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T-GADE: Thermodynamical Generative-AI-Driven Evolution of LLM Artifacts

Kyoko Ogawa, Naoki Mori

arXiv:2609.12286v1cs.AIcs.NE

TL;DR

Controlling diversity as well as generation is a challenge when evolving structured LLM outputs such as explanations paired with code. T-GADE combines LLM-based genetic operators with artifact-level diversity in a shared free-energy framework. Generational Bose-type T-GADE reduced median training excess relative to EoH, and validation selection among its top two candidates matched EoH’s median transfer excess.

  • Problem

    Artifact evolution must address which differences constitute useful diversity and how survival should control it, because distinct program texts may behave identically.

    Source: §I · p. 1

  • Method

    T-GADE extends thermodynamical genetic algorithms with LLM-based genetic operators and artifact-level diversity under a shared free-energy objective.

    Source: §I · p. 1, §VII · p. 9

  • Results

    0.815% median training excess for generational Bose-type T-GADE at T = 0.003 versus 1.152% for EoH; validation selection among its top two candidates reached 0.496% median transfer excess, matching EoH.

    Source: A. Training performance · p. 5, D. Final populations and individual… · p. 7, §VII · p. 9

  • Takeaways & Limitations

    The results identify population retention and post-search candidate selection as important alongside LLM generation.

    Source: §VII · p. 9

    The study evaluates single heuristics rather than jointly used artifacts and establishes neither universal superiority nor all interactions among temperature, occupancy, and update form.

    Source: D. Task suitability and scope · p. 8

Abstract

from arXiv · show

Integrating evolutionary computation and large language models (LLMs) requires control of population diversity as well as generative capability. Among LLM outputs, those with explicit structure, such as a description paired with code, are structured artifacts; we use artifact for short. We propose T-GADE, which evolves these artifacts by extending thermodynamical genetic algorithms through LLM-based genetic operators and artifact-level diversity evaluation. A common free-energy objective supports generational and steady-state updates, with Fermi-type occupancy excluding repeated genotypes and Bose-type occupancy permitting them. We establish exact one-member removal and conditions for recovering the zero-temperature survival rule of Evolution of Heuristics (EoH). On the online bin-packing task studied in the EoH paper, excess measures relative bin-count overhead above a volume lower bound. Training excess uses search instances; transfer excess uses instances with another bin capacity. Generational Bose-type T-GADE at $T=0.003$ reduced median training excess by approximately 29%, from 1.152% to 0.815%, over 20 runs per configuration (two-sided Mann-Whitney $p=0.042$, Cliff's $\delta=0.378$). Validation selection among its two highest-ranked final candidates reached the same median transfer excess as EoH, 0.496%. These results demonstrate the utility of thermodynamical selection and validation-based use of retained artifacts.

I. INTRODUCTION

T-GADE addresses the challenge of controlling diversity among LLM-generated artifacts, whose different program texts may behave identically. It extends thermodynamical selection with LLM-based genetic operators and artifact-level diversity, and compares its survival rule with EoH.

I. INTRODUCTION

  • Artifact evolution raises questions about which differences constitute useful diversity and how survival should control it, since distinct program texts can behave identically.Source: §I · p. 1
  • T-GADE extends thermodynamical genetic algorithms with LLM-based genetic operators and artifact-level diversity, separating representation, evaluation, variation, and survival.Its framework encompasses generational and steady-state updates and Fermi-type and Bose-type occupancy; it also establishes conditions for recovering EoH’s zero-temperature survival rule.Source: §I · p. 1

A. LLMs and evolutionary computation

B. Exploration and diversity control

  • T-GADE extends diversity-control approaches such as TDGA to LLM-based genetic operators, artifact-level diversity, and explicit occupancy rules.Related approaches include novelty-based selection, quality-diversity archives, and determinantal point processes.Source: B. Exploration and diversity control · p. 2

III. T-GADE

T-GADE evolves structured artifacts—here, paired explanations and executable code—using LLM variation and execution-based evaluation. A shared free-energy objective balances quality and artifact diversity, with occupancy rules controlling whether genotypes may repeat.

