# BRIDGE: Bridging Reasoning In Distillation Gap Elimination via Structure-Aware Masking

arXiv: https://arxiv.org/abs/2602.17686 · HTML: https://mlsanity.com/paper/2602.17686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 15 of 15)

- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Implicit Chain of Thought Reasoning via Knowledge Distillation](https://mlsanity.com/paper/2311.01460/) (2023)
- [Deep Research: A Survey of Autonomous Research Agents](https://mlsanity.com/paper/2508.12752/) (2025)
- [Implicit Reasoning in Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.02350/) (2025)
- [Making Slow Thinking Faster: Compressing LLM Chain-of-Thought via Step Entropy](https://mlsanity.com/paper/2508.03346/) (2025)
- [Navigate the Unknown: Enhancing LLM Reasoning with Intrinsic Motivation Guided Exploration](https://mlsanity.com/paper/2505.17621/) (2025)
- [Mixed Distillation Helps Smaller Language Model Better Reasoning](https://mlsanity.com/paper/2312.10730/) (2023)
- [SuperRL: Reinforcement Learning with Supervision to Boost Language Model Reasoning](https://mlsanity.com/paper/2506.01096/) (2025)
- [Align-GRAG: Anchor and Rationale Guided Dual Alignment for Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2505.16237/) (2025)
- [MiCoTA: Bridging the Learnability Gap with Intermediate CoT and Teacher Assistants](https://mlsanity.com/paper/2507.01887/) (2025)
- [From Reasoning LLMs to BERT: A Two-Stage Distillation Framework for Search Relevance](https://mlsanity.com/paper/2510.11056/) (2025)
- [Masked-and-Reordered Self-Supervision for Reinforcement Learning from Verifiable Rewards](https://mlsanity.com/paper/2511.17473/) (2025)

## Abstract (arXiv)

Chain-of-Thought (CoT) reasoning has significantly improved LLMs' mathematical problem-solving capabilities, but distilling such capabilities into smaller models remains challenging due to the capacity mismatch between verbose teachers and compact students. Directly copying teachers' lengthy reasoning chains causes capacity overload, resulting in truncated outputs or repetitive failure. Existing remedies each sacrifice a critical property of CoT: implicit reasoning methods (e.g., compressing reasoning into hidden states) trade away interpretability and verifiability, while heuristic compression strategies (e.g., random step pruning) destroy logical integrity. To address this, we propose BRIDGE, a curriculum framework that first establishes structural understanding via masked reconstruction, then uses GRPO-based reinforcement learning to guide students in self-discovering the optimal balance between accuracy and brevity, and finally internalizes complex reasoning through teacher-guided rewriting on failure cases. On GSM8K, BRIDGE enables Qwen2.5-3B to achieve 11.29% accuracy improvement and 27.4% token reduction over the original model, outperforming instruction-tuned variants and distillation baselines. Zero-shot transfer experiments on SVAMP and MATH-500 further confirm the generalization of internalized reasoning. Our code and model checkpoints are publicly available at https://github.com/Applied-Machine-Learning-Lab/SDM2026_BRIDGE and https://huggingface.co/bowen0815/BRIDGE.