecting their scale and query patterns:

###### VAE: Four specialized indices\.

The VAE system maintains four FAISS indices to support heterogeneous query types:

1. 1\.Dimension Index: 2,048 templated documents from Manifestation Units \(512 dimensions×\\times4 fields\)\. This is the primary index containing the core unit representations\.
2. 2\.Q&A Index: 144 curated question\-answer pairs covering general VAE architecture concepts, latent space interpretation, and common user questions\.
3. 3\.Interaction Index: 2,607 documents describing pairwise dimension relationships, conditional dependencies, and correlation patterns between specific dimension pairs\.
4. 4\.Narrative Index: 658 high\-level analysis documents including semantic family summaries, variance distribution insights, and correlation cluster narratives\.

This yields a total of5,457indexed documents across all VAE indices\.

###### CNN: Single unified index\.

The CNN system uses a single FAISS index containing all943templated documents\. The smaller scale \(224 filters vs\. 512 dimensions\) and simpler relationship structure do not require index separation; all template fields are searchable within one index\.

##### Hybrid retrieval strategy\.

Given a user queryqq, retrieval proceeds as follows:

1. 1\.Entity extraction: Apply regex patterns to detect explicit component references \(e\.g\., “dimension 63”, “filter 5 in conv1”\)\.
2. 2\.Query type classification: Classify query as conceptual, correlation\-focused, family\-related, or component\-specific based on keywords and extracted entities\.
3. 3\.Dynamic budget allocation\(VAE only\): Allocate retrieval slots across indices based on query type\. For specific dimension queries withk=20k=20total slots: - •Dimension Index:kdim=12k\_\{\\text\{dim\}\}=12\(60%\) - •Q&A Index:kqa=4k\_\{\\text\{qa\}\}=4\(20%\) - •Interaction Index:kint=2k\_\{\\text\{int\}\}=2\(10%\) - •Narrative Index:knarr=2k\_\{\\text\{narr\}\}=2\(10%\)
4. 4\.Exact match retrieval: For queries with explicit entity references, retrieve*all*documents for the referenced components and apply similarity boost \(×1\.5\\times 1\.5\)\.
5. 5\.Semantic search: Fill remaining slots via cosine similarity search across relevant indices\.
6. 6\.Re\-ranking: Sort final results by \(exact\_match, boosted\_similarity\) in descending order\.

##### Why multi\-index architecture \(VAE\)\.

Separating indices by content type enables targeted retrieval for different query intents:

- •*“What does dimension 63 encode?”*→\\rightarrowPrioritizes Dimension Index for unit\-specific data\.
- •*“How do VAE latent spaces work?”*→\\rightarrowPrioritizes Q&A Index for conceptual answers\.
- •*“What dimensions interact with 63?”*→\\rightarrowPrioritizes Interaction Index for relationship evidence\.
- •*“What is the Wearing\_Lipstick family?”*→\\rightarrowPrioritizes Narrative Index for family summaries\.

The ablation study \(Table[41](https://arxiv.org/html/2607.00089#A14.T41)\) confirms that removing any single index degrades performance, with the Dimension Index being most critical \(removing it causes recall to drop to 0% on dimension\-specific queries\)\.

##### Why multi\-field indexing\.

Each Manifestation Unit generates multiple documents \(one per field\), enabling queries to retrieve the most relevant*view*of a unit\. For example, “What does dimension 63 encode?” retrieves thesummarydocument, while “Which dimensions are redundant with dimension 63?” retrieves theredundancy\_notesdocument\. This yields higher precision than concatenating all fields into a single document \(see ablation: Unstructured Text baseline achieves only 20\.0% recall vs\. 94\.3% for structured retrieval\)\.

### C\.6Example Queries and Retrieval

##### Retrieval traces\.

To illustrate retrieval behavior, we present traces from 50 example queries per system, focusing on theRelationship\_Discoverycategory\. This illustrative set is separate from the main evaluation benchmark \(Appx\.[F\.3](https://arxiv.org/html/2607.00089#A6.SS3)\)\. The 50 example queries are distributed across three query types that test different retrieval capabilities\.

##### Query distribution\.

- •Pairwise correlation\(25 queries\): Single or paired component queries\. Ground truth field:pairwise\_interaction\.
- •Triple correlation\(20 queries\): Three\-component relationship queries\. Ground truth field:multi\_interaction\.
- •Family members\(5 queries\): Semantic grouping queries\. Ground truth field:summary\.

Table[8](https://arxiv.org/html/2607.00089#A3.T8)shows representative queries and their retrieval behavior\.

Table 8:Example queries and retrieval traces\. Exact matches \(EM\) receive1\.5×1\.5\\timessimilarity boost\.QueryTypeRetrieved FieldsRetrieval BehaviorVAE System \(512 dimensions, 4 indices, 5,457 total documents\)“What does dimension 63 encode?”pairwiseDim 63: summary, generation\_role, redundancy\_notes, manipulation\_guide \(all EM\)Exact match on dim\_id=63; all 4 fields retrieved with1\.5×1\.5\\timesboost“Why are dimensions 49, 4, and 215 correlated?”tripleDims 49, 4, 215: summary \(EM\) \+ Interaction docs for pairsExact match on 3 dims \+ semantic search in Interaction Index“Why are dimensions 154, 186, and 308 correlated?”familyDims 154, 186, 308: summary \(EM\) \+ Narrative family insightsFamily detected; Narrative Index allocation increasedCNN System \(224 filters, 1 index, 943 documents\)“What does filter 0 in conv1 encode?”pairwiseconv1\-f0: summary, technical, class\_responses, relationships, manipulation \(all EM\)Exact match on \(conv1, 0\); all 5 fields retrieved“Why are filters 0, 16, and 17 in conv1 correlated?”tripleconv1\-f0, f16, f17: summary, relationships \(EM\)Exact match on 3 filters \+ semantic expansion“Why are filters 0, 1, and 2 in conv1 correlated?”familyconv1\-f0, f1, f2: summary \(EM\)Summary fields contain family/grouping information

##### Retrieval workflow trace \(VAE\)\.

For the query “What does dimension 63 encode?”:

1. 1\.Entity extraction: Regex detects “dimension 63”→\\rightarrowtarget\_dims = \[63\]
2. 2\.Query classification: Single dimension query→\\rightarrowtype = specific
3. 3\.Budget allocation:k=20k=20allocated as: dim=12, qa=4, int=2, narr=2
4. 4\.Exact match: All 4 documents for dimension 63 retrieved with1\.5×1\.5\\timesboost
5. 5\.Semantic fill: Remaining 8 dim slots filled with similar dimension summaries \(dims 67, 351, 332, …\); Q&A slots filled with related questions \(“What does dimension 64 encode?”\)
6. 6\.Final retrieval: 20 documents total, 4 exact matches, avg similarity 60\.15%
7. 7\.Context assembly: Documents grouped by dimension ID for coherent LLM input

##### Retrieval workflow trace \(CNN\)\.

For the query “What does filter 0 in conv1 detect?”:

1. 1\.Entity extraction: Regex detects “filter 0 in conv1”→\\rightarrowtarget = \[\(conv1, 0\)\]
2. 2\.Field detection: Query contains “what does”→\\rightarrowprimary field =summary
3. 3\.Exact match: All 5 documents for conv1\-filter0 retrieved with1\.5×1\.5\\timesboost
4. 4\.Semantic fill: Remaining slots filled with related filters \(conv1\-f1, conv1\-f16, conv2\-f0, …\)
5. 5\.Final retrieval: 10 documents total, 1 exact match in required field, avg similarity 58\.86%

### C\.7Generation Prompt

The language model \(Qwen3\-8B\) receives the query along with retrieved evidence grouped by entity\. The prompt enforces grounded answering: the model must answer based only on retrieved content and must cite numeric values from retrieved fields\.

##### System prompt structure\.

The system prompt specifies:

- •Model context: Architecture description \(VAE with 512 dimensions / CNN with 224 filters across 3 layers\)
- •Grounding rules: Cite specific data from retrieved documents; distinguish facts from interpretation
- •Domain knowledge: Architecture\-specific concepts \(semantic families, layer hierarchy, correlation semantics\)
- •Response format: Quote exact numeric values; explain relationships using retrieved evidence

##### VAE context format\.

Retrieved documents are provided grouped by dimension:

```
=== RETRIEVED EVIDENCE ===

  Dimension 63
   summary: Dimension 63 primarily encodes ’Wearing_Lipstick’
    with correlation 0.303. Family: Wearing_Lipstick.
    Variance: 0.0174. Strong correlations: 368.
   generation_role: During face generation, this dimension
    primarily controls ’Wearing_Lipstick’. Hub dimension with
    extensive connections to other dimensions.
   redundancy_notes: This dimension has 156 very high
    correlations (>0.9). Redundant with dims 320, 241, 310.
   manipulation_guide: To manipulate ’Wearing_Lipstick’:
    adjust dimension 63. Co-manipulate correlated dims.

  Q&A Knowledge
   Q: What does dimension 64 encode? [similarity: 72.2%]
   Q: What does dimension 96 encode? [similarity: 70.5%]

  Narrative Insights
   Family Wearing_Lipstick: 35 dimensions encoding makeup...

=== END EVIDENCE ===
```

##### CNN context format\.

For CNN queries, evidence is grouped by layer and filter:

```
=== RETRIEVED EVIDENCE ===

  CONV1 Filter 0
   summary: Filter 0 in conv1 is a general-purpose low-level
    feature detector. Selectivity: 0.16. Mean activation: 0.128.
   technical_properties: Sparsity: 0.0009 (dense activation).
    Std: 0.048. Range: [0.0, 0.31].
   class_responses: Top classes - automobile ($\mu$=0.154),
    frog ($\mu$=0.142), truck ($\mu$=0.138).
   relationships: 4 synergistic partners. Strongest:
    filter 16 (r=0.75), filter 17 (r=0.74), filter 3 (r=0.71).
   manipulation_guide: Enhance automobile/frog detection
    by amplifying filter 0. Co-amplify filters 16, 17.

  CONV1 Filter 16   [semantic match, similarity: 65.2%]
   summary: Filter 16 in conv1 specializes in edge detection...

=== END EVIDENCE ===
```

The model is instructed to quote numeric values verbatim from these fields \(e\.g\., “correlation 0\.303”, “selectivity 0\.16”\), ensuring traceability from response to extracted statistics\.

## Appendix DSLM Configuration and Ablation Study

This appendix documents the Small Language Model \(SLM\) configuration used in the conversational interface and presents comprehensive ablation studies evaluating the impact of generation parameters on response quality\.

