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

arXiv: https://arxiv.org/abs/2606.04823 · HTML: https://mlsanity.com/paper/2606.04823/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 12 of 12)

- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [ChatDev: Communicative Agents for Software Development](https://mlsanity.com/paper/2307.07924/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [AutoChip: Automating HDL Generation Using LLM Feedback](https://mlsanity.com/paper/2311.04887/) (2023)
- [How Can Large Language Models Help Humans in Design and Manufacturing?](https://mlsanity.com/paper/2307.14377/) (2023)
- [Symbolic Intermediaries as a Linguistic-Numerical Interface for LLM-Driven Geometric Reasoning](https://mlsanity.com/paper/2505.17607/) (2025)
- [Reflective Reasoning for SQL Generation](https://mlsanity.com/paper/2601.06678/) (2026)
- [Language Models Refine Mechanical Linkage Designs Through Symbolic Reflection and Modular Optimisation](https://mlsanity.com/paper/2604.27962/) (2026)

## Abstract (arXiv)

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.