STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery
Jiarui Su, Songjun Tu, Bei Sun, Xiaojun Liang
Abstract
LLM-based equation discovery offers a promising route to recovering symbolic laws from data, but many systems still rely on generation-centered loops that propose candidates, fit parameters, score results, and reuse selected examples. Such loops can misjudge useful skeletons under unreliable fitting, discard near-correct equations that require repair, and accumulate redundant memories that provide limited guidance. We propose STRIDE, a self-reflective agent framework that improves reliability by coordinating data-aware generation, mixed-fitting evaluation, critic--executor repair, and diversity-preserving semantic memory. By turning fitted scores and candidate behavior into shared feedback, STRIDE enables equations to be proposed, assessed, refined, and reused within a closed-loop discovery process. Experiments on representative symbolic-regression benchmarks and LSR-Synth suites show that STRIDE improves accuracy, OOD robustness, and structural recovery across multiple LLM backbones, with ablations and analyses confirming the contribution of its core components.
AI Impact Assessments
(1 model)Scientific Impact Assessment: STRIDE
1. Core Contribution
STRIDE frames LLM-based equation discovery as a multi-role reflective agent workflow rather than a generation-centered loop. It introduces four coordinated mechanisms: (I) data-aware generation that extracts statistical hints (mean, parity, dominant terms) to condition the LLM generator; (II) a mixed-fitting evaluator that decomposes parameters into linear and nonlinear subsets via AST analysis, solving each with appropriate methods; (III) a critic–executor repair stage that diagnoses promising-but-imperfect candidates and applies constrained symbolic edits (REMOVE, SIMPLIFY, ADD); and (IV) a TF-IDF-based semantic memory that clusters equations by structural similarity rather than score alone, preserving diversity.
The key insight is that existing LLM-SR pipelines conflate multiple roles—proposal, evaluation, repair, memory—into a single generation-and-score loop, leading to premature rejection of structurally correct but poorly-fitted candidates, missed repair opportunities, and redundant memory. STRIDE explicitly decomposes these into distinct agent roles with shared feedback.
2. Methodological Rigor
Strengths in experimental design:
Concerns:
3. Potential Impact
Direct applications: The framework addresses a genuine need in scientific discovery—recovering interpretable symbolic laws from data. The OOD robustness improvements are particularly valuable since real scientific equations should generalize beyond observed regimes.
Broader influence: The decomposition of equation discovery into distinct agent roles (generator, evaluator, critic, executor, memory) provides an architectural template that could be adapted to other LLM-guided search problems in science (program synthesis, materials design, drug discovery). The mixed-fitting insight—that structural proposals should be judged on better-fitted parameters rather than raw optimizer output—is independently useful and could improve any SR pipeline.
Limitations of impact: The framework is tightly coupled to the symbolic regression setting. The semantic memory and mixed-fitting components are domain-specific engineering rather than broadly transferable algorithmic innovations. The reliance on expensive API calls (GPT-5.1) limits accessibility.
4. Timeliness & Relevance
The paper arrives at a moment of active interest in LLM-based scientific discovery. LLM-SR (ICLR 2025 Oral), LLM-SRBench, SR-Scientist, and DrSR all represent very recent work, and STRIDE builds directly on this wave. The identification that generation-centered loops are insufficient and that multi-role agent coordination is needed aligns with broader trends in agentic AI systems.
The use of GPT-5.1 (released 2025) and evaluation on LSR-Synth (from LLM-SRBench) demonstrates currency. However, the rapid pace of both LLM capability improvements and SR method development means the specific gains may be transient.
5. Strengths & Limitations
Key Strengths:
Notable Weaknesses:
Additional Observations
The paper would benefit from: (1) analysis of failure cases where STRIDE doesn't improve over baselines; (2) scaling analysis beyond 2000 candidates; (3) evaluation on noisy data, which is more realistic for scientific applications; (4) comparison with equation discovery methods that use different LLM paradigms (e.g., fine-tuned models rather than prompting).
Generated May 19, 2026
Comparison History (24)
Paper 1 focuses on automating symbolic regression, a foundational tool for scientific discovery. Improving the reliability of extracting physical laws from data has profound, cross-disciplinary implications for physics, biology, and chemistry. While Paper 2 offers a strong technical advancement for vehicle routing problems with high industrial utility, Paper 1's contribution directly accelerates fundamental scientific research itself, granting it a broader and more fundamental scientific impact.