### D\.1Conversational Architecture

Figure[14](https://arxiv.org/html/2607.00089#A4.F14)and[15](https://arxiv.org/html/2607.00089#A4.F15)illustrate the RAG conversational architectures for the VAE and CNN systems, respectively\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x11.png)Figure 14:VAE RAG Conversational Architecture and SLM Ablation Study Design\.Top: The system processes user queries \(e\.g\., “What does dimension 63 encode?”\) through: \(1\) Query Reformulation with structure\-based state tracking, \(2\) Entity Extraction detecting query types \(dimensions, families, correlations\), \(3\) Hybrid Retrieval combining Exact Match \(family\-aware\), Semantic Search \(context\-enhanced embedding\), Dynamic Allocation \(query\-adaptivekkwith 4\-tier budget\), and Family Retrieval \(pre\-computed mapping\), \(4\) Multi\-FAISS Index Search across 4 databases \(Dimensions, Interactions, Q&A, Narratives\), and \(5\) Conversation State Management tracking current dimensions, families, focus entities, and discussed correlations\. The SLM \(Qwen3\-8B\) generates grounded responses citing specific statistics from retrieved Manifestation Units\.Bottom: Ablation study design showing parameter configurations for Temperature Study \(varying 0\.1–1\.0\), Prompt Study \(minimal, structured, cot, detailed\), and Max Tokens Study \(500–4000\)\.![Refer to caption](https://arxiv.org/html/2607.00089v1/fig/cnn-arch-exp.png)Figure 15:CNN RAG Manifestation Architecture and SLM Ablation Study Design\.Top: The architecture processes filter queries \(e\.g\., “What does filter 10 in conv2 detect?”\) through: \(1\) Query Reformulation with conversation tracking \(pronoun resolution\), \(2\) Entity Extraction identifying filter IDs and layers, \(3\) Hybrid Retrieval with Exact Match \(filter \+ layer lookup\), Semantic Search \(FAISS vector\), and Dynamic Allocation \(query\-adaptivekk\), \(4\) Single unified FAISS index \(Conv\-Filter: 3 layers, 5 MU fields\), and \(5\) Filtering & Ranking with similarity threshold \(0\.3\), exact match boosting \(1\.5×1\.5\\times\), and over\-retrieval \(5×5\\timescandidates\)\. The SLM generates responses grounded in retrieved context with appropriate source citations\.Bottom: Identical ablation study design to VAE, enabling cross\-architecture comparison\.
### D\.2SLM Configuration Parameters

Both conversational systems use Qwen3\-8B as the generation backbone with configurable parameters for ablation studies\. Table[9](https://arxiv.org/html/2607.00089#A4.T9)summarizes the parameter space explored\.

Table 9:SLM configuration parameters and their ablation ranges\.##### Ablation study experimental design\.

Table[10](https://arxiv.org/html/2607.00089#A4.T10)summarizes the experimental configurations for each ablation study\. Each study varies one parameter while holding others constant, enabling isolated analysis of parameter effects\.

Table 10:Ablation study experimental design\. Each study varies one parameter \(bold\) while holding others at default values\.
##### Parameter definitions\.

- •temperature: Controls randomness in token sampling\. Lower values \(0\.1–0\.3\) produce more deterministic, focused outputs; higher values \(0\.7–1\.0\) increase diversity and creativity\.
- •max\_tokens: Maximum number of tokens the model can generate per response\. Affects response comprehensiveness and detail level\.
- •prompt\_method: Strategy for constructing the generation prompt from retrieved context: - –*minimal*: Raw context concatenation with simple question\-answer format - –*structured*: Organized sections with clear field delineation - –*cot*\(Chain\-of\-Thought\): Step\-by\-step reasoning instructions - –*detailed*: Comprehensive system instructions with grounding rules, domain knowledge, and structured output format \(default\)

### D\.3Prompt Engineering Methods

We evaluate four prompt engineering strategies, each representing a different level of instruction specificity\.

##### Minimal prompt\.

Direct context injection with no system instructions:

```
Context:
{retrieved_documents}

Question: {query}

Answer:
```

##### Structured prompt\.

Organized sections separating context by source type:

```
You are a {VAE/CNN} analysis assistant.

[DIMENSION/FILTER DATA]
{dimension/filter context grouped by entity}

[REFERENCE Q&A]
{qa context}

[QUESTION]
{query}

[ANSWER]
```

##### Chain\-of\-Thought \(CoT\) prompt\.

Explicit reasoning steps before final answer:

```
You are analyzing a {VAE/CNN} trained on {CelebA/CIFAR-10}.

Available information:
{bulleted context items}

Question: {query}

Think step by step:
1. What specific information from the context is relevant?
2. What does this information tell us?
3. What can we conclude?

Final Answer:
```

##### Detailed prompt\.

Comprehensive instructions including grounding rules, domain knowledge, and output format specifications\. This method includes:

- •System role definition with architecture\-specific expertise
- •Explicit grounding rules \(“cite specific data”, “distinguish facts from interpretation”\)
- •Domain terminology \(semantic families, layer hierarchy, correlation semantics\)
- •Structured output format with metric tags for automatic verification
- •Example question\-answer pairs demonstrating expected response style

See Appx\.[C\.7](https://arxiv.org/html/2607.00089#A3.SS7)for the complete detailed prompt template\.

### D\.4Ablation Study: Maximum Token Length

We evaluate the impact of maximum token limits on generation quality while holding retrieval parameters constant \(k=20k=20\)\. All experiments use 50 queries per system\.

Table[11](https://arxiv.org/html/2607.00089#A4.T11)presents the VAE system results across token settings\.

Table 11:VAE system: Maximum token ablation results\. Retrieval metrics remain constant across all token settings\. Best results per metric arebolded\.Table[12](https://arxiv.org/html/2607.00089#A4.T12)shows the stability analysis across token settings\.

Table 12:VAE system: Stability analysis across maximum token settings\. Retrieval metrics show zero variance \(perfect stability\), while generation metrics exhibit controlled variability\.##### Key findings\.

- •Retrieval stability: All retrieval metrics show zero variance across token settings, confirming that generation parameters do not affect retrieval quality\.
- •Optimal balance: Token limit of 1000 achieves the best trade\-off between generation quality \(highest F1, ROUGE\-L\) and faithfulness \(highest factual accuracy at 98\.4%\)\.
- •Diminishing returns: Increasing beyond 1000 tokens improves BERTScore marginally \(0\.837\) but decreases Attribution \(0\.571 at 4000 vs\. 0\.618 at 500\), suggesting longer responses include more content not directly grounded in retrieved evidence\.

### D\.5Ablation Study: Prompt Engineering Methods

We evaluate four prompt engineering strategies while holding other parameters constant \(temperature=0\.7, max\_tokens=3000,k=20k=20\)\.

Table[13](https://arxiv.org/html/2607.00089#A4.T13)compares prompt methods across key metrics for both systems\.

Table 13:Prompt engineering comparison across VAE and CNN systems\. Best values per metric arebolded\.Table[14](https://arxiv.org/html/2607.00089#A4.T14)shows the stability analysis across prompt methods\.

Table 14:Stability analysis across prompt engineering methods\. Retrieval metrics show zero variance, while generation metrics exhibit controlled variability\.##### Key findings\.

- •Generation quality: Detailed prompting consistently achieves highest F1 and ROUGE\-L scores across both systems, with particularly strong gains on CNN \(\+0\.234 F1 vs\. Minimal\)\.
- •Faithfulness trade\-off: Minimal prompting achieves perfect Attribution on CNN \(1\.000\) but lower generation quality\. This suggests minimal prompts produce responses that closely mirror retrieved content but lack interpretive depth\.
- •Factual accuracy: CoT achieves highest factual accuracy on VAE \(0\.991\), while Minimal achieves perfect accuracy on CNN \(1\.000\)\. Both demonstrate that explicit grounding instructions improve factual reliability\.
- •System differences: CNN shows higher variance across prompt methods than VAE, indicating the simpler architecture is more sensitive to prompt engineering choices\.

### D\.6Ablation Study: Temperature

We evaluate six temperature settings from deterministic \(0\.1\) to high creativity \(1\.0\) while holding other parameters constant \(prompt\_method=detailed, max\_tokens=3000,k=20k=20\)\.

Table[15](https://arxiv.org/html/2607.00089#A4.T15)presents the VAE temperature ablation results\.

Table 15:VAE system: Temperature ablation results\. Best results per metric arebolded\.Table[16](https://arxiv.org/html/2607.00089#A4.T16)presents the CNN temperature ablation results\.

Table 16:CNN system: Temperature ablation results\. Best results per metric arebolded\.Table[17](https://arxiv.org/html/2607.00089#A4.T17)shows stability analysis with coefficient of variation\.

Table 17:Temperature stability analysis\. All generation metrics exhibit CV below 5%, indicating high stability across temperature range\.##### Key findings\.

- •High stability: All generation metrics exhibit coefficient of variation \(CV\) below 5% across the temperature range, indicating the SLM produces consistent quality outputs regardless of sampling temperature\.
- •System\-specific optima: VAE prefers moderate temperatures \(0\.5–0\.7\) while CNN prefers higher temperatures \(0\.9–1\.0\) for generation quality\. This difference may reflect the complexity of the underlying analysis: VAE’s richer semantic structure benefits from more focused generation, while CNN’s simpler filter descriptions benefit from more diverse phrasing\.
- •Factual accuracy: Both systems achieve highest factual accuracy at lower temperatures \(0\.3\), suggesting deterministic generation reduces hallucination risk\.
- •Default recommendation: Temperature 0\.7 provides a robust default balancing generation quality, faithfulness, and response diversity for both systems\.

### D\.7Implementation Details

##### Conversation state management\.

Both systems maintain structured conversation state for context\-aware query handling:

```
# VAE conversation state
conversation_state = {
    "current_dimensions": set(),      # e.g., {63, 501}
    "current_families": set(),        # e.g., {"Male"}
    "last_focus_entity": str,         # e.g., "dimension_63"
    "discussed_correlations": list    # e.g., [(63, 501)]
}

# CNN conversation state
conversation_state = {
    "current_filters": set(),         # e.g., {("conv2", 10)}
    "current_layers": set(),          # e.g., {"conv2"}
    "current_classes": set(),         # e.g., {"automobile"}
    "last_focus_entity": str,         # e.g., "filter_conv2_10"
    "discussed_relationships": list   # e.g., [(("conv1", 5), ("conv1", 16))]
}
```

##### Query reformulation\.

The system resolves pronouns and implicit references using conversation state:

- •“its correlation”→\\rightarrow“dimension 63’s correlation” \(VAE\)
- •“in the same family”→\\rightarrow“in the Male family” \(VAE\)
- •“filter 10’s partners”→\\rightarrow“filter 10 in conv2’s partners” \(CNN\)
- •“other filters in this layer”→\\rightarrow“other filters in conv2 besides filter 10” \(CNN\)

##### Response generation\.

The SLM is invoked via Ollama’s local API:

```
response = requests.post(
    "http://localhost:11434/api/generate",
    json={
        "model": "qwen3:8b",
        "prompt": grounded_prompt,
        "stream": False,
        "options": {
            "temperature": 0.7,
            "num_predict": 3000,
            "max_tokens": 2000,
            "top_p": 0.9,
            "top_k": 20
        }
    }
)
```

##### Thinking tag removal\.

Qwen3’s reasoning traces \(enclosed in<think\>\.\.\.</think\>tags\) are stripped from responses unless explicitly requested, ensuring clean output for evaluation and user interaction\.

