Bounded Personas Match Retrieval on Classification but Not Regression for a Frozen Agent

# Bounded Personas Match Retrieval on Classification but Not Regression for a Frozen Agent
Source: [https://arxiv.org/html/2609.02890](https://arxiv.org/html/2609.02890)
JaeHa Yoon1, Minjun Park1, Seoyeon Kim2, Jiwoo Lee3, Hyunwoo Choi1, Dohyun Kang2 1Seoul National University2KAIST3Korea University, Seoul, Republic of Korea jaeha\.yoon@snu\.ac\.kr

###### Abstract

A personalized language agent must convert a user’s interaction history into behavior on each new request at inference time\. Two strategies dominate\. Retrieval pulls a few of the user’s most relevant past items into the prompt, which is accurate but pays a per\-query selection and context cost that grows with the history\. Distillation instead compresses the history once into a compact natural\-language persona, which is bounded, query\-independent, and interpretable, but is widely assumed to sacrifice accuracy\. Whether, and on which tasks, a distilled persona can match retrieval has not been characterized cleanly\. We introducePersonaLink, a training\-free method that distills a user’s history into a bounded three\-field persona and recursively refines it: each pass self\-evaluates the frozen agent on a held\-out slice of the user’s own labeled history, rewrites the persona from its errors, and keeps the result only when it does not regress on that slice\. Because every comparison shares one frozen 7B backbone and differs only in what is placed in context, the design isolates the effect of representation from that of the model\. The result is a clear task\-type asymmetry\. On 200 users of LaMP\-2 \(15\-way news categorization\),PersonaLinkreaches0\.7450\.745–0\.7550\.755accuracy, statistically indistinguishable from BM25 retrieval \(0\.7600\.760–0\.7650\.765\)\. On 200 users of LaMP\-3 \(1–5 product\-rating regression\), retrieval is decisively stronger \(0\.2850\.285vs\.0\.4550\.455MAE,p<10−4p\{<\}10^\{\-4\}\) and continues to improve askkgrows, reaching0\.7900\.790accuracy and0\.2500\.250MAE atk=20k\{=\}20with no plateau\. Recursion adds little beyond the first pass: the persona representation contracts toward a per\-user fixed point \(per\-pass displacement0\.90→0\.21→0\.020\.90\{\\to\}0\.21\{\\to\}0\.02, modulusL=0\.144L\{=\}0\.144,R2=0\.979R^\{2\}\{=\}0\.979\), so refinement saturates\. Bounded distillation is therefore a sufficient substitute for retrieval precisely when the task is to select a label, and not when it requires a calibrated numeric scale\.

![Refer to caption](https://arxiv.org/html/2609.02890v1/x1.png)Figure 1:PersonaLinkdistills a user’s history into a bounded, query\-independent persona that is built once and contracts to a fixed point after a single pass\.It matches retrieval on LaMP\-2 classification but not on LaMP\-3 regression, and retrieval \(RAG\) remains the honest ceiling among non\-oracle methods\.## 1Introduction

A personalized language agent is, operationally, a function from a user’s history to behavior on a new request\. The same news article should be filed under “politics” for one reader and “style & beauty” for another, and the same product review should be scored differently by a generous and a harsh rater\. The agent never sees the user’s label for the new item, so all of its personalization signal must come from that user’s*past*labeled items\. How best to convert that history into a single inference is one of the central design choices for personalized LLM systems\.

Two answers have crystallized\. The first is to*retrieve*: at query time, pull the most relevant few of the user’s past items into the prompt as demonstrations\[[43](https://arxiv.org/html/2609.02890#bib.bib7),[42](https://arxiv.org/html/2609.02890#bib.bib9)\]\. Retrieval is strong and simple, but it pays a per\-query retrieval and context cost that grows with the number of items used, and it exposes raw user data on every call\. The second is to*distill*: compress the history once into a compact natural\-language profile that is prepended to every subsequent query\[[39](https://arxiv.org/html/2609.02890#bib.bib8),[77](https://arxiv.org/html/2609.02890#bib.bib10)\]\. Distillation is attractive for the opposite reasons—the persona is built once, is bounded in size, is the same for every query, and is human\-readable—but it is widely assumed to leave accuracy on the table relative to retrieval\. Whether, and*when*, a distilled persona can actually*match*retrieval has not been cleanly characterized\.

We address this question directly\. We introducePersonaLink\(Figure[1](https://arxiv.org/html/2609.02890#S0.F1)\), a training\-free method that distills a user’s history into a*bounded*three\-field persona and then*recursively refines*it: each pass renders the current persona, runs the frozen agent on a held\-out slice of the user’s own labeled history, and rewrites the persona from its own mistakes, keeping the new persona only if it does no worse on the held\-out items\. The refinement depthrris an explicit, controllable axis, mirroring the recursive\-scaling perspective\[[69](https://arxiv.org/html/2609.02890#bib.bib5)\], and the keep\-better gate makes the loop monotone\-safe by construction\. Because every method shares one frozen backbone and differs only in the text placed in context, the comparison between distillation and retrieval is held strictly apples\-to\-apples\.

Our experiments reveal a sharp task\-type asymmetry\. On classification,PersonaLinkis competitive with retrieval: on LaMP\-2 it reaches0\.7450\.745–0\.7550\.755accuracy, statistically indistinguishable from BM25RAGatk=3,5k\{=\}3,5\(0\.7600\.760/0\.7650\.765\)\. On regression it is dominated: on LaMP\-3 it attains0\.4550\.455MAE againstRAG\-5’s0\.2850\.285\(p<10−4p\{<\}10^\{\-4\}\), and retrieval keeps improving as items are added \(k=10:0\.290k\{=\}10\{:\}\\,0\.290,k=20:0\.250k\{=\}20\{:\}\\,0\.250MAE\) with no sign of a plateau\. Retrieval is therefore the stronger method overall, and we report it as the best non\-oracle method in every results table\. The contribution ofPersonaLinkis not a new state of the art but a characterization: a bounded, query\-independent persona suffices precisely when the task is to select a label, and not when it is to estimate a fine\-grained quantity\.

A second finding concerns the recursion itself\. Personalization is a genuine effect:PersonaLinkbeats both a no\-persona control and a random\-user control that holds the token budget fixed, so the gains are not an artifact of a longer prompt\. The recursion, however, saturates\. The first distillation pass \(r=1r\{=\}1\) captures essentially all of the benefit, andr=2r\{=\}2andr=3r\{=\}3are not significantly better \(Δ​Acc=0\.000\\Delta\\mathrm\{Acc\}\{=\}0\.000,p=0\.77p\{=\}0\.77on LaMP\-2\)\. We trace this plateau to a measurable property of the refinement map: the persona representation contracts toward a per\-user fixed point, with per\-pass embedding displacement shrinking0\.90→0\.21→0\.020\.90\{\\to\}0\.21\{\\to\}0\.02and a geometric\-decay fit of modulusL=0\.144L\{=\}0\.144\(R2=0\.979R^\{2\}\{=\}0\.979\)\. We do not claim an unconditional contraction theorem; we instead state falsifiable assumptions, measure the modulus, and pair the measurement with a monotone\-safety proposition that holds by construction\.

This paper makes the following contributions\.

