规则更多、清单更长？在隐藏规则课程上对自我进化智能体进行基准测试

# More Rules, Longer Lists? Benchmarking Self-Evolving Agents on a Hidden-Rule Curriculum
Source: [https://arxiv.org/html/2610.40758](https://arxiv.org/html/2610.40758)
,Boyan XuAffiliation:Guangdong University of Technology,Guangzhou,Chinaemail:[hpakyim@gmail\.com](mailto:[email protected]),Shaobin ShiAffiliation:Guangdong University of Technology,Guangzhou,Chinaemail:[d7inshi@gmail\.com](mailto:[email protected]),Bingfeng ChenAffiliation:Guangdong University of Technology,Guangzhou,Chinaemail:[chenbf@gdut\.edu\.cn](mailto:[email protected]),Ruichu CaiAffiliation:Guangdong University of Technology,Guangzhou,Chinaemail:[cairuichu@gmail\.com](mailto:[email protected])andDongsheng LuoNote:Corresponding author\.Affiliation:Singapore Management University,Singaporeemail:[dsluo@smu\.edu\.sg](mailto:[email protected])

###### Abstract\.

Self\-evolving agents rewrite a persistent state from feedback, but it is largely untested whether this lets them learn a rule nobody told them\. An agent can also pass by writing down each correction as an exception, and its list then grows with every new rule\. We introduceCLR\-Bench, a Curriculum of Latent Rules benchmark\. Each chain adds one hidden rule per level on top of the earlier ones\. A rule acts on an opaque label that stands for a named grouping published on the Web, such as the founding members of an airline alliance\. The task gives one example value, practice feedback reveals one more member and one non\-member, and the test checks unseen members and similar non\-members\. Probes certify that the base model knows the members of each grouping and does not guess it without feedback, and that the evidence identifies the grouping once labels are read as named groupings\. Four other base models rarely guess the groupings either\. An automated pipeline builds chains from a new data domain, and we release 20 chains over 10 domains, each with four levels that pair a hidden rule with a practice task and a test task\. We evaluate six recent self\-evolution methods\. With the certifying model they barely learn\. The best gain at most 5 points over a frozen agent and exclude only 6–12% of the unseen members from the count, fewer than the 20% reached by simply keeping the raw practice history\. A fixed lesson that states the named\-grouping convention lifts the same methods by 14\.5 to 16\.5 points\. Their states hold the revealed member in 75–98% of cases and almost never the class name, and when practice exposes a member the list misses, they add that member to the list\. With the stronger GPT\-6\-Sol, ACE and Dynamic Cheatsheet learn from feedback alone\. They reach 78% accuracy and solve 59–60% of the single cells, against 53% and 8% with the certifying model, and they surpass the raw history\.CLR\-Benchtherefore measures how well an agent learns, and this ability differs across models\. Code and data are available at[https://github\.com/yausankit/clr\-bench](https://github.com/yausankit/clr-bench)\.

###### Keywords:

large language models, self\-evolving agents, benchmark

## 1\.Introduction

Large language model agents are increasingly expected to get better with use\. Self\-evolving methods give an agent a persistent state that it rewrites after each attempt\. The state can be an evolving playbook of strategies\([Zhang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib27)\), an optimized system prompt\([Agrawal et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib2)\), a cumulative cheatsheet\([Suzgun et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib17)\), a library of skills\([Alzubi et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib3)\), a bank of distilled reasoning memories\([Ouyang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib13)\), or a set of experiences extracted from groups of rollouts without updating weights\([Cai et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib5)\)\. All of these methods expect feedback from the environment to become knowledge the agent did not have before, and expect that knowledge to carry over to new cases\.

Current evaluations rarely test this expectation in isolation, for four reasons\. First, a score that rises over a stream can come from memorizing recurring instances, from following rules the task already states, or from fixing output formats and tool calls\. None of these requires inferring anything new\. Second, benchmarks do not measure what the model knew before the feedback, so a gain is hard to credit to the feedback and a failure hard to blame on the method\. Third, aggregate accuracy hides what was learned: an agent that memorizes the corrected cases can score like one that infers the rule behind them\. Fourth, few benchmarks check that the evidence determines what should be learned, and a low score may then reflect an ambiguous target\. We study a narrower question that is central to learning from experience\.*Given sparse corrective feedback, can a self\-evolving agent induce a hidden rule and apply it to cases it has never seen?*

Figure 1\.Overview ofCLR\-Bench\. \(a\) A level hides a published grouping behind an opaque label, with one exampleAA; practice reveals one member \(m0m\_\{0\}\) and one non\-member \(npn\_\{p\}\), and the test checks unseen members \(m1,m2m\_\{1\},m\_\{2\}\) and test non\-members \(NtN\_\{t\}\)\. \(b\) Rules accumulate over four levels; the agent practices, learns, and is tested\. \(c\) Four probes certify each candidate\.We introduceCLR\-Bench\(Curriculum ofLatentRules Benchmark\) to answer it\. Its chains consist of aggregation tasks over realistic records, such as counting reimbursable flight segments per department or reviewable medication records per patient\. Each level adds a rule that excludes records whose field value falls under an opaque label, for instance “segments in review queue B8 are not counted\.” The task gives one example value for the label,*Lufthansa*, and short factual descriptions of the values that appear\. The label stands for a real\-world named grouping taken from public sources, here the founding members of Star Alliance, but the task never names it\. Practice feedback comes from small edits of a public example\. The agent learns that*Thai Airways*belongs to review queue B8 like*Lufthansa*and that*ITA Airways*does not\. The test then asks it to apply the rule to the remaining members, such as*United Airlines*, which never appeared in feedback, and to keep counting similar\-looking non\-members\. To succeed, the agent has to turn two pieces of evidence into the right category and write that category into its state\.

The hidden classes come from the Web\. Agents increasingly act on Web data and services, and the categories behind their tasks are groupings that organizations and standards bodies publish and maintain online: the airlines of an alliance, the countries of an economic bloc, the weaknesses of a security taxonomy, the companies of a stock index\. A task rarely spells such a grouping out, and an agent meets it through examples and corrections\. Recovering a Web grouping from a few seed members is the classic problem of set expansion\([Wang and Cohen, 2007](https://arxiv.org/html/2610.40758#bib.bib21);[Zhang et al\., 2020](https://arxiv.org/html/2610.40758#bib.bib28)\), and learning a concept from a few positive examples has long been studied in cognitive science\([Tenenbaum, 1999](https://arxiv.org/html/2610.40758#bib.bib18)\)\.CLR\-Benchmoves this problem into the self\-evolution loop\. The seeds arrive as feedback, and the agent should store the grouping so that later decisions use it\. Hidden classes are published groupings or values tied to their members, for instance the currencies of BRICS member states\. The benchmark’s lists define them and record their sources and snapshot dates\.