### D\.8Architectural Differences Summary

Table[18](https://arxiv.org/html/2607.00089#A4.T18)summarizes the key architectural differences between the VAE and CNN conversational systems\.

Table 18:Architectural comparison between VAE and CNN conversational systems\.

## Appendix EManipulation Details

### E\.1VAE Manipulation

Given a target conceptctargetc\_\{\\text\{target\}\}\(e\.g\., “Smiling”\):

1. 1\.Retrieve dimensions where\|sd,ctarget\|\>τs\|s\_\{d,c\_\{\\text\{target\}\}\}\|\>\\tau\_\{s\}\(defaultτs=0\.3\\tau\_\{s\}=0\.3\)\.
2. 2\.Select top\-nndimensions by\|sd,ctarget\|\|s\_\{d,c\_\{\\text\{target\}\}\}\|\(defaultn=3n=3\)\.
3. 3\.For each selected dimensiondd, modify: zd′=zd\+sign​\(sd,ctarget\)⋅step⋅σdz^\{\\prime\}\_\{d\}=z\_\{d\}\+\\text\{sign\}\(s\_\{d,c\_\{\\text\{target\}\}\}\)\\cdot\\text\{step\}\\cdot\\sigma\_\{d\}\(12\)whereσd\\sigma\_\{d\}is the standard deviation of dimensionddacross the training set, and step is fromGG\(default 2\.0\)\.
4. 4\.Decode:x′=pθ​\(z′\)x^\{\\prime\}=p\_\{\\theta\}\(z^\{\\prime\}\)\.

### E\.2CNN Manipulation

Given a target classctargetc\_\{\\text\{target\}\}\(e\.g\., “dog”\):

1. 1\.Retrieve filters where selectivity forctargetc\_\{\\text\{target\}\}exceeds threshold\.
2. 2\.Select top\-nnfilters by selectivity \(defaultn=3n=3\)\.
3. 3\.For each selected filterff, we apply amplification to the post\-ReLU feature map: af′=α⋅afa^\{\\prime\}\_\{f\}=\\alpha\\cdot a\_\{f\}\(13\)whereα0\\alpha\_\{0\}is a conservative starting gain stored inGGfor interactive use \(default 1\.5\)\. For evaluation, we override this and sweepα∈\{10,30,50,70,90,100\}\\alpha\\in\\\{10,30,50,70,90,100\\\}\(see Sec\.[5](https://arxiv.org/html/2607.00089#S5)\)\.
4. 4\.Forward pass with modified activations and measure probability shift\.

### E\.3Manipulation Validation

To validate that excavated knowledge is bothactionable\(enables successful manipulations\) andfaithful\(retrieved components are semantically correct\), we conducted comprehensive evaluation across both architectures\.

#### E\.3\.1CNN Automatic Evaluation

We systematically tested all 90 source→\\totarget class pairs \(10 classes×\\times9 targets\) across 6 amplification levels \(α∈\{10,30,50,70,90,100\}\\alpha\\in\\\{10,30,50,70,90,100\\\}\), yielding 540 total manipulation attempts\.

##### Success Rate by Amplification\.

Figure[16](https://arxiv.org/html/2607.00089#A5.F16)shows success rates by amplification level\. Performance increases sharply from 44% atα=10\\alpha=10to approximately 80% atα≥70\\alpha\\geq 70, with optimal performance in the 70–100×\\timesrange\. The overall success rate across all amplification levels is 72%\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x12.png)Figure 16:CNN manipulation success rate by amplification factor\. Performance plateaus around 80% forα≥70\\alpha\\geq 70\.
##### Baseline Comparison: RAG\-Guided vs Random Selection\.

To validate that success stems from meaningful filter\-class mappings rather than noise exploitation, we compared RAG\-guided filter selection against a random baseline\. Both methods used identical conditions: same amplification factors \(α∈\{30,50,70\}\\alpha\\in\\\{30,50,70\\\}\), same number of filters, and same source images\. Theonlydifference was the filter selection criterion \(Figure[17](https://arxiv.org/html/2607.00089#A5.F17)\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x13.png)Figure 17:RAG\-guided vs\. random baseline \(single seed,n=270n\{=\}270\)\. Random filter selection achieves 0% success; RAG\-guided achieves 76\.3%\. The three\-seed mean for random \(Table[2](https://arxiv.org/html/2607.00089#S5.T2)\) is 6\.7%, confirming the≈70\{\\approx\}70pp gap is robust\. Correct filter selection—not arbitrary amplification—is what drives the difference\.Table 19:Baseline comparison validates that excavated knowledge is meaningful\. This visualisation run used a single random seed and obtained 0% success \(0/270\)\. The three\-seed mean reported in Table[2](https://arxiv.org/html/2607.00089#S5.T2)is 6\.7% \(18/270\); single seeds vary between 0 and∼\\sim10%, confirming the large gap to RAG\-guided selection \(76\.3%\) is robust to seed choice\.Table 20:Detailed baseline comparison by amplification factor\.Table[20](https://arxiv.org/html/2607.00089#A5.T20)shows the breakdown by amplification factor for this single\-seed visualisation run\. The near\-zero random success \(0% here; 6\.7% three\-seed mean in Table[2](https://arxiv.org/html/2607.00089#S5.T2)\) provides strong evidence that MANIFESTATION’s excavated filter\-class mappings capture genuine semantic structure rather than reflecting noise exploitation\.

#### E\.3\.2Class\-Pair Analysis

Figure[18](https://arxiv.org/html/2607.00089#A5.F18)shows the manipulation success rate for each source→\\totarget class pair, revealing systematic patterns in manipulation difficulty\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x14.png)Figure 18:Manipulation success rate by class pair\. Values indicate success rate \(%\) across amplification levels\. Notable patterns include high success for horse and truck as sources, and difficulty with automobile as target\.##### Category\-Level Analysis\.

We grouped CIFAR\-10 classes into vehicles \(airplane, automobile, ship, truck\) and animals \(bird, cat, deer, dog, frog, horse\) to analyze cross\-category manipulation patterns \(Figure[19](https://arxiv.org/html/2607.00089#A5.F19)\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x15.png)Figure 19:Success rate by transformation category\. V→\\toA \(vehicle to animal\) achieves highest success \(78%\), while A→\\toV \(animal to vehicle\) is most challenging \(36%\)\.Table 21:Manipulation success rate by category transformation\.Table[21](https://arxiv.org/html/2607.00089#A5.T21)summarizes the results\. The asymmetry between V→\\toA \(78%\) and A→\\toV \(36%\) suggests that vehicle features are more easily suppressed than animal features, possibly because the CNN encodes animal classes with more distributed, redundant filter responses\.

##### Asymmetric Manipulability\.

Figure[20](https://arxiv.org/html/2607.00089#A5.F20)reveals that classes differ significantly in both source manipulability \(how easily they can be transformed away from\) and target vulnerability \(how easily other images can be transformed into them\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x16.png)Figure 20:\(a\) Source manipulability: automobile and cat are easiest to transform\. \(b\) Target vulnerability: deer and airplane are easiest targets\.Key observations:

- •Most manipulable sources: automobile, cat, truck, horse
- •Least manipulable sources: deer, bird, frog
- •Most vulnerable targets: deer, airplane, bird
- •Least vulnerable targets: truck, automobile

#### E\.3\.3CNN Human Evaluation

To validate that automatic metrics align with human perception, evaluators assessed manipulation quality on a subset of tasks \(14 evaluations\)\.

##### Metrics\.

Evaluators rated each manipulation on:

- •Classification Success: Did the manipulation achieve the requested class change? \(Yes/Partially/No\)
- •Filter Explanation Quality: Were the selected filters meaningfully explained? \(Yes/Partially/No\)
- •Manipulation Coherence: Did the manipulation make logical sense? \(1–5 scale\)
- •Task Difficulty: Perceived difficulty of the transformation \(Easy/Medium/Hard/Very Hard\)
- •Iterations Needed: Number of attempts required \(1/2/3–4/5\+\)

##### Results\.

Table[22](https://arxiv.org/html/2607.00089#A5.T22)summarizes the CNN human evaluation results\.

Table 22:CNN human manipulation evaluation results \(14 evaluations\)\.
##### Human\-Automatic Alignment\.

Table[23](https://arxiv.org/html/2607.00089#A5.T23)shows that human coherence ratings correlate with automatic classification success, validating that automatic metrics serve as reliable proxies for manipulation quality\.

Table 23:Human\-automatic alignment for CNN manipulation\. Human coherence ratings correlate strongly with automatic classification success\.The 2\-point gap in coherence ratings between successful and failed manipulations validates that automatic classification success serves as a reliable proxy for human\-perceived manipulation quality\. Furthermore, 93% of evaluators rated filter explanations as at least partially satisfactory, indicating that the SLM\+RAG system provides meaningful justifications for its filter selections\.

#### E\.3\.4VAE Human Evaluation

Unlike CNN where classification shift provides an objective success criterion, VAE manipulation quality requires human assessment of visual outputs\. We conducted human evaluation with 17 manipulation attempts across diverse instructions \(“smile face”, “make her old”, “add glasses”, “give beard”, etc\.\)\.

##### Metrics\.

Evaluators assessed each manipulation on:

- •Visual Faithfulness: Does the modification match the requested change? \(1–5\)
- •Degree of Change: How visible is the modification? \(1–5\)
- •Identity Preserved: Is it recognizably the same person? \(Yes/Partial/No\)
- •Artifact Quality: Visual distortions present? \(None/Mild/Moderate/Severe\)
- •Interaction Quality: How smooth was the interaction? \(1–5\)
- •Instruction Clarity: How clear was the instruction interpretation? \(1–5\)

##### Results\.

Table[24](https://arxiv.org/html/2607.00089#A5.T24)summarizes VAE manipulation evaluation results\.

Table 24:VAE human manipulation evaluation results \(17 evaluations\)\. Visual faithfulness is moderate, limited by VAE reconstruction quality rather than retrieval accuracy\. Identity preservation is high, indicating targeted manipulation without global distortion\.
##### Key Findings\.

- •High identity preservation\(94% Yes\): Manipulations are targeted to specific attributes without distorting the overall face structure\.
- •Low artifact rate: 76% of manipulations had no or only mild artifacts\.
- •Moderate visual faithfulness\(2\.12/5\): This reflects VAE reconstruction limitations rather than retrieval errors the system correctly identifies relevant dimensions but the decoder struggles to render subtle attribute changes\.
- •Good interaction quality\(3\.47/5\): Users found the conversational interface responsive and logical\.

##### Retrieval Consistency\.

A key validation finding: the same semantic instruction consistently retrieves the same dimensions across different evaluators\. For example, all “smiling” requests \(“smile face”, “add smile”, “enhance smiling”\) retrieved dimensions 483, 9, 489, 357, and 446 the “Smiling” semantic family identified during excavation\. This consistency demonstrates that the SLM\+RAG system reliably grounds natural language instructions in the correct latent dimensions\.

