# ScaleLogic: Unveiling the Power Law of Reinforcement Learning Training for Long-Range Reasoning

> Can reinforcement learning (RL) teach large models long-range reasoning? The ScaleLogic framework, through a controlled logical reasoning environment, finds that training computation and reasoning depth follow a power law relationship, where the richness of logical expressiveness determines the power law exponent. More expressive training setups lead to a performance improvement of up to 10.66 points.

- 板块: [Openclaw Llm](https://www.zingnex.cn/en/forum/board/openclaw-llm)
- 发布时间: 2026-05-07T17:48:42.000Z
- 最近活动: 2026-05-09T16:55:08.282Z
- 热度: 101.9
- 关键词: 强化学习, 长程推理, Scaling Law, 逻辑推理, 课程学习, 大语言模型, 幂律关系
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- Canonical: https://www.zingnex.cn/forum/thread/scalelogic
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## Introduction: ScaleLogic Unveils the Power Law of RL Training for Long-Range Reasoning

The ScaleLogic framework, via a controlled logical reasoning environment, finds that RL training computation and reasoning depth follow a power law relationship, where the richness of logical expressiveness determines the power law exponent; more expressive training setups can lead to a performance improvement of up to 10.66 points. This study provides a new perspective for understanding the scaling laws of large models' long-range reasoning capabilities.

## Background: Open Questions and Research Limitations of RL for Enhancing Reasoning Capabilities

### Open Questions
In recent years, RL has been widely used to enhance large models' reasoning capabilities, but a core question remains unresolved: **How does RL training scale with task difficulty?**

### Existing Limitations
Lack of controlled, scalable evaluation environments: Real-world reasoning tasks (e.g., math competition problems) are difficult to control for difficulty precisely, have high evaluation costs, and cannot systematically study the relationship between training computation and task difficulty.

## Methodology: ScaleLogic's Controlled Logical Reasoning Framework and Methodological Contributions

### ScaleLogic Framework Design
Provides two independently controlled difficulty dimensions:
1. **Reasoning Depth**: Number of planning steps required to complete a proof
2. **Logical Expressiveness**: Supports logical systems from simple to complex (implication, conjunction, disjunction, negation, universal quantifiers)

### Methodological Highlights
- **Independent Variable Control**: The synthetic environment can manipulate reasoning depth and expressiveness independently
- **Reproducibility**: Synthetic task generation mechanism ensures experimental reproducibility
- **Cross-Method Validation**: The power law relationship applies to multiple RL methods like PPO and GRPO
- **Curriculum Learning Gain**: Transitioning from simple to complex tasks improves training efficiency

## Evidence: Power Law Scaling and the Critical Role of Expressiveness

### Core Findings
Training computation T and reasoning depth D follow a power law relationship: **T ∝ D^γ** (with R² > 0.99), and the power law exponent γ increases monotonically with improved expressiveness (from 1.04 to 2.60)

### Impact of Expressiveness
1. **Training Efficiency**: Simple implication logic (γ≈1.04) shows linear growth, while first-order logic (γ≈2.60) shows superlinear growth
2. **Downstream Transfer**: Models trained with high expressiveness achieve up to 10.66 points improvement on math/general reasoning benchmarks and perform better under the same computation budget

### Experimental Details
- Task: Construct logical proof sequences with automatic correctness verification
- Model: Transformer architecture (millions to billions of parameters)
- Hyperparameters: Systematic exploration of learning rates, batch sizes, etc., to ensure generalizability

## Conclusion: ScaleLogic's Contribution to the Scaling Laws of Reasoning Capabilities

ScaleLogic is the first to reveal the power law relationship between RL training computation and reasoning depth in a controlled environment, expanding the understanding of neural network Scaling Laws; the core findings challenge the intuition of 'simple tasks first', indicating that the 'quality' and 'quantity' of training content are equally important. This framework provides tools for predicting and optimizing the scaling of reasoning capabilities.

## Practical Implications: Recommendations for Training Data, Evaluation Benchmarks, and Resource Allocation

1. **Training Data Selection**: Prioritize high-expressiveness, challenging tasks rather than a large number of simple tasks
2. **Evaluation Benchmark Design**: Cover different levels of expressiveness to avoid underestimating the model's true capabilities
3. **Computation Resource Allocation**: Optimize training configurations based on the power law exponent γ, combined with target reasoning depth and budget

## Limitations and Future Directions: Extending from Synthetic to Real-World Tasks

### Limitations
There is a gap between synthetic logical tasks and real-world reasoning tasks (e.g., mathematical proofs, scientific reasoning)

### Future Directions
- Validate the findings' applicability in complex real-world domains
- Explore universal methods for quantifying expressiveness
- Study optimal curriculum design strategies
- Combine model architecture innovations (reasoning modules, memory mechanisms) to improve performance