AlgoEvolve: LLM-driven Meta-evolution of Algorithmic Trading Programs

# AlgoEvolve: LLM-driven Meta-evolution of Algorithmic Trading Programs
Source: [https://arxiv.org/html/2606.26173](https://arxiv.org/html/2606.26173)
Dr\. Gautam Shroff21Indraprastha Institute of Information Technology, Delhi 2Indraprastha Institute of Information Technology, Delhi \{dhruv22170, gautam\.shroff\}@iiitd\.ac\.in

###### Abstract

Recent work shows that Large Language Models \(LLMs\) can act as semantic mutation operators for the evolutionary discovery of programs and proofs\. Most current applications focus on static coding benchmarks\. We extend this paradigm to algorithmic trading\. This domain is uniquely challenging because it is noisy, non\-stationary, and highly discontinuous\. We present AlgoEvolve, an LLM\-driven evolutionary framework that generates, evaluates, and iteratively improves executable trading strategies\. These strategies are expressed as Python code and evaluated through a rigorous testing protocol\. Across multiple experiments, the system exhibits emergent regime\-adaptive strategy logic, including autonomous shifts in trading rules\. We further introduce a meta\-evolutionary outer loop that evolves the prompts guiding program synthesis in the inner loop\. This outer loop discovers improved search heuristics\. These heuristics balance exploration and exploitation while reducing zero\-trade failures\. They consistently outperform initial human\-designed instructions\. The results demonstrate that LLM\-based semantic evolution provides a viable approach for continual program synthesis in complex environments\.

## 1Introduction

Procedures that aim to discover optimal strategies for algorithmic trading in financial markets, e\.g\., using machine\-learning, need to synthesize and select heterogeneous market signals as well as adapt to non\-stationary regimesHamblyet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib10)\); Yuet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib30)\); Liet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib11)\)\. A trading strategy’s performance \(i\.e\., profit and loss\) is most often a non\-differentiable and highly discontinuous function of any parameters it may choose to use \(e\.g\., thresholds, model weights etc\.\)Zhanget al\.\([2020](https://arxiv.org/html/2606.26173#bib.bib12)\), due to the noisy character of the domain, i\.e\., a very low signal\-to\-noise ratioLim and Zohren \([2021](https://arxiv.org/html/2606.26173#bib.bib13)\)\. Traditional deep learning and reinforcement learning \(RL\) approaches are also limited by their reliance on ’black\-box’ parametric optimization, lacking the transparency often required by regulatory frameworksArsenaultet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib15)\)\. These are also prone to overfitting to historical noiseDe Prado \([2018](https://arxiv.org/html/2606.26173#bib.bib14)\), leading to severe degradation during abrupt regime shifts\.

Recently, Large Language Models \(LLMs\) have demonstrated their potential in financial decision\-making and addressing the limitations of parametric models: Beyond serving as multi\-modal feature extractorsChenet al\.\([2021](https://arxiv.org/html/2606.26173#bib.bib18)\); Yanget al\.\([2023b](https://arxiv.org/html/2606.26173#bib.bib19)\), LLMs exhibit emergent capabilities in capturing long\-range temporal dependencies and generalizing across diverse market regimes through in\-context learningJinet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib20)\); Yuet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib21)\)\. However, while these models are being increasingly used as ”agentic” controllers, they have primarily been evaluated as one\-shot generators or static predictors\. We propose using LLMs as semantic mutation operators capable of iterative program refinement\. By drawing inspiration from recent breakthroughs in symbolic discovery such as FunSearchRomera\-Paredeset al\.\([2024](https://arxiv.org/html/2606.26173#bib.bib22)\)and AlphaEvolveNovikovet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib23)\), as well as the scaling of test\-time compute through iterative editingEhrlichet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib27)\), we demonstrate that LLMs can participate in an iterative evolutionary discovery process, generating and continually improving executable algorithmic trading strategies\.

![Refer to caption](https://arxiv.org/html/2606.26173v1/x1.png)Figure 1:The AlgoEvolve Framework\.Our hierarchical architecture co\-evolves symbolic trading policies and their discovery heuristics\. \(A\) The Inner Loop utilizes an LLM as a semantic mutation operator to iteratively refine executable Python strategies, evaluated via a rigorous walk\-forward protocol\. \(B\) The Outer Loop performs meta\-evolution on the Prompt Genome, discovering superior search instructions that adapt to market non\-stationarity and stabilize the discovery process against common failure modes like ”zero\-trade” stagnation\.We introduceAlgoEvolve, a hierarchical framework where the LLM functions as a semantic mutation operator to discover executable trading policies\. Building upon the ”coding agent” paradigm established by AlphaEvolveNovikovet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib23)\), which orchestrates LLM pipelines for scientific discovery, we propose a specialized bi\-level meta\-evolutionary architecture: An inner loop evolves strategies using LLMs provided with a search prompt, strategy code, and recent performance data\. Additionally, an outer loop evolves the search prompt itself\. Unlike existing approaches that rely on static instructions or unstructured feedbackFernandoet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib42)\); Yanget al\.\([2023a](https://arxiv.org/html/2606.26173#bib.bib17)\), AlgoEvolve treats the prompt as a structuredprompt genome, enabling the system to autonomously discover and refine its own discovery heuristics across shifting market regimes\.

As AlgoEvolve is run continually and iteratively over time, it exhibits qualitative shifts in strategy logic that suggest a departure from simple historical fitting\. We observe autonomous transitions in trading paradigms, where the system independently moves beyond human\-provided trend\-following priors, discovering complex, regime\-adaptive rules such as multi\-factor scoring and price\-action heuristics\. These discovered strategies frequently utilize multi\-bar patterns that mirror human\-engineered structures, yet are optimized for the specific volatility profiles of the target assets\. At the outer level, the meta\-evolutionary layer discoversevolved promptsthat stabilize reasoning and effectively mitigate the ’zero\-trade’ failure modes observed in static LLM\-based search\.

Our contributions are as follows:\(1\)we introduce an end\-to\-end LLM\-driven evolutionary framework for discovering and improving algorithmic trading strategies, resulting in an annualized Sharpe ratio of 5\.60;\(2\)we demonstrate that AlgoEvolve independently abandons human\-designed trend\-following priors to discover superior, regime\-adaptive logic;\(3\)we propose a meta\-evolutionary Outer Loop that evolves the inner loop’s Evolver Prompt itself, enabling autonomous refinement of the search heuristic; and\(4\)we submit that LLM\-based semantic evolution is a viable approach for program synthesis in noisy, non\-differentiable, and high\-dimensional environments such as algorithmic trading\.