Paper 2 has higher potential impact due to its clear, broadly relevant conceptual contribution: it separates prompt-level behavior, decodable representations, and causal control, showing that linear readout does not imply behavioral reliance. This directly informs interpretability, behavioral evaluation, and the use of LLMs as human simulators across many domains (cog sci, econ, AI safety, mechanistic interpretability). The methodology (prompt tests, generalizing readouts, activation steering with sign/scale controls) is rigorous and timely. Paper 1 is useful but more incremental and narrower to symbolic regression workflows.
STRIDE addresses the fundamental challenge of automated scientific discovery through symbolic regression with a comprehensive multi-component framework. Its contributions—data-aware generation, mixed-fitting evaluation, critic-executor repair, and diversity-preserving memory—represent meaningful methodological advances in AI-driven equation discovery, with demonstrated improvements across multiple benchmarks and LLM backbones. Paper 2, while addressing a practical concern (agent robustness to environmental corruptions), is primarily a benchmark contribution with a narrower scope. STRIDE has broader scientific impact potential as it advances automated scientific reasoning, a high-impact research direction with applications across sciences.
SMDD-Bench addresses a critical gap in evaluating LLM agents for drug design—a high-stakes, real-world application domain. Its benchmark (502 tasks, 102 protein targets, 5 task types) provides standardized infrastructure that can catalyze an entire subfield, similar to how ImageNet transformed computer vision. The public leaderboard and guaranteed-solvable design encourage community adoption. While STRIDE offers meaningful methodological improvements for symbolic regression, it is more incremental within an established research area. SMDD-Bench's direct relevance to pharmaceutical discovery and its potential to redirect LLM agent development toward autonomous drug design gives it broader and higher impact potential.
Paper 1 advances AI-driven equation discovery, offering a practical framework that directly accelerates scientific research by reliably recovering symbolic laws from data. Its potential to automate and enhance scientific discovery across physics, biology, and engineering gives it a broader and more transformative scientific impact compared to Paper 2, which primarily focuses on evaluating LLM concept alignment and safety.
Paper 2 likely has higher scientific impact: it proposes a broadly applicable, constructive framework for reliable automatic equation discovery with clear real-world use in scientific modeling, engineering, and automated discovery. Its agentic loop (generation, mixed fitting, repair, and semantic memory) is methodologically rich and can generalize across domains and LLM backbones, supporting breadth and durability. Paper 1 is novel and rigorous but primarily advances jailbreak/refusal-evasion techniques, which may face limited publish-and-deploy applicability due to safety constraints and narrower positive downstream adoption.
Paper 1 introduces foundational architectural concepts and design patterns for integrating LLMs into production software, addressing a widespread engineering challenge across multiple domains. Its broad applicability to general agent design gives it a higher potential for widespread scientific and practical impact compared to Paper 2, which focuses on a narrower, albeit valuable, application of LLMs to symbolic regression.
Paper 1 (PTRM) demonstrates a more novel and impactful contribution: a simple, task-agnostic method that achieves dramatic accuracy improvements without retraining, using only 7M parameters while nearly doubling frontier LLM accuracy at a fraction of the cost. The approach of stochastic exploration in recursive models is elegant and broadly applicable. Paper 2 (STRIDE), while solid, is more incremental—combining known components (reflection, repair, memory) into an LLM-based equation discovery pipeline. PTRM's efficiency gains and paradigm-challenging results (tiny models outperforming massive LLMs) have broader implications for the field.
STRIDE addresses a fundamental scientific challenge—automated equation/law discovery from data—with broad applicability across physics, biology, and engineering. Its self-reflective agent framework for symbolic regression introduces methodological innovations (mixed-fitting evaluation, critic-executor repair, semantic memory) that advance both AI and scientific discovery. Paper 1 (SimGym) is a well-executed engineering contribution but is narrowly focused on e-commerce A/B test simulation with limited generalizability beyond that domain. STRIDE's potential to accelerate scientific discovery across multiple fields gives it substantially broader and deeper impact.
STRIDE addresses the well-established and growing field of AI-driven scientific discovery (symbolic regression/equation discovery), which has broad applicability across physics, biology, and engineering. Its self-reflective agent framework with coordinated components (generation, evaluation, repair, memory) offers a more generalizable and clearly validated contribution. Paper 1 introduces an interesting but niche framework for personalized language systems with commitment validation, but its narrow scope (personalization recall), unusual metrics (zero failures at low availability), and limited practical applicability reduce its broader impact potential compared to STRIDE's contribution to automated scientific discovery.