Towards Mechanistically Understanding Why Memorized Knowledge Fails to Generalize in Large Language Model Finetuning

# Towards Mechanistically Understanding Why Memorized Knowledge Fails to Generalize in Large Language Model Finetuning
Source: [https://arxiv.org/html/2607.08393](https://arxiv.org/html/2607.08393)
Lu Dai2,1Ziyang Rao1Yili Wang1Hanqing Wang1 Hao Liu1,2Hui Xiong1,2 1HKUST\(GZ\)2HKUST ldaiae@connect\.ust\.hk\{liuh,xionghui\}@ust\.hk

###### Abstract

Fine\-tuning LLMs to inject new knowledge faces a critical challenge: LLMs can quickly memorize new facts, yet fail to use them for downstream reasoning tasks\. We formalize this failure as theKnowing–Using Gap, characterized by an accuracy gap and a temporal lag between memorization and generalization\. To understand this phenomenon, we fine\-tune LLMs with unseen knowledge and monitor the spatial permeation dynamics of the knowledge internally using a novel intervention technique called self\-patching\. Self\-patching identifies activation locations where relocating representations substantially improves failed generalization cases\. These results are consistent with a knowledge\-circuit misalignment hypothesis: memorized representations can exist internally but may not be routed to computation\-effective layers\. To demonstrate the practicality of this diagnostic finding, we design a simple heuristic strategy which recovers 58–75% of the oracle headroom in generalization failure\. Experiments are done cross\-domain for the robustness of this finding\. Code and data are open at[https://anonymous\.4open\.science/r/Mem2Gen\-71FF](https://anonymous.4open.science/r/Mem2Gen-71FF)\.

## 1Introduction

Large language models \(LLMs\) excel at varieties of tasks but face significant challenges in adapting to unseen information, necessitating effective methods for post\-training knowledge updates\. While there are approaches like retrieval\-augmented generation \(RAG\) and knowledge editing[Meng et al\.](https://arxiv.org/html/2607.08393#bib.bib17); Gupta et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib13)\), fine\-tuning remains a fundamental paradigm for knowledge updating, as it not only operates on parametric memory end\-to\-end but also injects knowledge in a way that can be reused by the model’s existing reasoning capabilities\.

Despite sufficient capacity to fit new dataMorris et al\. \([2025](https://arxiv.org/html/2607.08393#bib.bib19)\);[Allen\-Zhu and Li](https://arxiv.org/html/2607.08393#bib.bib3), LLMs exhibit a “remembering but not using” failureOvadia et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib23)\); Soudani et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib28)\); Zhong et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib36)\); Cohen et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib7)\);[Berglund et al\.](https://arxiv.org/html/2607.08393#bib.bib5)as shown in Figure[1](https://arxiv.org/html/2607.08393#S1.F1): models can memorize new facts \(e\.g\.,“Sydney is located in \[Entity\]”\) but fail to reliably*use*them in downstream reasoning \(e\.g\.,“The capital of the country Sydney located is …”\)Zhong et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib36)\); Cohen et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib7)\); Yao et al\. \([2025](https://arxiv.org/html/2607.08393#bib.bib34)\), creating a gap between simple memorization and flexible generalization\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/x1.png)Figure 1:Illustration of the Knowing–Using Gap\.We term this phenomenon theKnowing–Using Gap, characterized by two distinct disparities: 1\) anaccuracy gap, where generalization accuracy remains significantly lower than memorization; and 2\) atemporal lag, where generalization emerges significantly later after remembering\.

This observation raises fundamental research questions on the mechanics of fine\-tuning:Once a fact is memorized, when and why does it become accessible to the model’s existing reasoning circuits?

To address these questions, we conduct a fine\-grained analysis of the training dynamics during knowledge injection\. We construct datasets from two real\-world domain knowledge bases and eliminate overlap with pretraining\. We define two types of reasoning QA tasks to evaluate how LLMs generalize the learned knowledge:chaining taskrequires resolving a bridge entity in the first hop to solve the second; andintersection taskrequires retrieving attributes for two entities and filtering by a required relation\. These tasks explicitly test whether injected knowledge can be propagated to reasoning beyond recalled in isolation\.

To investigate the underlying mechanics, we introduceself\-patching, a variant of activation patchingGhandeharioun et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib12)\);[Zhang and Nanda](https://arxiv.org/html/2607.08393#bib.bib35)which copies the hidden layer representation of an anchor position from a source run and substitutes it into a target run at a target layer, then measures the probability change of the correct answer\. By thoroughly scanning layers in LLM and across fine\-tuning, self\-patching yields a time\-evolving fine\-grained spatial map of the permeation of knowledge, identifying which layers and positions contain representations that can unlock the correct answer when routed into an appropriate position\.

Based on the observation, we propose theknowledge–circuit misalignmenthypothesis regarding the Knowing–Using Gap\. Self\-patching reveals that after memorization saturates, injected information is retrievable from certain layers but is not reliably integrated into the computation required by multi\-hop reasoning\. Continued fine\-tuning after memorization sometimes brings these usable representations into mid\-layer computation, coinciding with the emergence of generalization, while in other cases it fails because the representations remain stranded after natural gradient vanishes\. Further interventional experiments provide causal\-intervention evidence supporting this hypothesis: by simply relocating memorized representations yields immediate and substantial gains across models and tasks even after natural fine\-tuning convergence\. This suggests that the capability to generalize injected knowledge can be activated artificially, even if it does not naturally emerge during fine\-tuning\. Moreover, the gains substantially exceed prompting baselines like CoT and generic perturbation controls, reinforcing the hypothesis that improvements arise from transferring knowledge\-relevant information to the reasoning computation path, rather than from superficial decoding effects\. To showcase the practical value of this finding, we show that a simple heuristic strategy exploiting the structure of patch locations can still recover 58–75% of the oracle headroom \(§[5\.5](https://arxiv.org/html/2607.08393#S5.SS5)\), moving the contribution from pure diagnosis toward a practical remedy\. To conclude:

- •We identify and quantify theKnowing–Using Gapduring LLM fine\-tuning\.
- •We introduceself\-patching, an intervention\-based method that maps where injected knowledge becomes*causally usable*across layers, including on failed generalization cases\.
- •We propose theknowledge–circuit misalignment hypothesis, providing mechanistic evidence that manual relocation of memorized representations can recover generalization, and demonstrate its practicality by designing afixed non\-oracle heuristicthat recovers 58–75% of oracle headroom\. The phenomena and results are robust across domains and architectures through comprehensive experiments\.
- •We release a specializedMemorization\-to\-Generalization datasetfor evaluating multi\-hop reasoning on injected knowledge\.

Table 1:Overview of task definitions\.Memorization Task\(s\)are for finetuning andGeneralization Task\(s\)for evaluation\. Graphs on the left illustrate topological structures of supporting facts\.Memorization Task\(s\)Generalization Task\(s\)Chaining1\.Which protein is expressed inembryo?IGFBP3\.
2\.Which drug targets the proteinIGFBP3?Mecasermin\.1\.Which drug targets the protein that are expressed inembryo?Mecasermin\.Intersection1\.What exposure is linked toglioma?Trifluralin\.
2\.What exposure is linked tohypothyroidism?Trifluralin\.
3\.\(Noise\)Which gene is associated withglioma?PLK1\.1\.What is the exposure linked to the diseasegliomaand linked tohypothyroidism?Trifluralin\.
## 2Related Work

Mechanistic interpretability\.Mechanistic interpretability aims to reverse\-engineer neural networks into human\-understandable components, moving beyond behavioral analysis to causal explanations of model internals\. Previous methods can be categorized into observation\-based methods, such as logit\-lensnostalgebraist \([2020](https://arxiv.org/html/2607.08393#bib.bib21)\); Wendler et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib31)\), linear probesAlain and Bengio \([2017](https://arxiv.org/html/2607.08393#bib.bib2)\); Belinkov \([2022](https://arxiv.org/html/2607.08393#bib.bib4)\), and sparse auto\-encodersHuben et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib14)\); Gao et al\. \([2025](https://arxiv.org/html/2607.08393#bib.bib9)\)which disentangles the polysemantic features; and intervention\-based methods, such as causal tracingMeng et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib18)\); Palit et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib24)\)and activation patchingWang et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib30)\)\. Recent research has shifted from analyzing individual neurons to circuitsYao et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib33)\), which are subgraphs of the model responsible for specific behaviors\. For instance, "induction heads" have been identified as the primary mechanism for in\-context learningOlsson et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib22)\), while other studies have mapped circuits responsible for indirect object identificationWang et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib30)\)and entity trackingPrakash et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib27)\)\. However, most of the methods rely on large\-scale data to probe features and circuits\. Tangible tools for locating and extracting atomic knowledge remain sparse\.

