$\varepsilon$-MemEvo: Adaptive Cross-Task Memory Transfer for LLM Program Evolution

# Adaptive Cross-Task Memory Transferfor LLM Program Evolution
Source: [https://arxiv.org/html/2608.12522](https://arxiv.org/html/2608.12522)
## ε\\varepsilon\-MemEvo: Adaptive Cross\-Task Memory Transfer for LLM Program Evolution

###### Abstract

LLM\-based program evolution systems such as FunSearch and AlphaEvolve have shown strong ability to discover novel algorithms, but typically optimize each task in isolation, discarding search experience after completion\. We introduceε\\varepsilon\-MemEvo, a framework for*cross\-task knowledge transfer*in LLM program evolution\.ε\\varepsilon\-MemEvostores prior experience as*task\-agnostic tactic memories*: compact natural\-language summaries of successful algorithmic strategies rather than raw code, enabling transfer across tasks with different APIs and evaluators\. To avoid negative transfer from semantically mismatched memories,ε\\varepsilon\-MemEvouses an adaptive injection gate that decides whether retrieved memories should be injected, and at what intensity\. We evaluateε\\varepsilon\-MemEvoon 8 diverse optimization benchmarks spanning mathematical optimization and systems engineering, using a content\-level Leave\-One\-Out protocol that excludes target\-task memory entries\. On the primary GPT\-5 backbone,ε\\varepsilon\-MemEvoimproves AUCC over AdaEvolve on all 8 tasks, with a mean relative gain of\+8\.7%\+8\.7\\%, and improves early\-stage convergence by\+9\.4%\+9\.4\\%on average\. Ablations show that naive memory injection can fail catastrophically, while adaptive gating remains safe across all five ablation tasks\. The data\-updated posterior is interpretable in observed states: it favors*skip*during improving search and shifts from*skip*to*hint*across early and late plateaus\. These gains incur<1%<\\\!1\\%computational overhead\.

## 1Introduction

Large language models \(LLMs\) have emerged as powerful engines for automated algorithm discovery\. Systems like FunSearch\([26](https://arxiv.org/html/2608.12522#bib.bib1)\)and AlphaEvolve\([22](https://arxiv.org/html/2608.12522#bib.bib2)\)use LLMs to iteratively generate, evaluate, and refine programs, achieving breakthroughs in combinatorial optimization, matrix multiplication, and scientific computing\. More recent work such as AdaEvolve\([4](https://arxiv.org/html/2608.12522#bib.bib3)\)introduces adaptive island models and paradigm breakthroughs to further improve search diversity\.

Despite these advances, a fundamental limitation persists:every task starts from scratch\. When an LLM evolution system finishes one optimization task and moves to a related task, it retains nothing—no memory of which strategies worked, no intuition about search structure, no reusable heuristics\. This “amnesic” behavior leads to redundant exploration across related tasks, slow cold\-start convergence, and wasted API budget\.

Figure 1:Motivating example\.On circle packing after solving a related geometric task,ε\\varepsilon\-MemEvoretrieves a geometric arrangement heuristic from memory and reaches 90% of its final score in 3 iterations \(vs\. 9 for AdaEvolve\)\. The Tactic Memory Bank stores strategy summaries \(not code\), enabling transfer across tasks with different APIs and metrics\.Consider a concrete scenario: after optimizing a geometric packing problem, the system has learned that “structured grid layouts with symmetric offsets minimize overlap\.” This geometric intuition can also benefit a related packing task, yet existing systems cannot leverage it\. Human researchers naturally build on prior experience—why shouldn’t LLM evolution systems? We proposeε\\varepsilon\-MemEvo\(ε\\varepsilon\-Memory\-augmentedEvolution\), a framework for cross\-task knowledge transfer in LLM\-based program evolution\.ε\\varepsilon\-MemEvomakes two methodological moves tailored to evolutionary coding:

- •Content\-level transfervia a*Tactic Memory Bank*that stores LLM\-extracted natural\-language strategy summaries \(not raw code\) from completed tasks, enabling transfer across heterogeneous APIs and evaluators\.
- •Strategy\-level gatingvia an*Adaptive Injection Gate*that treats memory usage as an adaptive gating problem whose primary role is to avoid negative transfer: it learns when retrieved memories should be withheld, softly suggested, or strongly imposed based on search state\.

The key insight behindε\\varepsilon\-MemEvois that*cross\-task transfer in evolutionary coding is a safety problem, not a retrieval problem alone*\. Naïvely injecting cross\-task strategies every iteration can cause catastrophic negative transfer—in our ablation, two of five tasks see the search fail to produce*any*score\-improving program under always\-inject, and the same two fail under a rule\-based stagnation policy \(Section[4\.5](https://arxiv.org/html/2608.12522#S4.SS5)\)\. The adaptive gate addresses this by posterior\-sampling over Beta arms, so theguidearm is down\-weighted after a few unsuccessful injections, recoveringskip\-like behavior on mismatched tasks while retaining injection benefits elsewhere\. Although the adaptive gate is not uniformly better than hand\-tuned rules on benign tasks, it is the only variant in our study that remains safe across all five tasks without requiring per\-task threshold tuning\.