Practice and test reward different things by design\. An agent can pass practice by recording the two revealed values as exceptions\. Only an agent that asks which category explains a correction also handles the unseen members\. Earlier rules stay in force, so the gap grows with depth\. A list\-keeping agent adds another list at every level and misses the unseen members of every rule, while an agent that writes categories carries them forward\. Real feedback has the same shape: an agent is corrected on individual cases and has to infer the rule behind them\.

Three design choices make the benchmark diagnostic\. The evidence is sufficient under one convention\. If labels denote named groupings, the example, the revealed member, and the rejected non\-member single out one grouping of the domain’s library, and the base model knows which of the described values belong to it\. The evidence is also necessary\. Language\-model probes certify during construction that the label and the example alone do not give the class away\. Finally, the same tasks run under several conditions that show where learning fails\. A*frozen*agent never updates\. Each method learns from feedback alone \(*self*\), and again with a fixed*lesson*in its update step that states the convention and a procedure for using the evidence without naming any class\. A method\-free reference keeps the raw practice history in the prompt\. Value\-level diagnostics tell under\-generalization, where unseen members stay in the count, apart from over\-generalization, where non\-members are removed\.

An automated pipeline assembles and certifies chains from a new data domain\. A chain holds the records of one domain, with entities such as departments, employees, claims, and flight segments, a base task that counts records per entity, and four levels\. Each level adds a rule over one field with an opaque label, describes every value involved, and comes with a practice task and a test task\. We release 20 chains, two in each of 10 domains that range from travel expense audits and pharmacy reviews to system logs, chemical imports, and port state control\. Together they contain 80 hidden rules, 80 practice tasks, and 80 test tasks\.

Our contributions are as follows\.

\(1\)Task definition\.We define curriculum chains in which each level hides a rule over an opaque label that stands for a published grouping\. Practice and test ask for different outputs, so only an inferred rule transfers \(Section[3](https://arxiv.org/html/2610.40758#S3)\)\.

\(2\)Probe\-certified construction\.An automated pipeline builds chains from a new data domain and uses language\-model probes to certify that the model knows the members of each class and does not guess the class without feedback\. Under the named\-grouping convention the evidence identifies the class\. We release 20 chains over 10 domains with 80 hidden rules, each paired with a practice task and a test task \(Section[4](https://arxiv.org/html/2610.40758#S4)\)\.

\(3\)Diagnostic metrics and conditions\.Single\-cell accuracy and value\-level diagnostics separate under\- from over\-generalization\. A frozen agent, the raw history, and a lesson that states the convention bound what the evidence supports \(Section[5](https://arxiv.org/html/2610.40758#S5)\)\.

\(4\)Evaluation of six methods with two base models\.With the certifying model, ACE, GEPA, and Dynamic Cheatsheet gain 2 to 5 points and exclude fewer unseen members from the count than the raw history does\. Their states record corrections as a growing list of exceptions\. A fixed lesson in the update step lifts them by 14\.5 to 16\.5 points, and its convention part alone lifts ACE and Dynamic Cheatsheet by 13 to 19 points, or by 11 points when it is stated at level 1 only\. With the stronger GPT\-6\-Sol, ACE and Dynamic Cheatsheet solve 59–60% of the single cells from feedback alone, against 8% with GPT\-6\-Luna\. The benchmark therefore separates learning ability across models \(Sections[6](https://arxiv.org/html/2610.40758#S6)and[7](https://arxiv.org/html/2610.40758#S7)\)\.

## 2\.Related Work

Table 1\.Comparison with related benchmarks\.BenchmarkVenueFbStateHiddenPriorDiagLLF\-Bench\([Cheng et al\., 2023](https://arxiv.org/html/2610.40758#bib.bib6)\)arXiv’23✓\\checkmark––––MINT\([Wang et al\., 2024b](https://arxiv.org/html/2610.40758#bib.bib22)\)ICLR’24✓\\checkmark––––StreamBench\([Wu et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib26)\)NeurIPS’24✓\\checkmark✓\\checkmark–––Evo\-Memory\([Wei et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib25)\)arXiv’25✓\\checkmark✓\\checkmark–––EvoMemBench\([Wang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib23)\)arXiv’26✓\\checkmark✓\\checkmark–––EvoAgentBench\([Gao et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib8)\)arXiv’26✓\\checkmark✓\\checkmark–––MemoryAgentBench\([Hu et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib9)\)ICLR’26–✓\\checkmark∘\\circ––WILT\([Banatt et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib4)\)NeurIPS\-W’24✓\\checkmark–✓\\checkmark∘\\circ–InductionBench\([Hua et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib10)\)ACL’25––✓\\checkmark––CLR\-Bench\(ours\)–✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark
Fb: learns from feedback on its own attempts; State: knowledge persists across tasks; Hidden: the rule is never stated; Prior: prior knowledge is certified; Diag: value\-level diagnostics\.✓\\checkmarkyes,∘\\circpartly, – no\.

Table 2\.Evaluated self\-evolution methods\.Reflect: an LLM reflects on failures to write the update; Incr\.: the state is edited, not rewritten; Gate: an update is kept only if a condition holds; Retr\.: the solver sees only retrieved entries; Code: the state holds executable code\.

##### Self\-evolving agents\.

Several methods let a frozen language model improve across episodes by rewriting a persistent, non\-parametric state\. Reflexion keeps verbal self\-reflections in an episodic buffer\([Shinn et al\., 2023](https://arxiv.org/html/2610.40758#bib.bib15)\)\. ExpeL extracts insights from successful and failed trajectories\([Zhao et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib29)\)\. Voyager and EvoSkill grow libraries of executable skills\([Wang et al\., 2024c](https://arxiv.org/html/2610.40758#bib.bib19);[Alzubi et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib3)\), and Agent Workflow Memory induces reusable workflows from past episodes\([Wang et al\., 2024a](https://arxiv.org/html/2610.40758#bib.bib24)\)\. More recent methods change what is stored and how it is updated\. Dynamic Cheatsheet rewrites a cumulative cheatsheet after every attempt\([Suzgun et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib17)\), and ACE curates an itemized playbook with incremental edits\([Zhang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib27)\)\. ReasoningBank distills strategies from both successes and failures\([Ouyang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib13)\)\. Training\-Free GRPO extracts experiences by contrasting rollouts within a group\([Cai et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib5)\), and GEPA evolves the system prompt by reflective search over a Pareto front\([Agrawal et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib2)\)\. We evaluate six of these methods, and Table[2](https://arxiv.org/html/2610.40758#S2.T2)summarizes how each one writes and uses its state\. They all assume that feedback contains knowledge worth keeping\.CLR\-Benchtests whether they extract it when the knowledge is a category that the feedback only points at\.

