# ALIVE: Awakening LLM Reasoning via Adversarial Learning and Instructive Verbal Evaluation

arXiv: https://arxiv.org/abs/2602.05472 · HTML: https://mlsanity.com/paper/2602.05472/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 49 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 37)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Orca: Progressive Learning from Complex Explanation Traces of GPT-4](https://mlsanity.com/paper/2306.02707/) (2023)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Secrets of RLHF in Large Language Models Part II: Reward Modeling](https://mlsanity.com/paper/2401.06080/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [Reinforcement Learning Enhanced LLMs: A Survey](https://mlsanity.com/paper/2412.10400/) (2024)
- [QuestBench: Can LLMs ask the right question to acquire information in reasoning tasks?](https://mlsanity.com/paper/2503.22674/) (2025)

## Built on by (most cited first, 1 of 1)

- [PopuLoRA: Co-Evolving LLM Populations for Reasoning Self-Play](https://mlsanity.com/paper/2605.16727/) (2026)

## Abstract (arXiv)

The quest for expert-level reasoning in Large Language Models (LLMs) has been hampered by a persistent textitreward bottleneck: traditional reinforcement learning (RL) relies on scalar rewards that are costly to scale, brittle across domains, and blind to the underlying logic of a solution. This reliance on external, impoverished signals prevents models from developing a deep, self-contained understanding of reasoning principles. We introduce ALIVE (Adversarial Learning with Instructive Verbal Evaluation), a hands-free alignment framework that moves beyond scalar reward optimization toward intrinsic reasoning acquisition. Grounded in the principle of Cognitive Synergy, ALIVE unifies problem posing, solving, and judging within a single policy model to internalize the logic of correctness. By coupling adversarial learning with instructive verbal feedback, ALIVE enables models to internalize evaluative criteria directly from raw corpora, effectively transforming external critiques into an endogenous reasoning faculty. Empirical evaluations across mathematical reasoning, code generation, and general logical inference benchmarks demonstrate that ALIVE consistently mitigates reward signal limitations. With identical data and compute, it achieves accuracy gains, markedly improved cross-domain generalization, and higher self-correction rates. These results indicate that the reasoning trinity fosters a self-sustaining trajectory of capability growth, positioning ALIVE as a scalable foundation for general-purpose reasoning alignment without human-in-the-loop supervision.