Knowledge Representation in LLM\.The "Linear Representation Hypothesis"Park et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib25)\)and the "Key\-Value Memory"Gershman et al\. \([2025](https://arxiv.org/html/2607.08393#bib.bib10)\)framework posits that LLMs encode factual knowledge \(e\.g\., "A is B"\) as linear directions in the activation space, often stored within the weights of MLP layersMeng et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib18)\); Dai et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib8)\)\. Based on this localization, Model Editing techniques like ROMEMeng et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib18)\)were developed to directly update specific facts by modifying MLP weights\. However, a critical limitation of these approaches is the gap between storing a fact and utilizing it for reasoningGupta et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib13)\)\. Recent benchmarks like MQuAKEZhong et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib36)\)and RippleEditsCohen et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib7)\)reveal that while models can recall edited facts \(high memorization\), they fail to propagate these updates to multi\-hop reasoning tasks\.

Grokking and Learning dynamics\.GrokkingPower et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib26)\); Wang et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib29)\); Liu et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib16)\)refers to the phenomenon that generalization performance on validation sets suddenly improves long after training accuracy has saturated\. Originally observed in small algorithmic tasksPower et al\. \([2022](https://arxiv.org/html/2607.08393#bib.bib26)\), grokking has recently been confirmed in pre\-training and fine\-tuning of large transformersLi et al\. \([2025](https://arxiv.org/html/2607.08393#bib.bib15)\); Nanda et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib20)\); Wang et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib29)\)\. Unlike grokking which concerns the emergence of new capabilities that underlies datasets, our setting concerns the generalizability of single piece of knowledge to be used by common logics\. We posit that this generalization failure stems not from learning new reasoning circuits, but from aligning with them\.

## 3Dataset preparation

### 3\.1Preliminaries

To investigate the dynamics of memorization and generalization in LLMs, we construct a dataset comprising diverse pairs of memorization and generalization QA tasks\. Memorization QA tasks serve as the finetuning materials for LLM to memorize new knowledge, while generalization QA tasks, which are not explicitly memorized, test LLM’s ability to apply newly acquired knowledge\.

The dataset is adapted from STaRKWu et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib32)\), a real\-world semi\-structured knowledge base comprising millions of entities and relations of diverse heterogeneous types\. We use the biomedical \(STaRK\-Prime\) and academic \(STaRK\-MAG\) subset to ensure the robustness of our findings across domains\. The generation pipeline is detailed in Appendix\.

### 3\.2Tasks definition

We define two types of generalization QA tasks in table[1](https://arxiv.org/html/2607.08393#S1.T1)to evaluate how LLMs generalize the learned knowledge in various scenarios\.

The atom unit of knowledge in our setting is defined as a fact triplet:f=\(n1,e12,n2\)f=\(n\_\{1\},e\_\{12\},n\_\{2\}\)wheren1,n2∈Nn\_\{1\},n\_\{2\}\\in Nrepresent the head and tail entities ande12e\_\{12\}the relation between them\. For example, fact triplet \(MRE11, ppi, ATRX\) indicates the fact "protein MRE11 interacts with protein ATRX"\.

Each generalization task is based on a set of supporting fact triplets, paired with a memorization task per fact\. LLMs first learn about the supporting facts through finetuning on the memorization QA tasks, and then are evaluated on the generalization task that requires applying the learned knowledge\.

Memorization Task\.For eachffa corresponding memorization QA taskm​e​mfmem\_\{f\}is generated as the material to memorize the knowledge\. Specifically, the task presents the head entityn1n\_\{1\}and relatione12e\_\{12\}as the query, requiring the model to predict the tail entityn2n\_\{2\}as the correct answer\. E\.g\.,m​e​mfmem\_\{f\}= \{Q: "What protein interacts \(e12e\_\{12\}\) with MRE11 \(n1n\_\{1\}\)?", A: "ATRX \(n2n\_\{2\}\)\."\}

Generalization Task\.We design two types of generalization QA tasks in table[1](https://arxiv.org/html/2607.08393#S1.T1)from comprehensive meta paths:\(1\) Chaining Task\.This task depends on two supporting tasks on which the model is required to perform sequential reasoning to derive the final answer\. This assesses the model’s chain reasoning capabilities\.\(2\) Intersection Task\.This task depends on multiple supporting tasks and requires the model to identify shared entities with specific relations out of noise confounders\. This tests the model’s ability to perform intersection in its knowledge set\.

### 3\.3Knowledge Novelty Validation

Table 2:Evaluation of dataset novelty\.All models score below 6% on both dataset even before active leakage filtering, confirming the injected knowledge is genuinely novel\.ModelSTaRK\-Prime\(%\)STaRK\-MAG\(%\)Qwen\-2\.5\-1\.5B4\.205\.50Qwen\-2\.5\-3B3\.806\.00Qwen\-2\.5\-7B4\.405\.80LLaMA\-3\.2\-1B4\.905\.40LLaMA\-3\.2\-3B3\.805\.00LLaMA\-3\.1\-8B4\.805\.50

To ensure the injected knowledge is genuinely novel, we first verified that pre\-trained models score around or below 6% zero\-shot accuracy on 1,000 randomly sampled memorization tasks before any fine\-tuning, on bothSTaRK\-PrimeandSTaRK\-MAG\(Table[2](https://arxiv.org/html/2607.08393#S3.T2)\)\. Furthermore, during our patching experiments \(§[5](https://arxiv.org/html/2607.08393#S5)\), we explicitly filter out instances where the base model can already answer the memorization or generalization questions, ruling out potential data leakage\.

Evaluation separation\.Memorization and generalization tasks are disjoint by construction: memorization tasks present single\-hop\(entity, relation→\\toentity\)queries, while generalization tasks require multi\-hop reasoning over*different*query templates unseen in training\. Only fact entities may overlap because chaining inherently requires shared bridge entities, but the compositional query structure is always novel\.

## 4The Phenomenon: Characterizing the Knowing–Using Gap

### 4\.1Formalizing the Knowing–Using Gap

Letθt\\theta\_\{t\}denote model parameters aftertttraining steps \(or epochs\) of knowledge injection on a set of injected facts𝒦=\{fi\}i=1n\\mathcal\{K\}=\\\{f\_\{i\}\\\}\_\{i=1\}^\{n\}\. We evaluate two time\-dependent performance curves\.Memorization accuracyAmem​\(t\)A\_\{\\text\{mem\}\}\(t\): performance on direct recall queries for injected facts \(e\.g\., single\-hop completion of a trained triple\), andGeneralization \(use\) accuracyAgen​\(t;𝒯\)A\_\{\\text\{gen\}\}\(t;\\mathcal\{T\}\): performance on a downstream task𝒯\\mathcal\{T\}that requires reasoning with injected facts\.

We characterize the Knowing–Using Gap along two complementary dimensions:

Accuracy gap\.At the end of trainingt=Tmaxt=T\_\{\\max\}, define the difference after convergence as

Δ​A​\(𝒯\)=Amem​\(Tmax\)−Agen​\(Tmax;𝒯\)\.\\Delta A\(\\mathcal\{T\}\)\\;=\\;A\_\{\\text\{mem\}\}\(T\_\{\\max\}\)\\;\-\\;A\_\{\\text\{gen\}\}\(T\_\{\\max\};\\mathcal\{T\}\)\.\(1\)
#### Temporal lag\.

To ensure robustness against training fluctuations, we define the saturation time as the earliest point where performance remains stable for at leastwwconsecutive epochs\. Specifically, the saturation time of task𝒯\\mathcal\{T\}is defined as:

Tgen​\(𝒯\)=min⁡\{t:Agen​\(t′;𝒯\)=1,∀t′∈\[t,t\+w\]\}\.T\_\{\\text\{gen\}\}\(\\mathcal\{T\}\)=\\min\\\{t:A\_\{\\text\{gen\}\}\(t^\{\\prime\};\\mathcal\{T\}\)=1,\\forall t^\{\\prime\}\\in\[t,t\+w\]\\\}\.\(2\)The temporal lag is then defined asΔ​T​\(𝒯\)=Tgen​\(𝒯\)−Tmem\\Delta T\(\\mathcal\{T\}\)=T\_\{\\text\{gen\}\}\(\\mathcal\{T\}\)\-T\_\{\\text\{mem\}\}\. We exclude failed cases to ensureTgen​\(𝒯\)T\_\{\\text\{gen\}\}\(\\mathcal\{T\}\)reflects the point where generalizable facts are reliably mastered\.