A. Individuals and evaluation

  • An artifact pairs a natural-language explanation with executable code; execution on training instances supplies behavior and objective value for evaluation.The explanation and code form the genotype, while measured features represent artifact differences.Source: A. Individuals and evaluation · p. 2

B. Genetic operators

  • Four operator templates provide crossover-like proposals and mutation-like changes, with operators chosen equally and parents sampled by quality rank.The experiment reuses EoH templates but does not restrict T-GADE to them; it uses no post-generation consistency repair or additional mutation.Source: B. Genetic operators · p. 2

C. Free-energy minimization

  • T-GADE minimizes mean energy minus temperature-weighted artifact diversity, using temperature to control the quality–diversity trade-off.At T = 0 selection uses quality alone; at T > 0 it includes diversity, and selection temperature is distinct from LLM sampling temperature.Source: C. Free-energy minimization · p. 2

D. Fermi-type and Bose-type occupancy

  • Fermi-type occupancy permits one individual per genotype, whereas Bose-type occupancy permits repeats; either rule can accompany either update form.Genotype identity requires identical explanations and code, not code equality alone; generational Bose-type selection can select a candidate repeatedly, while steady-state selection does not create copies.Source: D. Fermi-type and Bose-type occupancy · p. 2, Figure 1 · p. 3

E. Generational update

The generational update freezes the parent population, generates children, and greedily constructs survivors by minimizing free energy. Fermi-type selection excludes repeated genotypes, while Bose-type selection leaves candidates available for repeated selection.

E. Generational update

  • The update pools N parents with N + 1 proposed children, then constructs a new population by selecting evaluated candidates in sequence.It first selects a minimum-energy candidate; each later addition minimizes the free-energy increment for the selected set.Source: E. Generational update · p. 3
  • Fermi-type selection removes every candidate with a selected genotype, whereas Bose-type selection leaves candidates available for repeated selection.Fermi-type construction requires N distinct valid genotypes.Source: E. Generational update · p. 3
  • Given feature inner products, the Schur complement evaluates each diversity increment in O(|P|^2) operations per block, but a global approximation guarantee remains future work.The objective is submodular on a fixed labeled candidate set, but normalization, quality-based initialization, and occupancy constraints are not covered by the stated monotone-submodular greedy guarantee.Source: E. Generational update · p. 3

F. Steady-state update

The steady-state update registers evaluated candidates in completion order and repeatedly removes the individual whose removal leaves the lowest-free-energy survivors. Its one-member optimality result applies to a single removal from a fixed pool.

F. Steady-state update

  • Steady-state selection filters candidates by occupancy rule and, when more than N remain, removes the individual whose removal minimizes survivor free energy.Fermi-type filtering keeps the first per genotype, Bose-type does not deduplicate, and the EoH rule keeps the first per objective value.Source: F. Steady-state update · p. 3
  • For a fixed pool of N + 1 labeled individuals where every one-member removal is admissible, the rule minimizes free energy over all N-member subpopulations.Each such subpopulation is the complement of exactly one individual, so the rule compares all possible complements.Source: F. Steady-state update · p. 3
  • The one-member result concerns one removal from a fixed pool; removal from a larger pool is sequential.Source: F. Steady-state update · p. 3

G. Relation to EoH

The section establishes when steady-state T-GADE reproduces EoH’s ordered survivors. The identity depends on shared candidate ordering and filtering, monotone energy, and specified tie-breaking.

G. Relation to EoH

  • EoH’s manager filters failures, keeps the first candidate at each recorded objective value, and retains up to N candidates in ascending objective order.Source: G. Relation to EoH · p. 4
  • Steady-state selection at T = 0 returns EoH’s ordered survivors under the stated filtering, energy, tie-breaking, and output-order conditions.Energy must be nondecreasing in objective, and ties remove the larger objective first.Source: G. Relation to EoH · p. 4
  • At zero temperature, minimizing mean survivor energy removes a worst individual repeatedly, leaving the lowest objective values after tie resolution.Stable output ordering then gives the same result.Source: G. Relation to EoH · p. 4
  • The identity concerns common input and does not guarantee identical search trajectories.Source: G. Relation to EoH · p. 4

A. Task and measurements

The experiment adopts EoH’s online bin-packing task and evaluator, then compares population-management settings under shared generation conditions. It also specifies the diversity representation and evaluation protocol.

A. Task and measurements

  • The online task assigns each arriving item to a feasible bin that cannot later be changed; fewer bins are better.Training uses five Weibull instances, each with 5,000 items and bin capacity 100, and measures bin use relative to a volume lower bound.Source: A. Task and measurements · p. 4
  • Five capacity-100 instances provide confirmation evaluation, while five capacity-500 instances provide transfer evaluation.Confirmation and transfer average instance-wise excess ratios; training inherits EoH’s ratio-of-sums evaluator.Source: A. Task and measurements · p. 4
  • Diversity is represented by a normalized 10,000-dimensional vector concatenating fill ratio and tightness rank across 5,000 placement decisions on the first training instance.Fill ratio measures post-placement occupancy; tightness rank is the normalized position among feasible bins ordered by residual capacity.Source: A. Task and measurements · p. 4

B. Comparison conditions

  • All configurations share Qwen3-32B, eight initial individuals, four operator templates, and the evaluator; generated programs run in isolation with a 30-second training timeout.The lexical gate rejects recognized random-number APIs but does not remove stochasticity from LLM generation; confirmation and transfer have 180-second per-instance timeouts.Source: B. Comparison conditions · p. 4
  • Generational updates freeze eight parents and propose nine children, while steady-state updates begin when the first new candidate is registered.Steady-state runs use 800 logical requests and generational runs use 792; additional controls test independent generation and evolution without quality selection.Source: B. Comparison conditions · p. 4

C. Aggregation and statistical comparison

The paper compares run-level training outcomes and evaluates how candidates are selected from final populations. It reports a training advantage for one generational Bose-type setting and distinguishes validation selection from test-informed diagnostics.