To evaluate content\-level cross\-task transfer, we use a*Leave\-One\-Out \(LOO\) protocol*: when evaluating on taskkk, the memory bank excludes all experience from taskkkitself\.

We evaluateε\\varepsilon\-MemEvoon 8 benchmarks spanning circle packing, signal processing, load balancing, SQL optimization, and more, on two LLM backbones \(GPT\-5 and Gemini\-3\-Pro\)\. Our key findings:

1. 1\.Consistent convergence improvement\.ε\\varepsilon\-MemEvoachieves higher AUCC on*all*8 tasks \(p=0\.0078p=0\.0078, Wilcoxon signed\-rank\) with\+8\.7%\+8\.7\\%mean relative improvement on GPT\-5 and\+11\.7%\+11\.7\\%on Gemini\-3\-Pro\.
2. 2\.Strongest early\-stage acceleration\.On GPT\-5, AUC@20 improves by\+9\.4%\+9\.4\\%on average, with circle packing\+26\.0%\+26\.0\\%and transaction scheduling\+27\.2%\+27\.2\\%, showing that the largest gains occur during cold\-start convergence\.
3. 3\.TS prevents catastrophic negative transfer\.Fullε\\varepsilon\-MemEvoimproves over AdaEvolve on all 5 ablation tasks; both naïve always\-inject and rule\-based stagnation variants fail to produce any score\-improving program on 2/5 tasks\.
4. 4\.Negligible overhead\.Cross\-task transfer adds<1%<\\\!1\\%per\-iteration cost \(∼\\sim0\.77 s vs\. 80–140 s baseline\); aggregate wall\-clock time across the 8 main tasks is0\.69×0\.69\\timesthat ofAdaEvolve\.

## 2Related Work

#### LLM\-based program evolution\.

Building on genetic programming\([14](https://arxiv.org/html/2608.12522#bib.bib16)\), recent work replaces hand\-designed variation operators with LLMs\. FunSearch\([26](https://arxiv.org/html/2608.12522#bib.bib1)\), AlphaEvolve\([22](https://arxiv.org/html/2608.12522#bib.bib2)\), and OpenEvolve\([29](https://arxiv.org/html/2608.12522#bib.bib17)\)establish LLM\-based evolutionary search on math and systems benchmarks; ShinkaEvolve\([15](https://arxiv.org/html/2608.12522#bib.bib19)\), CodeEvolve\([3](https://arxiv.org/html/2608.12522#bib.bib20)\), GEPA\([1](https://arxiv.org/html/2608.12522#bib.bib18)\), and AdaEvolve\([4](https://arxiv.org/html/2608.12522#bib.bib3)\)extend these via sample\-efficient sampling, island models, and adaptive paradigm breakthroughs\. Earlier work includes ELM\([16](https://arxiv.org/html/2608.12522#bib.bib5)\), Language Model Crossover\([21](https://arxiv.org/html/2608.12522#bib.bib9)\), EoH\([18](https://arxiv.org/html/2608.12522#bib.bib6)\), OPRO\([33](https://arxiv.org/html/2608.12522#bib.bib7)\), EvoPrompting\([6](https://arxiv.org/html/2608.12522#bib.bib4)\), and EvoX\([19](https://arxiv.org/html/2608.12522#bib.bib8)\)\.All operate per\-task without explicit cross\-task memory\.ε\\varepsilon\-MemEvoaddresses this gap by making cross\-task transfer first\-class at both the representation level \(tactic memories\) and the control level \(adaptive intervention\)\.

#### Selection in LLM\-based program evolution\.

Recent LLM\-evolution frameworks select*within\-task*programs for mutation through a variety of mechanisms\. FunSearch\([26](https://arxiv.org/html/2608.12522#bib.bib1)\)and OpenEvolve\([29](https://arxiv.org/html/2608.12522#bib.bib17)\)use island models with score\-weighted parent sampling and periodic island resets; AlphaEvolve\([22](https://arxiv.org/html/2608.12522#bib.bib2)\)extends this with multi\-model collaboration; ShinkaEvolve\([15](https://arxiv.org/html/2608.12522#bib.bib19)\)adds rejection\-sampled adaptive parent sampling for sample efficiency; AdaEvolve\([4](https://arxiv.org/html/2608.12522#bib.bib3)\)couples adaptive island models with paradigm breakthroughs that periodically inject conceptually different strategies into the next mutation prompt\.All operate within one task: selection uses programs discovered for the current problem, and memorisable artifacts reset between tasks\.ε\\varepsilon\-MemEvoinstead adds a cross\-task layer: a contextual Thompson Sampling gate\([31](https://arxiv.org/html/2608.12522#bib.bib11);[5](https://arxiv.org/html/2608.12522#bib.bib30);[12](https://arxiv.org/html/2608.12522#bib.bib31);[2](https://arxiv.org/html/2608.12522#bib.bib32)\)decides whether retrieved tactics should be withheld, suggested, or imposed\. The closest precedent is within\-run adaptive operator selection\([7](https://arxiv.org/html/2608.12522#bib.bib33);[9](https://arxiv.org/html/2608.12522#bib.bib34)\);ε\\varepsilon\-MemEvoinstead gates cross\-task interventions\.

