# LLM2: Let Large Language Models Harness System 2 Reasoning

arXiv: https://arxiv.org/abs/2412.20372 · HTML: https://mlsanity.com/paper/2412.20372/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 29 Dec 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 16 of 16)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [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)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [Distilling System 2 into System 1](https://mlsanity.com/paper/2407.06023/) (2024)
- [Rephrase and Respond: Let Large Language Models Ask Better Questions for Themselves](https://mlsanity.com/paper/2311.04205/) (2023)
- [A Thorough Examination of Decoding Methods in the Era of LLMs](https://mlsanity.com/paper/2402.06925/) (2024)
- [System 2 Attention (is something you might need too)](https://mlsanity.com/paper/2311.11829/) (2023)
- [Critical Tokens Matter: Token-Level Contrastive Estimation Enhances LLM's Reasoning Capability](https://mlsanity.com/paper/2411.19943/) (2024)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)
- [Language Models, Agent Models, and World Models: The LAW for Machine Reasoning and Planning](https://mlsanity.com/paper/2312.05230/) (2023)
- [Unchosen Experts Can Contribute Too: Unleashing MoE Models' Power by Self-Contrast](https://mlsanity.com/paper/2405.14507/) (2024)

## Built on by (most cited first, 12 of 12)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Reasoning RAG via System 1 or System 2: A Survey on Reasoning Agentic Retrieval-Augmented Generation for Industry Challenges](https://mlsanity.com/paper/2506.10408/) (2025)
- [Reasoning on a Spectrum: Aligning LLMs to System 1 and System 2 Thinking](https://mlsanity.com/paper/2502.12470/) (2025)
- [RL of Thoughts: Navigating LLM Reasoning with Inference-time Reinforcement Learning](https://mlsanity.com/paper/2505.14140/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [A Review of Incorporating Psychological Theories in LLMs](https://mlsanity.com/paper/2505.00003/) (2025)
- [Adapting Like Humans: A Metacognitive Agent with Test-time Reasoning](https://mlsanity.com/paper/2511.23262/) (2025)
- [The role of System 1 and System 2 semantic memory structure in human and LLM biases](https://mlsanity.com/paper/2604.12816/) (2026)
- [AMATA: Adaptive Multi-Agent Trajectory Alignment for Knowledge-Intensive Question Answering](https://mlsanity.com/paper/2605.17352/) (2026)
- [From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics](https://mlsanity.com/paper/2601.23048/) (2026)
- [Standing on the Shoulders of Giants: Stabilized Knowledge Distillation for Cross--Language Code Clone Detection](https://mlsanity.com/paper/2605.02860/) (2026)
- [Learning to Decide, Not to Reason: Parameter-Efficient Decision Operators via Low-Rank Activation Steering](https://mlsanity.com/paper/2610.06950/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have exhibited impressive capabilities across a myriad of tasks, yet they occasionally yield undesirable outputs. We posit that these limitations are rooted in the foundational autoregressive architecture of LLMs, which inherently lacks mechanisms for differentiating between desirable and undesirable results. Drawing inspiration from the dual-process theory of human cognition, we introduce LLM2, a novel framework that combines an LLM (System 1) with a process-based verifier (System 2). Within LLM2, the LLM is responsible for generating plausible candidates, while the verifier provides timely process-based feedback to distinguish desirable and undesirable outputs. The verifier is trained with a pairwise comparison loss on synthetic process-supervision data generated through our token quality exploration strategy. Empirical results on mathematical reasoning benchmarks substantiate the efficacy of LLM2, exemplified by an accuracy enhancement from 50.3 to 57.8 (+7.5) for Llama3-1B on GSM8K. Furthermore, when combined with self-consistency, LLM2 achieves additional improvements, boosting major@20 accuracy from 56.2 to 70.2 (+14.0).