Table 3:Comparison of Knowing–Using Gap between FFT and LoRA\.TaskTm​e​mT\_\{mem\}Tg​e​nT\_\{gen\}Δ​T\\Delta T𝒜g​e​n\\mathcal\{A\}\_\{gen\}LoRAChain\.10\.4±2\.810\.4\\pm 2\.815\.0±5\.215\.0\\pm 5\.24\.64\.60\.3030\.303Intersec\.8\.3±2\.18\.3\\pm 2\.18\.9±8\.08\.9\\pm 8\.00\.60\.60\.9100\.910FFTChain\.2\.4±1\.52\.4\\pm 1\.57\.9±4\.77\.9\\pm 4\.75\.55\.50\.3150\.315Intersec\.4\.1±1\.94\.1\\pm 1\.912\.9±9\.712\.9\\pm 9\.78\.88\.80\.8520\.852

### 4\.2The Knowing–Using Gap Across Tasks

Figure[1](https://arxiv.org/html/2607.08393#S1.F1)illustrates the Knowing–Using Gap under chaining: memorization reaches near\-ceiling accuracy within a few epochs, while downstream use stays low for an extended period\.

#### Across\-task pattern\.

Table[3](https://arxiv.org/html/2607.08393#S4.T3)shows the ubiquity of this dissociation in different downstream reasoning tasks\. Under LoRA, memorization saturates quickly for all tasks, but downstream use exhibits both delayed emergence and task\-dependent ceilings\. Intersection is close to an “ideal” regime, with minimal lag and high final use accuracy, since it does not require subsequent reasoning steps and often aligns with the memorization answer, with the complexity lies in filtering noises\. In contrast, chaining shows a clear two\-dimensional gap: it requires substantially more training to become usable and still converges to a low use accuracy despite near\-perfect memorization\. The central finding is consistent: memorization saturates early, while reliable downstream use is delayed and can remain substantially lower at convergence\.

#### Full fine\-tuning vs\. LoRA\.

As shown in Table[3](https://arxiv.org/html/2607.08393#S4.T3), FFT in general memorizes substantially faster than LoRA across tasks, but this advantage does not consistently translate into faster or better downstream use\. For chaining, FFT attains memorization much earlier yet shows a comparable lag magnitude and nearly identical final use accuracy\. For intersection, FFT memorizes earlier, but reaches reliable use markedly later, yielding a larger lag and lower𝒜g​e​n\\mathcal\{A\}\_\{gen\}\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/figures/datascale.png)

![Refer to caption](https://arxiv.org/html/2607.08393v1/figures/modelscale.png)

Figure 2:Results of know\-use gap on different data sizes and model sizes\.
#### Model and data scale\.

We also test the knowing\-using gap across different model scales and data scales\. Figure[2](https://arxiv.org/html/2607.08393#S4.F2)shows that increasing model size does not eliminate the temporal lagΔ​T\\Delta T\. Moreover, increasing the number of injected facts tends to widen the final accuracy gapΔ​A​\(𝒯\)\\Delta A\(\\mathcal\{T\}\), even when direct recall remains strong, indicating that scaling storage does not directly translate into proportional gains in reasoning\.

## 5Mechanistic Analysis for Knowledge–Circuit Misalignment

![Refer to caption](https://arxiv.org/html/2607.08393v1/x2.png)Figure 3:Method Comparison\.*Causal tracing*corrupts a run to identify causally relevant locations\.*Patchscope*interprets a hidden state by decoding it into natural language\.*Self\-patching*tests the effect position by swapping its internal representation across layers and contexts\.In this section, we propose the knowledge–circuit misalignment hypothesis to account for the observed Knowing–Using Gap through mechanistic interpretation\. We provide interventional evidence consistent with the hypothesis that, after fine\-tuning, answer\-relevant representations can be recovered from hidden states but are not always routed through computation\-effective layers\. This misalignment of knowledge storage and computation results in the generalization failure, but can be largely recovered by manually relocating knowledge to the correct layers\.

Knowledge–circuit misalignment hypothesis\.A Knowing–Using Gap is driven by a spatial misalignment of knowledge storage and reasoning circuits: fine\-tuning first encodes new facts in easy\-to\-fit storage states for memorization \(often early or very late layers\) that support direct recall, but are not reliably routed into the effective positions that are causally required for multi\-step reasoning, often in mid\-layer computation as shown in previous literature and our experiment in Figure[5](https://arxiv.org/html/2607.08393#S5.F5)\.

This hypothesis predicts that \(1\) after memorization saturates, there should exist*off\-path*representations that already contain injected information but do not yield correct reasoning end\-to\-end; and \(2\) explicitly relocating those representations into effective locations should immediately increase downstream use\. We test these predictions with several causal intervention tools, mainly self\-patching\.

### 5\.1Self\-Patching

Algorithm 1: Self\-patching scan

Input:modelMM, promptsPs,PtP\_\{s\},P\_\{t\}, anchorEE, answery∗y^\{\*\}, scoreII\.

Foreach layer pair\(ls,lt\)\(l\_\{s\},l\_\{t\}\):

- ⊳\\trianglerightLocate anchor tokensTs=T​\(Ps,E\)T\_\{s\}=T\(P\_\{s\},E\)andTt=T​\(Pt,E\)T\_\{t\}=T\(P\_\{t\},E\)\.
- ⊳\\trianglerightCache source statez=hTsls​\(Ps\)z=h^\{l\_\{s\}\}\_\{T\_\{s\}\}\(P\_\{s\}\)\.
- ⊳\\trianglerightRunPtP\_\{t\}and replaceh~Ttlt←z\\tilde\{h\}^\{l\_\{t\}\}\_\{T\_\{t\}\}\\leftarrow z\.
- ⊳\\trianglerightContinue the forward pass to obtainM~​\(Pt\)\\tilde\{M\}\(P\_\{t\}\)\.
- ⊳\\trianglerightRecordΔ​I=I​\(M~​\(Pt\),y∗\)−I​\(M​\(Pt\),y∗\)\\Delta I=I\(\\tilde\{M\}\(P\_\{t\}\),y^\{\*\}\)\-I\(M\(P\_\{t\}\),y^\{\*\}\)\.

Output:layer\-pair mapA​\[ls,lt\]=Δ​IA\[l\_\{s\},l\_\{t\}\]=\\Delta I\.

Self\-patching tests knowledge–circuit alignment through causal interventions: if a fact is already represented somewhere inside the model, can the target reasoning prompt use it when that representation is routed through a candidate computation layer?

LetMMbe anLL\-layer transformer and lethtl​\(P\)h\_\{t\}^\{l\}\(P\)denote the residual\-stream state at layerlland token positionttfor promptPP\. For an anchor substringEE\(e\.g\., the head entity\),T​\(P,E\)T\(P,E\)denotes its token span\. Given a source promptPsP\_\{s\}and a target promptPtP\_\{t\}, self\-patching copies only the anchor representation from source layerlsl\_\{s\}into target layerltl\_\{t\},h~T​\(Pt,E\)lt←hT​\(Ps,E\)ls\\tilde\{h\}^\{l\_\{t\}\}\_\{T\(P\_\{t\},E\)\}\\leftarrow h^\{l\_\{s\}\}\_\{T\(P\_\{s\},E\)\}, then resumes the target forward pass\. We measure the causal effect of this intervention as the change in an indicator functionI​\(⋅,y∗\)I\(\\cdot,y^\{\*\}\), which evaluates the correctness of the generated output againsty∗y^\{\*\}\(e\.g\., using Exact Match or Mean Reciprocal Rank\) withΔ​I=I​\(M~​\(Pt\),y∗\)−I​\(M​\(Pt\),y∗\)\\Delta I=I\(\\tilde\{M\}\(P\_\{t\}\),y^\{\*\}\)\-I\(M\(P\_\{t\}\),y^\{\*\}\)\.

We scan all layer pairs\(ls,lt\)\(l\_\{s\},l\_\{t\}\)after fine\-tuning\. A positive cell \(Δ​I\>0\\Delta I\>0\) has a concrete interpretation: layerlsl\_\{s\}contains a representation that becomes useful when placed at computation layerltl\_\{t\}\. This produces the permeation maps in Figure[4](https://arxiv.org/html/2607.08393#S5.F4)and the recoverable headroom in Table[4](https://arxiv.org/html/2607.08393#S5.T4)\. To rule out prompt\-specific shortcuts, we also patch across contexts from memorization promptsPmemP\_\{\\text\{mem\}\}into generalization promptsPgenP\_\{\\text\{gen\}\}; the transferred states preserve the same layer\-pair structure \(Figure[6](https://arxiv.org/html/2607.08393#S5.F6)\)\.