Related foundations include meta\-learning\([11](https://arxiv.org/html/2608.12522#bib.bib15);[10](https://arxiv.org/html/2608.12522#bib.bib26)\), retrieval\-augmented code generation\([17](https://arxiv.org/html/2608.12522#bib.bib12);[20](https://arxiv.org/html/2608.12522#bib.bib21);[25](https://arxiv.org/html/2608.12522#bib.bib22);[34](https://arxiv.org/html/2608.12522#bib.bib23)\), agentic memory\([30](https://arxiv.org/html/2608.12522#bib.bib13);[32](https://arxiv.org/html/2608.12522#bib.bib14);[23](https://arxiv.org/html/2608.12522#bib.bib24);[24](https://arxiv.org/html/2608.12522#bib.bib25)\), and continual learning\([13](https://arxiv.org/html/2608.12522#bib.bib27);[28](https://arxiv.org/html/2608.12522#bib.bib28);[8](https://arxiv.org/html/2608.12522#bib.bib29)\)\.

## 3Method

### 3\.1Problem Formulation

We consider a sequential setting where an LLM\-based evolution system solves tasks𝒯=\{T1,…,TN\}\\mathcal\{T\}=\\\{T\_\{1\},\\ldots,T\_\{N\}\\\}\. Each taskTiT\_\{i\}has descriptiondid\_\{i\}, evaluation functionfi:𝒫→ℝf\_\{i\}:\\mathcal\{P\}\\to\\mathbb\{R\}, and seed programpi0p\_\{i\}^\{0\}; the system runsMMiterations per task to maximizefif\_\{i\}\.ε\\varepsilon\-MemEvoaugments the standard \(per\-task\) setting with a persistent memory stateℳ=\(ℬ,π\)\\mathcal\{M\}=\(\\mathcal\{B\},\\pi\)comprising a Tactic Memory Bankℬ\\mathcal\{B\}and an Injection Policyπ\\pi\. The policy is updated during each task, while the bank is appended once at successful task completion; both are carried forward to subsequent tasks\.

### 3\.2Architecture Overview

![Refer to caption](https://arxiv.org/html/2608.12522v1/main_figure.png)Figure 2:ε\\varepsilon\-MemEvoarchitecture\.Prior\-task best programs are distilled into task\-agnostic tactics under LOO\. At each iteration, a state\-conditioned Thompson Sampling gate selectsskip,hint, orguide; retrieved tactics and the selected intensity augment the base prompt\. AdaEvolve evaluates each candidate and returns a delayed reward that updates the gate\. After a successful task run completes, its final best program contributes one tactic to memory for subsequent tasks\.ε\\varepsilon\-MemEvowraps around the AdaEvolve\([4](https://arxiv.org/html/2608.12522#bib.bib3)\)base framework, adding two cross\-task transfer modules \(Figure[2](https://arxiv.org/html/2608.12522#S3.F2)\): aTactic Memory Bankℬ\\mathcal\{B\}that stores strategy summaries from prior tasks \(retrieved by embedding similarity\), and anAdaptive Injection Gateπ\\pithat decides whether to inject memories and at what intensity\. At iterationttof taskTiT\_\{i\}, the controller \(1\) queriesπ\\pifor an actionat∈\{skip,hint,guide\}a\_\{t\}\\in\\\{\\texttt\{skip\},\\texttt\{hint\},\\texttt\{guide\}\\\}given search statests\_\{t\}; \(2\) ifat≠skipa\_\{t\}\\neq\\texttt\{skip\}, retrieves the top\-3 strategies fromℬ−i\\mathcal\{B\}\_\{\-i\}; \(3\) constructs an augmented prompt at intensityata\_\{t\}; \(4\) generates and evaluates a candidate; \(5\) resolves delayed rewards and updatesπ\\pi\.

### 3\.3Tactic Memory Bank

#### Strategy extraction\.

After a successful task run completes, we use GPT\-4\.1\-mini to extract a task\-agnostic strategy summary from its final best program:

tactici=LLMextract​\(di,pibest,fi​\(pibest\)\)\.\\text\{tactic\}\_\{i\}=\\text\{LLM\}\_\{\\text\{extract\}\}\\\!\\left\(d\_\{i\},\\;p\_\{i\}^\{\\text\{best\}\},\\;f\_\{i\}\(p\_\{i\}^\{\\text\{best\}\}\)\\right\)\.\(1\)The extraction prompt asks for general algorithmic descriptions \(e\.g\., “two\-phase optimization with greedy initialization followed by gradient descent”\) rather than task\-specific code\. Each completed successful task contributes one entry containing the tactic, approach\-type label, task description, and embedding; the entry becomes available only to subsequent tasks\.