## 2Related Work

LLM\-Driven Program SynthesisProgram synthesis has increasingly expanded from one\-shot autoregressive generationNijkampet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib24)\)to iterative discovery, where LLMs act as semantically informed mutation operators within evolutionary architecturesRomera\-Paredeset al\.\([2024](https://arxiv.org/html/2606.26173#bib.bib22)\)\. To manage vast program search spaces, current research integrates LLM reasoning with formal constraints, including syntactic guidance for enumerative synthesisLiet al\.\([2024](https://arxiv.org/html/2606.26173#bib.bib25)\)and grammar\-based structural constraints in hybrid human–LLM workflowsBarkeet al\.\([2022](https://arxiv.org/html/2606.26173#bib.bib26)\)\. Performance in these frameworks is increasingly driven by test\-time compute, leveraging iterative editingEhrlichet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib27)\), population\-based exploration over program proposalsRealet al\.\([2020](https://arxiv.org/html/2606.26173#bib.bib39)\), and execution feedback cyclesYanget al\.\([2023a](https://arxiv.org/html/2606.26173#bib.bib17)\)to resolve complex logic\. Unlike classical Genetic Programming, LLM\-driven evolution better captures semantic intent required for high\-dimensional optimizationFernandoet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib42)\), providing a foundation for synthesis in noisy, discontinuous environments such as algorithmic trading\.

LLMs for Financial Decision MakingLarge language models \(LLMs\) have been increasingly applied to financial tasks, ranging from sentiment analysis and domain\-specific modelingAraci \([2019](https://arxiv.org/html/2606.26173#bib.bib28)\); Wuet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib29)\)to agentic trading systems that perform inference\-time decision makingYuet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib30)\); Zhanget al\.\([2024](https://arxiv.org/html/2606.26173#bib.bib31)\); Wuet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib45)\); Songet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib46)\)\. Recent frameworks further integrate reinforcement learningXionget al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib44)\)or internal competition mechanismsZhaoet al\.\([2025](https://arxiv.org/html/2606.26173#bib.bib47)\)to improve robustness in noisy markets, but rely on continuous model inference during deployment\.

In contrast,*AlgoEvolve*employs LLMs only at design time to synthesize explicit, executable trading strategies\. By evolving symbolic Python programs rather than querying an LLM at runtime, the framework achieves zero inference\-time latency, intrinsic interpretability, and improved robustness to non\-stationary market regimes\. This formulation reframes LLMs as symbolic strategy designers rather than real\-time trading agents, better aligning language\-based reasoning with the operational constraints of algorithmic trading\.

Evolutionary Computation for Financial Strategy DiscoveryEvolutionary methods for trading range from Genetic Programming for symbolic rulesKoza \([1992](https://arxiv.org/html/2606.26173#bib.bib32)\); Potvinet al\.\([2004](https://arxiv.org/html/2606.26173#bib.bib33)\); Brabazon and O’Neill \([2006](https://arxiv.org/html/2606.26173#bib.bib34)\)to portfolio optimizationChanget al\.\([2000](https://arxiv.org/html/2606.26173#bib.bib35)\); Brabazonet al\.\([2008](https://arxiv.org/html/2606.26173#bib.bib36)\)and neuroevolutionary policiesStanley and Miikkulainen \([2002](https://arxiv.org/html/2606.26173#bib.bib37)\); Manahovet al\.\([2019](https://arxiv.org/html/2606.26173#bib.bib38)\)\. While interpretable, these approaches rely on stochastic operators that can yield unstable or brittle strategies in noisy financial environments\. Recent co\-evolutionary frameworks jointly optimize rules and risk, but remain limited to syntactic search without semantic guidance\. AlgoEvolve addresses this gap by replacing random mutation with reasoning\-driven LLM transformations, producing logically consistent modifications informed by execution feedback, thus improving stability in non\-stationary markets\.

Meta\-Evolution and Automated SearchBeyond evolving solutions, research explores optimizing the search process itself through self\-improving frameworksRealet al\.\([2020](https://arxiv.org/html/2606.26173#bib.bib39)\), meta\-learning of optimizersAndrychowiczet al\.\([2016](https://arxiv.org/html/2606.26173#bib.bib40)\), and co\-evolutionary population\-based trainingJaderberget al\.\([2017](https://arxiv.org/html/2606.26173#bib.bib41)\)\. More recently, LLM\-driven systems such as PromptBreederFernandoet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib42)\)and OPROYanget al\.\([2023a](https://arxiv.org/html/2606.26173#bib.bib17)\)demonstrated prompt optimization via self\-referential loops in static textual domains\. AlgoEvolve extends this paradigm to executable program discovery through a hierarchical architecture in which an outer loop evolves a prompt genome\. This enables the autonomous discovery of search heuristics that stabilize exploration and adapt to non\-stationary market regimes, mitigating practical failure modes such as strategy degeneration or zero\-activity collapse\.

## 3Problem Formulation

We formalize the automated discovery of trading strategies as abi\-level, non\-stationary program synthesisproblem\. The goal is to evolve an agent \(strategy\) that adapts to shifting data distributions, and simultaneously evolve a search algorithm \(prompt\) that improves the efficiency of that adaptation\.

### 3\.1Strategy Representation \(The Inner Agent\)

A trading strategy is represented as an executable Python programf∈ℱf\\in\\mathcal\{F\}, whereℱ\\mathcal\{F\}denotes the space of all syntactically valid Python programs expressible under the system’s execution constraints\. Formally, let𝐱t∈ℝd\\mathbf\{x\}\_\{t\}\\in\\mathbb\{R\}^\{d\}be the feature vector at timett\(derived from 5\-minute OHLCV bars\)\. The strategy computes:

f​\(𝐱t\)→y^t∈𝒴,𝒴=\{0,1,2,3,4\}×\{0,1,2,3,4\}f\(\\mathbf\{x\}\_\{t\}\)\\rightarrow\\hat\{y\}\_\{t\}\\in\\mathcal\{Y\},\\quad\\mathcal\{Y\}=\\\{0,1,2,3,4\\\}\\times\\\{0,1,2,3,4\\\}wherey^t\\hat\{y\}\_\{t\}is a tuple where each component encodes a discrete trading signal over short and long horizons respectively\. Unlike parametric models \(e\.g\., Neural Networks\) where optimization occurs in weight spaceΘ\\Theta, here optimization occurs in the discrete, non\-differentiable program spaceℱ\\mathcal\{F\}Koza \([1992](https://arxiv.org/html/2606.26173#bib.bib32)\)\.

### 3\.2Non\-Stationary Objective \(Walk\-Forward\)

Financial markets are non\-stationary, meaning the optimal functionf⋆f^\{\\star\}changes over time\. We model this using aWalk\-Forward ValidationprotocolDe Prado \([2018](https://arxiv.org/html/2606.26173#bib.bib14)\)\. Let the lifespan of the system be divided intoKKtemporal epochs\. At each epochkk, the system has access to a historical window𝒟t​r​a​i​n\(k\)\\mathcal\{D\}\_\{train\}^\{\(k\)\}\. It must produce a strategyfkf\_\{k\}to be deployed on the unseen future window𝒟t​e​s​t\(k\)\\mathcal\{D\}\_\{test\}^\{\(k\)\}\.

