# From Spectral Saliency to Finite Deletion: Evaluating Selective Language Model Edits

arXiv: https://arxiv.org/abs/2610.18098 · HTML: https://mlsanity.com/paper/2610.18098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 13 Oct 2026.

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Negative Preference Optimization: From Catastrophic Collapse to Effective Unlearning](https://mlsanity.com/paper/2404.05868/) (2024)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Knowledge Unlearning for Mitigating Privacy Risks in Language Models](https://mlsanity.com/paper/2210.01504/) (2022)
- [Who's Harry Potter? Approximate Unlearning in LLMs](https://mlsanity.com/paper/2310.02238/) (2023)
- [MUSE: Machine Unlearning Six-Way Evaluation for Language Models](https://mlsanity.com/paper/2407.06460/) (2024)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [An Adversarial Perspective on Machine Unlearning for AI Safety](https://mlsanity.com/paper/2409.18025/) (2024)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Dissecting Language Models: Machine Unlearning via Selective Pruning](https://mlsanity.com/paper/2403.01267/) (2024)
- [The LLM Surgeon](https://mlsanity.com/paper/2312.17244/) (2023)
- [SVD-Surgeon: Optimal Singular-Value Surgery for Large Language Model Compression](https://mlsanity.com/paper/2606.23568/) (2026)

## Abstract (arXiv)

Deleting singular components offers a precise way to remove a capability from a language model, yet the first-order spectral saliency used to rank components predicts only a local loss change, whereas deletion is a finite intervention. In this paper, we study how prediction error affects selective editing, where selective editing requires degradation of a target task while preserving others. We decompose the error into derivative transfer across item splits and nonlinear response along the deletion path. We establish that outer interval screening retains every feasible candidate when every candidate's intervals contain its finite validation loss changes on every task. We evaluate these effects using one answer-only negative log-likelihood objective for search, validation, and test, with disjoint calibration and evaluation masks. The primary configuration targets arithmetic in Mistral-7B-Instruct-v0.3 while preserving code and question answering; extensions cover Llama-3.1-8B-Instruct and reversed target roles. In the primary study, which deletes 1024 coordinates from a support of 7168, calibrated intervals cover 968 of 1024 evaluation masks. Outer screening reaches the direct-selected edit after 25 verification checks, whereas direct verification abstains at a 32-check cap, but it rejects 4 of 74 feasible masks. All three selected edits pass validation, yet only one meets every test constraint. Interval coverage, feasible-candidate retention, and independent test preservation are therefore distinct properties and require separate assessment.