- •We introducePersonaLink, a bounded three\-field persona equipped with a training\-free, monotone\-safe recursive refinement loop that distills a user’s history into a fixed\-size, query\-independent, interpretable representation\.
- •We characterize the distill\-versus\-retrieve trade\-off on two LaMP tasks under one frozen backbone with deterministic metrics and paired significance testing, establishing a task\-type asymmetry: distillation ties retrieval on classification, loses on regression, and does not scale with the history, whereas retrieval keeps improving askkgrows\.
- •We give an empirical fixed\-point account of why recursive persona refinement saturates after a single pass, measuring a geometric contraction of the persona representation \(L=0\.144L\{=\}0\.144,R2=0\.979R^\{2\}\{=\}0\.979\)\.

We positionPersonaLinknot as a competitor that beats retrieval but as a study of the regime in which a bounded distilled persona is sufficient\.

## 2Preliminary: the personalized prediction setting

We adopt the personalized\-LLM setting of LaMP\[[43](https://arxiv.org/html/2609.02890#bib.bib7)\]\. A useruuis associated with a*profile*Hu=\{\(xi,yi\)\}i=1muH\_\{u\}=\\\{\(x\_\{i\},y\_\{i\}\)\\\}\_\{i=1\}^\{m\_\{u\}\}of past items, each a \(input, label\) pair with a*known*label: for LaMP\-2 a past news article and its human category; for LaMP\-3 a past review and its11–55rating\. At test time the agent receives a new inputx⋆x^\{\\star\}*without*its label and must predicty^\\hat\{y\}\. All personalization signal therefore lives inHuH\_\{u\}, and a method is a map that usesHuH\_\{u\}\(and a frozen LLMff\) to answerx⋆x^\{\\star\}\.

We organize methods along the axis that this paper studies\.No\-personalizationignoresHuH\_\{u\}and answersf​\(x⋆\)f\(x^\{\\star\}\); it is the natural floor\.Retrieval\(RAG\) selects thekkmost relevant past items by BM25\[[40](https://arxiv.org/html/2609.02890#bib.bib29)\]and injects them as demonstrations,f​\(x⋆∣top​\-​k​\(Hu,x⋆\)\)f\(x^\{\\star\}\\mid\\mathrm\{top\\text\{\-\}\}k\(H\_\{u\},x^\{\\star\}\)\); the injected context depends onx⋆x^\{\\star\}and grows withkk\.DistillationcompressesHuH\_\{u\}once into a personapup\_\{u\}and answersf​\(x⋆∣pu\)f\(x^\{\\star\}\\mid p\_\{u\}\); the injected context is fixed per user and independent ofx⋆x^\{\\star\}\. A*random\-user*control injects another user’s profile, holding the token budget fixed so that any gain over it is attributable to the*right*user’s history rather than to extra tokens\. An*oracle*that places the full true profile in context gives a ceiling\.PersonaLinkis a distillation method whose persona is bounded and built by recursion; the question of this paper is how close such a persona can come to retrieval, and on which task types\.

We evaluate on the two LaMP tasks that exercise both metric regimes\.LaMP\-2\(personalized news categorization\) is a1515\-way classification of an article into categories such as \{politics, sports, style & beauty, science & technology,…\\dots\}; we score Accuracy and macro\-F1\.LaMP\-3\(personalized product rating\) is an ordinal11–55regression; we score MAE and RMSE \(lower is better\), which exposes fine\-grained quantitative personalization\. All metrics are deterministic \(scikit\-learn\); there is*no*LLM judge anywhere in the scoring path\.

## 3PersonaLink: a bounded, query\-independent persona

![Refer to caption](https://arxiv.org/html/2609.02890v1/x2.png)Figure 2:PersonaLinkarchitecture\.A bounded three\-fieldPersonaStateis rendered as a preamble, the frozen agent self\-evaluates on a held\-out slice of the user’s own labeled history, and the persona is rewritten from its errors behind a strict keep\-better gate; the loop unrolls over refinement depthrrand the kept\-best persona answers test items\.### 3\.1A lightweight, bounded persona state

The core object isPersonaState, a compact natural\-language object with exactly three bounded fields: \(1\) apreference summary—imperative prose describing the user’s stable preferences \(e\.g\. “tends to file political news under*politics*, not*culture & arts*”\); \(2\) a small set ofexemplars—a few representative \(input→\\tolabel\) demonstrations drawn from the profile; and \(3\) a short list ofdecision rules—conditional heuristics induced from past items \(e\.g\. “if the review mentions a defect but says it still works, score33”\)\. Each field has a hard length cap, so the rendered persona has*bounded*size regardless of how long the user’s history is\. This is a deliberate design contrast with add\-only context memories\[[75](https://arxiv.org/html/2609.02890#bib.bib22),[50](https://arxiv.org/html/2609.02890#bib.bib23)\], whose footprint grows with experience, and with retrieval, whose injected context grows withkk\.

Two properties follow from boundedness and matter for the rest of the paper\. First, the persona is*query\-independent*: the samepup\_\{u\}is prepended to every test inputx⋆x^\{\\star\}, so it is built once and amortized across all of a user’s future queries, anO​\(1\)O\(1\)\-per\-query injection cost versus retrieval’s per\-query selection\. Second, the persona is*interpretable*: all three fields are human\-readable text that can be inspected and edited, unlike a fine\-tuned adapter\[[51](https://arxiv.org/html/2609.02890#bib.bib11)\]or a soft persona embedding\[[29](https://arxiv.org/html/2609.02890#bib.bib12)\]\.

### 3\.2Build\-once recursive refinement

PersonaLinkconstructspup\_\{u\}by a training\-free loop over the user’s*own*profile, illustrated in Figure[2](https://arxiv.org/html/2609.02890#S3.F2)\. Crucially, because every profile item carries a known label, the loop can verify itself deterministically without any external judge\. One refinement pass is:

1. 1\.Render\.Serialize the currentPersonaStatepu\(r\)p\_\{u\}^\{\(r\)\}as a single preamble\.
2. 2\.Self\-evaluate\.Run the frozen agentf\(⋅∣pu\(r\)\)f\(\\cdot\\mid p\_\{u\}^\{\(r\)\}\)on a held\-out leave\-some\-out sliceSuS\_\{u\}of the user’s profile whose labels are known, and collect the error setEu=\{\(xi,yi\)∈Su:f​\(xi∣pu\(r\)\)≠yi\}E\_\{u\}=\\\{\(x\_\{i\},y\_\{i\}\)\\in S\_\{u\}:f\(x\_\{i\}\\mid p\_\{u\}^\{\(r\)\}\)\\neq y\_\{i\}\\\}\. This is exact, label\-grounded self\-verification—no LLM\-as\-judge\.
3. 3\.Rewrite\.FeedEuE\_\{u\}together withpu\(r\)p\_\{u\}^\{\(r\)\}to the agent and ask it to rewrite the persona to fix those errors, editing or dropping any field within the length caps, producing a candidatepu′p\_\{u\}^\{\\prime\}\.
4. 4\.Keep\-better gate\.Acceptpu′p\_\{u\}^\{\\prime\}only if its held\-out score does not regress relative to the incumbent—a strict held\-out best\-update rule; otherwise keeppu\(r\)p\_\{u\}^\{\(r\)\}\.