The performance metricS​\(f,𝒟\)S\(f,\\mathcal\{D\}\)is defined as a composite fitness score:

S​\(f,𝒟\)=α⋅ℛ​\(f,𝒟\)\+\(1−α\)⋅𝒞​\(f,𝒟\)S\(f,\\mathcal\{D\}\)=\\alpha\\cdot\\mathcal\{R\}\(f,\\mathcal\{D\}\)\+\(1\-\\alpha\)\\cdot\\mathcal\{C\}\(f,\\mathcal\{D\}\)whereℛ\\mathcal\{R\}denotes theTotal Return\(cumulative Profit and Loss\) generated by the strategy, and𝒞\\mathcal\{C\}denotesConsistency, a robustness metric measuring the fraction of assets for which the strategy outperforms the median market performance\. Hereα\\alphais a weighting coefficient used to prioritize cross\-asset robustness over single\-asset outperformance, mitigating the risks of non\-stationary distribution shifts\. This also serves to avoid the trivial zero\-exposure optima observed in preliminary Pareto trials where inactivity satisfies risk constraints perfectly\. TheInner Loopoptimization problem at epochkkis to find:

fk⋆=arg⁡maxf∈ℱ⁡S​\(f,𝒟t​r​a​i​n\(k\)\)f\_\{k\}^\{\\star\}=\\arg\\max\_\{f\\in\\mathcal\{F\}\}S\(f,\\mathcal\{D\}\_\{train\}^\{\(k\)\}\)The ultimate objective, however, is to maximize thegeneralizationto the unseen future:∑k=1KS​\(fk⋆,𝒟t​e​s​t\(k\)\)\\sum\_\{k=1\}^\{K\}S\(f\_\{k\}^\{\\star\},\\mathcal\{D\}\_\{test\}^\{\(k\)\}\)\.

### 3\.3Meta\-Evolution \(The Outer Loop\)

The success of the Inner Loop depends on the search heuristic, governed by theEvolver PromptPP\. Let𝒜​\(P,𝒟t​r​a​i​n\)\\mathcal\{A\}\(P,\\mathcal\{D\}\_\{train\}\)denote the stochastic optimization procedure \(Inner Loop\) driven by promptPP\. TheOuter Looptreats the promptPPas a learnable hyper\-parameter\. Its goal is to find the promptP⋆P^\{\\star\}that maximizes the expected Inner Loop performance:

P⋆=arg⁡maxP∈𝒫⁡𝔼𝒟​\[S​\(𝒜​\(P,𝒟t​r​a​i​n\),𝒟t​e​s​t\)\]P^\{\\star\}=\\arg\\max\_\{P\\in\\mathcal\{P\}\}\\mathbb\{E\}\_\{\\mathcal\{D\}\}\\left\[S\\left\(\\mathcal\{A\}\(P,\\mathcal\{D\}\_\{train\}\),\\mathcal\{D\}\_\{test\}\\right\)\\right\]This formulation frames the problem asAlgorithm Discovery: finding a natural language instructionPPthat induces an effective search policy in the discrete program spaceℱ\\mathcal\{F\}\. This formulation explicitly captures both non\-stationary adaptation and self\-improving search within a unified optimization frameworkHospedaleset al\.\([2022](https://arxiv.org/html/2606.26173#bib.bib48)\)\.

## 4Methodology: The AlgoEvolve Framework

We proposeAlgoEvolve\(Figure[1](https://arxiv.org/html/2606.26173#S1.F1)\), a hierarchical evolutionary framework designed to discover trading strategies in non\-stationary environments\. The system consists of two interacting optimization loops: anInner Loopthat evolves executable Python strategies \(ff\) and anOuter Loopthat evolves the natural language instructions \(PP\) guiding the search\.

### 4\.1The Inner Evolutionary Loop

The Inner Loop functions as a semantic variation\-selection engine\. Its goal is to approximate the optimal strategyf⋆f^\{\\star\}for a given temporal window\. Inner loop execution is controlled by two distinct prompts:

- •The System Prompt \(Fixed\):Defines the immutable computational environment, including the dataset structure, allowed Python libraries, and strict I/O constraints \(signature enforcement\)\. This prompt is*never*evolved to ensure code validity\.
- •The Evolver Prompt \(Evolved\):Defines the search heuristic, reasoning style, and creative constraints\. This prompt \(PP\) is the object of meta\-evolution\.

#### 4\.1\.1Prompt Construction via In\-Context Learning

At generationtt, the system constructs the input context\. To ensure the LLM has access to historical performance data, the system architecture injects the Top\-2 Best and Top\-2 Worst strategies \(i\.e\., their python code\) from the previous generation accompanied by their historical fitness scores into the context window\. Contrastive signals from ’Worst’ performers enable the LLM to prune ineffective logical branchesRomera\-Paredeset al\.\([2024](https://arxiv.org/html/2606.26173#bib.bib22)\), preventing logic collapse during discovery\. Crucially, the Evolver Prompt \(PP\) determines attention; for example, a prompt might instruct a step\-by\-step analysis of the divergence between the Best and Worst strategies \(strong utilization\), or conversely, disregard local optima to propose a radically novel paradigm \(zero utilization\)\. This modulates the exploration–exploitation trade\-off\.

#### 4\.1\.2LLM as a Semantic Mutation Operator

Unlike random bit\-flipping in Genetic Programming, AlgoEvolve usesChain\-of\-Thought \(CoT\)promptingWeiet al\.\([2022](https://arxiv.org/html/2606.26173#bib.bib43)\)\. CoT enhances the LLM’s capacity for complex symbolic reasoning by enabling it to decompose high\-dimensional mutation tasks into intermediate logical steps\. The LLM must output a<reasoning\>block justifying its proposed changes before outputting the<code\>block\(s\)\. We make this reasoning\-action trajectory a fundamental requirement rather than an optional heuristic\. This ensures mutations are hypothesis\-driven \(e\.g\., ”The previous strategy over\-traded; I will add a volatility filter”\)\. The functional execution ofRunInnerLoop\(see Algorithm[1](https://arxiv.org/html/2606.26173#alg1)\) consists ofNNgenerations of semantic evolution\. At each iterationii, a candidate strategyfif\_\{i\}is synthesized via the mutation operatorℳ​\(fb​e​s​t,ℒ,P\)\\mathcal\{M\}\(f\_\{best\},\\mathcal\{L\},P\)\. The resulting population is then evaluated on𝒟t​r​a​i​n\(k\)\\mathcal\{D\}\_\{train\}^\{\(k\)\}and ranked by the composite fitnessSS, selecting the optimal individual as the parent for the subsequent generation\.

#### 4\.1\.3Walk\-Forward Evaluation

Candidate strategies are evaluated using the sliding\-window protocol defined in Section 3\. The selection pressure is driven by the composite fitness scoreS​\(f\)S\(f\), balancing Total Return \(ℛ\\mathcal\{R\}\) and Consistency \(𝒞\\mathcal\{C\}\)\. Strategies that trigger runtime errors or violate the System Prompt constraints are assigned a fitness of−∞\-\\infty\.