##### Why Automatic Evaluation is Difficult for VAE\.

Unlike CNN manipulation where classification provides an objective metric, VAE manipulation lacks ground\-truth success criteria:

- •“More smiling” is inherently subjective
- •VAE reconstruction introduces artifacts unrelated to manipulation
- •Attribute entanglement means dimensions affect multiple attributes

For these reasons, we rely on human evaluation for VAE validation and acknowledge that baseline comparison \(random dimension selection\) would require prohibitively large human studies\.

### E\.4Optimization Strategies for Resistant Pairs

For the 25 class pairs that failed at all initial amplification levels, we applied a systematic optimization protocol\. Critically, the filter set retrieved by the SLM\+RAG system was held constant; only intervention parameters were varied\.

Figure[21](https://arxiv.org/html/2607.00089#A5.F21)shows the improvement from optimization, with 23 of 25 resistant pairs resolved\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x17.png)Figure 21:Manipulation success before and after optimization\. Green\-bordered cells in \(b\) indicate pairs resolved through parameter optimization\. Only airplane→\\toautomobile and ship→\\totruck remain resistant\.##### Strategies Tested\.

1. 1\.Higher amplifications:α∈\{150,200,300,500\}\\alpha\\in\\\{150,200,300,500\\\}with single iteration
2. 2\.Multiple iterations: 2–5 sequential amplification applications atα∈\{30,50,70,100\}\\alpha\\in\\\{30,50,70,100\\\}
3. 3\.Different source images: 3 distinct test images per source class
4. 4\.Query variations: 6 alternative phrasings \(e\.g\., “transform into”, “convert to”\)
5. 5\.Two\-step transformations: Source→\\tointermediate→\\totarget via high\-vulnerability classes
6. 6\.Extreme settings:α=1000\\alpha=1000single iteration,α=200\\alpha=200with 5 iterations

##### Results\.

Of 25 resistant pairs, 23 were resolved through parameter optimization alone \(Table[25](https://arxiv.org/html/2607.00089#A5.T25)\)\. The most effective strategies were higher amplification \(resolved 15 pairs\) and different source images \(resolved 5 pairs\)\. Two pairs remained resistant: airplane→\\toautomobile and ship→\\totruck\.

Table 25:Optimization strategy effectiveness for resistant pairs\.
##### Analysis of Persistent Failures\.

The two unresolved pairs \(airplane→\\toautomobile, ship→\\totruck\) are both vehicle→\\tovehicle transitions\. Analysis of the retrieved filters shows high overlap: filters selective for “airplane” also respond strongly to “automobile” \(both encode metallic surfaces, geometric shapes\)\. This represents a genuine limitation of the CNN’s learned representations the model encodes vehicles in a shared feature subspace rather than a failure of the retrieval system\.

### E\.5Filter Selectivity and Class Overlap

During manipulation experiments, we observed that some filters respond to multiple classes with different selectivity strengths\. For example, Filter 81 in Conv3 responds to bothdog\(primary,s=0\.92s=0\.92\) andcat\(secondary,s=0\.31s=0\.31\)\.

##### The Shared Filter Problem\.

Naïvely retrieving “filters associated with cat” would include Filter 81, since cat appears in its top\-kkclass responses\. However, amplifying Filter 81 strengthensdogclassification more thancat, potentially producing the opposite of the intended effect\. We observed this failure mode early in development: requesting “make this a cat” on a dog image sometimesincreaseddog probability\.

##### Solution: Primary\-Class Retrieval Rule\.

Our system addresses this by selecting only filters where the target class is theprimary response\(highest selectivity\), not merely present in the top\-kkresponses\. Formally, for target classcc, we retrieve:

ℱc=\{f:arg⁡maxc′⁡sf,c′=c\}\\mathcal\{F\}\_\{c\}=\\\{f:\\arg\\max\_\{c^\{\\prime\}\}s\_\{f,c^\{\\prime\}\}=c\\\}\(14\)wheresf,c′s\_\{f,c^\{\\prime\}\}is the selectivity of filterfffor classc′c^\{\\prime\}\. This rule is the typed retrieval primitive isolated in the H2 decomposition \(Sec\.[5\.2](https://arxiv.org/html/2607.00089#S5.SS2), Table[2](https://arxiv.org/html/2607.00089#S5.T2), condition C3 vs A\): selectivity\-only ranking achieves 58\.9% success; adding the primary\-class rule on top of the same selectivity raises success to 76\.3% \(\+17\.4\+17\.4pp\)\. The rule is only*expressible*becauseSSis a typed ranking with a well\-defined “primary class”—an unstructured feature store does not admit it\.

##### Implication for Framework Design\.

This finding validates the importance of the Semantics fieldSSin Manifestation Units: storingrankedassociations rather than binary presence enables disambiguation of shared components\. The\(E,S,R,D,G\)\(E,S,R,D,G\)structure explicitly supports this through ordered concept lists with quantified strengths\.

### E\.6Validation Metrics

VAE:Human evaluation of visual faithfulness, identity preservation, and artifact quality\. The consistent retrieval of semantically correct dimensions validates analysis faithfulness even when visual quality is limited by VAE reconstruction\.

CNN:We measure the probability shift toward the target class:

Δ​p=p​\(ctarget\|x,a′\)−p​\(ctarget\|x,a\)\\Delta p=p\(c\_\{\\text\{target\}\}\|x,a^\{\\prime\}\)\-p\(c\_\{\\text\{target\}\}\|x,a\)\(15\)Manipulation is considered successful if both \(i\) the predicted class switches to the target, i\.e\.,arg⁡maxc⁡p​\(c∣x,a′\)=ctarget\\arg\\max\_\{c\}p\(c\\mid x,a^\{\\prime\}\)=c\_\{\\text\{target\}\}, and \(ii\)Δ​p\>0\.1\\Delta p\>0\.1\. TheΔ​p\\Delta pthreshold prevents counting marginal flips caused by near\-ties among classes\. The baseline comparison \(Table[19](https://arxiv.org/html/2607.00089#A5.T19)\) validates that success requires correct filter selection from MANIFESTATION analysis random selection achieves 0% success under identical conditions\.

## Appendix FAdditional Experimental Details

### F\.1Model Architectures

VAE \(CelebA\):

- •Encoder: 4 residual blocks \(128, 256, 512, 512 channels\), GroupNorm, SiLU activation
- •Latent:512×32×32512\\times 32\\times 32\(spatially\-averaged toℝ512\\mathbb\{R\}^\{512\}for analysis\)
- •Decoder: 4 residual blocks with upsampling, symmetric to encoder
- •Training:β\\beta\-VAE withβ=1\\beta=1, Adam optimizer, 3 epochs

CNN \(CIFAR\-10\):

- •Conv1: 32 filters,3×33\\times 3, BatchNorm, ReLU, MaxPool
- •Conv2: 64 filters,3×33\\times 3, BatchNorm, ReLU, MaxPool
- •Conv3: 128 filters,3×33\\times 3, BatchNorm, ReLU, MaxPool
- •FC: 2048→\\to256→\\to10
- •Training: Adam optimizer \(lr=10−3\\text\{lr\}=10^\{\-3\}, weight decay5×10−45\\times 10^\{\-4\}\), 50 epochs, 84\.66% test accuracy

### F\.2Manifestation Unit Statistics

Table 26:Manifestation Unit statistics by architecture\.
### F\.3Evaluation Query Sets

We constructed two query sets per architecture:

Automatic Evaluation \(50 single\-turn queries\):Used for retrieval and generation metrics \(Precision@k, Recall@k, NDCG, BLEU, ROUGE, BERTScore, faithfulness\)\.

- •Entity queries\(20\): “What does dimension 47 encode?”
- •Concept queries\(15\): “Which dimensions relate to smiling?”
- •Relationship queries\(10\): “What dimensions are antagonistic to eyeglasses?”
- •Manipulation queries\(5\): “How do I make a face smile?”

Human & LLM\-as\-Judge Evaluation \(50 multi\-turn conversational queries\):Organized into conversations testing conversational capabilities:

- •Pronoun resolution: “What does dimension 63 encode?”→\\to“Is it part of a family?”
- •Context switching: Tracking multiple dimensions across turns
- •Multi\-dimension tracking: “Compare these two dimensions”
- •Progressive deep\-dive: “Show me its top correlations”→\\to“Tell me more about the first one”
- •Implicit references: “Any other dimensions with similar behavior?”

Note:The retrieval traces in Appx\.[C\.6](https://arxiv.org/html/2607.00089#A3.SS6)use a separate set of 50 example queries for illustration purposes; these are distinct from the evaluation sets described above\.

### F\.4GPT\-2 Manipulation: Per\-Behaviour Summary

Table[27](https://arxiv.org/html/2607.00089#A6.T27)is the headline result for the GPT\-2 instantiation: across five distinct IOI\-style behaviours, framework\-retrieved heads at recommended budgetkkbeat matched\-budget random head sets by1\.751\.75–4\.49×4\.49\\times\. TheGG\-field intervention method \(mean ablation or path patching\) is chosen per behaviour based on the oracle signal type stored in the MU’sDD\-field\. All five experiments were pre\-registered with SHA\-256\-hashed predictions before outcomes were computed; hashes are stored inGPT2/output/validation\_phases/\.

Table 27:GPT\-2 manipulation results\. Framework versus matched\-budget random heads \(mean of33random trials throughout\); “intervention” is theGG\-field method\. Lift=\|=\|framework shift\|/\|\|/\|random shift\|\|\. Absolute scale: IOI path\-patching restores40\.9%40\.9\\%versus23\.3%23\.3\\%random; bigram adds\+0\.211\+0\.211versus\+0\.051\+0\.051nats\.\*Bounded by baseline ceiling0\.970\.97\.##### Per\-behaviour setup\.

Sample sizes:2020Olsson\-style repeated\-token sequences \(length3030\) for induction\-copying tests;3030Wang\-style IOI templates for IO\-token routing and IOI logit\-difference;8080paired clean/corrupted prompts \(BABA corruption\) for path\-patching IOI;2020WikiText samples for bigram\-prediction loss\. Ablation budgetskkper behaviour are derived from the head\-count sweep on the same data and stored in each MU’sDD\-field asrecommended\_budget\_k\. Random\-head baselines use matched budget with seeds\{4242,4243,4244\}\\\{4242,4243,4244\\\}\(mean ablation experiments\) and\{9000,9017,9034\}\\\{9000,9017,9034\\\}\(path\-patching experiments\)\. The concept\-vocabulary pivot that populatesSS\(3/16→13/163/16\\to 13/16reference\-head recovery\) is documented below\.

### F\.5Per\-Architecture Instantiation Table

Table[28](https://arxiv.org/html/2607.00089#A6.T28)gives the per\-architecture instantiation of the MU schema across the three studied architectures\.\(E,S,R,D,G\)\(E,S,R,D,G\)are preserved;TTis populated only for transformer architectures, the only field whose*content type*substantively changes isSS\(categorical class\-associations→\\tofunctional/positional pattern scores\), with corresponding shifts inDD\(Transformer\-derived metrics\) andGG\(architecture\-natural intervention type\)\.