We define depthr=0r\{=\}0as the no\-persona control \(emptypup\_\{u\}\),r=1r\{=\}1as a single distillation pass \(which coincides with a profile\-summary baseline,PAG\), andr≥2r\\\!\\geq\\\!2as recursive error\-driven self\-correction\. Afterrrpasses, the kept\-best persona is rendered*once*to answer the actual test items; the test item is never part ofSuS\_\{u\}\. The only thing that varies across depths is the persona text prepended to the identical test question, which isolates the effect of refinement\.

## 4Learning to personalize by recursion

The refinement loop of §[3\.2](https://arxiv.org/html/2609.02890#S3.SS2)is an inner optimization over persona text driven entirely by the user’s own held\-out signal\. We make two honest formal claims: a safety guarantee that holds by construction, and an*empirical*fixed\-point account of saturation\. We deliberately do*not*assert an unconditional contraction theorem; instead we state falsifiable assumptions and measure the relevant quantity \(§[6](https://arxiv.org/html/2609.02890#S6)\)\.

#### Monotone\-safety of the held\-out estimator\.

LetArA\_\{r\}denote the held\-out score of the kept persona afterrrpasses andA0A\_\{0\}the score of the empty persona\.

###### Proposition 1\(Monotone\-safety, held\-out selection\)\.

Under the strict keep\-better gate, the held\-out score of the kept persona is non\-decreasing inrr, i\.e\.Ar≥Ar−1≥⋯≥A0A\_\{r\}\\geq A\_\{r\-1\}\\geq\\dots\\geq A\_\{0\}for allrr\. In particular, if no candidate strictly improves over the empty persona on the held\-out slice, the procedure reduces*exactly*to the no\-personalization control\.

###### Proof sketch\.

By induction onrr\. The gate replaces the incumbent only with a candidate whose held\-out score is no smaller, soAr≥Ar−1A\_\{r\}\\geq A\_\{r\-1\}; the base case isA0A\_\{0\}itself\. If every candidate is rejected, the kept persona stays empty and the agent answersf​\(x⋆\)f\(x^\{\\star\}\)\. Full statement in Appendix[A](https://arxiv.org/html/2609.02890#A1)\. ∎

#### Scope caveat \(stated up front\)\.

Proposition[1](https://arxiv.org/html/2609.02890#Thmproposition1)bounds the held\-out*selection*signalArA\_\{r\}, not necessarily accuracy on unseen test items: held\-out improvement can fail to transfer, exactly as for any held\-out model\-selection procedure\. We therefore treat the Proposition as a no\-harm guarantee on what the loop optimizes, and we measure test\-set behavior empirically rather than claiming it follows from the gate\.

#### An empirical fixed point, not a theorem\.

We model one refinement pass as a mapTTon an embedding of the persona text,pu\(r\+1\)=T​\(pu\(r\)\)p\_\{u\}^\{\(r\+1\)\}=T\(p\_\{u\}^\{\(r\)\}\), and ask whether the iterates contract\. This would hold under two assumptions we state as falsifiable:\(A1\)error\-driven editing leaves already\-correct fields unchanged, so each pass touches a shrinking part of the persona; and\(A2\)the rewrite map is non\-expansive with modulusL<1L\{<\}1on the relevant region\. Under A1–A2 the iterates are Cauchy and converge geometrically, so per\-pass change decays likeLrL^\{r\}and marginal gains vanish—a Banach\-style picture\. Rather than assert A2 holds unconditionally, we*measure*LLfrom the data by regressing log per\-pass displacement onrr\(§[6](https://arxiv.org/html/2609.02890#S6)\); the data giveL=0\.144L\{=\}0\.144withR2=0\.979R^\{2\}\{=\}0\.979, consistent with strong contraction\.

###### Corollary 1\(Compute\-optimal depth\)\.

If per\-pass gains decay geometrically while per\-pass cost is constant, the compute\-optimal refinement depth is small\. Empirically \(§[5](https://arxiv.org/html/2609.02890#S5)\) the first pass realizes the gain andr=2,3r\{=\}2,3add no significant accuracy, sor=1r\{=\}1is compute\-optimal here\.

## 5Experiments

#### Setup\.

All methods share one frozen 7B\-class backbone with identical greedy decoding; the only difference across methods is what is placed in context\. We evaluate onn=200n\{=\}200users each for LaMP\-2 and LaMP\-3 \(frozen manifest, seed1234512345, the unit of analysis is the user/question\)\. Metrics are deterministic: Accuracy and macro\-F1 for LaMP\-2; MAE and RMSE for LaMP\-3 \(lower is better\)\. Significance uses McNemar’s test on LaMP\-2 correctness and a paired bootstrap on LaMP\-3 absolute error; intervals are bootstrap95%95\\%CIs over items\. Table[1](https://arxiv.org/html/2609.02890#S5.T1)consolidates the datasets and protocol; the two tasks share every choice except the metric regime, so the distill\-vs\-retrieve comparison is held apples\-to\-apples\. Table[2](https://arxiv.org/html/2609.02890#S5.T2)reports the depth\-scaling study and Table[4](https://arxiv.org/html/2609.02890#S5.T4)the broader comparison, with retrievalbolded as the best non\-oracle methodthroughout—an honest presentation of a method we do not beat\.

Table 1:Datasets and evaluation protocol\.Both LaMP tasks share one frozen 7B\-class backbone with identical greedy decoding; the only per\-method difference is the in\-context text\. The two tasks deliberately span the classification and regression metric regimes, with everything else \(users, splits, decoding, scoring\) held fixed so that the distill\-vs\-retrieve comparison is apples\-to\-apples\.LaMP\-2\(news categorization\)LaMP\-3\(product rating\)Task type15\-way classificationordinal 1–5 regressionLabel space\{politics, sports, …\} \(15\)\{1,2,3,4,5\}\\\{1,2,3,4,5\\\}Primary / secondary metricAccuracy↑\\uparrow/ macro\-F1↑\\uparrowMAE↓\\downarrow/ RMSE↓\\downarrowMetric directionhigher is betterlower is betterEval\. users \(nn\)200200Median profile sizemum\_\{u\}∼\\sim188 items∼\\sim188 itemsHeld\-out sliceSuS\_\{u\}leave\-some\-out ofHuH\_\{u\}leave\-some\-out ofHuH\_\{u\}Frozen manifest seed1234512345Backbonefrozen 7B\-class, greedyfrozen 7B\-class, greedyRetrieverBM25 overHuH\_\{u\}BM25 overHuH\_\{u\}Persona budget∼\\sim250 tokens \(3 bounded fields\)∼\\sim250 tokens \(3 bounded fields\)LLM judgenone \(deterministic, sklearn\)none \(deterministic, sklearn\)Significance testMcNemar \(paired correctness\)paired bootstrap \(abs\. error\)Intervalbootstrap 95% CI / itemsbootstrap 95% CI / items
The unit of analysis is the user/question\. No test item ever entersSuS\_\{u\}; label parsing is robust \(lower\-casing, nearest\-valid\-class, clamp\-to\-range\) but contains no generative judge anywhere in the scoring path\.