### 4\.2The Meta\-Evolutionary Outer Loop

While the Inner Loop optimizes the solution, the Outer Loop optimizes the search itself by evolving the Evolver PromptPP\.

#### 4\.2\.1The Prompt Genome

We represent the search algorithm as a structured Prompt GenomeGGconsisting of four mutable genes \(θ\\theta\) representing a minimal spanning set for autonomous searchFernandoet al\.\([2023](https://arxiv.org/html/2606.26173#bib.bib42)\)\. Each geneθi\\theta\_\{i\}represents a categorical choice from a curated subspace of natural language instructions\. The functionG\.build\_prompt​\(\)G\.\\text\{build\\\_prompt\}\(\)maps these discrete selections into a concatenated, coherent executive directive\. This formalization allows the outer loop to perform targeted optimization over specific search behaviors:

1. 1\.θm​u​t​a​t​i​o​n\\theta\_\{mutation\}: The instruction for modifying code \(e\.g\., ”Propose five MINOR variants” vs\. ”Explore BOLD new paradigms”\)\.
2. 2\.θf​o​c​u​s\\theta\_\{focus\}: The creative directive \(e\.g\., ”Focus on combining momentum with volatility”\)\.
3. 3\.θc​o​n​s​t​r​a​i​n​t​s\\theta\_\{constraints\}: Negative search constraints \(e\.g\., ”Do not use look\-ahead bias”\)\.
4. 4\.θr​e​a​s​o​n​i​n​g\\theta\_\{reasoning\}: The analytical framework \(e\.g\., ”Analyze the learning curve”\)\.

#### 4\.2\.2Informed Meta\-Mutation

Standard meta\-learning often treats the optimizer as a black box\. AlgoEvolve employsInformed Meta\-Mutation, where a ”Meta\-LLM” acts as a research scientist rewriting the genome based on empirical evidence\. After an Inner Loop run, the Meta\-LLM receives aPerformance Reportcontaining:

- •Learning Curve Trajectory:To detect stagnation or instability\.
- •Failure Rate:The percentage of candidates that errored \(indicating overly restrictive constraints\)\.
- •Champion Anatomy:The breakdown of Return vs\. Consistency\.

The Meta\-LLM is instructed to rewrite exactly one gene to address specific deficiencies identified in the report \(e\.g\., ”The search stagnated; rewriteθm​u​t​a​t​i​o​n\\theta\_\{mutation\}to increase exploration”\)\. By grounding mutations in the Performance Report, this mechanism mitigates meta\-learning credit assignment challenges\. Rather than performing a stochastic random walk in the prompt space, the Meta\-LLM identifies the causal drivers of search failure—such as gradient stagnation or logic collapse—and applies a targeted update to the relevant gene\.

#### 4\.2\.3Meta\-Crossover

To combine successful heuristics, we employ uniform crossover in the prompt space\. Given two elite genomes, a child genome is created by independently sampling genes from either parent, allowing the system to combine, for example, theReasoning Styleof a stable parent with theCreative Focusof a high\-return parent\.

Algorithm 1AlgoEvolve Meta\-Learning ProcedureInput:Initial Prompt Population𝒫0\\mathcal\{P\}\_\{0\}, Meta\-GenerationsKKOutput:Best Found Prompt GenomeG⋆G^\{\\star\}

1:Initialize population

𝒫←𝒫0\\mathcal\{P\}\\leftarrow\\mathcal\{P\}\_\{0\}
2:formeta\-generation

k=1k=1to

KKdo

3:

ℱ←∅\\mathcal\{F\}\\leftarrow\\emptyset,

ℒ←∅\\mathcal\{L\}\\leftarrow\\emptyset
4:foreachGenome

G∈𝒫G\\in\\mathcal\{P\}do

5:

Pt​e​x​t←G\.build\_prompt​\(\)P\_\{text\}\\leftarrow G\.\\text\{build\\\_prompt\}\(\)
6:

logs,ℋ←RunInnerLoop​\(Pt​e​x​t,𝒟t​r​a​i​n\(k\)\)\\text\{logs\},\\mathcal\{H\}\\leftarrow\\text\{RunInnerLoop\}\(P\_\{text\},\\mathcal\{D\}\_\{train\}^\{\(k\)\}\)\{

ℋ\\mathcal\{H\}is the trajectory of candidate programs\}

7:

f⋆←argmaxf∈ℋ​S​\(f,𝒟t​r​a​i​n\(k\)\)f^\{\\star\}\\leftarrow\\text\{argmax\}\_\{f\\in\\mathcal\{H\}\}S\(f,\\mathcal\{D\}\_\{train\}^\{\(k\)\}\)\{Extract strategy maximizing composite fitness

SS\}

8:

ℱ​\[G\]←CalculateFitness​\(f⋆,𝒟t​e​s​t\(k\)\)\\mathcal\{F\}\[G\]\\leftarrow\\text\{CalculateFitness\}\(f^\{\\star\},\\mathcal\{D\}\_\{test\}^\{\(k\)\}\)
9:

ℒ​\[G\]←logs\\mathcal\{L\}\[G\]\\leftarrow\\text\{logs\}
10:endfor

11:

𝒫n​e​x​t←\{argmaxG​ℱ​\[G\]\}\\mathcal\{P\}\_\{next\}\\leftarrow\\\{\\text\{argmax\}\_\{G\}\\mathcal\{F\}\[G\]\\\}\{Elitism\}

12:while

\|𝒫n​e​x​t\|<\|𝒫\|\|\\mathcal\{P\}\_\{next\}\|<\|\\mathcal\{P\}\|do

13:

p1,p2←SelectTop​\(𝒫,ℱ\)p\_\{1\},p\_\{2\}\\leftarrow\\text\{SelectTop\}\(\\mathcal\{P\},\\mathcal\{F\}\)
14:

c​h​i​l​d←MetaCrossover​\(p1,p2\)child\\leftarrow\\text\{MetaCrossover\}\(p\_\{1\},p\_\{2\}\)
15:

report←GenerateReport​\(ℒ​\[p1\]\)\\text\{report\}\\leftarrow\\text\{GenerateReport\}\(\\mathcal\{L\}\[p\_\{1\}\]\)
16:

c​h​i​l​d←MetaMutate​\(c​h​i​l​d,report\)child\\leftarrow\\text\{MetaMutate\}\(child,\\text\{report\}\)
17:

𝒫n​e​x​t\.add​\(c​h​i​l​d\)\\mathcal\{P\}\_\{next\}\.\\text\{add\}\(child\)
18:endwhile

19:

𝒫←𝒫n​e​x​t\\mathcal\{P\}\\leftarrow\\mathcal\{P\}\_\{next\}
20:endfor

21:return

argmaxG​ℱ​\[G\]\\text\{argmax\}\_\{G\}\\mathcal\{F\}\[G\]

## 5Experiments

### 5\.1Experimental Setup

#### 5\.1\.1Market Environment and Feature Representation

We evaluate AlgoEvolve on the NUMIN111[https://pypi\.org/project/numin/](https://pypi.org/project/numin/)platform, a publicly availableintradaypaper trading environment with open programmatic access, providing anonymized multi\-asset equity market data and programmatic strategy evaluation via a Python SDK\. The dataset consists of over 200 trading days of discretized 5\-minute data that includes OHLCV candles, standard technical indicators, as well as 5 and 10 candle returns, normalized by the first close price of each day\. Each trading day is represented by 150 time steps, where rows 0–74 correspond to historical prior\-day context and rows 75–149 represent the active trading session\. Each day’s data is for a different set of 5 \(obfuscated\) stock symbols\. Normalized and obfuscated market data ensures numerical stability and prevents leakage\. The back\-testing SDK takes as input a strategy function and computes its returns for a given set of days as follows: The strategy function is provided data prior to a given 5\-minute tick \(omitting returns that are unavailable at that time\), and decides to buy, sell or hold a stock\. Each position exits 10 candles after entry, and a single open position per stock symbol is enforced\. A fixed0\.1%0\.1\\%\(10bps\) transaction plus slippage cost is enforced to prioritize high\-conviction signals over noise\.

