# Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning

arXiv: https://arxiv.org/abs/2504.08672 · HTML: https://mlsanity.com/paper/2504.08672/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 45 of its 62 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [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)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [From Crowdsourced Data to High-Quality Benchmarks: Arena-Hard and BenchBuilder Pipeline](https://mlsanity.com/paper/2406.11939/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Beam Search Strategies for Neural Machine Translation](https://mlsanity.com/paper/1702.01806/) (2017)
- [WildBench: Benchmarking LLMs with Challenging Tasks from Real Users in the Wild](https://mlsanity.com/paper/2406.04770/) (2024)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [OS-Genesis: Automating GUI Agent Trajectory Construction via Reverse Task Synthesis](https://mlsanity.com/paper/2412.19723/) (2024)
- [Chain of Hindsight Aligns Language Models with Feedback](https://mlsanity.com/paper/2302.02676/) (2023)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)

## Built on by (most cited first, 24 of 24)

- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [VisPlay: Self-Evolving Vision-Language Models from Images](https://mlsanity.com/paper/2511.15661/) (2025)
- [Seek in the Dark: Reasoning via Test-Time Instance-Level Policy Gradient in Latent Space](https://mlsanity.com/paper/2505.13308/) (2025)
- [Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data](https://mlsanity.com/paper/2602.21320/) (2026)
- [OS-Sentinel: Towards Safety-Enhanced Mobile GUI Agents via Hybrid Validation in Realistic Workflows](https://mlsanity.com/paper/2510.24411/) (2025)
- [Direct Reasoning Optimization: Token-Level Reasoning Reflectivity Meets Rubric Gates for Unverifiable Tasks](https://mlsanity.com/paper/2506.13351/) (2025)
- [MUR: Momentum Uncertainty guided Reasoning for Large Language Models](https://mlsanity.com/paper/2507.14958/) (2025)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [Skill Self-Play: Pushing the Frontier of LLM Capability with Co-Evolving Skills](https://mlsanity.com/paper/2607.22529/) (2026)
- [SketchVL: Policy Optimization via Fine-Grained Credit Assignment for Chart Understanding and More](https://mlsanity.com/paper/2601.05688/) (2026)
- [Wisdom of the Crowd: Reinforcement Learning from Coevolutionary Collective Feedback](https://mlsanity.com/paper/2508.12338/) (2025)
- [OdysseyArena: Benchmarking Large Language Models For Long-Horizon, Active and Inductive Interactions](https://mlsanity.com/paper/2602.05843/) (2026)
- [CodeEvo: Interaction-Driven Synthesis of Code-centric Data through Hybrid and Iterative Feedback](https://mlsanity.com/paper/2507.22080/) (2025)
- [Audio-Zero: Label-Free Self-Evolution for Fine-Grained Audio Reasoning](https://mlsanity.com/paper/2607.20166/) (2026)
- [Improving Text-to-Image Generation with Intrinsic Self-Confidence Rewards](https://mlsanity.com/paper/2603.00918/) (2026)
- [TTSR: Test-Time Self-Evolving via Reflection](https://mlsanity.com/paper/2603.03297/) (2026)
- [MAXS: Meta-Adaptive Exploration with LLM Agents](https://mlsanity.com/paper/2601.09259/) (2026)
- [Soft-SVeRL: Self-Verified Reinforcement Learning with Soft Rewards](https://mlsanity.com/paper/2605.28561/) (2026)
- [Continual Self-Improvement with Lightweight Experiential Latent Memories](https://mlsanity.com/paper/2606.17803/) (2026)
- [CoRE: Consensus Rewards via Equilibrium for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2608.09324/) (2026)
- [Unsupervised Post-Training of Foundation Models: A Survey](https://mlsanity.com/paper/2608.24982/) (2026)

## Abstract (arXiv)

Advancing LLM reasoning skills has captivated wide interest. However, current post-training techniques rely heavily on supervisory signals, such as outcome supervision or auxiliary reward models, which face the problem of scalability and high annotation costs. This motivates us to enhance LLM reasoning without the need for external supervision. We introduce a generalizable and purely unsupervised self-training framework, named Genius. Without external auxiliary, Genius requires to seek the optimal response sequence in a stepwise manner and optimize the LLM. To explore the potential steps and exploit the optimal ones, Genius introduces a stepwise foresight re-sampling strategy to sample and estimate the step value by simulating future outcomes. Further, we recognize that the unsupervised setting inevitably induces the intrinsic noise and uncertainty. To provide a robust optimization, we propose an advantage-calibrated optimization (ACO) loss function to mitigate estimation inconsistencies. Combining these techniques together, Genius provides an advanced initial step towards self-improve LLM reasoning with general queries and without supervision, revolutionizing reasoning scaling laws given the vast availability of general queries. The code will be released at https://github.com/xufangzhi/Genius.