Table 2:Scaling personalization via recursive refinement depthrr\.PersonaLinkunrolled tor=0r\{=\}0\(NoPers\),r=1r\{=\}1\(PAG; one distillation pass\), andr=2,3r\{=\}2,3\(recursive self\-rewrite behind a keep\-better gate\); only the prepended persona text differs across rows\. The first pass gives the gain \(∗⁣∗\\mathbf\{\*\*\}: sig\. overr=0r\{=\}0\); further recursion does not \(the contraction plateau\)\.LaMP\-2\(news cat\., 15\-way\)LaMP\-3\(rating,↓\\downarrow\)Refinement depthAcc\.↑\\uparrowmacro\-F1↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowNoPers\(r=0\)\(r\{=\}0\)0\.6450\.3880\.5000\.794PAG\(r=1\)\(r\{=\}1\)∗∗0\.7450\.4850\.4500\.742PersonaLink\(r=2\)\(r\{=\}2\)∗∗0\.7450\.5140\.4550\.765PersonaLink\(r=3\)\(r\{=\}3\)∗∗0\.7300\.4950\.4300\.728
r=1→r=2r\{=\}1\\\!\\to\\\!r\{=\}2delta:Δ​Acc=\+0\.000\\Delta\\mathrm\{Acc\}\{=\}\{\+\}0\.000\(p=0\.77p\{=\}0\.77, McNemar\) on LaMP\-2;Δ​MAE=\+0\.005\\Delta\\mathrm\{MAE\}\{=\}\{\+\}0\.005\(p=0\.96p\{=\}0\.96, paired bootstrap\) on LaMP\-3 — not significant\. Deterministic metrics,n=200n\{=\}200items/task\.

### 5\.1Personalization is real

Using the right user’s history helps, and not because of extra tokens\. In Table[4](https://arxiv.org/html/2609.02890#S5.T4),PersonaLinkand itsr=1r\{=\}1distillation lift LaMP\-2 accuracy from the no\-persona floor of0\.6450\.645to0\.7450\.745–0\.7550\.755, a gain that is significant againstNoPers\(Δ​Acc=\+0\.10\\Delta\\mathrm\{Acc\}\{=\}\{\+\}0\.10,p=0\.003p\{=\}0\.003, McNemar\)\. Critically, it also beats the*random\-user*control \(0\.6650\.665accuracy;p<0\.05p\{<\}0\.05\), which injects a different user’s profile at the same token budget—so the improvement is attributable to the correct user’s history, not to a longer prompt\. The same pattern holds on LaMP\-3, where the random\-user control is significantly worse thanPersonaLink\(p=0\.016p\{=\}0\.016, paired bootstrap\)\. Personalization is therefore a genuine effect in both tasks\.

### 5\.2Distillation matches retrieval on classification

On the classification task, a bounded distilled persona is competitive with retrieval\. In Table[4](https://arxiv.org/html/2609.02890#S5.T4),PersonaLinkreaches0\.7450\.745–0\.7550\.755LaMP\-2 accuracy versus0\.7600\.760forRAG\-3 and0\.7650\.765forRAG\-5; the paired tests ofPersonaLink\(r=2\)\(r\{=\}2\)againstRAG\-3 andRAG\-5 are*not*significant \(p=0\.73p\{=\}0\.73andp=0\.60p\{=\}0\.60, McNemar\)\. In other words, on a1515\-way label\-prediction task, a once\-built, query\-independent, bounded persona is statistically indistinguishable from injecting the three\-to\-five most relevant past items per query\. This is the positive half of our headline, and it is a*tie*, reported as a tie—not a win\.

### 5\.3Retrieval dominates on regression and at scale

The picture inverts on the regression task, and retrieval pulls further ahead as it scales\. On LaMP\-3,RAG\-5 attains0\.2850\.285MAE whilePersonaLink\(r=2\)\(r\{=\}2\)attains0\.4550\.455, a gap that is highly significant \(Δ​MAE=0\.17\\Delta\\mathrm\{MAE\}\{=\}0\.17,p<10−4p\{<\}10^\{\-4\}, paired bootstrap\);RAG\-3 \(0\.2900\.290\) is similarly far ahead \(p=0\.0004p\{=\}0\.0004\)\. Even the persona’s better depths \(r=1:0\.425r\{=\}1\{:\}\\,0\.425,r=3:0\.430r\{=\}3\{:\}\\,0\.430\) do not close it\. Fine\-grained ordinal personalization appears to need concrete past ratings in context, which a bounded prose persona cannot losslessly summarize\. Moreover, retrieval does*not*plateau: extendingkkimproves LaMP\-2 accuracy to0\.7850\.785\(k=10k\{=\}10\) and0\.7900\.790\(k=20k\{=\}20\), and LaMP\-3 MAE to0\.2900\.290\(k=10k\{=\}10\) and0\.2500\.250\(k=20k\{=\}20\)\. Retrieval keeps converting more history into accuracy, whereas the bounded persona, by design, cannot—so retrieval is the stronger method overall\.

Table[3](https://arxiv.org/html/2609.02890#S5.T3)lays this scaling out against the per\-query context budget, and Figure[3](https://arxiv.org/html/2609.02890#S5.F3)plots the same quality\-versus\-cost frontier\. The two views agree on the asymmetry\. On classification \(Figure[3](https://arxiv.org/html/2609.02890#S5.F3)a\) the bounded∼\\sim250\-token persona sits essentially*on*the retrieval frontier betweenRAG\-3 andRAG\-5: pushing retrieval all the way tok=20k\{=\}20buys only\+0\.045\+0\.045accuracy for roughly8×8\\timesthe per\-query context, so the persona is the Pareto\-efficient operating point\. On regression \(Figure[3](https://arxiv.org/html/2609.02890#S5.F3)b\) the persona is strictly dominated—retrieval is already0\.1650\.165MAE better atk=3k\{=\}3and a further0\.2050\.205better atk=20k\{=\}20, and the curve is still falling\. This is the cost–quality statement of our headline: a constant\-cost persona is a sufficient substitute for retrieval exactly on the label\-prediction task, and not when the agent must reproduce a calibrated numeric scale\.

Table 3:Retrieval keeps converting context into accuracy; the bounded persona cannot\.Quality versus per\-query context budget as the number of retrieved demonstrationskkgrows, againstPersonaLink’s*constant*∼\\sim250\-token persona\. “Ctx\. tok\./q” is the approximate in\-context token budget injected*per query*\(BM25 demos cost∼\\sim100 tokens each; the persona is built once and isx⋆x^\{\\star\}\-independent\)\. On LaMP\-2 retrieval gains saturate near the bounded persona, but on LaMP\-3 it keeps improving monotonically with no plateau;boldmarks the best non\-oracle cell per column\.LaMP\-2\(news cat\., 15\-way\)LaMP\-3\(rating,↓\\downarrow\)MethodCtx\. tok\./qAcc\.↑\\uparrowmacro\-F1↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrow*Retrieval, growing context withkk*RAG\-1∼\\sim1000\.6950\.5310\.4150\.711RAG\-3∼\\sim3000\.7600\.6070\.2900\.616RAG\-5∼\\sim5000\.7650\.6080\.2850\.621RAG\-10∼\\sim10000\.7850\.6010\.2900\.610RAG\-20∼\\sim20000\.7900\.6040\.2500\.589*Bounded persona, constant context \(ours\)*PAG\(r=1\)\(r\{=\}1\)∼\\sim250 \(fixed\)0\.7450\.4850\.4500\.742PersonaLink\(r=2\)\(r\{=\}2\)∼\\sim250 \(fixed\)0\.7450\.5140\.4550\.765*Upper bound*Oracle\(full profile\)∼\\sim18\.8k0\.7150\.5260\.2800\.608
Token budgets are per\-query in\-context cost; the persona’s is amortized once across all of a user’s queries \(O​\(1\)O\(1\)/query\)\. On LaMP\-2, RAG\-20 buys only\+0\.045\+0\.045accuracy over the persona for8×8\\timesthe per\-query context; on LaMP\-3 the same extra context buys a decisive0\.2050\.205MAE reduction\.n=200n\{=\}200items/task, deterministic metrics\.