Table 28:Per\-architecture instantiation of the MU schema\. Base Slot structure\(E,S,R,D,G\)\(E,S,R,D,G\)is preserved;TTextends the schema for GPT\-2; theSS\-field’s content type adapts \(categorical→\\tofunctional/positional\), and theGG\-field stores architecture\-natural intervention parameters \(amplification→\\toablation/path\-patching\)\. Indexed\-template counts: 4 retrieval fields per component plus pairwise relationship docs\.AspectVAE \(CelebA\)CNN \(CIFAR\-10\)GPT\-2 \(124M\)ArchitectureEncoder/Latent/Decoder3 conv layers \(32/64/128 filters\)12 layers×\\times12 headsComponent shape512 latent dims224 filters total144 attention headsManifestation Unit fieldsSS\-primitive typecategorical \(class\-assoc\.\)categorical \(class\-assoc\.\)functional/positional patternSS\-contentPearson corr\. with 40 attrsclass\-selectivity over 10 labelsattn\. to induction\-target / IO\-pos / prev / selfRR\-content5122512^\{2\}activation corr\.pairwise corr\. within / cross layerhead\-head corr\. \+ joint\-ablation synergyDD\-metadatavariance, family IDcluster ID, layer positioninduction / copying scores,Δ\\Deltappl, rec\.kkFamily structure20 Ward clustersper\-layer clustersinduction / name\-mover / prev / sink rolesGG\-interventionlatent edit,σ\\sigma\-stepfilter amplification \(α\\alpha\)zero / mean / path\-patchingSamples forSS1,000 \(val\)10,000 \(test\)30 Olsson \+ 30 IOI \+ 30 WikiText†Retrieval / interface\# of MUs512224144Indexed templates2,048 docs943 docs583 docs \(4 doc\-types per head \+ 7 rel\.\)Embedding modelSentence\-BERT \(384d\)Sentence\-BERT \(384d\)Sentence\-BERT \(384d\)LLM backendQwen3\-8BQwen3\-8BQwen3\-8B \(RAG built; pilot validates retrieval\+manipulation, not full LLM\-grounded chat\)Manipulation exampleQuery example“make smile”“make this look like a dog”“which heads copy earlier tokens?”Selected componentsDims 424, 229Filters 81, 39, 122L05\_H05, L06\_H09, L05\_H01Validationdecode→\\tovisualforward→\\toprobability shiftbehavioural metric vs\. random
†For GPT\-2 theSS\-field’s content type required a vocabulary pivot from surface linguistic concepts to MI\-derived functional concepts; details below\.

##### GPT\-2 concept\-vocabulary pivot: details\.

The GPT\-2 row of Table[28](https://arxiv.org/html/2607.00089#A6.T28)required a vocabulary pivot during pilot construction\. We document the pivot here as a methodological lesson rather than a finding: the schema\(E,S,R,D,G,T\)\(E,S,R,D,G,T\)transfers across architectures, but theSS\-primitive must match the architecture’s natural feature axes\.

InitialSS\-primitive \(surface\)\.The first GPT\-2 extraction populatedSSfor each of the 144 attention heads with associations to 48 surface linguistic concepts, computed over 3,000 WikiText\-103 samples\. The surface vocabulary covered standard linguistic categories: part\-of\-speech tags \(e\.g\.,noun,verb,adjective\), syntactic dependency labels \(subject,object,modifier\), token\-level features \(punctuation,capitalized,numeric,rare\_token\), and corpus\-frequency bands\. Association strength was Pearson correlation between per\-token attention weights and the binary concept indicator\. This vocabulary is well\-suited to feed\-forward analyses of token representations but proved inadequate for attention heads, whose computation is positional and relational rather than categorical over surface form\.

Reference set\.We evaluatedSSagainst a literature reference set of 16 attention heads with documented mechanistic roles: induction heads fromOlssonet al\.\([2022](https://arxiv.org/html/2607.00089#bib.bib75)\)and the IOI\-circuit heads fromWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\), including name\-mover heads \(L09 H06, L09 H09, L10 H00\), backup\-name\-mover heads \(L10 H10, L11 H02\), S\-inhibition heads \(L07 H03, L07 H09, L08 H06, L08 H10\), and induction heads \(L05 H05, L05 H08, L06 H09, L07 H02\)\. A head was scored as “recovered” if its primarySS\-association exceededr\>0\.30r\{\>\}0\.30on the corresponding functional axis\. The surface\-concept vocabulary recovered only3/163/16heads at this threshold; the recovered three were heads whose surface correlations happened to align with their functional role \(e\.g\., a name\-mover head correlating with proper\-noun tokens\)\.

RevisedSS\-primitive \(functional\)\.We pivoted to four MI\-derived functional concepts, defined relative to attention output rather than token surface form:

- •Attention\-to\-induction\-target: per\-head fraction of attention mass placed on the token whose copy would complete an induction pattern \(e\.g\., for promptA B …A, attention toB\)\. Computed on Olsson\-style repeated\-token sequences\.
- •IO\-position: per\-head fraction of attention mass placed on the indirect\-object position in IOI templates\(Wanget al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib70)\), distinguishing IO\-attending heads from S\-attending and end\-token\-attending heads\.
- •Previous\-token: per\-head fraction of attention mass placed at offset−1\-1from the current position, capturing the previous\-token\-attending pattern documented inElhageet al\.\([2021](https://arxiv.org/html/2607.00089#bib.bib76)\)\.
- •Self: per\-head fraction of attention mass placed at the current position \(offset0\), which decomposes attention sinks and copy\-suppression heads\.

These four primitives were measured on a smaller multi\-distribution sample \(30 Olsson\-style sequences \+ 30 IOI templates \+ 30 WikiText samples; see Table[28](https://arxiv.org/html/2607.00089#A6.T28)\)\. With this vocabulary,SSrecovered13/1613/16reference heads atr\>0\.30r\{\>\}0\.30\. The three unrecovered heads \(one backup\-name\-mover and two S\-inhibition heads\) require richer relational primitives that the four functional concepts do not capture; these are documented in App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)and would naturally be addressed by SAE\-featureSSat scale\.

Lesson\.The vocabulary\-pivot is reported in this paper because it is the methodologically informative part of the GPT\-2 pilot\. The schema\(E,S,R,D,G\)\(E,S,R,D,G\)is preserved without modification; only theSS\-content adapts, and the appropriateSS\-primitive is determined by the architecture rather than chosen in advance\. We expect the same observation to apply at frontier scale, where SAE features computed against the model’s own residual stream are likely to be the naturalSS\-primitive for transformer\-based MI\(Lieberumet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib67); Cunninghamet al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib74)\)\.

Practical guidance forSS\-primitive selection\.The concept vocabulary forSSshould be drawn from the space of*outputs*a component type produces, not the surface features of inputs that happen to activate it\. Forattention heads: attention\-routing primitives over position\-types \(induction\-target, IO\-position, previous\-token, self\)\. Forconvolutional filters: class\-conditional activation statistics \(selectivity scores over the label space\)\. ForSAE featuresorlinear projections: reconstruction weights over a fixed basis\. Surface linguistic features \(POS tags, dependency labels\) are appropriate only for components whose primary function is categorical discrimination over surface form; using them for positional routers \(attention heads\) causes the3/16→13/163/16\\to 13/16failure documented here\. When the right primitive is unclear, a pilot recovery test against a small literature reference set \(as used here\) provides a principled falsification criterion before committing to the full extraction\.

### F\.6CNN Categorical Structure

The conv3 cosine similarity matrix on CIFAR\-10, computed directly from the stored selectivity vectors, recovers the vehicle/animal block structure \(Fig\.[22](https://arxiv.org/html/2607.00089#A6.F22)\): vehicles \(airplane, automobile, ship, truck\) form a cluster with mean off\-diagonal cosine0\.860\.86\(peak0\.920\.92at auto↔\\leftrightarrowtruck\), animals \(bird, cat, deer, dog, frog, horse\) cluster with mean0\.850\.85\(peak0\.970\.97at cat↔\\leftrightarrowdog\), and cross\-category pairs are markedly less similar \(mean0\.720\.72, min0\.590\.59at airplane↔\\leftrightarrowfrog\)\. This is the CNN analogue of GPT\-2’s per\-layer IOI mediation result \(§[F\.4](https://arxiv.org/html/2607.00089#A6.SS4), Fig\.[23](https://arxiv.org/html/2607.00089#A6.F23)\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/fig/class_similarity_heatmap.png)Figure 22:Pairwise cosine similarity of conv3 class\-selectivity vectors from the stored MU class\-conditional means\. Vehicle and animal blocks emerge without supervision and mirror the within\-category failure pattern in Fig\.[3](https://arxiv.org/html/2607.00089#S5.F3)\.
### F\.7GPT\-2 Per\-Layer IOI Mediation

We patch all 12 attention heads in each layer simultaneously with their corrupted\-prompt activations \(BABA corruption,n=80n=80prompt pairs\) and measure the fraction of clean\-prompt IOI logit\-difference effect restored\(Goldowsky\-Dillet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib77); Heimersheim and Nanda,[2024](https://arxiv.org/html/2607.00089#bib.bib78)\)\. Per\-layer mediation peaks at layers77\(16\.9%16\.9\\%\),88\(22\.3%22\.3\\%\), and99\(29\.4%29\.4\\%\), matching the layer hotspot ofWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)for GPT\-2’s IOI circuit \(Fig\.[23](https://arxiv.org/html/2607.00089#A6.F23)\)\. Layers0–55contribute marginally; layers1010–1111show small or slightly negative effects \(consistent with backup\-name\-mover behaviour at these positions\)\. Random matched\-budget head sets recover−0\.3%\-0\.3\\%to\+1\.6%\+1\.6\\%across trials, providing a clean null baseline\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x18.png)Figure 23:Per\-layer IOI mediation in GPT\-2 under BABA path\-patching \(n=80n\{=\}80prompt pairs\)\. The framework’s retrieval surfaces a peak at layers 7\-9 \(16\.9%16\.9\\%,22\.3%22\.3\\%,29\.4%29\.4\\%effect restored\), reproducing the IOI\-circuit hotspot documented byWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)\.
### F\.8Embedding Stability: Default vs Qwen3\-Embedding\-8B

Figure[24](https://arxiv.org/html/2607.00089#A6.F24)compares per\-field paraphrase stability under two embedding models: the default Sentence\-BERT \(MiniLM, v5\) and Qwen3\-Embedding\-8B \(v6\)\. Stability is measured as Spearmanρ\\rhobetween head rankings on paraphrase query pairs \(left panel\) and as Jaccard@30 \(right panel\)\. TheTTfield was not run under v5\. Qwen3 resolves the instability ofEE\(0\.35→\\to0\.84\) andDD\(0\.58→\\to0\.80\) while preserving the already\-high stability ofRR\(0\.86→\\to0\.93\)\. Fused\-query stability also improves substantially \(0\.50→\\to0\.85\)\. The 0\.7 threshold line marks the minimum acceptable stability for production use; all v6 fields clear this threshold\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x19.png)Figure 24:Embedding sensitivity: per\-field paraphrase stability \(Spearmanρ\\rho, left; Jaccard@30, right\) for default Sentence\-BERT \(light blue\) vs Qwen3\-Embedding\-8B \(dark blue\)\. Fused\-query bars shown separately \(orange/red\)\. Dashed line at 0\.7 marks acceptable stability threshold\.TTfield was not run in v5; Qwen3 resolves instability inEEandDDand raises fused stability from 0\.50 to 0\.85\.
### F\.9Decomposition Quality: Field Merging Comparison

Figure[25](https://arxiv.org/html/2607.00089#A6.F25)shows that the six\-field ESRDGT decomposition is a strict optimum: merging fields into coarser groupings degrades oracle recall@30 significantly\. Pair merging \(ES\|\|RD\|\|GT\) drops recall by−0\.071\-0\.071\(p=0\.005∗∗p\{=\}0\.005^\{\*\*\}\); type merging \(text\|\|struct\|\|num\) by−0\.054\-0\.054\(p=0\.028∗p\{=\}0\.028^\{\*\}\)\. All\-merged reduces recall similarly \(−0\.054\-0\.054\) but is not individually significant \(p=0\.128p\{=\}0\.128\), likely due to overlap with the other merged conditions\. The result supports keeping individual field granularity: the decomposition is not arbitrary—collapsing it loses retrieval power\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x20.png)Figure 25:Field decomposition quality: oracle recall@30 for the ESRDGT 6\-field baseline vs three merged\-field configurations\. All merges degrade recall; pair\-merge and type\-merge are statistically significant \(p<0\.05p<0\.05\)\. Dashed line marks baseline recall\. Significant reductions confirm that the individual\-field decomposition is the optimal granularity\.