Strategy agents are required to output predictions for the dual multi\-horizon targets defined in Section 3\.1\. We maintain the same five\-class discrete scale𝒴\\mathcal\{Y\}for all discovered logic, ensuring that the semantic mutation process remains grounded in the established numerical stability constraints\.

#### 5\.1\.2Model Configuration and Hyperparameters

We employ a heterogeneous LLM architecture to decouple the high\-latency reasoning required for prompt optimization \(Gemini Pro\) from the high\-throughput generation required for strategy discovery \(Gemini Flash\)\. Critically, since the Gemini Flash ’generator’ remains constant across all ablation stages, the performance gains observed in Stage 4 are isolated to the quality of the evolved instructions rather than a shift in model\-tier capacity\. The Outer Loop utilizes the Pro family for its superior reasoning capabilities and long\-context window, while the Inner Loop leverages the Flash family for rapid iterative refinement\. We set the consistency weighting coefficient empirically asα=0\.7\\alpha=0\.7, as defined in Section 3\.2\.

### 5\.2Evaluation Metrics and Protocols

To rigorously assessAlgoEvolve, we utilize a multi\-dimensional evaluation framework that accounts for absolute profitability, risk exposure, and structural stability across non\-stationary regimes\.

#### 5\.2\.1Performance Metrics

We evaluate strategies using standard financial performance measures that jointly assess return potential and downside risk:Average Daily Profit and Loss \(Avg\. PnL\), the arithmetic mean of daily portfolio returns;Sharpe Ratio, measuring the consistency of alpha generation via risk\-adjusted returns;Return Volatility, representing the variability of portfolio returns; andMaximum Drawdown \(MDD\), quantifying the worst\-case cumulative capital loss from a local peak to a subsequent trough\. All Sharpe ratios are reported on a daily basis unless otherwise stated; annualized values useSann=Sdaily×252S\_\{\\text\{ann\}\}=S\_\{\\text\{daily\}\}\\times\\sqrt\{252\}for industry\-standard comparison\.

#### 5\.2\.2Temporal Evaluation Protocols

We assess the framework across two paradigms:Fixed \(Disjoint\) Window, where the evaluation windowWWshifts by its total length \(e\.g\., 13 days\) to establish long\-term logic stability; andSliding Window, where the window shifts by a single day\. The latter provides high\-frequency feedback, enabling the mutation operator to adapt to immediate market regime shifts\. Together, these protocols provide a view of both economic value and robustness\.

Unlike static ML benchmarks, intraday markets exhibit frequent regime shifts\. We prioritize rapid adaptation under continual distribution shift over asymptotic convergence, utilizing high\-frequency rolling windows to assess semantic mutation\.

### 5\.3Results and Ablation Study

In this section, we analyze the performance of theAlgoEvolveframework through an incremental ablation study\. By isolating the impact of temporal windowing, feedback granularity, and meta\-evolutionary optimization, we demonstrate how the system systematically overcomes market non\-stationarity\.

Prior to the longitudinal study, preliminary calibration experiments were conducted to evaluate the impact of temporal windowing\. Comparing 13\-day disjoint and 5\-day sliding windows, we established that a high\-frequency, 1\-day feedback protocol optimizes for recency bias and minimizes drawdown\. This configuration serves as our ’Standard Evol’ baseline \(Mean:0\.104%0\.104\\%, Daily Sharpe:0\.360\.36, MDD:0\.42%0\.42\\%\), representing the limits of inner\-loop semantic evolution without the adaptive guidance of the meta\-evolutionary outer loop\.

#### 5\.3\.1Meta\-Evolutionary Optimization

![Refer to caption](https://arxiv.org/html/2606.26173v1/selection_pressure_chart.png)Figure 2:Evolution of the Prompt Genome\. Meta\-evolutionary selection identifies elite heuristics achieving anannualized Sharpe of 5\.60against a population mean of 1\.21, representing a363% improvementin risk\-adjusted search efficiency over six meta\-generations\.AlgoEvolve successfully navigates non\-stationary search spaces through autonomous self\-correction, exhibiting a significantselection advantage\(Fig\.[2](https://arxiv.org/html/2606.26173#S5.F2)\)\. If the synthesis was unreliable, resulting in incorrect code being generated, our system treated the prompt genome as having−∞\-\\inftyfitness\.

![Refer to caption](https://arxiv.org/html/2606.26173v1/longitudinal_robustness_ijcai.png)Figure 3:Equity curves under a rolling walk\-forward evaluation\. AlgoEvolve \(Outer Loop\) maintains a stable upward trajectory, while static and parametric baselines exhibit high variance and suffer drawdowns following the regime shift after Day 10\.

### 5\.4Comparative Performance Analysis

To assess robustness under market non\-stationarity, we evaluateAlgoEvolveagainst four standardized baselines: a staticSeedheuristic, a single\-levelStandard Evolablation, and two tuned parametric models \(RF,LSTM\)\. The parametric baselines were trained on a 95\-day dataset \(June–Oct 2024\) utilizing 59 market features: theRandom Forest \(RF\)employs 250 estimators with a depth of 8 over a 30\-candle window, while theLSTMutilizes a 2\-layer architecture \(128 hidden units\) with a 20\-step temporal lookback\. Additionally, we include “Frozen” inner\-loop champions \(G​e​ni→20Gen\_\{i\}\\rightarrow 20\) to measure the rate of strategy decay in the absence of meta\-adaptation \(Table[1](https://arxiv.org/html/2606.26173#S5.T1), Fig\.[3](https://arxiv.org/html/2606.26173#S5.F3)\)\.