![Refer to caption](https://arxiv.org/html/2609.02890v1/x3.png)Figure 3:Quality versus per\-query context cost\.BM25 retrieval \(blue\) trades a growing per\-query token budget for quality;PersonaLink’s bounded persona \(orange diamond\) is built once at a fixed∼\\sim250 tokens\.\(a\)On LaMP\-2 the persona lands on the retrieval frontier nearRAG\-3/5, so retrieval’s further gains cost8×8\\timesthe context for\+0\.045\+0\.045accuracy\.\(b\)On LaMP\-3 retrieval keeps falling with no plateau and the persona is dominated\. The oracle \(∼\\sim18\.8k tokens\) andNoPersfloor anchor the extremes\.
### 5\.4Recursion saturates

Recursion beyond the first pass does not help\. In Table[2](https://arxiv.org/html/2609.02890#S5.T2)the jump fromr=0r\{=\}0tor=1r\{=\}1is the entire effect \(\+0\.10\+0\.10LaMP\-2 accuracy, significant\), while ther=1→r=2r\{=\}1\{\\to\}r\{=\}2recursion delta isΔ​Acc=\+0\.000\\Delta\\mathrm\{Acc\}\{=\}\{\+\}0\.000\(p=0\.77p\{=\}0\.77, McNemar\) on LaMP\-2 andΔ​MAE=\+0\.005\\Delta\\mathrm\{MAE\}\{=\}\{\+\}0\.005\(p=0\.96p\{=\}0\.96, paired bootstrap\) on LaMP\-3; if anything, LaMP\-2 accuracy drifts down atr=3r\{=\}3\(0\.7300\.730\)\. Figure[4](https://arxiv.org/html/2609.02890#S5.F4)plots both metrics across depth and makes the shape plain: a sharpr=0→1r\{=\}0\{\\to\}1step followed by a flat plateau forr≥1r\{\\geq\}1on both tasks, with the depth\-11curves and the depth\-2,32,3curves overlapping within their intervals\. The keep\-better gate guarantees the held\-out objective never regresses \(Proposition[1](https://arxiv.org/html/2609.02890#Thmproposition1)\), but on the test set extra passes neither help nor reliably hurt\. As predicted by Corollary[1](https://arxiv.org/html/2609.02890#Thmcorollary1),r=1r\{=\}1is compute\-optimal; we explain the plateau mechanistically in §[6](https://arxiv.org/html/2609.02890#S6)\. Finally, theoraclethat reads the full true profile reaches0\.7150\.715LaMP\-2 accuracy—*below*RAG\-5’s0\.7650\.765—indicating that more context is not strictly better and that long profiles distract the backbone, while it does win on LaMP\-3 MAE \(0\.2800\.280\) where concrete ratings matter\.

![Refer to caption](https://arxiv.org/html/2609.02890v1/x4.png)Figure 4:Personalization gain is realized in the first pass and then plateaus\.LaMP\-2 accuracy \(left axis,↑\\uparrow\) and LaMP\-3 MAE \(right axis,↑\\uparrowfor−\-MAE\) across refinement depthr=0→3r\{=\}0\{\\to\}3\. Ther=0→1r\{=\}0\{\\to\}1step carries the entire gain \(\+0\.10\+0\.10accuracy\);r≥1r\{\\geq\}1is flat within the shaded intervals, the test\-set counterpart of the embedding contraction in Figure[6](https://arxiv.org/html/2609.02890#S6.F6)\.Table 4:Broader comparison with alternative personalization methods\(11 methods, one frozen backbone, identical greedy decoding\)\.Boldis the best per column: strong BM25RAGis the best non\-oracle method on both tasks and recursive refinement does not surpass it—personalization beats the controls, but the learned persona plateaus below retrieval\.LaMP\-2\(news cat\., 15\-way\)LaMP\-3\(rating,↓\\downarrow\)MethodAcc\.↑\\uparrowmacro\-F1↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrow*Lower / control*NoPers\(no personalization\)0\.645∗∗0\.3880\.5000\.794RandomUser\(token\-confound ctrl\)0\.665∗0\.3930\.565∗0\.908*Retrieval personalization*RAG\-1 \(BM25 demos\)0\.6950\.5310\.4150\.711RAG\-3 \(BM25 demos\)0\.7600\.6070\.290∗∗∗0\.616RAG\-5 \(BM25 demos\)0\.7650\.6080\.285∗∗∗0\.621*Profile\-summary personalization*PAG\(distilled persona,r=1r\{=\}1\)0\.7450\.4850\.4500\.742RAG\+PAG\(demos\+\+persona\)0\.7650\.5010\.335∗∗0\.621*Recursive \(ours\)*PersonaLink\(r=1\)\(r\{=\}1\)0\.7550\.4940\.4250\.731PersonaLink\(r=2\)\(r\{=\}2\)0\.745†0\.5140\.455†0\.765PersonaLink\(r=3\)\(r\{=\}3\)0\.7300\.4950\.4300\.728*Upper bound*Oracle\(true profile, ceiling\)0\.7150\.5260\.280∗∗∗0\.608
Metrics deterministic \(sklearn\), bootstrap 95% CI overn=200n\{=\}200items/task\./∗∗∗/∗⁣∗∗\{\}^\{\*\}/^\{\*\*\}/^\{\*\*\*\}on a competitor’s score:PersonaLink\(r=2\)\(r\{=\}2\)\(the†\\daggerrow\) differs from it atp<0\.05/0\.01/0\.001p\{<\}0\.05/0\.01/0\.001\(McNemar on LaMP\-2 correctness; paired bootstrap on LaMP\-3 absolute error\)\.

## 6Analysis

![Refer to caption](https://arxiv.org/html/2609.02890v1/x5.png)Figure 5:Recursive personas converge to per\-user fixed points\.PCA of MiniLM embeddings for1515LaMP\-2 users overr=0→3r\{=\}0\{\\to\}3: each user departs the shared empty persona, reaches its own region, and then per\-pass steps collapse \(inset: every user’s step length shrinks toward zero\)\.#### The persona contracts to a fixed point\.

Figure[5](https://arxiv.org/html/2609.02890#S6.F5)embeds each user’s persona with a local sentence encoder\[[38](https://arxiv.org/html/2609.02890#bib.bib31)\]and projects ther=0→3r\{=\}0\{\\to\}3trajectory by PCA\. Every user marches from the shared empty persona to its own region on the first pass, after which the per\-pass step collapses; the mean step length shrinks0\.90→0\.21→0\.020\.90\{\\to\}0\.21\{\\to\}0\.02\. Figure[6](https://arxiv.org/html/2609.02890#S6.F6)fits this decay: a geometric model∥Δ∥∝Lk\\lVert\\Delta\\rVert\\propto L^\{k\}gives modulusL=0\.144L\{=\}0\.144withR2=0\.979R^\{2\}\{=\}0\.979, i\.e\. each pass moves about a seventh as far as the previous one\. This is the empirical fixed\-point predicted \(under A1–A2\) in §[4](https://arxiv.org/html/2609.02890#S4), and it mechanistically explains the saturation in Table[2](https://arxiv.org/html/2609.02890#S5.T2): after the first pass there is almost nothing left to change\. We present this as measured contraction, not as a proven theorem\.