##### Benchmarks for learning from feedback\.

Self\-evolving methods are usually evaluated on coding, web navigation, app\-based agent tasks, and financial reasoning\([Zhang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib27);[Ouyang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib13);[Wang et al\., 2024a](https://arxiv.org/html/2610.40758#bib.bib24)\)\. StreamBench treats the setting as online learning from a feedback stream\([Wu et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib26)\), and LLF\-Bench and MINT test learning from language feedback\([Cheng et al\., 2023](https://arxiv.org/html/2610.40758#bib.bib6);[Wang et al\., 2024b](https://arxiv.org/html/2610.40758#bib.bib22)\)\. Recent benchmarks for self\-evolving agents measure memory over task streams\([Wei et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib25);[Wang et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib23);[Hu et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib9)\)and the transfer of learned procedures across tasks\([Gao et al\., 2026](https://arxiv.org/html/2610.40758#bib.bib8)\)\. These benchmarks ask whether scores rise over a stream\.CLR\-Benchasks what was learned and tests it on values that never appear in feedback\. Table[2](https://arxiv.org/html/2610.40758#S2.T2)compares them withCLR\-Bench\.

##### Inductive reasoning and rule learning\.

Rule induction from few examples has long served to evaluate intelligence, from concept learning to the Abstraction and Reasoning Corpus\([Chollet, 2019](https://arxiv.org/html/2610.40758#bib.bib7)\)\. Qiu et al\. find that language models propose good hypotheses but struggle to apply them\([Qiu et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib14)\)\. InductionBench reports failures on the simplest classes of string functions\([Hua et al\., 2025](https://arxiv.org/html/2610.40758#bib.bib10)\)\. WILT asks models to discover a hidden rule by proposing test cases over several turns\([Banatt et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib4)\), and DiscoveryWorld hides regularities in a virtual environment for discovery agents\([Jansen et al\., 2024](https://arxiv.org/html/2610.40758#bib.bib11)\)\. Two methods come closest to whatCLR\-Benchasks of an agent\. Hypotheses\-to\-Theories builds a rule library on training problems and reuses it at test time\([Zhu et al\., 2023](https://arxiv.org/html/2610.40758#bib.bib30)\), and hypothesis search proposes natural\-language hypotheses and checks them as programs\([Wang et al\., 2024d](https://arxiv.org/html/2610.40758#bib.bib20)\)\. Both learn from labeled examples given in a batch\. InCLR\-Bench, evidence reaches an agent’s update step one correction at a time, and we evaluate methods built for that loop\. The feedback consists of counterexamples to the agent’s program, as in counterexample\-guided synthesis\([Solar\-Lezama et al\., 2006](https://arxiv.org/html/2610.40758#bib.bib16)\), and the groupings consistent with the evidence form a version space\([Mitchell, 1982](https://arxiv.org/html/2610.40758#bib.bib12)\)\. Most of the benchmarks above evaluate one episode of reasoning or exploration\.CLR\-Benchplaces induction inside an agent’s interaction loop\. The evidence is feedback on the agent’s own programs, and the rule has to be stored and then applied to a separate test task with a different output\. Because the hidden classes are real groupings that the model may already know, success depends on linking feedback to world knowledge\.

##### Set expansion and concept learning\.

Expanding a few seed entities into the full Web grouping they belong to is a classic Web mining task\. It has been solved with wrapper induction over Web pages\([Wang and Cohen, 2007](https://arxiv.org/html/2610.40758#bib.bib21)\)and with class names generated by language models\([Zhang et al\., 2020](https://arxiv.org/html/2610.40758#bib.bib28)\)\. Cognitive science models concept learning from a few positive examples as Bayesian inference over nested hypotheses, in which the size principle favors the smallest consistent concept\([Tenenbaum, 1999](https://arxiv.org/html/2610.40758#bib.bib18)\)\.CLR\-Benchgives this problem to an agent that receives the seeds one at a time as feedback and keeps the inferred grouping in its state\. Its diagnostics measure the two errors these fields study: expanding too little, which misses unseen members, and expanding too much, which includes non\-members\.

## 3\.Preliminaries and Task Definition

### 3\.1\.Curriculum Chains

A chain is set in a data domain with entities and records, such as departments, employees, claims, and flight segments\. Its base task asks for a program that counts records per entity\. A chain has four levels, and the rules accumulate\. Leveljjadds a rule over a fieldfjf\_\{j\}, its*trap field*, with an opaque labelℓj\\ell\_\{j\}, for example “segments in review queue B8 are not counted\.” We call a position in a chain a*slot*, andCLR\-Benchhas 80 slots\. Behind each label is a hidden classCjC\_\{j\}, a named grouping published on the Web \(Section[4](https://arxiv.org/html/2610.40758#S4)\)\. The task never namesCjC\_\{j\}\. It gives one exampleaj∈Cja\_\{j\}\\in C\_\{j\}and a one\-sentence factual description of every value that can appear in the level’s inputs, including the unseen members and the non\-members, so an agent that knows the class can recognize its members\. Each class also has three further membersm0,m1,m2m\_\{0\},m\_\{1\},m\_\{2\}, a practice non\-membernpn\_\{p\}, and seven test non\-membersNtN\_\{t\}\. The non\-members come preferentially from competing groupings that also contain the example \(Figure[1](https://arxiv.org/html/2610.40758#S1.F1)a\)\.

### 3\.2\.Practice and Test

At levelkkthe agent practices on the same records and rules, but the practice task asks for the largest entity total\. The agent may submit up to three programs\. Each program runs on a public example and on2​k\+12k\+1hidden inputs\. One hidden input moves the example values to other records\. For each rulej≤kj\\leq k, one input insertsm0m\_\{0\}and another inserts bothm0m\_\{0\}andnpn\_\{p\}\. Every failing input comes back as a counterexample that says, for each changed value, whether it belongs to the label like the example\. The first attempt usually fails, becausem0m\_\{0\}has not been shown yet\. Appendix[A\.4](https://arxiv.org/html/2610.40758#A1.SS4)reproduces a task and its feedback\. The method runs its update step after every attempt, and a gated method may reject the update\. Practice at a level ends at the first passing attempt or after three attempts\. The state at that point writes the test program, which returns the sum of the entity totals\.

