# Token Utility Is Selection-Conditioned: Coupled Selection of Prompt Context and Response Supervision for Instruction Tuning

arXiv: https://arxiv.org/abs/2609.22943 · HTML: https://mlsanity.com/paper/2609.22943/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [LongLLMLingua: Accelerating and Enhancing LLMs in Long Context Scenarios via Prompt Compression](https://mlsanity.com/paper/2310.06839/) (2023)
- [Is Attention Interpretable?](https://mlsanity.com/paper/1906.03731/) (2019)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [LLMLingua-2: Data Distillation for Efficient and Faithful Task-Agnostic Prompt Compression](https://mlsanity.com/paper/2403.12968/) (2024)
- [Superfiltering: Weak-to-Strong Data Filtering for Fast Instruction-Tuning](https://mlsanity.com/paper/2402.00530/) (2024)
- [Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small LLMs](https://mlsanity.com/paper/2412.13337/) (2024)
- [Token Cleaning: Fine-Grained Data Selection for LLM Supervised Fine-Tuning](https://mlsanity.com/paper/2502.01968/) (2025)
- [Instruction Fine-Tuning: Does Prompt Loss Matter?](https://mlsanity.com/paper/2401.13586/) (2024)
- [ProFit: Leveraging High-Value Signals in SFT via Probability-Guided Token Selection](https://mlsanity.com/paper/2601.09195/) (2026)
- [T-SHIRT: Token-Selective Hierarchical Data Selection for Instruction Tuning](https://mlsanity.com/paper/2506.01317/) (2025)
- [GIST: Targeted Data Selection for Instruction Tuning via Coupled Optimization Geometry](https://mlsanity.com/paper/2602.18584/) (2026)

## Abstract (arXiv)

Token selection for instruction tuning is coupled: supervision utility depends on retained context, and vice versa. Existing methods largely optimize prompt compression or response supervision separately. Combining selectors can value supervision using removed context, or context using excluded supervision, creating selection-state mismatch. BRIDGE (Budgeted Response-Prompt Interaction via Directional Gradient-guided Efficient Token Selection) models selection-conditioned token utility through a shared validation-directed surrogate objective. BRIDGE routes response utility to supporting prompt tokens through attention, then alternates budgeted selection to revalue each side under the other's retained subset. Updates reuse precomputed interactions without repeated model scoring, while structure-aware projection promotes coherent supervision spans. Across three model families and three task domains, BRIDGE performs best overall among evaluated selection methods. Its MATH advantage over independent selection grows with compression, reaching 1.66 percentage points on Llama-3.2-3B.