# When Does Critique Improve AI-Assisted Theoretical Physics? SCALAR: Structured Critic--Actor Loop for Agentic Reasoning

arXiv: https://arxiv.org/abs/2605.06772 · HTML: https://mlsanity.com/paper/2605.06772/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- 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, 21 of 21)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [PhysReason: A Comprehensive Benchmark towards Physics-Based Reasoning](https://mlsanity.com/paper/2502.12054/) (2025)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [Accelerating Scientific Research with Gemini: Case Studies and Common Techniques](https://mlsanity.com/paper/2602.03837/) (2026)
- [Persona is a Double-edged Sword: Mitigating the Negative Impact of Role-playing Prompts in Zero-shot Reasoning Tasks](https://mlsanity.com/paper/2408.08631/) (2024)
- [MathChat: Benchmarking Mathematical Reasoning and Instruction Following in Multi-Turn Interactions](https://mlsanity.com/paper/2405.19444/) (2024)
- [Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning](https://mlsanity.com/paper/2601.02902/) (2026)
- [ACC-Collab: An Actor-Critic Approach to Multi-Agent LLM Collaboration](https://mlsanity.com/paper/2411.00053/) (2024)
- [Improving Physics Reasoning in Large Language Models Using Mixture of Refinement Agents](https://mlsanity.com/paper/2412.00821/) (2024)
- [Have Large Language Models Learned to Reason? A Characterization via 3-SAT Phase Transition](https://mlsanity.com/paper/2504.03930/) (2025)
- [Can Theoretical Physics Research Benefit from Language Agents?](https://mlsanity.com/paper/2506.06214/) (2025)
- [A Comment On "The Illusion of Thinking": Reframing the Reasoning Cliff as an Agentic Gap](https://mlsanity.com/paper/2506.18957/) (2025)
- [Advancing AI-Scientist Understanding: Multi-Agent LLMs with Interpretable Physics Reasoning](https://mlsanity.com/paper/2504.01911/) (2025)
- [Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories](https://mlsanity.com/paper/2603.11164/) (2026)
- [Asymmetric Actor-Critic for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.00304/) (2026)
- [Learning to Unscramble Feynman Loop Integrals with SAILIR](https://mlsanity.com/paper/2604.05034/) (2026)
- [The DNA of nuclear models: How AI predicts nuclear masses](https://mlsanity.com/paper/2508.08370/) (2025)

## Abstract (arXiv)

As large language models (LLMs) show increasing promise on research-level physics reasoning tasks and agentic AI becomes more common, a practical question emerges: How does the interaction between researchers and agents affect the results? We study this using SCALAR (Structured Critic--Actor Loop for Agentic Reasoning), an Actor--Critic--Judge pipeline applied to quantum field theory and string theory problems. The Actor proposes solutions, the Critic provides iterative feedback, and an independent Judge evaluates the transcript against reference solutions. We vary the Actor persona, the Critic feedback strategy, and the Actor model family and scale. Multi-turn dialogue improves over single-shot attempts throughout, but both the mechanism of improvement and the value of different prompting choices depend strongly on the Actor--Critic pairing. Increasing the scale within one model family (e.g. from the 8B-parameter DeepSeek-R1 variant to DeepSeek-R1 70B) improves some easier-problem behavior, but does not remove the hardest bottleneck we observe. Critic feedback strategy matters most clearly in the asymmetric Actor--Critic setting (e.g, a lightweight Haiku Actor guided by a stronger Sonnet Critic), where constructive feedback improves mean-score outcomes. In same-family Actor--Critic settings, strategy effects are weaker: lenient feedback is sometimes favored, while strict and adversarial feedback are not beneficial. Taken together, SCALAR provides a controlled testbed for evaluating which interaction structures help or hinder AI-assisted reasoning on known-answer scientific problems.