The test has five hidden inputs, which we call*cells*\. Each cell is a full set of records\. The5−k5\-k*clean cells*contain only example values\. Each of thekk*single cells*adds, for one rule, its two unseen members and its seven test non\-members\. A program that applies every rule only to its example scores\(5−k\)/5\(5\-k\)/5, which gives the frozen staircase of 0\.80, 0\.60, 0\.40, and 0\.20\. Any gain above it comes from applying a rule to unseen members while keeping the non\-members\. Recording the example andm0m\_\{0\}is enough to pass practice, so practice never rewards generalization directly\. The test measures whether the agent infers which category explains its corrections, which is what a deployed agent would have to do\.

## 4\.Benchmark Construction

Figure 2\.Composition ofCLR\-Bench\. \(a\) Hidden classes by domain \(inner\), trap field \(middle\), and kind of grouping \(outer\)\. \(b\) Other published lists that contain each example\. \(c\) Size of each value universe\. \(d\) Length of the test task per level\.Writing hidden\-rule chains by hand does not scale, and it invites shortcuts such as classes that the example gives away or members that share a visible prefix\. We therefore build chains with a pipeline that turns a domain description into certified chains \(Figure[1](https://arxiv.org/html/2610.40758#S1.F1)c\)\. The domain is the only manual input\.

### 4\.1\.Domain Inputs and Candidates

A domain provides three inputs\. The records come from a seeded generator or a public research release; two domains use Synthea’s synthetic patient records and Loghub system logs, and no personal data is involved\. Each trap field has a universe of values with one\-sentence descriptions\. A library of named lists supplies the candidate classes, such as organization rosters, alliance memberships, index constituents, official classifications, and sections of standards, each with its source and snapshot date \(Table[5](https://arxiv.org/html/2610.40758#A1.T5)\)\. For each level the pipeline draws a classCCand picks the example, three members, the practice non\-member, and seven test non\-members\. Several constraints block shortcuts\. The example must lie in at least two other lists, and no single attribute may separate members from non\-members\. Different levels use disjoint value pools, and non\-members come preferentially from competing lists that contain the example\. Disputed or recently changed members are never used\.

Table 3\.Probes that certify every hidden class \(sampled over the three choices of the revealed member\)\.
### 4\.2\.Probe Certification

Each candidate passes four probes run with the evaluated model \(Table[3](https://arxiv.org/html/2610.40758#S4.T3)\)\. The Known probe runs first, on every candidate list\. It shows the model the list’s pool values with their descriptions, one round of feedback, and the lesson, and asks it to name the grouping and mark which values belong to it\. The soft score is the share of pool values whose membership the model gets right, and the probe requires at least 0\.8 on average and 0\.6 in every rotation of the revealed member\. A list passes only if the model both identifies the grouping and knows its members\. The other three probes run in the context of the full chain\. The Hidden probe gives only the label and the example, and the model must not recover the class\. The Learnable probe gives practice feedback alone and requires the model to assign between 1/6 and 2/3 of the unseen members\. The Solvable probe adds the lesson and requires a soft score of at least 0\.8 on the remaining pool values\. A candidate that fails is replaced\. Together the probes place each class where feedback matters, between classes the model guesses outright and classes it cannot learn\. Built chains are checked for consistency and reproduce bit for bit from their seeds\. A frozen agent scores 0\.80, 0\.57, 0\.34, and 0\.20 on them, close to the designed staircase\.

### 4\.3\.Benchmark Statistics

Figure[2](https://arxiv.org/html/2610.40758#S4.F2)shows the composition ofCLR\-Bench\. The 20 chains cover ten domains with two chains each\. Every domain contributes three trap fields, whose value universes range from about 100 values for medicines and materials to several thousand for airports, ports, and universities\. The 80 hidden classes span seven kinds of published grouping\. Intergovernmental memberships make up the largest share with 35 classes, followed by 18 standards and official classifications, 10 airline alliances, and 8 stock indices and sports clubs\. The rest are software products and ports, university networks, and language families\. Every example also belongs to other published lists, 6\.5 on average and up to 20, so the evidence has to separate the class from real competitors\. Under the named\-grouping convention it does\. Tasks grow with depth as rules and records accumulate, from a median of about 3\.3k tokens at level 1 to 4\.9k at level 4\. Table[4](https://arxiv.org/html/2610.40758#A1.T4)lists all classes\.

## 5\.Evaluation Metrics and Conditions

### 5\.1\.Level and Single\-Cell Accuracy

The level score is the share of the five hidden test inputs for which a program returns the correct sum\. The share of clean cells falls with depth, so we also report single\-cell accuracy, the share of correct single cells pooled over the 20 chains and levels 1–4\. It is zero for an agent that applies every rule only to the example, and the mixture of cells does not affect it\.

### 5\.2\.Value\-Level Diagnostics

For every value in a class pool we build an input that adds only that value to the example values\. We run the level\-kktest program on it for every rulej≤kj\\leq kand record two outcomes\. For a member we record whether it is excluded, writteninc\\mathrm\{inc\}, orincu\\mathrm\{inc\}\_\{u\}for the two unseen membersm1m\_\{1\}andm2m\_\{2\}\. For a non\-member we record whether it is kept, writtenexc\\mathrm\{exc\}\. Both are pooled over chains, levels, and rules\. A lowincu\\mathrm\{inc\}\_\{u\}signals under\-generalization, and a low exc signals over\-generalization\.

### 5\.3\.Conditions

The main comparison varies two things, the method and the base model \(Table[6](https://arxiv.org/html/2610.40758#A1.T6)in the appendix\)\. Each method runs*self*, learning from feedback alone, and again with a*lesson*added to its update step\. The lesson is a fixed text that names no class\. It states the benchmark’s convention, namely that a label denotes a well\-known named grouping that contains the example and the confirmed member and excludes the rejected value, and it gives a procedure for applying this convention\. Certification requires the lesson to make every class learnable, so it marks what the evidence can support\. A method\-free*history*reference puts the raw practice programs and feedback into the solver prompt, with or without the lesson\. Under*rewarded practice*, the hidden practice inputs of the second and third attempts also insertm1m\_\{1\}\. An exception list built from the first attempt’s feedback then fails a second time, and onlym2m\_\{2\}stays unseen\. The appendix reports two further reference conditions, the parts of the lesson and the class names\.