#### Comparison with similar methods\.

We compare the most similar causal intervention based mechanistic interpretation method in Fig[3](https://arxiv.org/html/2607.08393#S5.F3)\. Unlike causal tracing, self\-patching does not require a “clean” correct trajectory and is therefore applicable to failed generalization cases\. Unlike PatchScope, it focuses on the accuracy of target prompts instead of interpreting the source prompt with auxiliary decoding prompts; it evaluates whether the representation can unlock the downstream computation when routed into the model\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/x3.png)Figure 4:Permeation dynamics of know–use transition, aligned with fine\-tuning process\.Cell\(lsrc,ltgt\)\(l\_\{\\text\{src\}\},l\_\{\\text\{tgt\}\}\)measures whether patching the head\-entity representation fromlsrcl\_\{\\text\{src\}\}toltgtl\_\{\\text\{tgt\}\}increases generalization accuracy, with red indicating full recovery, blue for no effect, and white for partial gain\.Top:a natural failed instance\. The red region indicates the position of knowledge storage, which permeates but halts before reaching the diagonal, indicating generalization failure\.Bottom:a successful instance, patch\-effective regions expand and cover diagonal before training stabilizes\.

### 5\.2Knowledge Dynamics in Fine\-Tuning

We first trace the knowledge permeation of two atomic knowledge during fine\-tuning to understand*after a fact is memorized, when, where and how does it become accessible to the model’s pre\-existing reasoning logic\.*We save checkpoints each epoch and perform layer\-to\-layer self\-patching at the head\-entity positionsEh​e​a​dE\_\{head\}onPgenP\_\{\\text\{gen\}\}, producing a heatmap over\(lsrc,ltgt\)\(l\_\{\\text\{src\}\},l\_\{\\text\{tgt\}\}\)at each step\.

Before memorization, patching rarely helps as indicated by the all\-blue map: injected knowledge is not yet available internally at all, thus swapping can not help\.

On the moment in training curve when two facts are memorized, we can observe clear*off\-diagonal*red region appear in Figure[4](https://arxiv.org/html/2607.08393#S5.F4)that says the needed information is already stored in certain layers and can take effect if routed into particular target layers\. However, the model still fails end\-to\-end in the natural fine\-tuning process: diagonal cells remains blue \(fail with no intervention\)\.

As fine\-tuning continues, the red region expands wider towards the heatmap diagonal, indicating the gradual permeation of knowledge into more layers\. In successful cases, the red region covers the diagonal line, which means the natural emergence of generalization from fine\-tuning\. In failed cases, while still expanding, the red region halts before reaching the diagonal\. This is due to the fine\-tuning nature that after memorization whereM​\(P\)M\(P\)matchesy∗y^\{\*\}, loss will diminish soon and become too small to drive further gradient updates for internal change\. The model will stuck and fail to generalize unless manually relocating the representation, as shown in the next section\. This knowledge permeation dynamics aligns well with the training phases in time, which validates the prediction from our hypothesis: knowledge is stored but not used until the representation becomes available in locations effective for the reasoning computation\.

ModelSTaRK\-PrimeSTaRK\-MAGMem\.ChainingIntersectionMem\.ChainingIntersectionw/opat\.w/opat\.w/opat\.w/opat\.Qwen\-2\.5\-1\.5B0\.9980\.0780\.4400\.7930\.9870\.9910\.0460\.2860\.9280\.994Qwen\-2\.5\-3B0\.9970\.1140\.5420\.7980\.9860\.9860\.0520\.2880\.9580\.994Qwen\-2\.5\-7B0\.9960\.1240\.5040\.7740\.9560\.9820\.0680\.3100\.9760\.994LLaMA\-3\.2\-1B0\.9940\.1020\.3160\.8740\.9750\.9750\.0820\.1820\.9820\.994LLaMA\-3\.2\-3B0\.9930\.1260\.4040\.8150\.9690\.9740\.0640\.2400\.9821\.000LLaMA\-3\.1\-8B0\.9860\.1820\.4580\.7950\.9210\.9750\.0720\.2220\.9820\.994Table 4:Oracle self\-patching recovers downstream use across models, architectures, and knowledge domains\.“pat\.” denotes head\-entity self\-patching at the most effective layer, averaged over 1000 injected facts\. Full 95% Wilson score confidence intervals are in Appendix[12](https://arxiv.org/html/2607.08393#A6.T12)\.
### 5\.3Manually Trigger Generalization

We then quantify the*oracle upper bound*at convergence to see how much downstream use can be activated by relocating representations\. Since self\-patch do not introduce new information but only relocates existing representations, the substantial improvement in downstream use after patching indicates that the generalization failure is not due to the absence of knowledge but rather a misalignment between storage and computation\. We systematically fine\-tune on different architectures, scales, and knowledge domains, and perform self\-patching at convergence to measure the recoverable headroom\. Experiments are computed with 1,000 samples to avoid randomness, detailing in Appendix[B](https://arxiv.org/html/2607.08393#A2)\.

Table[4](https://arxiv.org/html/2607.08393#S5.T4)shows that memorization saturates near\-perfectly across models and domains, yet downstream use without intervention remains low, especially for chaining\. Oracle self\-patching yields large and consistent improvements along all architectures, model scales and knowledge domains\. Chaining accuracy lifts by 1\.5–6×\\timesin every cell, and the smaller know\-use gap in intersection is nearly eliminated\. The uniform improvement again points to a structural origin rather than an random artifact, showing causal evidence for the knowledge–circuit misalignment hypothesis\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/figures/position_distribution.png)Figure 5:Effective patch locations concentrate into two clusters\.Location of most effective patching\.We further draw the spatial positions with most effective patching in Figure[5](https://arxiv.org/html/2607.08393#S5.F5), revealing a clear two\-cluster pattern: one cluster of source layers in early layers and another cluster in late layers, both patching into a middle cluster of target layers\. While the later one is intuitiveGhandeharioun et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib12)\); Biran et al\. \([2024](https://arxiv.org/html/2607.08393#bib.bib6)\)since moving latter representation backwards inherently brings in enriched information, the other cluster is surprising: moving from early layers into middle layers also triggers the generalization ability\. This means that it is not that the need information emerges too late – the model can even succeed skipping several layers\. Instead, the information is already stored in both early and late layers, but fail to align with the computation in middle layers, which is the bottleneck for use\. Moreover, relocating to late layers is useless as shown in the empty space at right, which can be illustrated by the three\-step theory in previous work that the reasoning stream has moved to the last token in late layersGeva et al\. \([2023](https://arxiv.org/html/2607.08393#bib.bib11)\)\.

### 5\.4Ablations and Sanity Checks

We perform several ablations to rule out other potential explanations such as position, prompting and perturbation artifacts\.

Table 5:Token\-position ablation\.McNemar’s test on patching at different positions against random baseline\.PositionMeanpp\-valueSignificanceRandom0\.1359––<BOS\>0\.04851\.0000n\.s\.<EOS\>0\.40290\.0000\*\*\*First Relation0\.19900\.0235\*Second Relation0\.19900\.0121\*Entity0\.64080\.0000\*\*\*

Token\-position Ablations\.We experimentally prove that injected factual information is tightly tied to entity mentions but not position\-agonistic\. Table[5](https://arxiv.org/html/2607.08393#S5.T5)shows that patching at the head\-entity position yields the largest and most significant improvements, far exceeding random and <BOS\>\. The <EOS\> position exhibits a secondary signal, consistent with late positions aggregating information relevant for generation\.

ChainingIntersectionModelw/o pat\.CoTIrrelevant pat\.Self pat\.w/o pat\.CoTIrrelevant pat\.Self pat\.Qwen\-2\.5\-1\.5B0\.0780\.0780\.1320\.1320\.1500\.1500\.4400\.4400\.7930\.7930\.2430\.2430\.8730\.8730\.9870\.987Qwen\-2\.5\-3B0\.1140\.1140\.2880\.2880\.1840\.1840\.5420\.5420\.7980\.7980\.3870\.3870\.8560\.8560\.9860\.986Qwen\-2\.5\-7B0\.1240\.1240\.3900\.3900\.1940\.1940\.5040\.5040\.7740\.7740\.3980\.3980\.8900\.8900\.9560\.956

Table 6:Prompting and perturbation ablations\.Direct/no patching and self\-patching are shared anchors; CoT tests prompt effects, and irrelevant patching controls for generic activation perturbations\.Control experiment on prompting and perturbation\.