#### Semantic retrieval\.

Given a new task with descriptiondjd\_\{j\}, we embed𝐞j=Embed​\(dj\)\\mathbf\{e\}\_\{j\}=\\text\{Embed\}\(d\_\{j\}\)via text\-embedding\-3\-small \(1536\-dim\) and rank memory entries by a score\-weighted similarity:

rk=cos⁡\(𝐞j,𝐞k\)⋅\(1\+0\.3⋅log⁡\(1\+max⁡\(Δk,0\.01\)\)\),r\_\{k\}=\\cos\(\\mathbf\{e\}\_\{j\},\\mathbf\{e\}\_\{k\}\)\\cdot\\left\(1\+0\.3\\cdot\\log\(1\+\\max\(\\Delta\_\{k\},0\.01\)\)\\right\),\(2\)whereΔk\\Delta\_\{k\}is the score improvement of entrykk’s strategy over its baseline; we return the top\-3\.

### 3\.4Adaptive Injection Gate

The injection gate is implemented as a contextual bandit with Beta\-distributed arms updated by Thompson sampling\. We design it primarily as a*gate against negative transfer*rather than a reward\-maximizing controller: on tasks where retrieved strategies are mismatched, the posterior forguidecollapses within a handful of unsuccessful injections and the policy reverts to predominantlyskipactions\.

#### State space\.

Six discrete states from two features:search phase∈\{improving,plateau,stagnating\}\\in\\\{\\texttt\{improving\},\\texttt\{plateau\},\\texttt\{stagnating\}\\\}from global improvement rateρ=improvementsevaluations\\rho=\\frac\{\\text\{improvements\}\}\{\\text\{evaluations\}\}\(ρ\>0\.1⇒improving\\rho\>0\.1\\Rightarrow\\texttt\{improving\};0\.02<ρ≤0\.1⇒plateau0\.02<\\rho\\leq 0\.1\\Rightarrow\\texttt\{plateau\};ρ≤0\.02⇒stagnating\\rho\\leq 0\.02\\Rightarrow\\texttt\{stagnating\}\); andtask stage∈\{early,late\}\\in\\\{\\texttt\{early\},\\texttt\{late\}\\\}, wheret/M<0\.4t/M<0\.4is early and the remaining iterations are late\.

#### Action space\.

Three injection intensities:skip\(no injection, base prompt\),hint\(retrieved strategies as optional references\), andguide\(top strategy as recommended approach plus injection into paradigm breakthrough generation\)\.

#### Informative priors\.

Each\(s,a\)\(s,a\)pair isBeta​\(αs,a,βs,a\)\\text\{Beta\}\(\\alpha\_\{s,a\},\\beta\_\{s,a\}\)\. We setPrior​\(improving,skip\)=Beta​\(3,1\)\\text\{Prior\}\(\\texttt\{improving\},\\texttt\{skip\}\)=\\text\{Beta\}\(3,1\)andPrior​\(stagnating,guide\)=Beta​\(3,1\)\\text\{Prior\}\(\\texttt\{stagnating\},\\texttt\{guide\}\)=\\text\{Beta\}\(3,1\), withBeta​\(1,1\)\\text\{Beta\}\(1,1\)for other pairs\.

#### Decision and reward\.

At each iteration we sampleθs,a∼Beta​\(αs,a,βs,a\)\\theta\_\{s,a\}\\sim\\text\{Beta\}\(\\alpha\_\{s,a\},\\beta\_\{s,a\}\)and picka∗=arg⁡maxa⁡θs,aa^\{\*\}=\\arg\\max\_\{a\}\\theta\_\{s,a\}\. Before applying the action, we record the current best scorefpre∗f^\{\*\}\_\{\\mathrm\{pre\}\}\. The reward is delayed: after windoww=5w=5iterations,Rt=𝟏\[ft\+w∗\>fpre∗\+ϵ\]R\_\{t\}=\\mathbf\{1\}\[f^\{\*\}\_\{t\+w\}\>f^\{\*\}\_\{\\mathrm\{pre\}\}\+\\epsilon\]withϵ=10−8\\epsilon=10^\{\-8\}; on success,αst,at\+=1\\alpha\_\{s\_\{t\},a\_\{t\}\}\\mathrel\{\+\}=1, otherwiseβst,at\+=1\\beta\_\{s\_\{t\},a\_\{t\}\}\\mathrel\{\+\}=1\. Concurrent pending decisions are resolved via a FIFO queue𝒬\\mathcal\{Q\}\. At the task boundary, unresolved records are evaluated against the final best score before the queue is cleared\.

### 3\.5Leave\-One\-Out Evaluation Protocol

When evaluatingε\\varepsilon\-MemEvoon taskTkT\_\{k\}: \(1\) the memory bankℬ−k\\mathcal\{B\}\_\{\-k\}excludes any entries fromTkT\_\{k\}; \(2\) the policyπ\\piretains its full posterior, since it learns task\-agnostic state\-action mappings rather than task\-specific content or task identity; \(3\) all methods share the same seed program and evaluator\. Thus, the protocol leaves out target\-task memory content while retaining the globally warm\-started policy\.

