# PRIME: Policy-Reinforced Iterative Multi-agent Execution for Algorithmic Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2602.11170 · HTML: https://mlsanity.com/paper/2602.11170/

## 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 39 of its 96 references that are in the map.
- First posted on arXiv 19 Jan 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, 30 of 39)

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- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
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- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
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- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [Effective Long-Context Scaling of Foundation Models](https://mlsanity.com/paper/2309.16039/) (2023)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [On the Measure of Intelligence](https://mlsanity.com/paper/1911.01547/) (2019)

## Abstract (arXiv)

Large language models have demonstrated remarkable capabilities across diverse reasoning tasks, yet their performance on algorithmic reasoning remains limited. To handle this limitation, we propose PRIME (Policy-Reinforced Iterative Multi-agent Execution), a framework comprising three specialized agents, an executor for step-by-step reasoning, a verifier for constraint checking, and a coordinator for backtracking control, optimized through group relative policy optimization. For comprehensive evaluation, we introduce PRIME-Bench, the largest algorithmic reasoning benchmark to date, comprising 86 tasks across 12 categories with 51,600 instances. Tasks span sorting algorithms, graph and tree structures, automata and state machines, symbolic reasoning, and constraint-based puzzles, with execution traces reaching over one million steps. Compared to baseline approach, PRIME improves average accuracy from 26.8% to 93.8%, a 250% relative gain. The largest improvements occur on tasks requiring sustained state tracking, with Turing machine simulation improving from 9% to 92% and long division from 16% to 94%. Ablation studies identify iterative verification as the primary contributor, preventing the error propagation that causes baseline approaches to fail catastrophically. Analysis across model scales (8B-120B parameters) reveals that smaller models benefit disproportionately, achieving accuracy comparable to models 8x larger.