C. Aggregation and statistical comparison

  • The unit of analysis is one search run, with median excess, IQR, and threshold counts reported; the six-setting comparison is not a complete factorial experiment.Rank comparisons round excess fractions to five decimal places, preserving ranks and ties.Source: C. Aggregation and statistical… · p. 5

D. Choosing an individual from the final population

  • Validation selection ranks the top k final individuals by training objective, chooses among them using one fixed capacity-500 instance, and scores the selected candidate on the other four tests.Test-informed selection instead chooses and reports one candidate using its mean excess on all five transfer instances; this is a diagnostic, not a per-instance ensemble oracle.Source: D. Choosing an individual from the… · p. 5

A. Training performance

  • Generational Bose-type T-GADE at T = 0.003 had the lowest median training excess among tested configurations: 0.815% versus EoH’s 1.152%, a 0.337-percentage-point or approximately 29% decrease.The two-sided Mann–Whitney comparison yielded p = 0.042 and Cliff’s δ = 0.378.Source: A. Training performance · p. 5
  • The median relative gap to the offline optimum is at most 0.815% for this T-GADE setting over the five training instances in aggregate.This follows from the offline optimum lying between the volume lower bound and any feasible bin count.Source: A. Training performance · p. 5
  • 15/20 runs for this T-GADE setting reached at most 1% training excess, compared with 8/20 for EoH; raising its temperature to 0.03 gave a 1.056% median.Figure 2(a) plots training excess against the fraction of runs at or below each excess.Source: A. Training performance · p. 5

B. Search progress and offspring quality

Search progress, steady-state survival, and final-population selection show different aspects of T-GADE’s performance: best-so-far training excess declines, survival sometimes departs from quality-only truncation, and validation selection improves transfer results.

C. Steady-state selection activity

  • 28.5% was the median run-level cutoff-change rate for Bose-type steady-state selection at T = 0.003, versus no changes across 13,032 removals under the EoH occupancy rule at T = 10^-5.The contrast changes both occupancy and temperature; cutoff changes describe departures from quality truncation, not better performance.Source: Figure 2 · p. 6, C. Steady-state selection activity · p. 7

B. Search progress and offspring quality

  • 2.8% of E1 children and 13.0% of M2 children improved on their best recorded parent; run-level median improvement fractions were 2.4% and 10.8%, respectively.Operators use different parent sets and counts, so these are not comparisons on identical parents.Source: B. Search progress and offspring quality · p. 6
  • 1.02% median best-so-far training excess was reached by 540 calls, 0.84% by 720 calls, and 0.815% at 792 calls for generational Bose-type T-GADE at T = 0.003.Figure 3 tracks historical best values; generational endpoints in Table II use final populations, which can differ when the historical best is not retained.Source: B. Search progress and offspring quality · pp. 5–6, Figure 3 · p. 7

D. Final populations and individual selection

  • 0.496% median transfer excess was reached by validation selection among the top two generational Bose-type candidates at T = 0.003, matching EoH under the same procedure.Training selection yielded 0.962%; the 0.496% result remained unchanged at shortlist lengths 4 and 8.Source: Figure 4 · p. 7, D. Final populations and individual… · p. 7
  • 18% of generational Bose-type slots at T = 0.003 had mean transfer excess above 10%, compared with 6% for Fermi-type selection, 31% for Bose-type at T = 0.03, and 9% for EoH.Training quality and the prevalence of transfer-poor individuals exhibited different patterns.Source: D. Final populations and individual… · pp. 7–8, Table IV · p. 8

E. Independent generation and evolution without quality selection

Additional controls compare evolutionary variation and quality-based retention with independent generation. The paper also describes how occupancy and update timing shape T-GADE’s population management.

