# Optimizing Language Model's Reasoning Abilities with Weak Supervision

arXiv: https://arxiv.org/abs/2405.04086 · HTML: https://mlsanity.com/paper/2405.04086/

## Key facts

- Cited by 15 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 42 of its 60 references that are in the map.
- First posted on arXiv 7 May 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 42)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Semi-Supervised Semantic Segmentation with Cross Pseudo Supervision](https://mlsanity.com/paper/2106.01226/) (2021)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)

## Built on by (most cited first, 15 of 15)

- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Weak-to-Strong Reasoning](https://mlsanity.com/paper/2407.13647/) (2024)
- [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://mlsanity.com/paper/2503.17439/) (2025)
- [Towards Acyclic Preference Evaluation of Language Models via Multiple Evaluators](https://mlsanity.com/paper/2410.12869/) (2024)
- [ExPO: Unlocking Hard Reasoning with Self-Explanation-Guided Reinforcement Learning](https://mlsanity.com/paper/2507.02834/) (2025)
- [The Quest for Efficient Reasoning: A Data-Centric Benchmark to CoT Distillation](https://mlsanity.com/paper/2505.18759/) (2025)
- [Diagnosis Before Recovery: Turning Agent Failures into Selective Self-Correction](https://mlsanity.com/paper/2608.11772/) (2026)
- [How to Train a Real-World Silicon Concierge? Internalizing Complex Business Workflow to Only OneModel](https://mlsanity.com/paper/2608.20350/) (2026)
- [HuggingR4: A Progressive Reasoning Framework for Discovering Optimal Model Companions](https://mlsanity.com/paper/2511.18715/) (2025)
- [CURA: Clinical Uncertainty Risk Alignment for Language Model-Based Risk Prediction](https://mlsanity.com/paper/2604.14651/) (2026)
- [Trust Functions: Near-Lossless Weak-to-Strong Generalization by Learning When to Trust the Weak Teacher](https://mlsanity.com/paper/2606.01000/) (2026)
- [ARC: Fair Relative Advantage Comparison in Open-Ended Real-World Interaction](https://mlsanity.com/paper/2608.13622/) (2026)
- [Ask, Condition or Abstain: Reinforcement Learning for Missing-Premise Reasoning](https://mlsanity.com/paper/2608.16554/) (2026)
- [Grounded Skill Synthesis from Code at Scale for Agentic Intelligence](https://mlsanity.com/paper/2609.05571/) (2026)

## Abstract (arXiv)

While Large Language Models (LLMs) have demonstrated proficiency in handling complex queries, much of the past work has depended on extensively annotated datasets by human experts. However, this reliance on fully-supervised annotations poses scalability challenges, particularly as models and data requirements grow. To mitigate this, we explore the potential of enhancing LLMs' reasoning abilities with minimal human supervision. In this work, we introduce self-reinforcement, which begins with Supervised Fine-Tuning (SFT) of the model using a small collection of annotated questions. Then it iteratively improves LLMs by learning from the differences in responses from the SFT and unfinetuned models on unlabeled questions. Our approach provides an efficient approach without relying heavily on extensive human-annotated explanations. However, current reasoning benchmarks typically only include golden-reference answers or rationales. Therefore, we present textscPuzzleBen, a weakly supervised benchmark that comprises 25,147 complex questions, answers, and human-generated rationales across various domains, such as brainteasers, puzzles, riddles, parajumbles, and critical reasoning tasks. A unique aspect of our dataset is the inclusion of 10,000 unannotated questions, enabling us to explore utilizing fewer supersized data to boost LLMs' inference capabilities. Our experiments underscore the significance of textscPuzzleBen, as well as the effectiveness of our methodology as a promising direction in future endeavors. Our dataset and code will be published soon on textttAnonymity Link.