## Appendix GPath\-Patching Analysis

This appendix reports the full path\-patching causal\-mediation analysis on GPT\-2’s IOI circuit, supplementing the scope paragraph in §[5\.4](https://arxiv.org/html/2607.00089#S5.SS4)and the limitations discussion in §[6](https://arxiv.org/html/2607.00089#S6)\.

### G\.1Budget\-Matched Comparison at Variablekk

Table[29](https://arxiv.org/html/2607.00089#A7.T29)compares the fraction of clean\-prompt IOI logit\-difference restored \(frac\_restored\) for three head sets across retrieval budgetsk∈\{7,15,20,30\}k\\in\\\{7,15,20,30\\\}: FRAMEWORK\_NL \(top\-kkheads retrieved by our structured query\); the oracle set \(the 7 canonical IOI name\-mover heads fromWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)\); and random matched\-budget heads \(mean of 3 seeds\)\.

Table 29:Path\-patchingfrac\_restoredat variable retrieval budgetkk\(n=80n\{=\}80BABA prompt pairs\)\. Oracle set is fixed at 7 heads regardless ofkk; framework and random vary withkk\.At the oracle\-set\-matched point \(k=7k\{=\}7, set size of the canonical circuit, not the retrieval budget\), FRAMEWORK\_NL restores only0\.0370\.037vs the oracle’s0\.1170\.117—the framework*loses*to the oracle at oracle\-set\-matchedk=7k\{=\}7\. The apparently strongk=30k\{=\}30result \(0\.4090\.409vs random0\.2330\.233\) reflects a4\.3×4\.3\\timeslarger head set rather than per\-head causal enrichment, and should not be read as evidence of mechanistic precision\.

### G\.2Layer\-Wise Mediation

Per\-layer IOI mediation \(all 12 heads per layer simultaneously patched\) peaks at layers 7 \(16\.9%16\.9\\%\), 8 \(22\.3%22\.3\\%\), and 9 \(29\.4%29\.4\\%\), consistent with the L7–9 name\-mover hotspot ofWanget al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib70)\)\. Layers 10–11 show small or slightly negative contributions, consistent with backup\-name\-mover behaviour\. This layer\-wise curve is shown in Fig\.[23](https://arxiv.org/html/2607.00089#A6.F23)\(App\.[F\.4](https://arxiv.org/html/2607.00089#A6.SS4)\)\.

### G\.3Per\-Field Causal Enrichment \(test\_g\)

Table[30](https://arxiv.org/html/2607.00089#A7.T30)reports whether heads retrieved by each individual field are causally enriched for IOI mediation, tested against a field\-matched random baseline using a one\-sidedtt\-test with Bonferroni correction across fields and strategies\.

Table 30:Per\-field causal enrichment \(test\_g\): Bonferroni\-correctedpp\-values across all 6 fields and retrieval strategies\. All tests fail to reject the null \(H0H\_\{0\}: field\-retrieved heads are not causally enriched over matched\-budget random\)\.All 6 fields producep=1\.0p\{=\}1\.0after Bonferroni correction: no individual field retrieves a head set that is causally enriched for IOI path\-patching beyond what a random matched\-budget set would achieve\.

### G\.4Mechanistic Interpretation

Three factors explain this null result without invalidating the framework:

\(1\) The IOI circuit is intrinsically distributed\.The 7 canonical oracle name\-mover heads themselves restore onlyfrac\_restored=0\.117\\texttt\{frac\\\_restored\}\{=\}0\.117\. No small head set, however well\-chosen, will restore a large fraction of the IOI logit\-difference because the circuit distributes the computation across many heads and layers\.

\(2\)TT\-field primitives are correlated with but not equal to path\-patching scores\.TheTT\-field encodes attention\-pattern features \(induction/copying scores, QK/OV circuit norms, position ratios\)\. These correlate with mechanistic roles but are not optimised to predictfrac\_restored\. ATT\-field populated directly from path\-patching scores—possible in principle, costly in practice—would close this gap\.

\(3\) Retrieval enrichment≠\\neqcausal enrichment\.The framework is designed to surface heads with structured mechanistic descriptions, not to maximise path\-patching recovery\. The oracle recall result \(5/7 L7–9 name\-movers recovered atk=30k\{=\}30\) and the behavioural lift results \(Table[27](https://arxiv.org/html/2607.00089#A6.T27)\) confirm that retrieval enrichment is real; the path\-patching null result says only that this enrichment does not translate to per\-head causal superiority over random within the distributed IOI circuit\.

## Appendix HField\-Level Oracle Discriminability

This analysis tests whether oracle heads \(the 7 canonical IOI name\-mover heads\) are statistically distinguishable from randomly\-drawn heads using each field’s own stored statistics, independent of query\-based retrieval\. Two scoring modes are used:hand\(hand\-crafted per\-field scoring, query\-conditioned forDDandTT\) andlearned\(logistic\-regression probability fit on oracle vs\. non\-oracle heads\)\. A one\-sided Mann\-WhitneyUU\-test is used; no Bonferroni correction is applied \(exploratory\)\.

Table 31:Field\-level oracle discriminability \(pp\-values, Mann\-WhitneyUU, oracle vs\. random heads\)\.Dis significant in both modes;Tsignificant in learned mode only\. Bold =p<0\.05p\{<\}0\.05\.Interpretation\.DDis the only field whose stored statistics consistently discriminate oracle from random heads across both modes\. This is not contradicted by the ablation finding thatDD*interferes*with retrieval:DDencodes information correlated with oracle\-head identity \(induction scores, copying scores,Δ\\Deltappl\) but when used as a retrieval basis, its dynamics vocabulary attracts non\-oracle heads with high numeric activity, adding noise\.TTdiscriminates in learned mode only, suggesting its attention\-pattern features partially recover the oracle signal when fit to the oracle set—but not under general query\-based retrieval\.

Caveat\.Learned\-mode scores are fit directly on the oracle set and are not query\-conditioned; these results are exploratory and should not be read as retrieval benchmarks\.

## Appendix IPer\-Field Singleton Retrieval

This appendix reports field\-level singleton retrieval performance: each field queried alone, without combination, against the 7\-head IOI oracle set\. Data are from the Qwen3\-Embedding\-8B \(v6\) configuration\.

### I\.1Oracle Recall and MRR per Field

Table 32:Per\-field singleton oracle retrieval on GPT\-2 ESRDGT schema \(Qwen3\-Embedding\-8B\)\. Oracle set: 7 canonical IOI L7–9 name\-mover heads\. Each field queried independently; no field combination\.
### I\.2Field–Function Dissociation

Table[32](https://arxiv.org/html/2607.00089#A9.T32)reveals a dissociation between*set retrieval*\(recall@30\) and*first\-rank retrieval*\(MRR\):

R dominates set retrieval\.RRachieves the highest recall@30 \(0\.4290\.429, recovering3/73/7oracle heads\), indicating that the relational field—encoding head\-to\-head activation correlations and joint\-ablation synergies—captures the most oracle\-head signal when used alone\.

T and D lead first\-rank retrieval\.TTachieves the highest MRR \(0\.0570\.057\) followed byDD\(0\.0400\.040\), meaning that the attention\-pattern primitives and descriptor metadata are most likely to place an oracle head at the very top of the ranking\.RR’s MRR \(0\.0250\.025\) is notably lower than its recall@30, confirming thatRRrecovers oracle heads by casting a wide net rather than by precision ranking\.

E retrieves nothing\.EE\(entity name / head identifier\) achieves recall@30=0\.000=0\.000and MRR=0\.014=0\.014, consistent with the finding that entity labels do not carry mechanistic information at singleton resolution—and with the LOO result that removingEEfrom the full schema*improves*recall \(it actively interferes\)\.

This dissociation has a practical implication: if the goal is broad oracle head coverage \(retrieval recall\),RRis the single most informative field; if the goal is precise first\-hit ranking \(MRR\),TTandDDshould be weighted more heavily\. The minimal\-optimalS\+RS\{\+\}Rcombination benefits from both:RR’s wide net andSS’s complementary, weakly anti\-correlated head ranking \(ρ=−0\.20\\rho\{=\}\{\-\}0\.20, Fig\.[5](https://arxiv.org/html/2607.00089#S5.F5)B\)\.

Figure[26](https://arxiv.org/html/2607.00089#A9.F26)visualises both panels: grouped recall bars atk∈\{7,15,30\}k\\in\\\{7,15,30\\\}per field \(left\) and MRR per field \(right\)\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x21.png)Figure 26:Per\-field singleton oracle retrieval \(Qwen3\-Embedding\-8B\)\.Left:grouped oracle recall atk=7k\{=\}7\(light blue\),k=15k\{=\}15\(medium blue\),k=30k\{=\}30\(dark blue\)\.RRdominates recall@30 \(0\.430\.43\);EEretrieves nothing at anykk\.Right:per\-field MRR\.TTleads \(0\.0570\.057\), followed byDD\(0\.0400\.040\) andRR\(0\.0250\.025\)\. The dissociation between recall\-leadership \(RR\) and MRR\-leadership \(TT,DD\) reflects different retrieval modes:RRcasts a wide net;TT/DDplace oracle heads at the top of the ranking\.

## Appendix JMetric Definitions

We organize evaluation metrics into two groups: automatic metrics for system performance, and human/LLM rating dimensions for explanation quality\. Table[33](https://arxiv.org/html/2607.00089#A10.T33)summarizes both groups\.