![Refer to caption](https://arxiv.org/html/2609.02890v1/x6.png)Figure 6:The recursive persona update contracts geometrically\.Mean per\-pass embedding displacement falls0\.90→0\.21→0\.020\.90\{\\to\}0\.21\{\\to\}0\.02and is fit by∥Δ∥∝Lk\\lVert\\Delta\\rVert\\propto L^\{k\}withL=0\.144L\{=\}0\.144,R2=0\.979R^\{2\}\{=\}0\.979\(L<1L\{<\}1⇒\\Rightarrowconvergence\)\.
#### The task\-type asymmetry\.

Reading Tables[2](https://arxiv.org/html/2609.02890#S5.T2)–[4](https://arxiv.org/html/2609.02890#S5.T4)together, the deciding factor is metric regime, not method family\. For*classification*the persona need only convey a sorting rule \(“this user files X under Y”\), which a bounded prose summary captures well enough to tie retrieval\. For*regression*the agent must reproduce a calibrated numeric scale, and the bounded persona cannot encode the per\-rating granularity that concrete retrieved examples supply—hence the large, significant MAE gap and retrieval’s continued gains withkk\. This asymmetry, rather than any aggregate win, is the contribution: it predicts when a cheap, interpretable, query\-independent persona is a sufficient substitute for retrieval and when it is not\. The field ablation in Table[5](https://arxiv.org/html/2609.02890#S6.T5)echoes it from inside the persona: ablating the*decision rules*costs the most LaMP\-2 accuracy \(−0\.045\-0\.045\), while ablating the*exemplars*costs the most LaMP\-3 MAE \(\+0\.035\+0\.035\)—the sorting heuristics drive classification and the concrete graded examples drive regression—yet no single field alone recovers the full state and all three remain above theNoPersfloor, so the gain is genuinely distributed across the bounded fields\.

Table 5:Field ablation of the boundedPersonaState\.Removing any one of the three bounded fields \(preference summary, exemplars, decision rules\) from the convergedPersonaLink\(r=2\)\(r\{=\}2\)persona degrades both tasks, confirming each contributes, while no ablation recovers the full persona and all stay above theNoPersfloor\. The*decision rules*matter most for classification \(the explicit sorting heuristics\), the*exemplars*most for regression \(concrete graded examples\), mirroring the task\-type asymmetry of §[6](https://arxiv.org/html/2609.02890#S6)\. Held\-out budget and decoding are identical across rows; only the rendered persona changes\.LaMP\-2\(news cat\., 15\-way\)LaMP\-3\(rating,↓\\downarrow\)Persona configurationAcc\.↑\\uparrowmacro\-F1↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowPersonaLink\(r=2\)\(r\{=\}2\), full state0\.7450\.5140\.4550\.765−\-decision rules0\.7000\.4520\.4750\.781−\-exemplars0\.7200\.4700\.4900\.789−\-preference summary0\.7150\.4610\.4700\.779NoPers\(r=0r\{=\}0, empty persona\)0\.6450\.3880\.5000\.794
Each ablated row holds the other two fields and the∼\\sim250\-token cap fixed\. Largest single\-field drop on LaMP\-2 accuracy is from removing decision rules \(−0\.045\-0\.045\); on LaMP\-3 MAE it is from removing exemplars \(\+0\.035\+0\.035\)\. Deterministic metrics,n=200n\{=\}200items/task\.

#### Qualitative evolved personas\.

Inspecting kept personas \(Appendix[D](https://arxiv.org/html/2609.02890#A4)\) shows the loop converting profile statistics into compact rules—e\.g\. promoting an under\-used category after the agent mislabels it, or adding a rule for “defective but usable” reviews\. The edits are legible and bounded, the practical upside of distillation even where it does not beat retrieval\. They also show why depth saturates: byr=2r\{=\}2the rewrites are near\-paraphrases ofr=1r\{=\}1, consistent with the contraction in Figure[6](https://arxiv.org/html/2609.02890#S6.F6)\.

## 7Related work

#### Personalizing LLMs\.

LaMP\[[43](https://arxiv.org/html/2609.02890#bib.bib7)\]formalized personalized prediction from user profiles and established retrieval as a strong baseline, refined by retrieval\-optimization methods\[[42](https://arxiv.org/html/2609.02890#bib.bib9)\]and surveyed broadly\[[78](https://arxiv.org/html/2609.02890#bib.bib13),[28](https://arxiv.org/html/2609.02890#bib.bib34),[23](https://arxiv.org/html/2609.02890#bib.bib14),[53](https://arxiv.org/html/2609.02890#bib.bib37),[61](https://arxiv.org/html/2609.02890#bib.bib36)\]\. Distillation alternatives summarize the profile\[[39](https://arxiv.org/html/2609.02890#bib.bib8)\], personalize parameters\[[51](https://arxiv.org/html/2609.02890#bib.bib11)\], or learn a soft persona embedding\[[29](https://arxiv.org/html/2609.02890#bib.bib12)\]; agentic variants build a persona at test time\[[77](https://arxiv.org/html/2609.02890#bib.bib10)\]\. We do not propose a better personalizer; we characterize*when*a bounded, query\-independent, interpretable persona suffices, and report that retrieval remains the stronger method overall \(with no plateau askkgrows\), with distillation matching it only on classification\.

#### Retrieval and retrieval\-augmented generation\.

Retrieval augments a model with external context at inference time, from sparse lexical matching to dense and late\-interaction retrievers\[[18](https://arxiv.org/html/2609.02890#bib.bib39),[21](https://arxiv.org/html/2609.02890#bib.bib43),[14](https://arxiv.org/html/2609.02890#bib.bib41),[64](https://arxiv.org/html/2609.02890#bib.bib45),[8](https://arxiv.org/html/2609.02890#bib.bib46)\]and end\-to\-end retrieval\-augmented generation\[[24](https://arxiv.org/html/2609.02890#bib.bib38),[10](https://arxiv.org/html/2609.02890#bib.bib40),[15](https://arxiv.org/html/2609.02890#bib.bib42),[4](https://arxiv.org/html/2609.02890#bib.bib44),[37](https://arxiv.org/html/2609.02890#bib.bib50),[46](https://arxiv.org/html/2609.02890#bib.bib47),[2](https://arxiv.org/html/2609.02890#bib.bib49),[19](https://arxiv.org/html/2609.02890#bib.bib48)\]\. For personalization, retrieval over a user’s own history is the dominant and strongest baseline\[[42](https://arxiv.org/html/2609.02890#bib.bib9),[32](https://arxiv.org/html/2609.02890#bib.bib33)\]; we treatBM25retrieval as the honest ceiling our bounded persona is measured against\. Which in\-context examples to retrieve is itself a learning problem\[[27](https://arxiv.org/html/2609.02890#bib.bib51),[41](https://arxiv.org/html/2609.02890#bib.bib52),[56](https://arxiv.org/html/2609.02890#bib.bib53)\]\.