Table 1:Comparative performance of strategy discovery methods across a 20\-day benchmark and a 30\-day longitudinal \(6 MG\) evaluation\. AlgoEvolve demonstrates superior risk\-adjusted alpha \(Sharpe: 5\.60\) and autonomous resilience to non\-stationarity\. While parametric baselines \(RF, LSTM\) exhibit high\-variance decay and severe drawdowns \(7\.27%\), our meta\-evolutionary framework identifies elite heuristics that maintain capital preservation \(Max DD: 1\.59%\) while consistently capturing positive mean returns\. AlgoEvolve’s Sharpe here corresponds to the elite Prompt Genome selected under evolutionary pressure, while the population\-level mean Sharpe remains≈1\.21\\approx 1\.21; our claims are therefore comparative and selection\-based rather than reflective of average deployable performance\.Performance Benchmarking\.Table[1](https://arxiv.org/html/2606.26173#S5.T1)showsAlgoEvolve \(6 MG\)achieves the optimal risk\-return profile\. The*Seed Heuristic*fails catastrophically \(−15\.65%\-15\.65\\%loss\), while the*Standard Evol*baseline reveals single\-loop limits: high stability \(MDD0\.42%0\.42\\%\) but muted alpha \(0\.10%0\.10\\%mean\); it lacks the structural verticality required to capitalize on high\-alpha events\. Conversely, our bi\-level architecture unlocks significant “verticality,” increasing mean daily returns to0\.31%0\.31\\%—a3×\\timesimprovement—with an institutional\-grade5\.60 Sharpe\.

Baseline Fragility\.Parametric models exhibit regime\-shift decay: the*RF Baseline*suffers high volatility and severe drawdown \(7\.27%7\.27\\%\), while the*LSTM*fails to extract signal from intraday noise\. AlgoEvolve’s symbolic, rule\-based heuristics act as a natural regularizer, mitigating the high\-frequency overfitting inherent in black\-box models\.

Adaptation Dynamics\.Superior performance is driven by the outer loop’s strategic pivots\. As seen in Fig\.[3](https://arxiv.org/html/2606.26173#S5.F3), the*Standard Evol*curve plateaus, a trend mirrored byFrozen Strategy fossils\(Geni→20\\mathrm\{Gen\}\_\{i\}\\rightarrow 20\) which decay as distributions shift\. AlgoEvolve overcomes this “alpha silence” by identifying theMG 3 drawdown\(−1\.59%\-1\.59\\%\) and autonomously injecting search diversity\. This triggered aV\-shaped recoveryin MG 4, capturing a2\.53%2\.53\\%single\-day alpha event, demonstrating how design\-time reasoning can enable structural adaptation beyond runtime parametric inference\.

## 6Qualitative Analysis

### 6\.1Inner\-Loop Baseline Analysis

Preliminary calibration \(13\-day window\) established the framework’s ability to autonomously pivot from failed trend\-following to mean\-reversion logic, validating the high\-frequency protocol\. Subsequent ablative analysis of the “Standard Evol” \(Inner\-Loop only\) trajectory reveals a distinct three\-phase decay pattern\.

##### Phase 1: Rapid Heuristic Convergence \(Gens 1–4\)\.

In the initial generations, the LLM successfully synthesized a foundational suite of technical indicators\. By Generation 1, the system discovered the utility ofRSI/CMO momentum filtersandSMA trend confirmation\. Reasoning logs show the model attempting to “create high\-granularity signals” by aggregating multiple binary conditions\. However, the logic remained shallow, relying on fixed thresholds \(e\.g\.,buy\_threshold = 4\.0\) that lacked sensitivity to intraday volatility regimes\.

##### Phase 2: The “Zero\-Trade” Stagnation Trap \(Gens 5–12\)\.

The most significant finding in the baseline study was a prolonged period ofsemantic stagnation\. During these eight generations, the system produced a terminal return of0\.0%0\.0\\%\.

- •Logic Collapse:Reasoning traces indicate the LLM attempted to “enhance robustness” by adding increasingly complex conditional layers\. This resulted in unintentionalover\-regularizationof the trading logic\.
- •Syntactic Over\-Smoothing:Because the Evolver Prompt remained static, the LLM became trapped in a loop of minor threshold refinements\. The resulting programs were so conservative that they failed to trigger a single trade across validation assets, identifying a state of“Alpha Silence”: when executable logic could not be generated by the provided instructions\.

##### Analysis: Threshold Fragility and Bi\-Level Necessity\.

As illustrated in Table[2](https://arxiv.org/html/2606.26173#S6.T2), the baseline search eventually attempts to recover from stagnation throughThreshold Fragility\(Gen 20\)—performing stochastic parameter tuning on aggressive ’overextension’ rules rather than structural innovation\. This progression confirms that under static prompts, LLMs as mutation operators are prone to local optima convergence\. A meta\-evolutionary layer is therefore required to mutate the search instructions themselves, forcing the synthesizer to abandon redundant filters and discover the regime\-adaptive architectures seen in the full AlgoEvolve framework\.

Table 2:Evolution of symbolic logic\. The system autonomously transitioned from naive thresholds to weighted multi\-factor scoring architectures\.

### 6\.2Meta\-Evolutionary Dynamics

In contrast, as illustrated in Fig\.[2](https://arxiv.org/html/2606.26173#S5.F2), theAlgoEvolvemeta\-trajectory followedthree distinct evolutionary phasescharacterized by initial optimization, a regime crisis, and a strategic recovery breakthrough\. This corresponds to three distinct Prompt Genome Eras:

##### Era 1: The Refinement Paradigm \(MG1–MG2\)\.

In the initial phase, the meta\-population was dominated by “Convergent DNA” \(e\.g\.,prompt\_12e806c5\), characterized by instructions to“Propose MINOR variants… small, logical refinements\.”This search style was highly effective in stable regimes, identifying a “Confluence Filter” that successfully combined RSI and Bollinger Bands\. In MG2, the system autonomously discovered theHierarchical VWAP Filter\(prompt\_b1c7b1ac\)\. By mandating that all entry logic be gated by VWAP, the Meta\-LLM synthesized a regime\-aware search instruction\. This prevented inner\-loop models from trading against the dominant trend, leading to a cumulative PnL of\+1\.79%\+1\.79\\%\.

##### Era 2: The Resilience Pivot \(MG3–MG4\)\.

The system encountered a performance plateau due to a market regime shift in MG3, where previously optimized logic failed \(Champion loss:−1\.59%\-1\.59\\%, Population mean:−2\.90%\-2\.90\\%\)\. Detailed logs indicate the inner\-loop models were over\-fitting to prior volatility\. In response, the Meta\-LLM executed aStrategic Diversity Injectionin MG4 \(prompt\_94876739\)\. As shown below, the evolvedθf​o​c​u​s\\theta\_\{focus\}gene shifted the search paradigm to overcome the alpha plateau: e\.g\.,“Propose structurally diverse archetypes; explore non\-linear indicator combinations and inverse volatility signals to bypass the current zero\-trade stagnation\.”This transition provides empirical evidence of the system’s capacity to autonomously detect heuristic failure and execute a structural pivot, resulting in a recovery that captured a 2\.53% alpha event in MG4\.

