LLMs learn to think ahead like a boss, by doing math homework designed for kids.

Overview

Paper Summary › Explain Like I'm Five › Conflicts of Interest › Identified Limitations › Rating Explanation › Good to know › Topic Hierarchy › File Information ›

Paper Summary

Paperzilla title

This paper introduces a scalable method to teach large language models (LLMs) to reason over long, multi-step problems by composing existing simpler math problems into complex chains. The approach uses reinforcement learning with a curriculum that progressively increases problem difficulty, leading to significant accuracy boosts on challenging math and long-context benchmarks. The authors acknowledge that the initial training data, synthetically composed of 6th-grade level math problems, is somewhat artificial yet effective for demonstrating the method's capabilities.

Explain Like I'm Five

We taught smart computer programs to solve really long math problems by first having them solve many small math problems that build on each other, like a long puzzle. It's like learning to build big towers by first practicing with small blocks.

Possible Conflicts of Interest

One author is from 'Microsoft AI Frontiers', which is part of a company with significant interests in large language models. This could represent a conflict of interest, as the research aims to improve LLM capabilities.

Identified Limitations

Reliance on Synthetic Data Composition

The core training relies on synthetically composed GSM8K math problems, which the authors acknowledge are 'relatively artificial.' While transfer to harder benchmarks is shown, the method's effectiveness might vary for real-world long-horizon tasks where such clear atomic problems or simple chaining structures are not readily available.

Computational Cost Trade-off

The paper notes that using 'cheaper' (skewed towards shorter problems) data distributions to achieve similar performance requires 'more training compute.' This implies a trade-off where cost efficiency in data might lead to increased computational cost, which could be a limitation in resource-constrained environments.

Simplified Theoretical Model

The theoretical analysis relies on a simplified model of long-horizon correctness. While this provides valuable insights into sample complexity, it is a simplification that may not fully capture the complexities of real-world LLM reasoning.

Limited Skill and Dependency Diversity

The discussion section points to future work on incorporating new sources of atomic skills beyond GSM8K and expanding the serial dependency structure. This suggests current limitations in the diversity of skills learned and the complexity of dependencies the method can handle.

Base Model Capabilities

While the method shows significant improvements on Instruct models (Qwen-2.5-3B, Qwen-2.5-7B, Llama-3.2-3B), the LLM landscape evolves rapidly. The performance gains are relative to the chosen base models, and the absolute 'groundbreaking' nature might need re-evaluation with newer, more powerful foundation models.

Rating Explanation

This paper presents a groundbreaking and scalable method for improving large language models' long-horizon reasoning by composing existing short-horizon data into complex chains and applying curriculum reinforcement learning. It demonstrates significant empirical gains and offers strong theoretical backing, showing that models learn genuinely new capabilities and effectively transfer these skills to harder, unseen benchmarks. The approach directly addresses a critical challenge in scaling LLM reasoning.

Good to know

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Topic Hierarchy

Domain: Physical Sciences

Field: Computer Science

Subfield: Artificial Intelligence

File Information

Original Title: BOOTSTRAPPING LLMS TO REASON OVER LONGER HORIZONS VIA REINFORCEMENT LEARNING

Uploaded: October 09, 2025 at 06:06 PM

Privacy: Public