Algorithm 1ε\\varepsilon\-MemEvo: One Iteration of Cross\-Task Augmented Evolution\\ALC@lno\\ALC@tlmRequire:Memory bank

ℬ−k\\mathcal\{B\}\_\{\-k\}, policy

π\\piwith Beta counts

\{\(αs,a,βs,a\)\}\\\{\(\\alpha\_\{s,a\},\\beta\_\{s,a\}\)\\\}and pending queue

𝒬\\mathcal\{Q\}, iteration

tt, task description

dkd\_\{k\}, current best score

ft−1∗f^\{\*\}\_\{t\-1\}, reward window

ww, total iterations

MM
\\ALC@lno\\ALC@tlm

st←GetState​\(ρt,t/M\)s\_\{t\}\\leftarrow\\textsc\{GetState\}\(\\rho\_\{t\},t/M\)\{6\-state discretisation\}

\\ALC@lno\\ALC@tlmSample

θst,a∼Beta​\(αst,a,βst,a\)\\theta\_\{s\_\{t\},a\}\\sim\\text\{Beta\}\(\\alpha\_\{s\_\{t\},a\},\\beta\_\{s\_\{t\},a\}\)for

a∈\{skip,hint,guide\}a\\in\\\{\\texttt\{skip\},\\texttt\{hint\},\\texttt\{guide\}\\\}
\\ALC@lno\\ALC@tlm

at←arg⁡maxa⁡θst,aa\_\{t\}\\leftarrow\\arg\\max\_\{a\}\\theta\_\{s\_\{t\},a\}\{posterior sampling\}

\\ALC@lno\\ALC@tlm

fpre∗←ft−1∗f^\{\*\}\_\{\\mathrm\{pre\}\}\\leftarrow f^\{\*\}\_\{t\-1\};

tactics←∅\\text\{tactics\}\\leftarrow\\emptyset
\\ALC@lno\\ALC@tlmif

at≠skipa\_\{t\}\\neq\\texttt\{skip\}then

\\ALC@lno\\ALC@tlm

tactics←ℬ−k\.Retrieve​\(dk,top\_k=3\)\\text\{tactics\}\\leftarrow\\mathcal\{B\}\_\{\-k\}\.\\textsc\{Retrieve\}\(d\_\{k\},\\text\{top\\\_k\}\{=\}3\)
\\ALC@lno\\ALC@tlmendif

\\ALC@lno\\ALC@tlm

prompt←BuildPrompt​\(parent,context,tactics,at\)\\text\{prompt\}\\leftarrow\\textsc\{BuildPrompt\}\(\\text\{parent\},\\text\{context\},\\text\{tactics\},a\_\{t\}\)
\\ALC@lno\\ALC@tlm

pnew←LLM​\(prompt\)p\_\{\\text\{new\}\}\\leftarrow\\text\{LLM\}\(\\text\{prompt\}\);

score←fk​\(pnew\)\\text\{score\}\\leftarrow f\_\{k\}\(p\_\{\\text\{new\}\}\)
\\ALC@lno\\ALC@tlm

ft∗←UpdatePopulation​\(pnew,score\)f^\{\*\}\_\{t\}\\leftarrow\\textsc\{UpdatePopulation\}\(p\_\{\\text\{new\}\},\\text\{score\}\)
\\ALC@lno\\ALC@tlm

𝒬\.Append​\(\(,,,,,,,\)\)\\mathcal\{Q\}\.\\textsc\{Append\}\\bigl\(\(s\_\{t\},a\_\{t\},t,f^\{\*\}\_\{\\mathrm\{pre\}\}\)\\bigr\)
\\ALC@lno\\ALC@tlm

ResolvePending​\(𝒬,t,w,ft∗\)\\textsc\{ResolvePending\}\(\\mathcal\{Q\},t,w,f^\{\*\}\_\{t\}\)\{Beta updates for records witht≥τ\+wt\\geq\\tau\+w\}

## 4Experiments

### 4\.1Experimental Setup

#### Benchmarks\.

We evaluate 8 tasks across two categories:*mathematical optimization*\(4 from AlphaEvolve\([22](https://arxiv.org/html/2608.12522#bib.bib2)\): circle packing, signal processing, two inequality problems\) and*systems optimization*\(4 from ADRS: EPLB, LLM\-SQL, PRISM, transaction scheduling\)\. All task objective scores are higher\-is\-better\.

#### Methods\.

We compareε\\varepsilon\-MemEvo\(ours\), which augments AdaEvolve with LOO memory and a TS gate;AdaEvolve, the base adaptive evolution framework; andTopK, a simpler top\-KKmutation baseline\.

#### Protocol\.

GPT\-5 via LiteLLM is the primary generator, with Gemini\-3\-Pro replication runs reported in the tables; text\-embedding\-3\-small is used for retrieval\.Exp\. 1\(memory accumulation\): 8 tasks×\\times50 iterations×\\times2 methods, sequential\.Exp\. 2\(main\): 8 tasks×\\times80 iterations×\\times3 methods, using LOO memory from Exp\. 1\.Exp\. 3\(ablation\): 5 tasks×\\times50 iterations×\\times5 variants\. Each score is the mean over5 paired seeds\{42,0,1,2,3\}\\\{42,0,1,2,3\\\}\. Metrics are:Final Scoreat iteration 80;AUCC\(normalized area under the convergence curve\);AUC@20\(cold\-start efficiency\); andT90%T\_\{90\\%\}\(iterations to 90% of a method’s own final score\)\.