Table 33:Evaluation metrics organized by type\.TypeCategoryMetricsAutomaticRetrieval \(4\)Precision@k, Recall@k, F1@k, NDCGGeneration \(5\)Gen\-F1, BLEU, ROUGE\-1, ROUGE\-2, ROUGE\-LSemantic \(7\)BERT\-P, BERT\-R, BERT\-F1, 1/2/3\-gram overlap,Semantic Sim, Avg SimFaithfulness \(2\)Attribution Score, Factual AccuracyHuman/LLM \(7\)Comprehensibility, Faithfulness, Correctness,Usefulness, Specificity, Trustworthiness, Coherence### J\.1Retrieval Metrics

Precision@k: Fraction of retrieved units that are relevant\.

Precision@k=\|Retrievedk∩Relevant\|k\\text\{Precision@k\}=\\frac\{\|\\text\{Retrieved\}\_\{k\}\\cap\\text\{Relevant\}\|\}\{k\}\(16\)
Recall@k: Fraction of relevant units that are retrieved\.

Recall@k=\|Retrievedk∩Relevant\|\|Relevant\|\\text\{Recall@k\}=\\frac\{\|\\text\{Retrieved\}\_\{k\}\\cap\\text\{Relevant\}\|\}\{\|\\text\{Relevant\}\|\}\(17\)
F1@k: Harmonic mean of Precision@k and Recall@k\.

NDCG: Normalized Discounted Cumulative Gain, measuring ranking quality with position\-based discounting\.

Gold Set Construction\.Relevant units are defined as the gold set constructed by matching ground\-truth entity IDs, concept labels, and relationship structures for each query:

- •For entity queries \(e\.g\., “What does dimension 47 encode?”\), the gold set contains the single matching MU\.
- •For concept queries \(e\.g\., “Which dimensions relate to smiling?”\), the gold set contains all MUs where the target concept appears in the top\-mmassociations\.
- •For relationship queries \(e\.g\., “What dimensions are antagonistic to eyeglasses?”\), the gold set contains the top\-rrneighbors inRkR\_\{k\}whose correlation sign matches the query label \(synergistic or antagonistic\)\.

Gold sets were constructed programmatically from the extracted Manifestation Units\. The comparison against BM25\-hybrid and unstructured\-text baselines \(Table[1](https://arxiv.org/html/2607.00089#S5.T1)\) controls for the shared data: those baselines have identical access to the same per\-component statistics but achieve only 18–20% precision, confirming that the structuredSS\-field separation—not circular access to the gold\-set content—drives the retrieval advantage\.

### J\.2Generation Metrics

BLEU:nn\-gram precision with brevity penalty, computed using SacreBLEU\(Post,[2018](https://arxiv.org/html/2607.00089#bib.bib1)\)\.

ROUGE\-1/2/L: Recall\-orientednn\-gram overlap \(unigram, bigram, longest common subsequence\)\.

Gen\-F1: Token\-level F1 between generated and reference responses\.

### J\.3Semantic Similarity Metrics

BERTScore: Contextual embedding similarity using BERT\(Zhanget al\.,[2020](https://arxiv.org/html/2607.00089#bib.bib13)\)\. We report Precision \(BERT\-P\), Recall \(BERT\-R\), and F1 \(BERT\-F1\)\.

nn\-gram Overlap: Exactnn\-gram match ratios forn∈\{1,2,3\}n\\in\\\{1,2,3\\\}\.

Semantic Sim: Cosine similarity between sentence embeddings \(Sentence\-BERT\)\.

### J\.4Faithfulness Metrics

Factual Accuracy: Binary metric indicating whether all quoted statistics in the response exactly match values in the retrieved Manifestation Unit fields\. We verify both numeric values \(correlations, selectivity scores\) and discrete labels \(cluster IDs, synergistic/antagonistic classifications\)\. Computed by extracting values from responses and verifying against serialized\(E,S,R,D,G\)\(E,S,R,D,G\)fields\.

Attribution Score: Fraction of response claims that can be attributed to retrieved content\. We adapted the RAGAS faithfulness measure, which computes entailment between individual response statements and the retrieved context\(Eset al\.,[2024](https://arxiv.org/html/2607.00089#bib.bib14)\)\.

### J\.5Human and LLM\-as\-Judge Metrics

We adapt seven dimensions from the Explanation Satisfaction framework\(Hoffmanet al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib15)\):

- •Comprehensibility: Is the explanation easy to understand?
- •Faithfulness: Does the explanation accurately reflect the model’s behavior?
- •Correctness: Are the stated facts accurate?
- •Usefulness: Does the explanation help accomplish the user’s goal?
- •Specificity: Does the explanation provide sufficient detail?
- •Trustworthiness: Can the user trust this explanation?
- •Coherence: Is the explanation logically organized?

All dimensions are rated on 5\-point Likert scales \(1=Strongly Disagree, 5=Strongly Agree\)\.

## Appendix KHuman Evaluation Details

Tables[34](https://arxiv.org/html/2607.00089#A11.T34)and[35](https://arxiv.org/html/2607.00089#A11.T35)present complete human evaluation results across all seven dimensions and three expertise levels\.

Table 34:VAE system human evaluation scores by expertise level \(315 total evaluations\)\. Beginners rate most favorably; experts apply stricter standards across all metrics\.Table 35:CNN system human evaluation scores by expertise level \(297 total evaluations\)\. Pattern mirrors VAE results with expertise gap of 0\.65 points between beginners and experts\.Figure[27](https://arxiv.org/html/2607.00089#A11.F27)illustrates the expertise effect across metrics for the CNN system, showing consistent pattern where beginners rate highest and experts most critically\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x22.png)Figure 27:CNN system human evaluation scores by expertise level\. Beginners \(teal\) consistently rate higher than intermediates \(orange\) and experts \(purple\) across all seven metrics\.Figure[28](https://arxiv.org/html/2607.00089#A11.F28)shows score distributions via box plots, revealing that experts exhibit higher variance in their ratings, particularly for Trustworthiness and Usefulness\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x23.png)Figure 28:Score distribution by expertise level for CNN system\. Box plots reveal experts \(purple\) have wider score distributions, reflecting more nuanced evaluation criteria\.Figure[29](https://arxiv.org/html/2607.00089#A11.F29)presents the average scores across metrics for the VAE system\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/fig/vae-average.png)Figure 29:VAE system average evaluation scores across all seven metrics\. All dimensions exceed 3\.8/5\.0, with Coherence \(4\.16\) and Specificity \(4\.14\) rated highest; Usefulness \(3\.82\) rated lowest but still above neutral\.### K\.1Inter\-Rater Reliability Analysis

To assess the consistency of human evaluations, we compute standard inter\-rater reliability \(IRR\) metrics across all evaluators\. Tables[36](https://arxiv.org/html/2607.00089#A11.T36)and[37](https://arxiv.org/html/2607.00089#A11.T37)present comprehensive IRR statistics for both systems\.

#### K\.1\.1IRR Metrics

We report four complementary reliability measures:

- •ICC\(2,1\): Intraclass Correlation Coefficient for single rater reliability under a two\-way random effects model\(Shrout and Fleiss,[1979](https://arxiv.org/html/2607.00089#bib.bib61)\)\.
- •ICC\(2,k\): ICC for the average ofkkraters, indicating reliability of mean ratings\.
- •Krippendorff’sα\\alpha: A versatile reliability coefficient suitable for ordinal data\(Krippendorff,[2011](https://arxiv.org/html/2607.00089#bib.bib62)\)\.
- •Fleiss’κ\\kappa: Multi\-rater extension of Cohen’s kappa for categorical agreement\(Fleiss,[1971](https://arxiv.org/html/2607.00089#bib.bib63)\)\.

We additionally report pairwise agreement rates: exact agreement \(identical ratings\) and within\-1 agreement \(ratings differing by at most 1 point on the 5\-point scale\)\.

#### K\.1\.2VAE System Inter\-Rater Reliability

Table 36:Inter\-rater reliability metrics for VAE system \(9 evaluators, 315 evaluations\)\. Low traditional IRR metrics reflect systematic expertise\-level calibration differences rather than random disagreement; within\-1 agreement exceeds 75% across all dimensions\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x24.png)Figure 30:VAE system inter\-rater reliability heatmap\. Traditional metrics \(ICC, Krippendorff’sα\\alpha, Fleiss’κ\\kappa\) show low values due to systematic expertise\-level calibration differences, not random disagreement\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x25.png)Figure 31:VAE system pairwise agreement rates by quality dimension\. While exact agreement averages 32\.1%, within\-1 agreement exceeds 75% for all metrics\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x26.png)Figure 32:VAE system pairwise rater agreement matrix \(within±\\pm1 point\)\. E1–E9 represent anonymized evaluators\.
#### K\.1\.3CNN System Inter\-Rater Reliability

Table[37](https://arxiv.org/html/2607.00089#A11.T37)presents inter\-rater reliability metrics for the CNN system across 9 evaluators and 297 total evaluations\. The pattern closely mirrors VAE results, with low traditional IRR metrics but strong within\-1 agreement \(75\.9% average\), confirming that the expertise\-driven calibration effects observed in VAE evaluation generalize across architectures\.

Table 37:Inter\-rater reliability metrics for CNN system \(9 evaluators, 297 evaluations\)\. Pattern mirrors VAE results, confirming that expertise\-driven calibration differences are consistent across architectures\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x27.png)Figure 33:CNN system inter\-rater reliability heatmap\. Pattern mirrors VAE results, with low traditional metrics reflecting systematic expertise effects\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x28.png)Figure 34:CNN system pairwise agreement rates by quality dimension\. Within\-1 agreement exceeds 72% for all metrics\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x29.png)Figure 35:CNN system pairwise rater agreement matrix \(within±\\pm1 point\)\. E1–E9 represent anonymized evaluators\.
#### K\.1\.4Interpretation

Following established benchmarks\(Cicchetti,[1994](https://arxiv.org/html/2607.00089#bib.bib64); Landis and Koch,[1977](https://arxiv.org/html/2607.00089#bib.bib65)\), ICC values below 0\.40 indicate poor reliability, while Krippendorff’sα\\alphabelow 0\.667 suggests only tentative conclusions\. Our results show low traditional IRR metrics \(average ICC\(2,1\) = 0\.066 for VAE, 0\.060 for CNN\), which initially appears concerning\. However, this pattern reflects a well\-documented phenomenon in subjective evaluation studies:systematic rater calibration differencesrather than random disagreement\(Grahamet al\.,[2015](https://arxiv.org/html/2607.00089#bib.bib66)\)\.

#### K\.1\.5Understanding Low Traditional IRR with High Practical Agreement

Three key observations explain this apparent paradox:

\(1\) Systematic Expertise Effect:As documented in Sec\.[K](https://arxiv.org/html/2607.00089#A11), experts consistently rate 0\.4–0\.6 points lower than beginners across all metrics\. This systematic offset inflates between\-rater variance, reducing ICC and Krippendorff’sα\\alpha, even though raters agree on relative quality ordering\.