E. Independent generation and evolution without quality selection

  • Median training excess decreased from independent generation to evolution without quality selection and then to EoH in the ten-seed controls.The control without quality selection changes both parent and survivor selection, so it isolates neither component.Source: E. Independent generation and… · p. 8

A. Selecting for quality and diversity

  • Generational Bose-type T-GADE at T = 0.003 improved training performance over EoH, while additional controls support variation and evaluation-based retention beyond repeated independent generation.The controls support variation and evaluation-based retention of generated artifacts beyond repeated independent generation.Source: A. Selecting for quality and diversity · p. 8
  • Increasing temperature from 0.003 to 0.03 did not improve generational training performance; diversity supports useful exploration, not maximization without regard to quality.LLM operators modify artifacts while survival uses measured quality and diversity, allowing selection to change without replacing the model.Source: A. Selecting for quality and diversity · p. 8

B. Occupancy and update form

  • Fermi-type occupancy reserves room for distinct genotypes, whereas Bose-type occupancy allows repeated candidates without requiring repetition; temperature weights diversity within the quality–diversity balance.Intermediate integer occupancy caps define other admissible populations.Source: B. Occupancy and update form · p. 8
  • Evaluated candidates affect generation after a batch or at each registration; Bose-type repetition arises during generational construction or can be retained from steady-state inputs.Both update forms can also use the Fermi-type rule.Source: B. Occupancy and update form · p. 8

C. Using retained candidates

The section distinguishes retained-population selection for transfer from training optimization, then addresses T-GADE’s scope and future analysis of explanation–code inheritance.

C. Using retained candidates

  • Validation among the top two reduced median transfer excess from 0.962% to 0.496%; fewer Fermi slots above 10% transfer excess did not yield a lower validation-selected median.Population composition and selected-individual quality are complementary measures; test-informed selection uses information unavailable for deployment.Source: C. Using retained candidates · p. 8

D. Task suitability and scope

  • Online bin packing evaluates quality and behavior by execution; training-only diversity does not directly reward differences useful at another capacity, and causality remains untested.Near low excess, endpoint and candidate selection become consequential.Source: D. Task suitability and scope · p. 8
  • The task evaluates single heuristics, not jointly used artifacts; broader tasks and models, repeated validation splits, adaptive temperature, and interactions among design choices remain open.The present design establishes neither universal superiority nor all interactions among temperature, occupancy, and update form.Source: D. Task suitability and scope · p. 8
  • T-GADE requires an energy evaluator, diversity features, and LLM-based genetic operators, while feature blocks can represent documents, workflows, graph designs, and prompt sets.Evaluation may involve an LLM, making quality and diversity measurement a central design question.Source: D. Task suitability and scope · pp. 8–9

E. Directions for analyzing explanation–code inheritance

  • Proposed inheritance diagnostics include behavior-group entropy [23], valid-code rate, behavioral disagreement, objective distributions, and code–explanation–code round trips.These analyses remain future work.Source: E. Directions for analyzing… · p. 9

VII. CONCLUSION

  • T-GADE extends thermodynamical genetic algorithms through LLM-based genetic operators and artifact-level diversity, with one free-energy objective spanning generational and steady-state updates and Fermi- and Bose-type occupancy.The paper establishes exact one-member removal and conditions for recovering EoH’s zero-temperature survival rule.Source: §VII · p. 9
  • Across 20 runs per configuration, generational Bose-type T-GADE at T = 0.003 reduced median training excess by approximately 29% relative to EoH, and validation among its top two candidates reached EoH’s median transfer excess.The conclusion identifies population retention and post-search candidate selection as important alongside LLM generation.Source: §VII · p. 9
  • Future work includes richer structured artifacts, task-appropriate diversity representations, adaptive temperature control, and analysis of explanation–code inheritance stability.The framework supports analysis of temperature, occupancy, and update form alongside performance.Source: §VII · p. 9

APPENDIX A EVALUATION AND AGGREGATION DETAILS

The appendix specifies run accounting and selection aggregation, then gives the Schur-complement computation used for diversity increments.

A. Seeds, endpoints, and precision

B. Validation and test-informed selection

  • Validation and test-informed selection use a fixed validation index and report medians across runs of a five-instance mean; test-informed selection chooses one candidate for all five instances.Ties preserve training order.Source: B. Validation and test-informed… · p. 9

C. Generation and evaluation accounting

  • Generational runs make 88 × 9 = 792 generation requests; steady-state regeneration requests count toward an 800-request cap, while reevaluation uses no LLM generation.Unsuccessful proposals leave generational vacancies; transport retries are counted separately.Source: C. Generation and evaluation accounting · p. 9

APPENDIX B SCHUR-COMPLEMENT COMPUTATION

  • For each feature block, log dℓ(y) is the unnormalized log-determinant gain; combined with the mean-energy increment it gives diversity increment (3), computable in O(n^2) per block.Regularization makes each Gram matrix positive definite, so dℓ > 0 in exact arithmetic; the logarithm and normalized increment may be zero or negative.Source: Appendix B · p. 10
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