### 4\.2Main Results

Table 1:Final scores\(Exp\. 2, 80 iter, mean over 5 seeds\), on two LLM backbones\. Bold: best ofε\\varepsilon\-MemEvo/AdaEvolve\.On GPT\-5,ε\\varepsilon\-MemEvoachieves higher final scores thanAdaEvolveon7/8tasks, with large gains on EPLB \(\+46\.0%\+46\.0\\%\) and txn\_scheduling \(\+45\.2%\+45\.2\\%\)\. The single loss on PRISM \(−0\.04%\-0\.04\\%\) is negligible\.

### 4\.3Convergence Efficiency

AUCC \(full 80\)AUC@20T90%T\_\{90\\%\}\(iter\)Taskε\\varepsilon\-MemEvoAdaEvolveΔ\\Deltaε\\varepsilon\-MemEvoAdaEvolveΔ\\Deltaε\\varepsilon\-MemEvoAdaEvolveSpeedup*Backbone: GPT\-5*circle\_pack\.946\.885\+6\.9%\.861\.683\+26\.0%393\.0×\\timeseplb\.159\.135\+17\.9%\.124\.123\+1\.0%53500\.9×\\timesautocorr\.980\.979\+0\.1%\.942\.942\+0\.0%111\.0×\\timesllm\_sql\.708\.696\+1\.8%\.675\.669\+0\.8%111\.0×\\timesprism25\.9025\.31\+2\.3%24\.8422\.45\+10\.6%2178\.5×\\timessignal\.668\.651\+2\.5%\.573\.525\+9\.2%15231\.5×\\timestxn\_sched37662743\+37\.3%33582639\+27\.2%151‡—uncert\_ineq\.890\.882\+0\.9%\.855\.848\+0\.8%111\.0×\\timesWin/Total8/87/83/8‡‡MeanΔ\\Delta\+8\.7%\+9\.4%*Backbone: Gemini\-3\-Pro*circle\_pack\.947\.886\+6\.9%\.861\.684\+25\.9%4102\.5×\\timeseplb\.166\.146\+13\.3%\.129\.133−\-3\.0%56520\.9×\\timesautocorr\.907\.832\+8\.9%\.871\.801\+8\.8%221\.0×\\timesllm\_sql\.707\.693\+1\.9%\.674\.666\+1\.1%122\.0×\\timesprism25\.8725\.26\+2\.4%24\.8222\.41\+10\.8%3165\.3×\\timessignal\.618\.553\+11\.7%\.530\.446\+18\.8%14221\.6×\\timestxn\_sched37252683\+38\.8%33212581\+28\.7%161‡—uncert\_ineq\.823\.750\+9\.8%\.791\.721\+9\.7%221\.0×\\timesWin/Total8/87/84/8‡‡MeanΔ\\Delta\+11\.7%\+12\.6%
‡AdaEvolve’sT90%=1T\_\{90\\%\}\{=\}1when its final score is materially lower thanε\\varepsilon\-MemEvo’s—reaching 90% of a lower target is trivially faster\.

‡‡Excluding ties\.

Table 2:Convergence efficiency\(ε\\varepsilon\-MemEvovs\.AdaEvolveon 8 tasks, two backbones\)\.Δ\\Delta% = relative improvement\.#### AUCC\.

ε\\varepsilon\-MemEvowins onall 8 tasks\(mean\+8\.7%\+8\.7\\%on GPT\-5,\+11\.7%\+11\.7\\%on Gemini\-3\-Pro\)\. Largest gains are on txn\_scheduling \(\+37\.3%\+37\.3\\%/\+38\.8%\+38\.8\\%\) and EPLB \(\+17\.9%\+17\.9\\%/\+13\.3%\+13\.3\\%\)\.

#### AUC@20\.

Cold\-start improves on7/8 tasks\(mean\+9\.4%\+9\.4\\%/\+12\.6%\+12\.6\\%\), exceeding the full\-horizon AUCC gain and indicating that the largest improvements occur in the cold\-start phase\. The largest GPT\-5 gains are circle\_packing \(\+26\.0%\+26\.0\\%\), txn\_scheduling \(\+27\.2%\+27\.2\\%\), and PRISM \(\+10\.6%\+10\.6\\%\)\.

#### T90%T\_\{90\\%\}\.

On GPT\-5,ε\\varepsilon\-MemEvoreaches 90% faster on circle\_packing \(3 vs\. 9,3\.0×3\.0\\times\), PRISM \(2 vs\. 17,8\.5×8\.5\\times\), and signal\_processing \(15 vs\. 23,1\.5×1\.5\\times\)\.

### 4\.4Statistical Significance

On AUCC, the paired Wilcoxon signed\-rank givesp=0\.0078p=0\.0078\(the minimum two\-sidedpp\-value atn=8n\{=\}8when all task\-level differences share the same sign\); the bootstrap 95% BCa CI on mean relative improvement is\[\+2\.9%,\+21\.4%\]\[\+2\.9\\%,\+21\.4\\%\]; Cohen’sdz=0\.675d\_\{z\}=0\.675\(medium effect\)\.

### 4\.5Ablation Study

We compare five variants on 5 tasks \(50 iter\):ε\\varepsilon\-MemEvo\(full\)\(LOO bank \+ TS\),MemEvo\-always\(always guide\),MemEvo\-stagnation\(rule\-based: guide if stagnating, else skip\),AdaEvolve\(no memory\),TopK\(weak baseline\)\.