Table[6](https://arxiv.org/html/2607.08393#S5.T6)combines two complementary ablations on prompting and representation\. CoT prompting improves chaining but remains far below self\-patching, and sometimes even degrades intersection performance, and irrelevant patching that uses representation from unrelated fact still lags largely behind patching*correct*fact’s representation\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/figures/mem_self_patching_comparison.png)Figure 6:Cross\-context consistency\.Detect knowledge existence\. To rule out the chance that gains are driven by prompt artifacts or noises, we further cross\-context patch theEh​e​a​dE\_\{head\}representation fromPmemP\_\{\\text\{mem\}\}which contains knowledge representation toPgenP\_\{\\text\{gen\}\}\. Figure[6](https://arxiv.org/html/2607.08393#S5.F6)shows strong correlation in the effective layer\-pair patterns from both contexts, supporting that self\-patching transfers injected\-knowledge representations similar toPmemP\_\{\\text\{mem\}\}rather than some unknown noises\.

### 5\.5From Diagnosis to Practical Heuristic

While oracle self\-patching shows large headroom, it is a diagnostic tool rather than a practical method\. A natural question is whether the observation in Figure[5](https://arxiv.org/html/2607.08393#S5.F5)can be exploited for a practical strategy\.

Fixed heuristic\.Based on the concentration of effective patches into two clusters \(late→\\tomid and early→\\tomid\), we define a simple strategy using only two predetermined layer pairs per model architecture: \(i\) source at∼\\sim0\.8LLtargeting∼\\sim0\.5LL, and \(ii\) source at∼\\sim0\.1LLtargeting∼\\sim0\.5LL, whereLLis the total number of layers\. These pairs require no per\-instance search\.

Results\.Table[7](https://arxiv.org/html/2607.08393#S5.T7)shows that the fixed heuristic recovers 58–75% of oracle headroom across all models and tasks, confirming that the knowing–using gap can be partially bridged with a practical strategy\. The remaining gap between the fixed and oracle results reflects instance\-specific variation in where knowledge is stored, motivating future work on adaptive alignment methods\.

ModelMem\.ChainingIntersectionNo Pat\.FixedOracleNo Pat\.FixedOracleQwen\-2\.5\-1\.5B0\.9980\.0780\.3490\.4400\.7930\.9420\.987Qwen\-2\.5\-3B0\.9970\.1140\.4350\.5420\.7980\.9430\.986Qwen\-2\.5\-7B0\.9960\.1240\.4090\.5040\.7740\.9140\.956LLaMA\-3\.2\-1B0\.9940\.1020\.2520\.3160\.8740\.9470\.975LLaMA\-3\.2\-3B0\.9930\.1260\.3210\.4040\.8150\.9260\.969LLaMA\-3\.1\-8B0\.9860\.1820\.3750\.4580\.7950\.8860\.921Average—0\.1210\.3570\.4440\.8080\.9260\.966Table 7:Fixed heuristic vs\. oracle self\-patching\.“Fixed” uses two predetermined layer pairs \(late→\\tomid, early→\\tomid\) per model architecture, requiring no per\-instance search\.

## 6Conclusion

We identified the Knowing–Using Gap: fine\-tuned LLMs memorize injected facts yet fail to use them in multi\-hop reasoning\. Using self\-patching as a causal diagnostic, we trace this failure toknowledge–circuit misalignment—knowledge is encoded in storage\-oriented early or late layers but does not permeate into the mid\-layer circuits required for reasoning\. The gap is thus a routing problem, not a capacity one—knowledge resides in the model, just not where reasoning happens\. It is also partially reversible: a heuristic recovers 58–75% of oracle headroom, and the effect replicates across models, scales, and domains\. Together, these results recast fine\-tuning’s generalization failure as a tractable alignment problem, and point to alignment\-aware training as a principled path forward\.

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## Appendix ADataset details

### A\.1Construction pipeline

We present an automated pipeline designed to sample facts from the knowledge graph and generate QA pairs for the dataset\. Two distinct methods are designed for the generation process: an LLM\-based approach to ensure linguistic diversity, and a template\-based approach to maintain structural consistency\. The procedure comprises the following steps:

1. 1\.Sample Valid PathsFor each type of generalization task, we manually design a list of valid meta paths to guide the sampling process and generate meaningful and reasonable questions\. A meta path defines a sequence of entity types and relation types that outline the structure of the knowledge to be used for the task\. For instance, a meta\-path for chaining task may be denoted as\(anatomy→expression Present→gene/protein→target→drug\)\(\\text\{anatomy\}\\to\\text\{expression Present\}\\to\\text\{gene/protein\}\\to\\text\{target\}\\to\\text\{drug\}\)\. Concrete paths \(i\.e\., comprising specific entity sequences\) matching the meta paths are sampled from the knowledge graph accordingly, e\.g\.,\(female reproductive system→expression present→SLC12A6→target→potassium chloride\)\(\\text\{female reproductive system\}\\to\\text\{expression present\}\\to\\text\{SLC12A6\}\\to\\text\{target\}\\to\\text\{potassium chloride\}\)\.
2. 2\.Generate Memorization TasksWe randomly sample a path matching a meta path from the first step, and decompose it into a list of fact triplets, the minimal units of knowledge in our setting, as well as the material for finetuning LLMs\. For each fact triplet, we prompt an AI assistant or use a predefined template to generate the memorization task\. Specifically, for intersection tasks, some extra noise facts related to both head entities are added to the list for task complexity\.
3. 3\.Generate Generalization TasksFor the same sampled path, we use similar method to generate the corresponding generalization task question with AI assistant or templates\.

This pipeline is automated, efficient, and scalable, offering two alternative methods for QA pair generation\. The LLM\-based method yields diverse and more natural QA pairs, while the template\-based method ensures consistency and controllability for downstream interpretability studies\.

Table 8:Target prompt used in patchscopemeta path \(key\)in\-context prompt \(value\)\(’disease’, ’associated with’, ’gene/protein’\)cystic fibrosis\-\>CFTR; sickle cell disease\-\>HBB; Duchenne muscular dystrophy\-\>DMD; disease name\-\>\(’effect/phenotype’, ’associated with’, ’gene/protein’\)PTC bitter\-tasting ability\-\>TAS2R38; red\-green color vision defect\-\>OPN1LW; lactase persistence \(adult lactose digestion\)\-\>LCT; phenotype name\-\>\(’disease’, ’contraindication’, ’drug’\)G6PD deficiency\-\>primaquine; asthma\-\>propranolol; Parkinson’s disease\-\>metoclopramide; disease name\-\>
### A\.2Requirements validation

We validate that our dataset meets all 4 requirements mentioned in[3\.1](https://arxiv.org/html/2607.08393#S3.SS1)\.Scalabilityis guaranteed by the 8 million distinct fact triplets in STaRK\-Prime KG, from which we directly generate dataset samples from\. Fortask diversity, we manually design 3 generalization tasks organizing support facts in different ways, and generate them from 53 meta paths covering 10 entity types and 18 relation types\. Andreal\-world knowledgein our dataset is grounded by the biomedical KG\. For cross\-domain validation, we additionally construct an analogous dataset from STaRK\-MAG \(academic knowledge graph\) following the same pipeline with author–paper–field\-of\-study relations, generating 12,000 chaining and 4,390 intersection items\.

To validate that our dataset containsminimal prior knowledgeto the LLMs, we conducted an experiment to evaluate the novelty of the facts\. Specifically, we randomly sampled 1,000 facts and their corresponding memorization tasks from the dataset and assessed the evaluate the zero\-shot accuracy of pre\-trained LLMs on these tasks without any fine\-tuning\. As results shown in Table[2](https://arxiv.org/html/2607.08393#S3.T2), on bothSTaRK\-PrimeandSTaRK\-MAG, all models score around or below0\.060\.06, indicating that the models have little prior knowledge of the dataset samples\.

## Appendix BExperiment Setup Details

This section consolidates the experimental setup used by the phenomenon and mechanistic analyses in the main paper\. Unless otherwise stated, experiments are run on a fixed 1,000\-sample split of injected facts to reduce sampling noise; smaller counts only arise after task\-specific filtering or when a diagnostic scan is intentionally run on a smaller subset for computational cost\.

