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

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.

Controlled Agentic Planning & Reasoning for Mechanism Synthesis

This work presents a dual-agent Large Language Model (LLM)-based reasoning method for mechanism synthesis, capable of reasoning at both linguistic and symbolic levels to generate geometrical and dynamic outcomes. The model consists of a composition of well-defined functions that, starting from a natural language specification, references abstract properties through supporting equations, generates and parametrizes simulation code, and elicits feedback anchor points using symbolic regression and distance functions. This process closes an actionable refinement loop at the linguistic and symbolic layers. The approach is shown to be both effective and convergent in the context of planar mechanisms. Additionally, we introduce MSynth, a novel benchmark for planar mechanism synthesis, and perform a comprehensive analysis of the impact of the model components. We further demonstrate that symbolic regression prompts unlock mechanistic insights only when applied to sufficiently large architectures.