Table 3:Ablation: AUCC@50 and relative improvement overAdaEvolve\.Red= catastrophic failure \(AUCC=0=0\)\.Avg\.Δ\\Delta%averages per\-task relative improvements overAdaEvolve; AUCC=0=0failures are scored as−100%\-100\\%\.#### Both naive always\-inject and rule\-based stagnation fail catastrophically on mismatched tasks\.

MemEvo\-always and MemEvo\-stagnation both achieve AUCC=0\{\}=0on EPLB and LLM\-SQL—*no iteration in 50 produces a score\-improving program*on these tasks, whileε\\varepsilon\-MemEvo\(full\) andAdaEvolveboth produce valid programs on the same tasks\. MemEvo\-always injects every iteration; MemEvo\-stagnation injects whenever stagnation is detected\. These failures are consistent with static policies repeatedly injecting inapplicable code patterns\. TS limits this behavior because theguideposterior drops after unsuccessful injections, and the gate reverts to predominantlyskip\.

#### Memory injection is highly valuable when appropriate\.

On circle\_packing, signal, and txn\_scheduling, all three memory variants outperformAdaEvolveby\+2\.9%\+2\.9\\%to\+55\.3%\+55\.3\\%, demonstrating genuine value when semantically aligned memories are available\.

#### The adaptive gate trades peak upside for robustness\.

On circle\_packing \(\+13\.4%\+13\.4\\%vs\.\+9\.9%\+9\.9\\%\) and signal \(\+4\.0%\+4\.0\\%vs\.\+2\.9%\+2\.9\\%\), MemEvo\-stagnation edges outε\\varepsilon\-MemEvoby small margins; on txn\_scheduling, MemEvo\-always is best \(\+55\.3%\+55\.3\\%\)\. These results show that memory content is valuable when aligned, while the adaptive gate keeps that upside without exposing the system to static\-injection brittleness\.ε\\varepsilon\-MemEvois the only memory\-augmented variant that improves overAdaEvolveon all 5 tasks without per\-task threshold tuning\.

### 4\.6Analysis

#### Policy posterior and prior sensitivity\.

Figure[3](https://arxiv.org/html/2608.12522#S4.F3)shows the warm\-start policy posterior obtained from Exp\. 1\. The observed states recover an interpretable hierarchy:improving→\\toskip,plateau\_early→\\toskip, andplateau\_late→\\tohint\. These greedy actions are unchanged when the informative prior is replaced by uniform Beta\(1,1\), confirming that the observed\-state behavior is learned rather than inherited from initialization\. The unobservedstagnatingstates retain the informative prior that favors stronger memory use when progress stalls\.

Figure 3:Policy posterioras a posterior\-mean heatmap over 6 states×\\times3 actions after Exp\. 1\. Bold\-bordered cells mark the greedy arm per state\. Observed states yield the data\-driven hierarchy improving→\\toskip, plateau\_early→\\toskip, and plateau\_late→\\tohint; the unobservedstagnatingstates retain the prior\-initializedguideaction\.
#### Reward rate validation\.

Within theimproving\_earlydecisions in Exp\. 2,skipattains a 39\.6% positive reward rate \(99/250\), compared with 34\.0% forhint\(17/50\) and 19\.7% forguide\(15/76\)\.Over\-injection during productive search actively harms performance:guide’s reward rate is half that ofskip\.

#### Negative transfer avoided in practice\.

On EPLB, the closest retrievable memory \(from LLM\-SQL, cosine0\.4810\.481\) prescribes SQL\-style grouping; underMemEvo\-alwaysthis produces code that scores00every iteration, whereas the adaptive gate’sguide\-arm posterior collapses after a handful of failures and the policy reverts toskip, allowing normalAdaEvolvesearch to proceed\.

#### Retrieval forms semantic clusters\.

Retrieval similarity reveals two natural clusters:*geometric placement*\(similarities0\.4200\.420–0\.6460\.646\) and*numerical/systems*\(similarities0\.3750\.375–0\.5550\.555\)\. The catastrophic\-failure pair \(EPLB↔\\leftrightarrowLLM\-SQL at0\.4810\.481\) is a*post\-hoc diagnostic*, not an inference\-time cutoff:ε\\varepsilon\-MemEvoalways retrieves top\-3 by weighted similarity and lets TS gate the decision\.

#### Computational overhead\.

ε\\varepsilon\-MemEvoadds∼\\sim0\.77 s per iteration \(<1%<\\\!1\\%of the 80–140 s baseline\)\. Wall\-clock time is faster on 5/8 main tasks, with an aggregate ratio of0\.69×0\.69\\timesrelative toAdaEvolve\.

Figure 4:Convergence curveson four representative tasks\.ε\\varepsilon\-MemEvo\(blue\) converges faster thanAdaEvolve\(orange\) in early iterations; the gap is most pronounced on circle\_packing and txn\_scheduling\. Shaded region: AUC@20 zone\.