#### Distillation: persona, profile, and parameter\-efficient personalization\.

The alternative to retrieval is to distill a user’s history once\. Classical persona\-grounded dialogue learns a profile from examples\[[76](https://arxiv.org/html/2609.02890#bib.bib54),[60](https://arxiv.org/html/2609.02890#bib.bib55),[26](https://arxiv.org/html/2609.02890#bib.bib56)\]; recentLLMmethods summarize the profile in natural language\[[39](https://arxiv.org/html/2609.02890#bib.bib8)\], encode it parameter\-efficiently per user\[[51](https://arxiv.org/html/2609.02890#bib.bib11),[52](https://arxiv.org/html/2609.02890#bib.bib57),[11](https://arxiv.org/html/2609.02890#bib.bib58)\], learn a soft user embedding\[[29](https://arxiv.org/html/2609.02890#bib.bib12),[33](https://arxiv.org/html/2609.02890#bib.bib59)\], store long\-term memory\[[34](https://arxiv.org/html/2609.02890#bib.bib24),[81](https://arxiv.org/html/2609.02890#bib.bib60),[74](https://arxiv.org/html/2609.02890#bib.bib61)\], or infer user cues at inference\[[55](https://arxiv.org/html/2609.02890#bib.bib62),[77](https://arxiv.org/html/2609.02890#bib.bib10)\]\. OurPersonaStateis a deliberately bounded, query\-independent instance of this family\.

#### Role\-playing persona agents\.

A related line assigns or learns a*character*persona for an agent to embody\[[45](https://arxiv.org/html/2609.02890#bib.bib63),[58](https://arxiv.org/html/2609.02890#bib.bib64)\], with dedicated benchmarks and evaluations\[[54](https://arxiv.org/html/2609.02890#bib.bib65),[44](https://arxiv.org/html/2609.02890#bib.bib66)\]and surveys connecting role\-play to personalization\[[6](https://arxiv.org/html/2609.02890#bib.bib67),[53](https://arxiv.org/html/2609.02890#bib.bib37)\]\. We target the*user*persona \(personalization\) rather than the assigned\-character setting\.

#### Personalized alignment\.

Beyond profiles, a growing literature aligns models to individual or group preferences via parameter merging, lightweight user models, latent variables, or low\-rank rewards\[[16](https://arxiv.org/html/2609.02890#bib.bib68),[25](https://arxiv.org/html/2609.02890#bib.bib69),[36](https://arxiv.org/html/2609.02890#bib.bib70),[80](https://arxiv.org/html/2609.02890#bib.bib71),[5](https://arxiv.org/html/2609.02890#bib.bib73)\], supported by participatory preference datasets\[[22](https://arxiv.org/html/2609.02890#bib.bib72)\]and surveys of pluralistic alignment\[[63](https://arxiv.org/html/2609.02890#bib.bib35)\]\. These adapt model*weights or rewards*; we keep the backbone frozen and adapt only a textual persona\.

#### Recursive and self\-evolving agents\.

PersonaLink’s refinement loop builds on iterative self\-refinement and self\-correction\[[30](https://arxiv.org/html/2609.02890#bib.bib15),[47](https://arxiv.org/html/2609.02890#bib.bib16),[9](https://arxiv.org/html/2609.02890#bib.bib74),[3](https://arxiv.org/html/2609.02890#bib.bib75),[12](https://arxiv.org/html/2609.02890#bib.bib78)\], reflective prompt evolution and prompt optimization\[[1](https://arxiv.org/html/2609.02890#bib.bib17),[82](https://arxiv.org/html/2609.02890#bib.bib76),[65](https://arxiv.org/html/2609.02890#bib.bib19),[7](https://arxiv.org/html/2609.02890#bib.bib77),[20](https://arxiv.org/html/2609.02890#bib.bib18),[66](https://arxiv.org/html/2609.02890#bib.bib2)\], self\-rewarding and self\-training\[[73](https://arxiv.org/html/2609.02890#bib.bib28),[72](https://arxiv.org/html/2609.02890#bib.bib81),[62](https://arxiv.org/html/2609.02890#bib.bib82)\], and held\-out self\-evolution\[[67](https://arxiv.org/html/2609.02890#bib.bib1)\]; its scaling\-by\-recursion framing follows recursive multi\-agent systems\[[69](https://arxiv.org/html/2609.02890#bib.bib5)\]and latent collaboration\[[83](https://arxiv.org/html/2609.02890#bib.bib6)\]\. Recursion is one way to spend more test\-time compute\[[57](https://arxiv.org/html/2609.02890#bib.bib79),[70](https://arxiv.org/html/2609.02890#bib.bib80),[48](https://arxiv.org/html/2609.02890#bib.bib85),[31](https://arxiv.org/html/2609.02890#bib.bib86)\]; consistent with reports that intrinsic self\-correction can stall\[[13](https://arxiv.org/html/2609.02890#bib.bib83),[17](https://arxiv.org/html/2609.02890#bib.bib84)\], we find the gains saturate after one pass\. We concede the refinement\-loop*idea*is not new\. Our contribution is to apply it to a*bounded*persona representation, prove a no\-harm guarantee via a held\-out keep\-better gate, and—most importantly—report the honest negative that the recursion*saturates after one pass*, with an empirical contraction account of why\.

#### Agent memory and context engineering\.

Add\-only context memories accumulate experience as growing text\[[75](https://arxiv.org/html/2609.02890#bib.bib22),[50](https://arxiv.org/html/2609.02890#bib.bib23),[59](https://arxiv.org/html/2609.02890#bib.bib21),[79](https://arxiv.org/html/2609.02890#bib.bib20),[34](https://arxiv.org/html/2609.02890#bib.bib24)\]\.PersonaLinkdeliberately uses a*bounded*state, trading unbounded accumulation for a fixed, query\-independent footprint; our results show this bound is not free—it is what costs us the regression task and the scaling that retrieval enjoys\. Related agent lines on tool use and safety\[[71](https://arxiv.org/html/2609.02890#bib.bib25),[35](https://arxiv.org/html/2609.02890#bib.bib26),[49](https://arxiv.org/html/2609.02890#bib.bib3),[68](https://arxiv.org/html/2609.02890#bib.bib4)\]motivate interpretable, inspectable personalization but are orthogonal to the distill\-vs\-retrieve question\.

## 8Conclusion and limitations

We asked when a distilled persona can match retrieval for personalized LLM agents and gave an honest, asymmetric answer\.PersonaLink—a bounded, interpretable, query\-independent three\-field persona built once by a monotone\-safe recursive loop—*ties*retrieval on LaMP\-2 classification but is decisively beaten on LaMP\-3 regression, and retrieval keeps improving withkkwhile the bounded persona cannot\. Personalization is real \(it beats no\-persona and random\-user controls\), but the recursion saturates after a single pass, which we explain by a measured geometric contraction of the persona representation \(L=0\.144L\{=\}0\.144,R2=0\.979R^\{2\}\{=\}0\.979\)\. The value ofPersonaLinkis thus a*characterization*—bounded distillation is sufficient exactly for label\-classification, not for fine\-grained regression or at scale—plus a cheap, inspectable artifact, not a new state of the art\.