## 6\.Experimental Setup

### 6\.1\.Baselines

#### 6\.1\.1\.Self\-evolution methods

We evaluate six self\-evolution methods that differ in what they store and how they update it \(Table[2](https://arxiv.org/html/2610.40758#S2.T2)\)\. We follow the official prompts and algorithms and replace only the task\-specific placeholders\.

#### 6\.1\.2\.Reference conditions

A*frozen*agent writes every test program with an empty state and sets the floor\. The method\-free*history*reference puts the raw practice programs and feedback into the solver prompt\. It shows what the evidence supports without any update step\. The*lesson*in the update step shows what the evidence supports under the benchmark’s convention \(Section[5](https://arxiv.org/html/2610.40758#S5)\)\.

### 6\.2\.Experimental Settings

All methods, the frozen agent, and the references use GPT\-6\-Luna with high reasoning effort\. Section[7\.1\.2](https://arxiv.org/html/2610.40758#S7.SS1.SSS2)reruns the frozen agent, the history reference, and all six methods with GPT\-6\-Sol at high effort, both from feedback alone and with the lesson\. At each level a method gets up to three practice attempts and updates its state after every attempt\. An attempt is one submitted program, and Training\-Free GRPO samples its group of four rollouts within an attempt\. The state reached after practicing levelkkwrites the level\-kktest program, which is scored once\. The state carries over from one level to the next, and the history reference sees every earlier practice program and its feedback from all levels so far\. Practice feedback is explicit\. For every value that a hidden practice input changed, it says whether the value belongs to the label, for example “X belongs to review queue B8, like Lufthansa; its records are not counted\.” Each condition runs once per chain, and we report averages over the 20 chains\. Besides the level score we report single\-cell accuracy and the diagnosticsincu\\mathrm\{inc\}\_\{u\}and exc \(Section[5](https://arxiv.org/html/2610.40758#S5)\)\.

## 7\.Experimental Results

### 7\.1\.Main Results

#### 7\.1\.1\.Overall results

Figure 3\.Test accuracy per level \(20 chains\) from feedback alone \(open\) and with the lesson \(filled\), with GPT\-6\-Luna \(red\) and GPT\-6\-Sol \(blue\)\. Gray band: the designed staircase \(80, 60, 40, 20\) of an agent that applies each rule only to the example\.Figure[3](https://arxiv.org/html/2610.40758#S7.F3)shows the accuracy of every method per level with both base models, and Table[7](https://arxiv.org/html/2610.40758#A1.T7)in the appendix lists every condition per level\.

With GPT\-6\-Luna and feedback alone, the methods barely learn, and none of them generalizes better than the raw evidence\. The frozen agent passes 95\.5% of the clean cells and none of the single cells, so any point above it comes from applying a rule beyond the example\. ACE, GEPA, and Dynamic Cheatsheet gain only 1\.8 to 5\.0 points\. They solve 3–8% of the single cells, exclude 6–12% of the unseen members, and stay on the staircase at every level\. The method\-free history reference keeps every practice program and its feedback in the prompt\. Its accuracy is about the same at 52\.3%, and it excludes more unseen members, 20%\. The update steps make programs more precise, keeping 92–95% of the non\-members where the history keeps 82%, but they add no generalization\.

Three methods fail because of the way they accept updates\. Training\-Free GRPO extracts experiences only from groups with mixed outcomes, and EvoSkill accepts a skill only if it raises the practice score\. Practice outcomes are all\-or\-nothing\. As a result, no Training\-Free GRPO state ever contains an experience, and EvoSkill accepted no skill on 9 of the 20 chains; a third of its 449 proposals were malformed\. Every Training\-Free GRPO state is empty with both base models, and 70% of EvoSkill’s states hold no skill with GPT\-6\-Luna, against 14% with GPT\-6\-Sol\. ACE and Dynamic Cheatsheet, by contrast, update after every attempt\. ReasoningBank retrieves generic strategies such as “infer the full category behind a field\-note example,” and the solver then excludes values on the strength of their descriptions alone\. It keeps only 51% of the non\-members and falls 14 points below the frozen agent\.

#### 7\.1\.2\.Effect of the base model

We rerun the frozen agent, the history reference, and all six methods with GPT\-6\-Sol, from feedback alone and with the lesson \(Figure[3](https://arxiv.org/html/2610.40758#S7.F3), blue, and Table[10](https://arxiv.org/html/2610.40758#A1.T10)\)\. Without feedback, Sol guesses a class in only 1 of the 80 level scores\. Its frozen agent even falls below the staircase to 32\.5%, because its programs also drop non\-members that fit a guessed attribute category such as “airlines based in European countries\.”

From feedback alone, ACE and Dynamic Cheatsheet with Sol reach 78\.3% and 78\.5%\. They solve 59–60% of the single cells and exclude 68–76% of the unseen members, where Luna managed 8% and 12%\. They also overtake the history reference, which reaches 70\.3% and 49% of the single cells\. Most of the margin comes from keeping more non\-members, 90–95% against 83%\. Dynamic Cheatsheet also excludes more unseen members than the history, 76% against 68%, while ACE excludes as many\. The lesson adds only 3\.0 and 5\.5 points with Sol, compared with 14\.5 and 15\.5 with Luna\. The gap between the two models widens with depth, and at level 4 the self condition scores 59% with Sol and 24% with Luna\. The exception lists seen with Luna are what an update step writes when the model does not propose a category\. A model that proposes the category writes the category instead\. Difficulty was calibrated on the certifying model\. Sol scores above 80% on the first two levels, and level 4 still leaves 41 points to gain\.

Figure 4\.Generalization against specificity \(GPT\-6\-Luna, levels 1–4 pooled\): each method from feedback alone \(open\) to \+ lesson \(filled\)\. The inset enlarges the top\-left corner, where Training\-Free GRPO and the frozen agent overlap\.Figure 5\.GPT\-6\-Luna, learning from feedback alone\. \(a\) Exclusion of the revealed memberm0m\_\{0\}and of the unseen membersm1,m2m\_\{1\},m\_\{2\}\. \(b\) Exclusion ofm2m\_\{2\}, which is never shown, under standard and rewarded practice \(wherem1m\_\{1\}is revealed from the second attempt\)\.A stronger model does not help every update mechanism\. GEPA and EvoSkill with Sol exclude more unseen members, 48% and 41%, but keep only 66% and 53% of the non\-members and end at 58\.8% and 52\.3%\. Training\-Free GRPO still extracts no experience, and ReasoningBank’s strategies drop even more non\-members, keeping 21%\. Both end below their Luna scores, at 35\.8% and 24\.8%\. A model that proposes categories helps the methods whose update step records them and makes the others over\-generalize\. With the lesson, Sol raises History to 83\.8%, GEPA to 64\.8%, and EvoSkill to 70\.5%\. Training\-Free GRPO and ReasoningBank stay below their feedback\-only scores at 31\.2% and 20\.8%\. When the update step does not store a rule, neither a better model nor the convention helps\.

