# BRIDGE: Budget-aware Reasoning via Intermediate Distillation with Guided Examples

arXiv: https://arxiv.org/abs/2512.20403 · HTML: https://mlsanity.com/paper/2512.20403/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [On the Efficacy of Knowledge Distillation](https://mlsanity.com/paper/1910.01348/) (2019)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- ["My Answer is C": First-Token Probabilities Do Not Match Text Answers in Instruction-Tuned Language Models](https://mlsanity.com/paper/2402.14499/) (2024)
- [Universal Cross-Tokenizer Distillation via Approximate Likelihood Matching](https://mlsanity.com/paper/2503.20083/) (2025)
- [Lion: Adversarial Distillation of Proprietary Large Language Models](https://mlsanity.com/paper/2305.12870/) (2023)
- [PaD: Program-aided Distillation Can Teach Small Models Reasoning Better than Chain-of-thought Fine-tuning](https://mlsanity.com/paper/2305.13888/) (2023)
- [FinMTEB: Finance Massive Text Embedding Benchmark](https://mlsanity.com/paper/2502.10990/) (2025)
- [Pro-KD: Progressive Distillation by Following the Footsteps of the Teacher](https://mlsanity.com/paper/2110.08532/) (2021)
- [SelectLLM: Can LLMs Select Important Instructions to Annotate?](https://mlsanity.com/paper/2401.16553/) (2024)
- [In-context Learning vs. Instruction Tuning: The Case of Small and Multilingual Language Models](https://mlsanity.com/paper/2503.01611/) (2025)

## Abstract (arXiv)

Distilling knowledge from large proprietary models (e.g., GPT-4) to tiny deployable models (less than 1B parameters) faces a critical capacity-budget trap: the 1000x capacity gap between teachers and students prevents effective direct transfer, while API costs prohibit extensive data collection. We introduce BRIDGE (Budget-Aware Reasoning via Intermediate Distillation), a two-phase framework that resolves these constraints through strategic intermediation and budget asymmetry. In Phase 1, a mid-sized Teacher Assistant (TA; e.g., about 7B) learns from the black-box teacher on a strictly limited subset of data (e.g., 3-5%), selected via a zero-API-cost pipeline that balances entropic difficulty and semantic diversity using only local TA inference. In Phase 2, we exploit this asymmetry-teacher queries are expensive, whereas TA inference is free to amplify supervision: the refined TA generates synthetic rationales for the full dataset to train the tiny student. Crucially, we apply an instruction-tuning curriculum to establish behavioral alignment in the tiny student before transferring reasoning. Our theoretical analysis shows that BRIDGE yields tighter generalization bounds than direct distillation when data is abundant. Experiments across medical, legal, and financial benchmarks demonstrate consistent improvements: BRIDGE delivers student performance gains of 28-41%, closing the capability gap with proprietary teachers by 12-16% while using 10x fewer teacher queries. Notably, BRIDGE defies the conventional cost-performance frontier, surpassing direct distillation baselines that use 100% of the budget while consuming only 5% of the resources.