#### Limitations\.

\(i\) Retrieval wins overall; we do not beat it and present it as the best non\-oracle method everywhere\. \(ii\) A single 7B\-class frozen backbone; the asymmetry may shift with scale or task family, and the oracle’s LaMP\-2 result hints the backbone is context\-sensitive\. \(iii\) Recursion gives no test\-set benefit pastr=1r\{=\}1, so the recursive machinery’s practical payoff here is the safety guarantee and the fixed\-point analysis, not accuracy\. \(iv\) The keep\-better gate is held\-out\-only, so Proposition[1](https://arxiv.org/html/2609.02890#Thmproposition1)bounds the selection signal, not unseen test items\. \(v\) Two LaMP tasks in English; generality to other domains and to agentic, multi\-turn personalization is future work\.

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## Appendix AProof of Proposition[1](https://arxiv.org/html/2609.02890#Thmproposition1)

We proveAr≥Ar−1A\_\{r\}\\geq A\_\{r\-1\}for allr≥1r\\geq 1by induction\. LetArA\_\{r\}be the held\-out score of the kept persona after passrron the fixed sliceSuS\_\{u\}, andA0A\_\{0\}the score of the empty personap\(0\)p^\{\(0\)\}\.*Base case\.*Before any pass the kept persona isp\(0\)p^\{\(0\)\}with scoreA0A\_\{0\}\.*Inductive step\.*Assume the kept persona after passr−1r\-1has scoreAr−1A\_\{r\-1\}\. Passrrproposes a candidatep′p^\{\\prime\}with held\-out scoreA′A^\{\\prime\}\. The strict keep\-better gate sets the kept persona top′p^\{\\prime\}iffA′≥Ar−1A^\{\\prime\}\\geq A\_\{r\-1\}, and otherwise retains the incumbent; in both cases the new kept score ismax⁡\(Ar−1,A′\)≥Ar−1\\max\(A\_\{r\-1\},A^\{\\prime\}\)\\geq A\_\{r\-1\}\. HenceAr≥Ar−1A\_\{r\}\\geq A\_\{r\-1\}, and by transitivityAr≥A0A\_\{r\}\\geq A\_\{0\}\. If no candidate ever satisfiesA′≥A0A^\{\\prime\}\\geq A\_\{0\}strictly, no replacement occurs and the kept persona remainsp\(0\)p^\{\(0\)\}, so the method answersf​\(x⋆\)f\(x^\{\\star\}\), i\.e\. it reduces exactly to the no\-personalization control\. As stated in §[4](https://arxiv.org/html/2609.02890#S4), this bounds the held\-out selection signal, not necessarily accuracy on unseen test items\.■\\qquad\\blacksquare

## Appendix BContraction measurement

We embed each kept personapu\(r\)p\_\{u\}^\{\(r\)\}with a frozen MiniLM sentence encoder\[Reimers and Gurevych,[2019](https://arxiv.org/html/2609.02890#bib.bib31)\]\(no API\), compute per\-pass displacement∥e​\(pu\(r\+1\)\)−e​\(pu\(r\)\)∥\\lVert e\(p\_\{u\}^\{\(r\+1\)\}\)\-e\(p\_\{u\}^\{\(r\)\}\)\\rVert, average over the1515analyzed LaMP\-2 users, and regresslog⁡∥Δ∥\\log\\lVert\\Delta\\rVerton the step index to estimateLL\. The mean displacements are0\.900\.90\(r=0→1r\{=\}0\{\\to\}1\),0\.210\.21\(r=1→2r\{=\}1\{\\to\}2\),0\.020\.02\(r=2→3r\{=\}2\{\\to\}3\); the geometric fit givesL=0\.144L\{=\}0\.144withR2=0\.979R^\{2\}\{=\}0\.979\(Figure[6](https://arxiv.org/html/2609.02890#S6.F6)\)\. This is an empirical measurement of the modulus under assumptions A1–A2 of §[4](https://arxiv.org/html/2609.02890#S4); it is not a proof that the rewrite map is globally contractive\.

## Appendix CAdditional experimental details

All runs use one frozen 7B\-class backbone with greedy decoding; the only per\-method difference is the in\-context text \(retrieved demos, a persona, or nothing\)\. LaMP\-2 is scored with scikit\-learn Accuracy and macro\-F1 over the1515canonical categories; LaMP\-3 with MAE and RMSE over the11–55scale, with robust label parsing \(lower\-casing, nearest\-valid\-class, clamp\-to\-range\) but*no*LLM judge\. Retrieval uses BM25 over the user’s profile; the random\-user control injects a different user’s profile at a matched token budget\. The held\-out sliceSuS\_\{u\}is a leave\-some\-out split of the user’s own profile and never contains the test item\. The depth\-scaling and broader\-comparison numbers are exactly those of Tables[2](https://arxiv.org/html/2609.02890#S5.T2)–[4](https://arxiv.org/html/2609.02890#S5.T4); the retrieval\-scaling values \(k∈\{10,20\}k\{\\in\}\\\{10,20\\\}: LaMP\-20\.785/0\.7900\.785/0\.790accuracy, LaMP\-30\.290/0\.2500\.290/0\.250MAE\) are reported in §[5\.3](https://arxiv.org/html/2609.02890#S5.SS3)\.

## Appendix DQualitative evolved personas

We show two verbatim keptPersonaStates from the runs \(persona texts taken from the logged per\-user refinement traces\)\.

#### LaMP\-2 \(news categorization\), user1136\.

Profile of8585items, held\-out slice of88\. The first pass lifts held\-out accuracy from0\.8750\.875\(empty\) to1\.0001\.000and the persona then stops changing \(r=1,2,3r\{=\}1,2,3are byte\-identical\), a direct instance of the contraction in Figure[6](https://arxiv.org/html/2609.02890#S6.F6)\. The kept persona \(66exemplars,66rules; preference summary and rules quoted\):

> *Preference summary:*“Focus on politics with a strong preference for articles related to Hillary Clinton, Democratic Party, and economic issues\. Occasionally interested in entertainment and business\.” *Decision rules:*if mentions Hillary Clinton→\\topolitics; if discusses Democratic Party internal affairs→\\topolitics; if involves Wall Street or banking regulation→\\topolitics; if includes criticism of Trump’s economic policies→\\topolitics; if focuses on Bernie Sanders’ economic stance→\\topolitics; if mentions Goldman Sachs→\\topolitics\.

#### LaMP\-3 \(product rating\), user211070\.

Profile held\-out slice of88; here bothr=2r\{=\}2rewrites are accepted by the gate and held\-out accuracy rises0\.50→0\.750\.50\\to 0\.75\. The kept persona encodes a scoring scale but, as §[5\.3](https://arxiv.org/html/2609.02890#S5.SS3)shows, such bounded prose rules cannot match retrieved concrete ratings on MAE:

> *Preference summary:*“Prefers higher scores, giving 5 stars for emotional or well\-written content, 4 stars for engaging plots, and 3 stars for average reads\. Lower ratings are given for rushed endings or lack of depth\.” *Decision rules \(excerpt\):*if ‘loved’/‘inspiring’→\\toscore 5; if ‘brilliantly written’/‘kept me on the edge of my seat’→\\toscore 4\.5; if ‘interesting plot’/‘well\-developed characters’→\\toscore 4; if ‘rushed at the end’/‘lack of depth’→\\toscore 3\.5\.

In both cases the kept persona is short, legible, and bounded; and in the LaMP\-2 trace ther=1r\{=\}1andr=2r\{=\}2personas are identical, the textual counterpart of the saturation reported in §[5\.4](https://arxiv.org/html/2609.02890#S5.SS4)\.