##### Era 3: The Complexity Ceiling \(MG5–MG6\)\.

The final phase of the longitudinal study identifies a complexity saturation point at the frontier of autonomous synthesis\. As meta\-instructions evolved toward high\-density logic, the framework encountered its first syntactic boundary in the final generation\. Crucilly, this served as a validation of the system’s robustness\-aware selection: while a subset of the population errored\(no valid asset results\), the robustness filters successfully quarantined these candidates, assigning them−∞\-\\inftyfitness\. Despite this tail\-end complexity, the search remained productive, with the champion lineage remaining free of invalid code and capturing a significant\+2\.50%\+2\.50\\%alpha event\. This minor blip at the experimental frontier demonstrates that the framework is capable of safe continual discovery, prioritizing execution integrity over speculative complexity\.

Table 3:Qualitative Heuristic Evolution\. The table maps evolved search instructions to their quantitative impact, highlighting the autonomous pivot in MG4\.

## 7Conclusion and Outlook

AlgoEvolve provides a bi\-level evolutionary framework that reframes LLMs as symbolic architects capable of autonomous strategy discovery\. We demonstrated the system’s ability to navigate non\-stationary market regimes, achieving a peak annualized Sharpe ratio of 5\.60\. To address the constraints identified during our study, future work can exploreModular Program Synthesisto overcome the observed complexity ceiling by evolving discrete, reusablesub\-routines\.

