# LESSER: Post-Training Data Selection with Output-Layer Gradients

arXiv: https://arxiv.org/abs/2610.03702 · HTML: https://mlsanity.com/paper/2610.03702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 54 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 47)

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- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
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- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
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- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)

## Abstract (arXiv)

The choice of post-training data for large language models substantially affects downstream performance. Gradient-based data selection is a popular approach that ranks training data by how well their gradients align with those of a small validation set. However, ranking with full-parameter gradients requires an expensive backward pass on every sample, making computation intractable for large candidate pools. This raises a natural question: can we approximate full-gradient features at a fraction of the cost? Conveniently, we find that output-layer gradients suffice for effective data selection, yet require only the cheaper forward pass. We implement this as LESSER, a drop-in wrapper for selection methods that reduces the feature-extraction FLOP cost by 9.7× for SFT and 3.0× for RL benchmarks, while tracking full-gradient performance on downstream tasks. Empirically, we find that even when output-layer and full gradients rank individual samples differently, they select batches with aligned gradients.