Other models cannot guess the hidden classes either \(Table[9](https://arxiv.org/html/2610.40758#A1.T9)in the appendix\)\. Without feedback, frozen agents with four further base models stay at or below the staircase, and at most 4 of their 80 level scores lie above it\. Scores below the staircase come from programs that also drop values the clean cells must count\. When told the class names, these models apply them about as imprecisely as GPT\-6\-Luna, solving 40–45% of the single cells and keeping 51–63% of the non\-members\. The gap between knowing a grouping and applying it is therefore not specific to one model\. Table[10](https://arxiv.org/html/2610.40758#A1.T10)in the appendix lists every learning condition for both base models\.

### 7\.2\.Analysis

Figure 6\.\(a\) What the state says about each level’s label \(ACE and Dynamic Cheatsheet, 160 states per row, annotated without test results; names the class: the class, a broader grouping, or its members listed; wrong rule: another grouping or an attribute rule\)\. \(b\) Unseen members excluded and non\-members kept by the program, by state content, over all annotated states\.#### 7\.2\.1\.Why do the methods not learn?

With the lesson in their update step, ACE, GEPA, and Dynamic Cheatsheet reach 67\.0%, 66\.0%, and 68\.3% and solve 39–46% of the single cells, on par with History \+ lesson at 63\.5%\. The same evidence therefore suffices to learn the rules\. The gap to the self condition grows as rules accumulate\. At level 4, ACE scores 48% with the lesson and 23% without it, GEPA 42% and 22%, and Dynamic Cheatsheet 42% and 24%\. The lesson helps only methods whose update step stores a rule\. Training\-Free GRPO stays at 49\.5% because its gate never opens\. EvoSkill and ReasoningBank lose accuracy with the lesson, falling to 42\.0% and 30\.0% and keeping only 62% and 31% of the non\-members\. Once told that labels denote named groupings, they remove whole groupings they guess\. The gains hold across domains \(Table[11](https://arxiv.org/html/2610.40758#A1.T11)in the appendix\)\. The lesson raises ACE in 8 of the 10 domains and Dynamic Cheatsheet in 9, and web security is the exception for both\.

In the diagnostics, ACE excludes the member revealed in practice 92\.5% of the time but the two unseen members only 12\.2% of the time\. Dynamic Cheatsheet and GEPA behave the same way, at 80\.0% against 11\.8% and 87\.0% against 5\.8% \(Figure[5](https://arxiv.org/html/2610.40758#S7.F5)a\)\. The states record the revealed member as an exception\. Figure[4](https://arxiv.org/html/2610.40758#S7.F4)shows that all methods learning from feedback alone sit in the corner of high specificity and low generalization\. The lesson moves ACE, GEPA, and Dynamic Cheatsheet toward the learned category and pushes EvoSkill and ReasoningBank toward over\-generalization\. By string match, the revealed member appears in 75–98% of the final states of ACE, GEPA, and Dynamic Cheatsheet, and the full class name in at most 3%, or 8–18% with the lesson\. In a chain whose class is the founding members of Star Alliance, the ACE playbook after level 1 reads: “the confirmed members include Lufthansa and Thai Airways; ITA Airways is confirmed not to be a member and remains countable\. Apply membership by the exact airline value, not by name similarity\.” With the lesson it reads: “B8 is Star Alliance: exclude Lufthansa and Thai Airways, but count ITA Airways\.” The lesson state names Star Alliance, a slightly broader grouping than its founding members, which fits the lower exc of the lesson condition\. Test non\-members taken from competing groupings are kept as often as the others, 92\.2% against 92\.8% for ACE\. When asked directly in a single prompt, the bare model assigns 44% of the unseen members from the same feedback, as the Learnable probe shows\.

We annotated the state written after each level by what it says about that level’s label\. The annotator was GPT\-6\-Luna, which saw the hidden class and the practice evidence but no test result \(Appendix[A\.1](https://arxiv.org/html/2610.40758#A1.SS1)\)\. With GPT\-6\-Luna and feedback alone, 91% of the ACE and Dynamic Cheatsheet states hold only the values seen in practice or nothing about the label, and 6% name the class or list its members\. With GPT\-6\-Sol, 58% name the class or list its members \(Figure[6](https://arxiv.org/html/2610.40758#S7.F6)a\)\. State content predicts what the program does\. When a state names the class or lists its members, the program excludes 89% of the unseen members and keeps 93% of the non\-members\. When the state holds only the seen values, the program excludes 9% \(Figure[6](https://arxiv.org/html/2610.40758#S7.F6)b\)\. The methods fail to turn corrections into a category, and they apply a category well once it is stored\.

To see which part of the lesson matters, we split it inside the update step and give both parts under the same neutral heading, “UPDATE NOTE” \(Table[8](https://arxiv.org/html/2610.40758#A1.T8)\)\. The procedure alone tells the method to decide the class behind the example and apply it to every described value\. It leaves ACE and Dynamic Cheatsheet at 55\.0%, a gain of 2\.5 and 2\.2 points\. The convention alone says that a label denotes a well\-known named grouping chosen to fit the corrections\. It lifts them to 71\.5% and 65\.8%, a gain of 19\.0 and 13\.0 points, so its effect does not depend on the authority of the original heading\. With the raw history, the convention alone gives 64\.8%, as much as the whole lesson at 63\.5%, while the procedure alone adds 2\.0 points\. Giving the class names in the update step together with the feedback lifts ACE and Dynamic Cheatsheet to 73\.5% and 75\.8% and to 52–57% of the single cells\. A solver told the names without any feedback reaches only 58\.0%, with 40% of the single cells and 58% of the non\-members kept\. The methods fail at identifying the category, and once it is identified, the feedback sets its boundary\. The state annotations show the same split\. With the procedure alone, 76% of the states hold only the seen values or nothing, and with the convention, 52% name the class or list its members\. Dynamic Cheatsheet with the whole lesson under the neutral heading stays at 53\.8%\. Its states show why: 69% of them no longer mention the label, because the cheatsheet is rewritten as a whole and the rule gets dropped\.