Knowledge\-injection tasks\.The default domain isSTaRK\-Prime, withSTaRK\-MAGused for cross\-domain replication\. For the chaining experiments, each instance contains two support factsE1→r1→E2E\_\{1\}\\rightarrow r\_\{1\}\\rightarrow E\_\{2\}andE2→r2→E3E\_\{2\}\\rightarrow r\_\{2\}\\rightarrow E\_\{3\}\. The model is fine\-tuned on the corresponding memorization queries and evaluated on the held\-out compositional queryE1→r1→r2→?E\_\{1\}\\rightarrow r\_\{1\}\\rightarrow r\_\{2\}\\rightarrow?, which requires recovering the bridge entity before predicting the final answer\. Intersection uses the same memorization\-then\-use separation, but evaluates whether the model can identify the shared entity from multiple support facts and noise facts\. Before patching, we filter out instances already answered correctly by the base model on either the memorization or generalization prompt, so the measured gains cannot be attributed to pre\-existing knowledge leakage\.

Training setup for the Knowing–Using Gap\.For the temporal\-lag and accuracy\-gap measurements in Section[4\.2](https://arxiv.org/html/2607.08393#S4.SS2), we fine\-tune open\-weight LLaMA and Qwen models on randomly sampled knowledge\-injection tasks and track memorization and downstream\-use accuracy at each checkpoint\. The LoRA runs use AdamW with weight decay0\.010\.01; the practical injection setting in the original setup uses batch size1010, learning rate10−410^\{\-4\}, and5050epochs, long enough for direct memorization to saturate\. The full fine\-tuning comparison uses the same task split and evaluation protocol as the LoRA comparison\. For model\-scale and data\-scale experiments, we keep the task construction fixed while varying either the base model size or the number of injected facts, and report both the final accuracy gapΔ​A\\Delta Aand the temporal lagΔ​T\\Delta T\.

LoRA hyperparameters for the main multi\-fact runs\.The consolidated LoRA configuration uses rankr=16r=16,α=32\\alpha=32, dropout0\.050\.05, and target modules\{q,k,v,o,gate,up,down\}proj\\\{q,k,v,o,\\mathrm\{gate\},\\mathrm\{up\},\\mathrm\{down\}\\\}\_\{\\mathrm\{proj\}\}across all transformer blocks\. We use AdamW with defaultβ1=0\.9\\beta\_\{1\}=0\.9,β2=0\.999\\beta\_\{2\}=0\.999,ϵ=10−8\\epsilon=10^\{\-8\}, weight decay0\.010\.01, no warmup, and greedy evaluation decoding\. The reproduction scripts use learning rate2×10−42\{\\times\}10^\{\-4\}, per\-device batch size11, gradient accumulation88\(effective batch size88\), fp32 gradients, and random seed4242\. Main multi\-fact runs use the fixed 1,000\-fact split unless a table explicitly reports a filtered evaluation count\.

Permeation dynamics\.For the training\-dynamics heatmaps in Section[5\.2](https://arxiv.org/html/2607.08393#S5.SS2), we save checkpoints at every epoch and run layer\-to\-layer self\-patching at the head\-entity token positionsEheadE\_\{\\mathrm\{head\}\}\. For each checkpoint, we scan source and target layer pairs\(lsrc,ltgt\)\(l\_\{\\mathrm\{src\}\},l\_\{\\mathrm\{tgt\}\}\)and record whether replacing the target residual\-stream representation with the source representation improves the downstream answer\. This diagnostic scan is run on100100randomly sampled chaining tasks over3030epochs with parameter\-efficient tuning, which is sufficient to visualize when memorized representations become causally usable\.

Oracle and fixed self\-patching\.For the converged recoverable\-headroom results in Section[5\.3](https://arxiv.org/html/2607.08393#S5.SS3), each instance is evaluated by scanning all layer pairs on the head\-entity position in the generalization prompt and reporting the best\-performing pair as the oracle diagnostic upper bound\. The fixed heuristic in Section[5\.5](https://arxiv.org/html/2607.08393#S5.SS5)uses only two predetermined pairs per model,\(⌊0\.82L⌉,⌊0\.45L⌉\)\\bigl\(\\lfloor 0\.82L\\rceil,\\lfloor 0\.45L\\rceil\\bigr\)and\(⌊0\.10L⌉,⌊0\.45L⌉\)\\bigl\(\\lfloor 0\.10L\\rceil,\\lfloor 0\.45L\\rceil\\bigr\), whereLLis the number of transformer layers\. No per\-instance search is used by the fixed heuristic\. ForSTaRK\-MAG, we follow the same memorization, chaining, intersection, filtering, fine\-tuning, and self\-patching protocol asSTaRK\-Prime; the patching evaluation uses500500MAG chaining instances and166166MAG intersection instances after filtering, as detailed in Appendix[C](https://arxiv.org/html/2607.08393#A3)\.

Controls and statistical reporting\.The token\-position ablation uses the same converged checkpoints but changes the patched position among random,<BOS\>,<EOS\>, relation tokens, and the entity token\. Prompting and perturbation controls compare direct generation, CoT prompting, irrelevant\-fact patching, and self\-patching with the correct fact representation under the same exact\-match scoring rule\. For all aggregate proportions, Appendix[F](https://arxiv.org/html/2607.08393#A6)reports 95% Wilson confidence intervals; paired memorization–use gaps are tested with McNemar’s test and an exact binomial test on discordant pairs, and the temporal\-lag definition is checked under aτ,w\\tau,wsensitivity grid\.

## Appendix CCross\-Domain Replication Details \(STaRK\-MAG\)

### C\.1Domain comparison

Table[9](https://arxiv.org/html/2607.08393#A3.T9)compares the two knowledge domains used in this work\. STaRK\-Prime covers biomedical entities \(diseases, genes, drugs\) with rich relational structure, while STaRK\-MAG covers academic publications \(authors, papers, fields of study\)\. The domains differ in entity naming conventions \(concise biomedical terms vs\. verbose paper titles\), relation types, and graph density, providing a meaningful test of cross\-domain generality\.

Table 9:Comparison of the two knowledge domains\.STaRK\-PrimeSTaRK\-MAGSourcePrimeKGMicrosoft AcademicDomainBiomedicalAcademicEntity typesDisease, Gene, Drug,Author, Paper,Anatomy, PhenotypeField of StudyRelation types185Entity namingConcise termsVerbose titlesChaining items1,00012,000Intersection items9964,390
### C\.2Training dynamics

Figure[7](https://arxiv.org/html/2607.08393#A3.F7)shows epoch\-by\-epoch memorization and generation accuracy for the Qwen MAG training runs\.Chainingexhibits the starkest decoupling: memorization reaches\>\>0\.95 by epoch 15 while generation remains near zero throughout—a pattern that holds across Qwen model scales and mirrors the biomedical domain\.Intersectionshows memorization and generation rising in tandem, reaching similarly high final values—consistent with the small gap observed in both domains\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/x4.png)Figure 7:MAG training dynamics across tasks and model scales\.Each panel shows memorization \(red\) and generation \(blue\) accuracy over 50 training epochs; the shaded region visualizes the instantaneous KU gap\. Chaining exhibits a large, persistent gap; intersection shows near\-parallel learning curves\.

## Appendix DScaling Results on Knowing–Using Gap

We test the knowing\-using gap across different model scales and data scales, with results in Appendix\.

Table 10:Temporal Lag \(Δ​T\\Delta T\) across different tasks on Llama\-3\.2\-8B\. Values denote Epochs \(Mean±\\pmStd\)\.TaskTm​e​mT\_\{mem\}Tg​e​nT\_\{gen\}Δ​T\\Delta T\(Lag\)Chaining7\.23±1\.897\.23\\pm 1\.8911\.83±5\.4111\.83\\pm 5\.41\+4\.60\+4\.60Intersection6\.04±1\.326\.04\\pm 1\.327\.16±6\.967\.16\\pm 6\.96\+1\.12\+1\.12

Figure[2](https://arxiv.org/html/2607.08393#S4.F2)shows that increasing model size does not eliminate the temporal lagΔ​T\\Delta T\. Moreover, increasing the number of injected facts tends to widen the final accuracy gapΔ​A​\(𝒯\)\\Delta A\(\\mathcal\{T\}\), even when direct recall remains strong, indicating that scaling storage does not directly translate into proportional gains in usable reasoning\. Table[10](https://arxiv.org/html/2607.08393#A4.T10)gives the corresponding LLaMA\-3\.2\-8B lag estimates for chaining and intersection: chaining shows a larger delay, while intersection remains much closer to memorization time\.

## Appendix EMore results on knowledge\-circuit misalignment\.

![Refer to caption](https://arxiv.org/html/2607.08393v1/figures/patchscope_memorization.png)Figure 8:Patchscope views of memorization\-related layers at the head\-entity position\.We use PatchScope to interpret the hidden state in the memorization prompt\. We use the in\-context prompt shown in Table[8](https://arxiv.org/html/2607.08393#A1.T8), and test the head\-entity position\. Results in Figure[8](https://arxiv.org/html/2607.08393#A5.F8)show that for early\-layer knowledge storage, the detectable place in LLaMA is lower than that in Qwen across model scales, suggesting that LLaMA tends to store knowledge in early to middle layers\.