## 5Discussion

#### When does transfer help most?

Our results suggest cross\-task transfer is most beneficial when: \(1\) the memory bank contains strategies from semantically related tasks \(e\.g\.,circle\_packingbenefits from other geometric layout strategies at similarity≥0\.5\\geq 0\.5\); \(2\) the target task has a smooth fitness landscape where the base framework can make steady progress; \(3\) the search is in its early stages \(AUC@20 gains exceed full\-horizon AUCC gains on both backbones\)\. Transfer is less direct when available memories are from distant task domains, which is where the adaptive gate is most important\.

#### Theoretical safety guarantee\.

Specialising the standard regret bound for Bernoulli Thompson sampling\([27](https://arxiv.org/html/2608.12522#bib.bib10);[2](https://arxiv.org/html/2608.12522#bib.bib32)\)to our 3\-arm gating problem shows that, when retrieved tactics are mismatched \(sopskip\>pguidep\_\{\\texttt\{skip\}\}\>p\_\{\\texttt\{guide\}\}in a fixed search state\), the expected number ofguidepulls in the firstTTrounds satisfies𝔼⁡\[Tguide​\(T\)\]≤C​log⁡T/Δguide2\+o⁡\(log⁡T\)\\mathbb\{E\}\[T\_\{\\texttt\{guide\}\}\(T\)\]\\leq C\\log T/\\Delta\_\{\\texttt\{guide\}\}^\{2\}\+o\(\\log T\), so the per\-round probability of injecting a harmful tactic decays asO⁡\(1/t\)O\(1/t\)\. In a synthetic validation overT=500T\{=\}500rounds, the rolling selection frequency ofguidefalls below 5% byt≈100t\\approx 100in the mismatched setting\.

#### Why Thompson sampling?

Our gate needs to support delayed binary rewards, informative Beta priors, and rapid suppression of harmful actions\. Fixedε\\varepsilon\-greedy continues to select every arm with nonzero probability even after repeated failures, while UCB1 has no natural mechanism for incorporating the state\-specific priors used byε\\varepsilon\-MemEvo\. In matched and mismatched synthetic bandits, Thompson sampling is the only tested controller that combines near\-lowest regret in both regimes with a vanishing harmful\-arm selection rate\. This choice does not imply that Thompson sampling is universally optimal: our LLM\-in\-the\-loop experiments isolate adaptive gating against always\-inject and stagnation\-triggered controls, rather than replacing the gate with every bandit alternative\.

#### Limitations\.

We evaluate two LLM backbones \(GPT\-5, Gemini\-3\-Pro\)\. The memory bank is built at the task level: each entry distills a complete optimization run, and LOO evaluation tests transfer from other tasks\. We do not yet know how retrieval precision, gate calibration, or negative\-transfer frequency change as the bank grows to hundreds of entries\. Moreover,ε\\varepsilon\-MemEvoaugments rather than replaces its base evolution framework, so memory transfer cannot compensate for fundamental exploration failures in the underlying search\. A stronger rule\-based control not evaluated here would combine stagnation\-triggered injection with akk\-strike auto\-disable rule\. Such a controller could recover much of the observed safety benefit without posterior sampling, but would introduce a task\-dependent strike threshold; comparing it withε\\varepsilon\-MemEvois an important missing ablation\. The within\-paperAdaEvolvevs\.ε\\varepsilon\-MemEvocomparison \(Tables[1](https://arxiv.org/html/2608.12522#S4.T1)–[2](https://arxiv.org/html/2608.12522#S4.T2)\) remains the primary controlled test\.

## 6Conclusion

We presentedε\\varepsilon\-MemEvo, a framework that formalizes cross\-task knowledge transfer as an*adaptive intervention problem*in LLM\-based program evolution\. Through a Tactic Memory Bank for content\-level transfer and an Adaptive Injection Gate for strategy\-level transfer,ε\\varepsilon\-MemEvoachieves statistically significant convergence improvements across 8 diverse optimization benchmarks on GPT\-5 \(p=0\.0078p=0\.0078, 8/8 AUCC wins,\+8\.7%\+8\.7\\%average improvement\)\. The key insight is that*adaptive*injection control is essential: while cross\-task memories can provide substantial value \(up to\+55%\+55\\%\), uncontrolled injection can actively harm the search—in our ablation, two of five tasks fail to improve under naive always\-inject\. The adaptive gate resolves this tension with an interpretable posterior: data favor*skip*in improving and early\-plateau states and*hint*in late\-plateau states, while the unobserved stagnating states retain the prior\-initialized*guide*action\. This control incurs negligible overhead \(<1%<\\\!1\\%\)\. The content\-level LOO protocol excludes target\-task entries from the memory bank, so the transferred tactics come from other tasks rather than target solutions\.

These results establish adaptive cross\-task memory as a complementary layer for evolutionary coding agents\. Next steps include larger, more diverse banks, hierarchical memory, and transfer across base search frameworks and weaker LLM backbones\.

### Broader Impact Statement

ε\\varepsilon\-MemEvouses0\.69×0\.69\\timesthe aggregate wall\-clock time ofAdaEvolveacross the 8 main tasks but costs 2–34 GPU\-hours per task; scaling may raise energy use\. Cross\-task reuse lowers cost; gating reveals memory influence\.

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