FoE: The Forest of Errors Effect Reveals the 'First Solution is Optimal' Phenomenon in Large Reasoning Models

This study reveals the counterintuitive phenomenon of 'first solution being optimal' in large reasoning models. It proposes the Forest of Errors (FoE) theory to explain this phenomenon and designs the RED framework. By optimizing the first solution and pruning subsequent errors, it achieves a maximum 19% performance improvement and a 37.7%-70.4% reduction in token consumption.

In recent years, large reasoning models (LRMs) represented by DeepSeek-R1 have improved complex reasoning capabilities through multi-path exploration, which is considered a key factor in their excellent performance. However, the latest research finds that the first generated solution is often the best, and subsequent alternative solutions are not only not better but may even have negative impacts, challenging the test-time scaling law that 'more candidate solutions lead to better results'.

To explain the 'first solution is optimal' phenomenon, the study proposes the Forest of Errors (FoE) theory: Errors in reasoning paths grow synchronously with test time, and errors are interrelated and progressive, forming a forest-like structure. Early errors (tree roots) will have a chain effect on subsequent branches, leading to more error accumulation. This theory is supported by empirical analysis and mathematical modeling.

Based on the FoE theory, the study designs the RED (Reasoning Error Detection) framework:

1. Refining First: Identify and correct potential errors in the first solution to suppress the growth of the error forest from the source;
2. Discarding Subs: Prune subsequent error solutions through double consistency checks to avoid invalid exploration and focus resources on valuable paths.

The RED framework was validated on 5 benchmark tests and 6 models of different scales, compared with 8 baseline methods:

1. Performance: Up to 19.0% improvement in reasoning accuracy;
2. Efficiency: 37.7%-70.4% reduction in token consumption;
3. FoE Metrics: Significantly reduced the size of the error forest, verifying the effectiveness of its design principles.

The FoE study challenges the test-time scaling law that 'more test-time computing resources improve performance': When the error growth brought by expansion exceeds the benefits, more computing will instead have negative effects. It suggests that reasoning strategies need to be redesigned to pursue intelligent computing rather than simply increasing resources, especially applicable to resource-constrained scenarios.

Theoretical Contribution: FoE provides a new framework for reasoning failure analysis, and the 'first solution is optimal' phenomenon challenges existing reasoning paradigms; Future Directions: Refine the FoE mathematical model, explore error propagation laws across different tasks, and extend to tasks such as code generation; Practical Significance: RED reduces reasoning costs and response speed, suggesting that optimizing the first solution is more effective than generating more alternatives, which helps in the commercial deployment and large-scale application of large models.