We also report the controlled experiment for self\-patching for the LLaMA architecture same size as used in main text, as shown in Table[11](https://arxiv.org/html/2607.08393#A5.T11)\. The control confirms that self\-patching yields the strongest recovery on both chaining and intersection, while irrelevant patching remains below the knowledge\-specific intervention\.

Table 11:Control patching experiments\.for LLaMA\-3\.2\-3bChain\.Intersec\.No\-Patching0\.1260\.1260\.8150\.815Irrelevant\-Patching0\.2070\.2070\.9150\.915Self\-Patching0\.4040\.4040\.9690\.969

## Appendix FStatistical Significance and Confidence Intervals

We report 95% Wilson score confidence intervals for all main results\. Wilson intervals are preferred over normal approximation for proportions near 0 or 1Agresti and Coull \[[1998](https://arxiv.org/html/2607.08393#bib.bib1)\]\. Memorization is evaluated onn=1000n=1000facts; chaining and intersection onn=500n=500andn=1000n=1000respectively\. The per\-instance Knowing–Using Gap \(Mem\.−\-Chain\.\) is significant for all models under McNemar’s test on paired 0/1 outcomes \(p<10−50p<10^\{\-50\}for every model\)\. The gap magnitude is fully described by the difference of proportions Mem\.−\-Chain\., which is itself the McNemar effect\-size statistic and is shown in the right column\. An exact binomial test on the discordant pairs gives the same conclusion as McNemar\. Spearman correlation between model size and gap magnitude isr=−0\.90r=\-0\.90,p=0\.015p=0\.015\. For temporal\-lag sensitivity, recomputingΔ​T\\Delta Ton Qwen\-2\.5\-3B chaining overτ∈\{0\.9,0\.95,1\.0\}\\tau\\in\\\{0\.9,0\.95,1\.0\\\}andw∈\{1,2,3\}w\\in\\\{1,2,3\\\}yields lag values within±1\.0\\pm 1\.0epoch of the default \(τ=1\.0\\tau=1\.0,w=2w=2\) report; the qualitative patternTuse\>TmemT\_\{\\text\{use\}\}\>T\_\{\\text\{mem\}\}holds in all 9 grid cells\.

ModelMem\.Chain\.Intersec\.GapQwen\-2\.5\-1\.5B0\.998−0\.004\+0\.0020\.998^\{\+0\.002\}\_\{\-0\.004\}0\.078−0\.020\+0\.0250\.078^\{\+0\.025\}\_\{\-0\.020\}0\.793−0\.038\+0\.0320\.793^\{\+0\.032\}\_\{\-0\.038\}0\.920Qwen\-2\.5\-3B0\.997−0\.004\+0\.0020\.997^\{\+0\.002\}\_\{\-0\.004\}0\.114−0\.024\+0\.0300\.114^\{\+0\.030\}\_\{\-0\.024\}0\.798−0\.037\+0\.0320\.798^\{\+0\.032\}\_\{\-0\.037\}0\.883Qwen\-2\.5\-7B0\.996−0\.005\+0\.0030\.996^\{\+0\.003\}\_\{\-0\.005\}0\.124−0\.026\+0\.0310\.124^\{\+0\.031\}\_\{\-0\.026\}0\.774−0\.039\+0\.0340\.774^\{\+0\.034\}\_\{\-0\.039\}0\.872LLaMA\-3\.2\-1B0\.994−0\.006\+0\.0040\.994^\{\+0\.004\}\_\{\-0\.006\}0\.102−0\.023\+0\.0280\.102^\{\+0\.028\}\_\{\-0\.023\}0\.874−0\.032\+0\.0260\.874^\{\+0\.026\}\_\{\-0\.032\}0\.892LLaMA\-3\.2\-3B0\.993−0\.006\+0\.0040\.993^\{\+0\.004\}\_\{\-0\.006\}0\.126−0\.026\+0\.0310\.126^\{\+0\.031\}\_\{\-0\.026\}0\.815−0\.036\+0\.0310\.815^\{\+0\.031\}\_\{\-0\.036\}0\.867LLaMA\-3\.1\-8B0\.986−0\.009\+0\.0060\.986^\{\+0\.006\}\_\{\-0\.009\}0\.182−0\.031\+0\.0350\.182^\{\+0\.035\}\_\{\-0\.031\}0\.795−0\.038\+0\.0320\.795^\{\+0\.032\}\_\{\-0\.038\}0\.804

Table 12:95% Wilson score confidence intervals for Table[4](https://arxiv.org/html/2607.08393#S5.T4)\.![Refer to caption](https://arxiv.org/html/2607.08393v1/x5.png)Figure 9:More permeation dynamics cases on LLaMA\-3\.1\-8B\.![Refer to caption](https://arxiv.org/html/2607.08393v1/x6.png)Figure 10:More permeation dynamics cases on Qwen\-2\.5\-7B\.
## Appendix GMore cases on permeation dynamics

Fig[9](https://arxiv.org/html/2607.08393#A6.F9)and fig\.[10](https://arxiv.org/html/2607.08393#A6.F10)demonstrate more cases of the permeation dynamics of transitions from memorization to generalization on LLaMA\-3\.1\-8B and Qwen\-2\.5\-7B respectively\. The patterns are all coherence with results in[5\.2](https://arxiv.org/html/2607.08393#S5.SS2)where patch\-effective regions covering diagonal indicates the emergence of direct chaining ability\.

## Appendix HLimitations and Responsible Research Details

### H\.1Limitations

Self\-patching is deliberately constrained: we intervene at a fixed anchor position and move representations across layers\. Injected knowledge may also distribute across multiple positions or be redundantly encoded, so our estimates may understate the full recoverable headroom\.

Our oracle best\-pair results should be interpreted as a diagnostic upper bound\. While the fixed heuristic in Section[5\.5](https://arxiv.org/html/2607.08393#S5.SS5)demonstrates practical feasibility, developing fully adaptive non\-oracle alignment strategies remains an important direction\.

Our mechanism is mainly diagnostic: we can identify and partially repair the misalignment post hoc, but we do not yet offer an early\-training signal that forecasts which facts will fail to generalize\. Developing such a predictive metric would enable proactive interventions during fine\-tuning\.

Finally, our mechanistic analysis operates at the token\-layer level\. Finer\-grained localization to specific attention heads or MLP sublayers could further refine the knowledge–circuit misalignment hypothesis and inform more targeted interventions\.

### H\.2Reproducibility and Compute

Code, data, and reproduction instructions are included in the anonymous release at[https://anonymous\.4open\.science/r/Mem2Gen\-71FF](https://anonymous.4open.science/r/Mem2Gen-71FF)\. Appendix[B](https://arxiv.org/html/2607.08393#A2)reports the main data splits, filtering protocol, hyperparameters, evaluation rules, and statistical tests used to reproduce the experimental results\.

Experiments were run on a server with NVIDIA A800 GPUs, each with 81,920 MiB of memory, an Intel 128\-core CPU, and 512 GB system memory\. A typical primary experiment used 8 GPUs\. Depending on model scale and experiment type, the wall\-clock time for a single run ranged from about 5 hours to 1 day\.

### H\.3Assets, Licenses, and Released Artifacts

We release the derived memorization\-to\-generalization QA data and accompanying code as new artifacts under the MIT License in the anonymous repository\. The released data are generated from knowledge\-graph facts and templates or AI\-assisted wording; no consent\-bearing human\-subject data are collected for this work\.

### H\.4Ethics, Broader Impacts, and Safeguards

The authors reviewed the NeurIPS Code of Ethics and believe the work conforms to it\. The work does not involve crowdsourcing, human\-subject experiments, participant compensation, or IRB\-style review requirements\.