## References

- M\. Andrychowicz, M\. Denil, S\. Gomez Colmenarejo, M\. W\. Hoffman, D\. Pfau, T\. Schaul, B\. Shillingford, and N\. de Freitas \(2016\)Learning to learn by gradient descent by gradient descent\.InProceedings of the 30th International Conference on Neural Information Processing Systems,pp\. 3988–3996\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p5.1)\.
- D\. Araci \(2019\)FinBERT: financial sentiment analysis with pre\-trained language models\.arXiv preprint arXiv:1908\.10063\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- P\. Arsenault, S\. Wang, and J\. Patenaude \(2025\)A survey of explainable artificial intelligence \(xai\) in financial time series forecasting\.ACM Computing Surveys57\(10\),pp\. 1–37\.External Links:[Document](https://dx.doi.org/10.1145/3729531)Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1)\.
- S\. Barke, M\. B\. James, and N\. Polikarpova \(2022\)Grounded copilot: how programmers interact with code\-generating models\.arXiv preprint arXiv:2206\.15000\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p1.1)\.
- A\. Brabazon, M\. O’Neill, and I\. Dempsey \(2008\)An introduction to evolutionary computation in finance\.IEEE Computational Intelligence Magazine3\(4\),pp\. 42–55\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- A\. Brabazon and M\. O’Neill \(2006\)Biologically inspired algorithms for financial modelling\.Springer\-Verlag,Berlin, Heidelberg\.External Links:ISBN 3540262520Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- T\.\-J\. Chang, N\. Meade, J\. E\. Beasley, and Y\. M\. Sharaiha \(2000\)Heuristics for cardinality constrained portfolio optimisation\.Computers and Operations Research27\(13\),pp\. 1271–1302\.External Links:[Document](https://dx.doi.org/10.1016/S0305-0548%2899%2900074-X)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- L\. Chen, K\. Lu, A\. Rajeswaran, K\. Lee, A\. Grover, M\. Laskin, P\. Abbeel, A\. Srinivas, and I\. Mordatch \(2021\)Decision transformer: reinforcement learning via sequence modeling\.arXiv preprint arXiv:2106\.01345\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1)\.
- M\. L\. De Prado \(2018\)Advances in financial machine learning\.John Wiley & Sons\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1),[§3\.2](https://arxiv.org/html/2606.26173#S3.SS2.p1.6)\.
- R\. Ehrlich, B\. Brown, J\. Juravsky, R\. Clark, C\. Ré, and A\. Mirhoseini \(2025\)CodeMonkeys: scaling test\-time compute for software engineering\.arXiv preprint arXiv:2501\.14723\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1),[§2](https://arxiv.org/html/2606.26173#S2.p1.1)\.
- C\. Fernando, D\. Banarse, H\. Michalewski, S\. Osindero, and T\. Rocktäschel \(2023\)Promptbreeder: self\-referential self\-improvement via prompt evolution\.arXiv preprint arXiv:2309\.16797\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p3.1),[§2](https://arxiv.org/html/2606.26173#S2.p1.1),[§2](https://arxiv.org/html/2606.26173#S2.p5.1),[§4\.2\.1](https://arxiv.org/html/2606.26173#S4.SS2.SSS1.p1.4)\.
- B\. Hambly, R\. Xu, and H\. Yang \(2023\)Recent advances in reinforcement learning in finance\.Mathematical Finance33\(3\),pp\. 437–503\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1)\.
- T\. Hospedales, A\. Antoniou, P\. Micaelli, and A\. Storkey \(2022\)Meta\-learning in neural networks: a survey\.IEEE Transactions on Pattern Analysis and Machine Intelligence44\(9\),pp\. 5149–5169\.External Links:[Document](https://dx.doi.org/10.1109/TPAMI.2021.3079209)Cited by:[§3\.3](https://arxiv.org/html/2606.26173#S3.SS3.p1.7)\.
- M\. Jaderberg, V\. Dalibard, S\. Osindero, W\. M\. Czarnecki, J\. Donahue, A\. Razavi, O\. Vinyals, T\. Green, I\. Dunning, K\. Simonyan, C\. Fernando, and K\. Kavukcuoglu \(2017\)Population based training of neural networks\.arXiv preprint arXiv:1711\.09846\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p5.1)\.
- M\. Jin, S\. Wang, L\. Ma, Z\. Chu, J\. Y\. Zhang, X\. Shi, P\. Chen, and S\. Pan \(2023\)Time\-llm: time series forecasting by reprogramming large language models\.arXiv preprint arXiv:2310\.01728\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1)\.
- J\. R\. Koza \(1992\)Genetic programming: on the programming of computers by means of natural selection\.MIT Press\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1),[§3\.1](https://arxiv.org/html/2606.26173#S3.SS1.p1.7)\.
- Y\. Li, Y\. Yu, H\. Li, Z\. Chen, and K\. Khashanah \(2023\)TradingGPT: multi\-agent system with layered memory and distinct characters for enhanced financial trading performance\.arXiv preprint arXiv:2309\.03736\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1)\.
- Y\. Li, J\. Parsert, and E\. Polgreen \(2024\)Guiding enumerative program synthesis with large language models\.InProceedings of the International Conference on Computer Aided Verification,Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p1.1)\.
- B\. Lim and S\. Zohren \(2021\)Time\-series forecasting with deep learning: a survey\.Philosophical Transactions of the Royal Society A379\(2194\),pp\. 20200209\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1)\.
- V\. Manahov, R\. Hudson, and A\. Urquhart \(2019\)High\-frequency trading from an evolutionary perspective: financial markets as adaptive systems\.International Journal of Finance & Economics24\(2\),pp\. 943–962\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- E\. Nijkamp, B\. Pang, H\. Hayashi, L\. Tu, H\. Wang, Y\. Zhou, S\. Savarese, and C\. Xiong \(2023\)CodeGen: an open large language model for code with multi\-turn program synthesis\.InProceedings of the International Conference on Learning Representations,Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p1.1)\.
- A\. Novikov, N\. Vu, M\. Eisenberger, E\. Dupont, P\. Huang, A\. Z\. Wagner, S\. Shirobokov, B\. Kozlovskii, F\. J\. R\. Ruiz, A\. Mehrabian, M\. P\. Kumar, A\. See, S\. Chaudhuri, G\. Holland, A\. Davies, S\. Nowozin, P\. Kohli, and M\. Balog \(2025\)AlphaEvolve: a coding agent for scientific and algorithmic discovery\.arXiv preprint arXiv:2506\.13131\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1),[§1](https://arxiv.org/html/2606.26173#S1.p3.1)\.
- J\. Potvin, P\. Soriano, and M\. Vallée \(2004\)Generating trading rules on the stock markets with genetic programming\.Computers and Operations Research31\(7\),pp\. 1033–1047\.External Links:[Document](https://dx.doi.org/10.1016/S0305-0548%2803%2900063-7)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- E\. Real, C\. Liang, D\. R\. So, and Q\. V\. Le \(2020\)AutoML\-zero: evolving machine learning algorithms from scratch\.InProceedings of the 37th International Conference on Machine Learning,pp\. 8007–8019\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p1.1),[§2](https://arxiv.org/html/2606.26173#S2.p5.1)\.
- B\. Romera\-Paredes, M\. Barekatain, A\. Novikov, M\. Balog, M\. P\. Kumar, E\. Dupont, F\. J\. R\. Ruiz, J\. S\. Ellenberg, P\. Wang, O\. Fawzi, P\. Kohli, and A\. Fawzi \(2024\)Mathematical discoveries from program search with large language models\.Nature625,pp\. 468–475\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1),[§2](https://arxiv.org/html/2606.26173#S2.p1.1),[§4\.1\.1](https://arxiv.org/html/2606.26173#S4.SS1.SSS1.p1.2)\.
- Z\. Song, K\. Song, G\. Hu, D\. Qi, J\. Gao, X\. Wang, D\. Li, and C\. Zhao \(2025\)Trade in minutes\!: rationality\-driven agentic system for quantitative financial trading\.arXiv preprint arXiv:2510\.04787\.External Links:[Document](https://dx.doi.org/10.48550/arXiv.2510.04787)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- K\. O\. Stanley and R\. Miikkulainen \(2002\)Evolving neural networks through augmenting topologies\.Evolutionary Computation10\(2\),pp\. 99–127\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p4.1)\.
- J\. Wei, X\. Wang, D\. Schuurmans, M\. Bosma, B\. Ichter, F\. Xia, E\. H\. Chi, Q\. V\. Le, and D\. Zhou \(2022\)Chain\-of\-thought prompting elicits reasoning in large language models\.InAdvances in Neural Information Processing Systems,Vol\.35,pp\. 24824–24837\.Cited by:[§4\.1\.2](https://arxiv.org/html/2606.26173#S4.SS1.SSS2.p1.7)\.
- S\. Wu, O\. Irsoy, S\. Lu, V\. Dabravolski, M\. Dredze, S\. Gehrmann, P\. Kambadur, D\. Rosenberg, and G\. Mann \(2023\)BloombergGPT: a large language model for finance\.arXiv preprint arXiv:2303\.17564\.Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- S\. Wu, J\. Wang, Z\. Guan, L\. Zhao, X\. Song, X\. Ying, D\. Yu, J\. Wang, H\. Zhang, M\. Pak, Y\. He, Y\. Xin, J\. Wang, and T\. Shi \(2025\)MountainLion: a multi\-modal LLM\-based agent system for interpretable and adaptive financial trading\.arXiv preprint arXiv:2507\.20474\.External Links:[Document](https://dx.doi.org/10.48550/arXiv.2507.20474)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- G\. Xiong, Z\. Deng, K\. Wang, Y\. Cao, H\. Li, Y\. Yu, X\. Peng, M\. Lin, K\. E\. Smith, X\. Liu, J\. Huang, S\. Ananiadou, and Q\. Xie \(2025\)FLAG\-trader: fusion llm\-agent with gradient\-based reinforcement learning for financial trading\.InFindings of the Association for Computational Linguistics: ACL 2025,pp\. 13921–13934\.External Links:[Document](https://dx.doi.org/10.18653/v1/2025.findings-acl.716)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- C\. Yang, X\. Wang, Y\. Lu, H\. Liu, Q\. V\. Le, D\. Zhou, and X\. Chen \(2023a\)Large language models as optimizers\.arXiv preprint arXiv:2309\.03409\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p3.1),[§2](https://arxiv.org/html/2606.26173#S2.p1.1),[§2](https://arxiv.org/html/2606.26173#S2.p5.1)\.
- H\. Yang, X\. Liu, and C\. D\. Wang \(2023b\)FinGPT: open\-source financial large language models\.arXiv preprint arXiv:2306\.06031\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1)\.
- Y\. Yu, Z\. Yao, H\. Li, Z\. Deng, Y\. Jiang, Y\. Cao, Z\. Chen, J\. W\. Suchow, Z\. Cui, R\. Liu, Z\. Xu, D\. Zhang, K\. Subbalakshmi, G\. Xiong, Y\. He, J\. Huang, D\. Li, and Q\. Xie \(2025\)FinCon: a synthesized LLM multi\-agent system with conceptual verbal reinforcement for enhanced financial decision making\.InAdvances in Neural Information Processing Systems,Vol\.37,pp\. 137010–137045\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1),[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- Y\. Yu, Z\. Yao, H\. Li,et al\.\(2023\)FinMem: a multimodal agent with hierarchical memory for financial decision making\.arXiv preprint arXiv:2311\.11300\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p2.1)\.
- W\. Zhang, L\. Zhao, H\. Xia, S\. Sun, J\. Sun, M\. Qin, X\. Li, Y\. Zhao, Y\. Zhao, X\. Cai, Y\. Zhang, X\. Wang, and B\. An \(2024\)A multimodal foundation agent for financial trading: tool\-augmented, diversified, and generalist\.InProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining,pp\. 4314–4325\.External Links:[Document](https://dx.doi.org/10.1145/3637528.3671801)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.
- Z\. Zhang, S\. Zohren, and S\. J\. Roberts \(2020\)Deep reinforcement learning for trading\.The Journal of Financial Data Science2\(2\),pp\. 25–40\.Cited by:[§1](https://arxiv.org/html/2606.26173#S1.p1.1)\.
- L\. Zhao, R\. Sun, Z\. Jiang, B\. Yang, Y\. Bai, M\. Chen, X\. Wang, J\. Li, and Z\. Bai \(2025\)ContestTrade: a multi\-agent trading system based on internal contest mechanism\.arXiv preprint arXiv:2508\.00554\.External Links:[Document](https://dx.doi.org/10.48550/arXiv.2508.00554)Cited by:[§2](https://arxiv.org/html/2606.26173#S2.p2.1)\.