To test whether the methods learn a reusable inference policy, we give the convention in the update step at level 1 only and remove it from level 2 on \(Table[8](https://arxiv.org/html/2610.40758#A1.T8)\)\. ACE and Dynamic Cheatsheet reach 63\.8% and 64\.3%, between learning from feedback alone at 52\.5% and 52\.8% and receiving the convention at every level at 71\.5% and 65\.8%\. At levels 2–4, whose classes never came with the convention, ACE scores 75, 58, and 39%, compared with 64, 44, and 23% from feedback alone\. Most of the effect of one statement persists in the state\. Where it fades, the methods fall back on attribute rules, for example “airports in Africa” for airports in OPEC member states\.

#### 7\.2\.2\.Does rewarded practice change what the methods learn?

An exception list passes standard practice, and declining to generalize from two positives and one negative could be a cautious choice\. Under rewarded practice a further member,m1m\_\{1\}, appears from the second attempt on\. ACE, GEPA, and Dynamic Cheatsheet then exclude the newly revealedm1m\_\{1\}, ACE in 93\.5% of cases, but they still miss the member they never saw\. Their inc onm2m\_\{2\}is 9\.5%, 4\.0%, and 14\.0%, close to the 12\.0%, 4\.5%, and 11\.0% of standard practice \(Figure[5](https://arxiv.org/html/2610.40758#S7.F5)b\)\. With the same signal, the history reference more than doubles its inc onm2m\_\{2\}, from 19\.5% to 42\.0%\. The raw history uses the evidence that a list fails, and the methods do not\.

#### 7\.2\.3\.Failure modes, retention, and cost

In the self condition, 83–97% of the single cells of ACE, GEPA, Dynamic Cheatsheet, Training\-Free GRPO, and EvoSkill fail because an unseen member is still counted\. ReasoningBank fails just as often by dropping non\-members \(Figure[7](https://arxiv.org/html/2610.40758#A1.F7)a in the appendix\)\. Accuracy falls over the levels mostly because the share of single cells grows \(Figure[8](https://arxiv.org/html/2610.40758#A1.F8)in the appendix\)\. For ACE and Dynamic Cheatsheet, the exclusion of unseen rule\-1 members at level 4 stays within 3 points of its level\-1 value with both models\. ACE with Luna moves from 15\.0% to 17\.5%, and with Sol from 72\.5% to 70\.0%\. Keeping rule\-1 non\-members declines as rules accumulate, from 99\.4% to 77\.5% for Dynamic Cheatsheet with Sol and from 95\.0% to 84\.4% for ACE with Luna\. Older rules lose specificity and keep their members\. Passing practice says little about learning\. ACE passes 95% of the practice levels and the history reference 91%, yet they solve 8% and 13% of the single cells, because the exception list is enough to pass\. Training\-Free GRPO passes no practice level at all, so its mixed\-outcome gate never opens\. EvoSkill spends about 6M input tokens per chain on practice and learns nothing\. ACE spends about 0\.9M, and the history reference spends 0\.07M and generalizes best among the self conditions\.

## 8\.Conclusion

CLR\-Benchasks whether self\-evolving agents learn from feedback a rule they were never told\. Its hidden classes are groupings whose members the base model knows, which it does not guess without feedback, and which it can identify from the evidence once labels are read as named groupings\. With the certifying model, current methods record corrections as exceptions and gain at most 5 points over a frozen agent\. A lesson that states the convention lifts them to 66–68%, so the missing step is inferring that corrections point to a named grouping\. Gated updates starve under binary practice rewards, and retrieved generic strategies over\-generalize\. Practice reward is a poor signal of learning: with the certifying model, ACE passes 95% of the practice levels yet solves 8% of the single cells\. A stronger base model, GPT\-6\-Sol, makes the missing inference from feedback alone, and the benchmark can follow such progress as models improve\. Three directions follow from these results: update steps that propose named groupings and check them against the model’s knowledge, tools that let the agent look up published groupings during updates, and acceptance rules that do not depend on reward variation\. The construction pipeline lets others extend the benchmark to new domains and rerun it as methods improve\.

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## Appendix AAppendix

Table 4\.Hidden classes, one row per chain \(levels 1–4\)\. TR: Travel audit, SY: Pharmacy review, WS: Web security, LG: System logs, SP: Sponsorship, CH: Chemical imports, MN: Raw materials, SH: Port inspections, UN: Scholarships, GR: Travel grants\.Figure 7\.Failure modes and cost \(GPT\-6\-Luna, learning from feedback alone unless marked \+L\)\. \(a\) How single cells fail\. \(b\) Practice levels passed and \(c\) practice input tokens against single\-cell accuracy\.![Refer to caption](https://arxiv.org/html/2610.40758v1/retention.png)Figure 8\.Retention: unseen members excluded \(top\) and non\-members kept \(bottom\) for rulejj\(columns\) at levelkk\(rows\)\.Table 5\.The ten domains: value\-universe size and number of candidate lists per trap field\.Table 6\.Conditions: text added to the update step \(U\) or the solver prompt \(S\)\.Table 7\.All conditions, GPT\-6\-Luna \(%;Δ\\Delta: change over the frozen agent\)\. Rows without \+ learn from feedback alone\.†With a format note \(Appendix[A\.3](https://arxiv.org/html/2610.40758#A1.SS3.SSS0.Px1)\)\.∗m1m\_\{1\}is revealed in practice; incucountsm2m\_\{2\}only\.L1L2L3L4AvgΔ\\DeltaSingleincuexcFrozen8057342047\.8–0194History8465372352\.3\+4\.5132082rewarded practice∗9075513963\.8\+16\.0314287History \+ lesson8570554463\.5\+15\.8445975History \+ convention8868574664\.8\+17\.0475973History \+ procedure8267402854\.3\+6\.5183282Class\-name oracle8867473058\.0\+10\.3404958ACE7964442352\.5\+4\.881292\+ lesson7973684867\.0\+19\.3466286\+ convention8671674667\.5\+19\.8475784rewarded practice∗8362432653\.5\+5\.8101096GEPA†8158372249\.5\+1\.83696\+ lesson9283474266\.0\+18\.3395282\+ convention8870424260\.5\+12\.8394675rewarded practice∗8262362250\.5\+2\.84495Dynamic Cheatsheet8362422452\.8\+5\.081295\+ lesson8582644268\.3\+20\.5435684\+ convention9379585070\.0\+22\.3455989rewarded practice∗8367442554\.8\+7\.0121492Training\-Free GRPO8055381948\.0\+0\.30294\+ lesson8060391949\.5\+1\.81196EvoSkill7754371646\.0\-1\.81284\+ lesson8048261442\.0\-5\.871062ReasoningBank6836151533\.5\-14\.33951\+ lesson682816830\.0\-17\.881431Table 8\.Text added to the update step \(GPT\-6\-Luna\); columns as in Table[7](https://arxiv.org/html/2610.40758#A1.T7)\. Neutral heading: “UPDATE NOTE” instead of “VERIFIED LESSON”\.Table 9\.Other base models \(%\)\. Frozen: accuracy per level and level scores above the staircase \(of 80\)\. Oracle: the class\-name oracle\.∗Evaluated and certifying model\.Table 10\.Both base models \(%\)\. Methods learn from feedback alone unless marked \+ lesson\.†With a format note \(Appendix[A\.3](https://arxiv.org/html/2610.40758#A1.SS3.SSS0.Px1)\)\.Table 11\.Average test accuracy \(%, levels 1–4\) per domain, two chains each\. \+L: with the lesson\. The lesson adds little in web security and pharmacy review\.### A\.1\.State annotation