\(2\) High Within\-1 Agreement:Despite low traditional metrics, within\-1 agreement rates of 78\.4% \(VAE\) and 75\.9% \(CNN\) demonstrate that evaluators rarely disagree by more than one point\. For 5\-point Likert scales, this represents strong practical agreement—a difference between rating 4 vs\. 5 is qualitatively minor\.

\(3\) Metric Ranking Concordance:Kendall’sWWcoefficients of 0\.260 \(VAE\) and 0\.083 \(CNN\) indicate that while absolute scores differ by expertise level, evaluators show agreement on which quality dimensions perform better or worse\. All groups consistently rate Coherence and Specificity highest, while Usefulness and Trustworthiness receive the lowest ratings\.

#### K\.1\.6Precedent in XAI Evaluation Literature

Low traditional IRR metrics are common in explainable AI evaluation studies\.Hoffmanet al\.\([2023](https://arxiv.org/html/2607.00089#bib.bib15)\)report similar patterns when evaluating explanation satisfaction, noting that expertise\-driven calibration differences are expected and informative\. The systematic nature of our expertise effect—where experts apply stricter but internally consistent standards—validates our stratified evaluation design rather than indicating measurement failure\.

#### K\.1\.7Summary

Our IRR analysis reveals that traditional IRR metrics \(ICC≈\\approx0\.06, Krippendorff’sα\\alpha≈\\approx0\.01\) are low due to systematic expertise\-level calibration, not random noise\. Within\-1 agreement rates of 76–78% indicate strong practical consistency\. The expertise gap is a feature, not a bug: experts appropriately apply stricter evaluation criteria to AI\-generated explanations\. Cross\-architecture consistency \(similar patterns for VAE and CNN\) supports the reliability of our evaluation methodology\. We recommend that future XAI evaluation studies report both traditional IRR metrics and practical agreement rates, while stratifying by evaluator expertise to capture meaningful calibration differences\.

## Appendix LLLM\-as\-Judge Evaluation

We compare human evaluations with two LLM judges: Claude\-Opus and GPT\-5\.1\. Table[38](https://arxiv.org/html/2607.00089#A12.T38)and Table[39](https://arxiv.org/html/2607.00089#A12.T39)present the full comparison\.

Table 38:LLM\-as\-judge evaluation for VAE system\. Both LLM judges rate higher than humans, with Claude\-Opus showing optimism bias of \+0\.59 points overall\.##### GPT\-2 BM25 baseline \(oracle recall@kk\)\.

Table[42](https://arxiv.org/html/2607.00089#A14.T42)reports BM25 lexical retrieval on the GPT\-2 ESRDGT schema, using the same oracle set \(7 canonical IOI name\-mover heads\)\. BM25 recall@30 falls*below*the random\-partition mean, confirming that keyword\-based retrieval provides no signal on functional\-concept queries where surface form is uninformative\.

Table 39:LLM\-as\-judge evaluation for CNN system\. Claude\-Opus maintains consistent optimism bias \(\+0\.47 points\); GPT\-5\.1 shows similar pattern with \+0\.22 points overall\.The optimism bias is consistent with documented LLM judge tendencies toward fluent, well\-structured responses\(Zhenget al\.,[2023](https://arxiv.org/html/2607.00089#bib.bib17)\)\. Importantly, the relative ordering of metrics is preserved: both humans and LLM judges rate Comprehensibility and Coherence highest, while Usefulness and Trustworthiness receive lower \(but still positive\) ratings\.

Figure[36](https://arxiv.org/html/2607.00089#A12.F36)and Figure[37](https://arxiv.org/html/2607.00089#A12.F37)present heatmap visualizations comparing all evaluator groups across metrics\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/fig/heatmap-vae.png)Figure 36:VAE system evaluation heatmap across all evaluator groups\. Darker green indicates higher scores\. Claude\-Opus consistently rates highest; experts rate most critically\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x30.png)Figure 37:CNN system evaluation heatmap across all evaluator groups\. Pattern mirrors VAE results with LLM judges showing systematic optimism bias\.Figure[38](https://arxiv.org/html/2607.00089#A12.F38)directly compares human average scores with both LLM judges for the CNN system\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x31.png)Figure 38:Human vs LLM\-as\-Judge comparison for CNN system\. Human averages \(blue\) are consistently lower than Claude\-Opus \(purple\) and GPT\-5\.1 \(green\) across most metrics\.Figure[39](https://arxiv.org/html/2607.00089#A12.F39)and Figure[40](https://arxiv.org/html/2607.00089#A12.F40)show overall score comparisons across all evaluator types\.

![Refer to caption](https://arxiv.org/html/2607.00089v1/x32.png)Figure 39:Overall scores comparison for VAE system\. Claude\-Opus achieves highest overall \(4\.60\), followed by GPT\-5\.1 \(4\.25\), beginners \(4\.17\), intermediates \(4\.11\), human average \(4\.02\), and experts \(3\.76\)\.![Refer to caption](https://arxiv.org/html/2607.00089v1/x33.png)Figure 40:Overall scores comparison for CNN system\. Claude\-Opus achieves highest overall \(4\.52\), followed by beginners \(4\.40\), GPT\-5\.1 \(4\.27\), intermediates \(4\.00\), human average \(4\.05\), and experts \(3\.75\)\.
### L\.1Key Findings

Expertise Effect:Experts consistently rate 0\.4–0\.6 points lower than beginners across both systems, with largest gaps in Trustworthiness and Usefulness\. This reflects appropriate skepticism about AI\-generated explanations from knowledgeable users\.

LLM Optimism Bias:Both LLM judges exhibit systematic optimism, with Claude\-Opus showing larger bias \(\+0\.5–0\.6 points\) than GPT\-5\.1 \(\+0\.2–0\.3 points\)\. GPT\-5\.1 occasionally rates below human averages for Faithfulness and Correctness\.

Metric Ordering Preservation:Despite absolute score differences, relative metric rankings remain consistent across evaluator types\. Coherence and Comprehensibility receive highest ratings; Usefulness and Trustworthiness receive lowest\.

Cross\-Architecture Consistency:Both VAE and CNN systems show similar evaluation patterns, supporting the framework’s architecture\-agnostic design\.

## Appendix MAutomatic Evaluation Details

Table[40](https://arxiv.org/html/2607.00089#A13.T40)presents comprehensive automatic evaluation results across both architectures, LLM backends, and retrieval depthsk∈\{5,10,20\}k\\in\\\{5,10,20\\\}\.

Table 40:Comprehensive automatic evaluation results\. Bold: best per architecture\-kkcombination\. All systems achieve high retrieval recall and faithfulness, with Qwen showing strongest generation quality across both architectures\.Key observations:

- •The CNN system achieves higher retrieval precision than VAE \(96\.8% vs\. 89\.6% atk=5k=5\) due to the discrete nature of filter–class associations compared to continuous VAE dimensions\.
- •Precision naturally decreases askkincreases, while recall remains perfect \(100%\) because gold sets are small \(1–5 units\) and consistently captured within the top\-kkresults\.
- •Qwen3\-8B achieves the highest generation quality \(Gen\-F1 up to 50\.8%\) and attribution scores \(up to 70\.1%\), suggesting stronger adherence to retrieved evidence\.
- •Claude\-Opus demonstrates consistently superior factual accuracy \(99\.2–99\.6%\) but lower attribution, indicating a more conservative generation style that prioritizes correctness\.
- •We hypothesize that Qwen’s stronger generation performance may stem from its text\-only design explicitly optimized for natural language tasking, whereas multimodal\-capable LLMs such as Claude and GPT distribute representational capacity across multiple modalities, potentially reducing specialization for structured text\-based retrieval and generation\.
- •Despite these differences, all configurations maintain high factual accuracy \(\>94%\>94\\%\), suggesting that grounding quality may matter more than model scale when retrieval provides correct and structured context\.

## Appendix NFull Ablation Results

Table[41](https://arxiv.org/html/2607.00089#A14.T41)presents comprehensive ablation results across 14 configurations\.

Configuration descriptions\.

- •Full System \(Conversational\): Complete MANIFESTATION with all components including conversation state management\.
- •Manifestation \(Base\): Core system without conversational layer\.
- •No Reranking: Disables similarity threshold filtering; accepts all retrieved documents regardless of similarity score \(threshold set to 0\.0\)\.
- •No Over\-retrieval: Retrieves exactlykkdocuments instead of5​k5kcandidates with subsequent filtering \(search multiplier set to 1\)\.
- •No Exact Match Boosting: Disables the 1\.5×\\timessimilarity boost for exact\-match documents; exact matches still prioritized by flag but scores are not inflated\.
- •Dims Index Only: Uses only the dimension/filter index, excluding Q&A and interaction indices\.
- •No Query Reformulation: Disables context\-aware query reformulation; pronouns and references are not resolved using conversation history\.
- •No Exact Match: Disables entity\-aware exact matching; dimension/filter identifiers are extracted for statistics only, not used for retrieval prioritization\.
- •Semantic Search Only: Pure embedding\-based retrieval without exact matching, boosting, or threshold filtering\.
- •Exact Match Only: Retrieves only explicitly referenced entities via metadata lookup; no semantic expansion for conceptual queries\.
- •Unstructured Text: Same statistical content serialized as free\-form prose without\(E,S,R,D,G\)\(E,S,R,D,G\)structure or identifier normalization\.
- •Q&A Index Only: Uses only the pre\-computed question\-answer pair index\.
- •Interactions Index Only: Uses only the pairwise interaction/relationship index\.
- •BM25 Hybrid: Combines BM25 sparse retrieval \(term\-frequency\-based\) with dense semantic embeddings, merging results by combined score\.
- •ID Normalized \(Semantic\): Prepends normalized identifier tokens \(e\.g\.,DIM\_063,CONV2\_F23\) to document text before embedding, then performs semantic search\.

Critical failures \(bottom block\) are configurations where removing a component causes dramatic performance collapse\.

Table 41:Comprehensive evaluation atk=5k\{=\}5\. Top block: MANIFESTATION ablations \(14 configurations for VAE; 7 applicable configurations for CNN — the CNN pipeline is non\-conversational and uses a single hybrid retriever, making VAE\-specific conversational ablations inapplicable\)\. Bottom block: traditional retrieval baselines\. Cells marked “–” denote inapplicable configurations; see text for explanation of the Manifestation \(Base\) CNN entry\.##### Per\-Query\-Type Breakdown\.

Entity queries \(e\.g\., “What does dimension 47 encode?”\) achieve 95\.0% \(VAE\) and 100\.0% \(CNN\) precision with exact matching, but only 5\.0% and 10\.0% with semantic search alone\. Concept queries show the opposite: semantic search achieves 78\.0% \(VAE\) and 86\.7% \(CNN\), while exact matching drops to 20\.0% and 33\.3%\. This demonstrates why hybrid retrieval is necessary—neither strategy alone handles both query types\.

Table 42:GPT\-2 oracle recall@kkfor BM25 \(lexical\) vs baselines\. Oracle set: 7 canonical IOI L7–9 name\-mover heads\. BM25 recall@30=0\.143=0\.143falls below random \(0\.3040\.304\), confirming surface\-form retrieval carries no signal on functional\-concept queries\.