R-APS: Compositional Reasoning and In-Context Meta-Learning for Constrained Design via Reflective Adversarial Pareto Search

arXiv cs.AI Papers
large-language-models multi-objective-optimization agentic-ai constrained-design meta-learning compositional-reasoning robotics

Summary

R-APS (Reflective Adversarial Pareto Search) is a novel method for constrained design tasks that addresses three structural failures in LLM-based agentic systems—error propagation, robustness evaluation, and knowledge invalidation—through reasoning-mode decomposition across three timescales, requiring no fine-tuning. Evaluated on planar mechanism synthesis, it achieves 3.5x tighter robustness certificates, 46% faster iterations-to-first-admission, and 2.1x Chamfer-distance reduction over baselines.

arXiv:2606.04823v1 Announce Type: new Abstract: Large language models (LLMs) are fluent on open-ended tasks, yet in agentic settings, where a system must plan, use tools, and act over extended horizons, fluency does not ensure reliable delivery. We trace this gap to three coupled structural failures: errors propagate without localization, worst-case perturbations go unevaluated, and accumulated knowledge is never invalidated. We argue these share a root cause: abductive, counterfactual, meta-inductive, corrective, and inductive reasoning pull a shared context in incompatible directions. We introduce Reflective Adversarial Pareto Search (R-APS), to our knowledge the first method addressing all three failures jointly via reasoning-mode decomposition, allocating each reasoning mode its own context and orchestrating interaction across three timescales: staged compositional reasoning with a typed validation critic (failure localization), sensitivity-guided counterfactual stress-testing as a first-class Pareto objective (robustness), and meta-inductive rule extraction with explicit invalidation (persistent memory). R-APS requires no fine-tuning and operates on a frozen LLM purely via structured protocol design. We evaluate on planar mechanism synthesis (robotics, prosthetics, mechanical design), with every candidate checked by a kinematic solver. On 32 target trajectories, R-APS delivers robustness certificates 3.5x tighter than uniform-perturbation baselines, 46% faster iterations-to-first-admission, and 2.1x Chamfer-distance reduction over Enum+GA while jointly controlling bar-count and worst-case robustness. Small 4B reasoning-specialized models prove competitive with general-purpose 70B backbones inside the protocol, suggesting structured protocols can partially offset model scale.
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# R-APS: Compositional Reasoning and In-Context Meta-Learning for Constrained Design via Reflective Adversarial Pareto Search
Source: [https://arxiv.org/abs/2606.04823](https://arxiv.org/abs/2606.04823)
[View PDF](https://arxiv.org/pdf/2606.04823)

> Abstract:Large language models \(LLMs\) are fluent on open\-ended tasks, yet in agentic settings, where a system must plan, use tools, and act over extended horizons, fluency does not ensure reliable delivery\. We trace this gap to three coupled structural failures: errors propagate without localization, worst\-case perturbations go unevaluated, and accumulated knowledge is never invalidated\. We argue these share a root cause: abductive, counterfactual, meta\-inductive, corrective, and inductive reasoning pull a shared context in incompatible directions\. We introduce Reflective Adversarial Pareto Search \(R\-APS\), to our knowledge the first method addressing all three failures jointly via reasoning\-mode decomposition, allocating each reasoning mode its own context and orchestrating interaction across three timescales: staged compositional reasoning with a typed validation critic \(failure localization\), sensitivity\-guided counterfactual stress\-testing as a first\-class Pareto objective \(robustness\), and meta\-inductive rule extraction with explicit invalidation \(persistent memory\)\. R\-APS requires no fine\-tuning and operates on a frozen LLM purely via structured protocol design\. We evaluate on planar mechanism synthesis \(robotics, prosthetics, mechanical design\), with every candidate checked by a kinematic solver\. On 32 target trajectories, R\-APS delivers robustness certificates 3\.5x tighter than uniform\-perturbation baselines, 46% faster iterations\-to\-first\-admission, and 2\.1x Chamfer\-distance reduction over Enum\+GA while jointly controlling bar\-count and worst\-case robustness\. Small 4B reasoning\-specialized models prove competitive with general\-purpose 70B backbones inside the protocol, suggesting structured protocols can partially offset model scale\.

## Submission history

From: João Pedro Gandarela \[[view email](https://arxiv.org/show-email/fdf238d5/2606.04823)\] **\[v1\]**Wed, 3 Jun 2026 12:45:39 UTC \(362 KB\)

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