## NeurIPS Paper Checklist

1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]\.
4. Justification: The abstract and Introduction state the Knowing–Using Gap, self\-patching method, knowledge–circuit misalignment hypothesis, recovery claims, and dataset release\. Sections[4\.2](https://arxiv.org/html/2607.08393#S4.SS2)–[5\.5](https://arxiv.org/html/2607.08393#S5.SS5)and Appendix[B](https://arxiv.org/html/2607.08393#A2)define the experimental scope across model families and STaRK domains\.
5. Guidelines: - •The answer\[N/A\]means that the abstract and introduction do not include the claims made in the paper\. - •The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations\. A\[No\]or\[N/A\]answer to this question will not be perceived well by the reviewers\. - •The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings\. - •It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper\.
6. 2\.Limitations
7. Question: Does the paper discuss the limitations of the work performed by the authors?
8. Answer:\[Yes\]\.
9. Justification: Appendix[H](https://arxiv.org/html/2607.08393#A8)discusses limitations of the self\-patching diagnostic, the oracle upper\-bound interpretation, the KG\-style domain scope, the lack of an early predictive signal, and the layer\-level granularity of the analysis\.
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13. Answer:\[N/A\]\.
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16. 4\.Experimental result reproducibility
17. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper \(regardless of whether the code and data are provided or not\)?
18. Answer:\[Yes\]\.
19. Justification: The data construction, filtering, training, evaluation, patching protocol, and statistical tests are described in Sections[3\.1](https://arxiv.org/html/2607.08393#S3.SS1)–[5\.5](https://arxiv.org/html/2607.08393#S5.SS5)and Appendices[B](https://arxiv.org/html/2607.08393#A2)–[F](https://arxiv.org/html/2607.08393#A6)\. Code, data, and reproduction instructions are included in the anonymous release\.
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22. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
23. Answer:\[Yes\]\.
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27. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, how they were chosen, type of optimizer\) necessary to understand the results?
28. Answer:\[Yes\]\.
29. Justification: Section[3\.1](https://arxiv.org/html/2607.08393#S3.SS1)describes task construction and evaluation separation, while Appendix[B](https://arxiv.org/html/2607.08393#A2)specifies the splits, filtering, optimizer, LoRA configuration, learning rates, batch sizes, seed, checkpointing, and patching evaluation protocol\.
30. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them\. - •The full details can be provided either with the code, in appendix, or as supplemental material\.
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32. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
33. Answer:\[Yes\]\.
34. Justification: Appendix[F](https://arxiv.org/html/2607.08393#A6)reports 95% Wilson score confidence intervals, McNemar’s tests, exact binomial tests on discordant pairs, a Spearman correlation analysis, and temporal\-lag sensitivity checks\.
35. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The authors should answer\[Yes\]if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper\. - •The factors of variability that the error bars are capturing should be clearly stated \(for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions\)\. - •The method for calculating the error bars should be explained \(closed form formula, call to a library function, bootstrap, etc\.\) - •The assumptions made should be given \(e\.g\., Normally distributed errors\)\. - •It should be clear whether the error bar is the standard deviation or the standard error of the mean\. - •It is OK to report 1\-sigma error bars, but one should state it\. The authors should preferably report a 2\-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified\. - •For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range \(e\.g\., negative error rates\)\. - •If error bars are reported in tables or plots, the authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text\.
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37. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
38. Answer:\[Yes\]\.
39. Justification: Appendix[H](https://arxiv.org/html/2607.08393#A8)reports the NVIDIA A800 GPU hardware, 81,920 MiB GPU memory, Intel 128\-core CPU, 512 GB system memory, 8\-GPU primary run configuration, and 5\-hour to 1\-day single\-run wall\-clock range\.
40. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage\. - •The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute\. - •The paper should disclose whether the full research project required more compute than the experiments reported in the paper \(e\.g\., preliminary or failed experiments that didn’t make it into the paper\)\.
41. 9\.Code of ethics
43. Answer:\[Yes\]\.
44. Justification: Appendix[H](https://arxiv.org/html/2607.08393#A8)states that the authors reviewed the NeurIPS Code of Ethics and that the work does not involve crowdsourcing, human\-subject experiments, or participant compensation\.
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46. 10\.Broader impacts
47. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
48. Answer:\[Yes\]\.
49. Justification: Appendix[H](https://arxiv.org/html/2607.08393#A8)discusses positive impacts for diagnosing and mitigating LLM knowledge\-injection failures, and negative impacts from potentially improving adaptation to incorrect, unsafe, or harmful facts\.
50. Guidelines: - •The answer\[N/A\]means that there is no societal impact of the work performed\. - •If the authors answer\[N/A\]or\[No\], they should explain why their work has no societal impact or why the paper does not address societal impact\. - •Examples of negative societal impacts include potential malicious or unintended uses \(e\.g\., disinformation, generating fake profiles, surveillance\), fairness considerations \(e\.g\., deployment of technologies that could make decisions that unfairly impact specific groups\), privacy considerations, and security considerations\. - •The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments\. However, if there is a direct path to any negative applications, the authors should point it out\. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate Deepfakes for disinformation\. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster\. - •The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from \(intentional or unintentional\) misuse of the technology\. - •If there are negative societal impacts, the authors could also discuss possible mitigation strategies \(e\.g\., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML\)\.
51. 11\.Safeguards
52. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse \(e\.g\., pre\-trained language models, image generators, or scraped datasets\)?
53. Answer:\[N/A\]\.
54. Justification: The work releases code and KG\-derived QA data, but does not release trained model weights, pretrained language models, image generators, or scraped image datasets\. Appendix[H](https://arxiv.org/html/2607.08393#A8)notes that external model use remains governed by the corresponding model provider’s license and acceptable\-use terms\.
55. Guidelines: - •The answer\[N/A\]means that the paper poses no such risks\. - •Released models that have a high risk for misuse or dual\-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters\. - •Datasets that have been scraped from the Internet could pose safety risks\. The authors should describe how they avoided releasing unsafe images\. - •We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort\.
56. 12\.Licenses for existing assets
57. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
58. Answer:\[Yes\]\.
59. Justification: The paper cites STaRKWu et al\. \[[2024](https://arxiv.org/html/2607.08393#bib.bib32)\], and Appendix[H](https://arxiv.org/html/2607.08393#A8)identifies the public licenses or terms for STaRK, Qwen2\.5, and LLaMA assets\.
60. Guidelines: - •The answer\[N/A\]means that the paper does not use existing assets\. - •The authors should cite the original paper that produced the code package or dataset\. - •The authors should state which version of the asset is used and, if possible, include a URL\. - •The name of the license \(e\.g\., CC\-BY 4\.0\) should be included for each asset\. - •For scraped data from a particular source \(e\.g\., website\), the copyright and terms of service of that source should be provided\. - •If assets are released, the license, copyright information, and terms of use in the package should be provided\. For popular datasets,[paperswithcode\.com/datasets](https://arxiv.org/html/2607.08393v1/paperswithcode.com/datasets)has curated licenses for some datasets\. Their licensing guide can help determine the license of a dataset\. - •For existing datasets that are re\-packaged, both the original license and the license of the derived asset \(if it has changed\) should be provided\. - •If this information is not available online, the authors are encouraged to reach out to the asset’s creators\.
61. 13\.New assets
62. Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
63. Answer:\[Yes\]\.
64. Justification: The paper introduces and releases a memorization\-to\-generalization QA dataset and accompanying code\. Section[3\.1](https://arxiv.org/html/2607.08393#S3.SS1), Appendix[B](https://arxiv.org/html/2607.08393#A2), and Appendix[H](https://arxiv.org/html/2607.08393#A8)document construction, filtering, use, licensing, and release details\.
65. Guidelines: - •The answer\[N/A\]means that the paper does not release new assets\. - •Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates\. This includes details about training, license, limitations, etc\. - •The paper should discuss whether and how consent was obtained from people whose asset is used\. - •At submission time, remember to anonymize your assets \(if applicable\)\. You can either create an anonymized URL or include an anonymized zip file\.
66. 14\.Crowdsourcing and research with human subjects
67. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
68. Answer:\[N/A\]\.
69. Justification: The work does not involve crowdsourcing or research with human subjects\. The released QA data are generated from knowledge\-graph facts with templates or AI\-assisted wording, as described in Appendix[H](https://arxiv.org/html/2607.08393#A8)\.
70. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper\. - •According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector\.
71. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
72. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
73. Answer:\[N/A\]\.
74. Justification: The work does not involve crowdsourcing, research participants, human\-subject data collection, or IRB\-style review requirements, as stated in Appendix[H](https://arxiv.org/html/2607.08393#A8)\.
75. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Depending on the country in which research is conducted, IRB approval \(or equivalent\) may be required for any human subjects research\. If you obtained IRB approval, you should clearly state this in the paper\. - •We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution\. - •For initial submissions, do not include any information that would break anonymity \(if applicable\), such as the institution conducting the review\.
76. 16\.Declaration of LLM usage
77. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does*not*impact the core methodology, scientific rigor, or originality of the research, declaration is not required\.
78. Answer:\[N/A\]\.
79. Guidelines: - •The answer\[N/A\]means that the core method development in this research does not involve LLMs as any important, original, or non\-standard components\. - •Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described\.