For every chain and level we take the state a method holds after practicing levelkkand annotate what it says about the label of levelkk\. The annotator \(GPT\-6\-Luna, high reasoning effort\) sees the field, the label, the hidden class and its members, and the values revealed in practice, but no test program or score\. It assigns one of seven categories: the exact class or an equivalent description; a broader grouping that contains the class; another named grouping; an attribute rule \(region, country, size, name pattern\); only the values seen in practice; most members of the class listed without naming it; or nothing usable\. We annotate 1,280 states: ACE and Dynamic Cheatsheet learning from feedback alone, with the lesson, and under rewarded practice with GPT\-6\-Luna; with the procedure, the convention, and the whole lesson under the neutral heading with GPT\-6\-Luna; and from feedback alone and with the lesson with GPT\-6\-Sol\. Each state is then linked to the value\-level diagnostics of the program written from it at the same level\.

### A\.2\.The lesson

The \+ lesson condition appends the following text, under the heading “VERIFIED LESSON \(correct, from the task designers\)”, to the input of each method’s update step; the History \+ lesson reference places it in the solver prompt\. The text is the same for every chain and level and does not name any class\. It states a convention \(labels denote well\-known named groupings rather than attribute\-defined categories\) and a procedure for using the evidence\.

LessonWhen a level rule applies to a labelled class and the report gives only one example value, the class is a real\-world category that the label does not name: a named grouping that exists in this domain, such as an organisation, an alliance, an official list or a standard classification\. Feedback that another value is treated like the example, and that some other value is not, tells you which category it is: choose the best\-known named grouping that contains the example and the confirmed value and excludes the rejected one\. Do not construct a category from a property you read in the descriptions, such as a region, a type of government, a climate or a size\. Write that category by name into your notes together with the label\. Then apply the rule to every value the report describes that belongs to that grouping, using each description only to identify what the value is and your knowledge of the grouping to decide membership, including values that never appeared in feedback, and leave out values that are not in the grouping\. Before coding, go through every described value, decide membership for each one, and hard\-code the complete member set\.

##### Lesson parts\.

History \+ convention uses the first three sentences of the lesson \(up to “a climate or a size”\)\. History \+ procedure uses: “When a level rule applies to a labelled class and the report gives only one example value, decide which class the example and the feedback point to and write it into your notes together with the label\. Then apply the rule to every value the report describes that belongs to that class, including values that never appeared in feedback, and leave out values that are not in it\. Before coding, go through every described value, decide membership for each one, and hard\-code the complete member set\.”

### A\.3\.Implementation details

All methods use the official prompts and algorithms with task\-specific placeholders filled in; the frozen agent uses the same solver prompt with an empty state\. A practice attempt is one submitted program\. Training\-Free GRPO samples a group of four rollouts within each attempt and, as in the official implementation, extracts experiences only from groups with mixed outcomes\. ReasoningBank retrieves the top memory items by embedding similarity with a local sentence\-transformers model\. EvoSkill’s skill library can exceed the context window at the last levels; in that case we fall back to the previous level’s state and record the fallback\. In the \+ lesson condition, the lesson is appended to every update input and nothing else changes\. The history reference shows the solver every earlier practice program, from all levels so far, with its feedback; the class\-name oracle adds one line per label \(“review queue B8 stands for: founding member airlines of Star Alliance”\) and an instruction to apply each rule to exactly the members of the named grouping\.

##### GEPA note\.

GEPA folds every detail of the practice task into its evolved prompt, including the practice aggregation \(largest total\), which then overrides the test task \(sum\)\. All GEPA results in the main text therefore append one fixed note to its reflection input: “Note on the policy: it will also be used for this level’s test task, which has the same records and rules but may ask for a different output \(for example a different aggregation over the entities\)\. Keep the policy about which records count and which rules apply; do not state the output aggregation or format, and let each task’s own instructions decide them\.” Under explicit feedback, the original GEPA without any note reaches 6\.8% average accuracy \(self\), with 137 of its 160 test programs \(self and \+ lesson\) returning the practice aggregation\. A variant whose note gives the test aggregation as its example \(“for example the sum over all entities instead of the largest total”\) reaches 50\.8% \(self\) and 62\.5% \(\+ lesson\); the neutral note of the main results reaches 49\.5% and 66\.0%\.

### A\.4\.Example task and feedback

Excerpts from the level\-1 practice task of chain TR1 and the feedback on a first attempt that excluded no airline\.

Practice task \(excerpt\)Each flight segment on a submitted expense claim counts once toward the total of the department of the employee who filed that claim\. Return the largest total among the departments in the input, as an int\.Field notes: \- A segment whose airline is ’Lufthansa’ is in review queue B8\. Each label in the field notes stands for a real\-world category of values; a note gives one member of that category, and the label’s name does not say which category it is\.Level rules: L1: From this level on, segments in review queue B8 are not counted\.Value reference: \- Air Canada \-\- Airline based in Canada\. \- ITA Airways \-\- Airline based in Italy\. \- Thai Airways \-\- Airline based in Thailand\. \- United Airlines \-\- Airline based in US\. …

Feedback on attempt 1 \(excerpt\)Wrong\. Your submission gives a wrong result on the input below, which is one of the hidden test inputs\. …Compared with the example input, this input differs only in: segments\.airline: one value ’Air Dabia’ was replaced by ’Thai Airways’; segments\.airline: one value ’Air Burkina’ was replaced by ’ITA Airways’\. ’Thai Airways’ belongs to review queue B8, like ’Lufthansa’, so the record with this value is not counted\. ’ITA Airways’ does not belong to review queue B8, so the record with this value is still counted\.