# HeadEdit: Calibrating Language Model Behavior Through the Frozen Unembedding Matrix

arXiv: https://arxiv.org/abs/2610.01170 · HTML: https://mlsanity.com/paper/2610.01170/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 41 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 39)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [OR-Bench: An Over-Refusal Benchmark for Large Language Models](https://mlsanity.com/paper/2405.20947/) (2024)
- [SORRY-Bench: Systematically Evaluating Large Language Model Safety Refusal](https://mlsanity.com/paper/2406.14598/) (2024)
- [Improving Instruction-Following in Language Models through Activation Steering](https://mlsanity.com/paper/2410.12877/) (2024)
- [Semantics-Adaptive Activation Intervention for LLMs via Dynamic Steering Vectors](https://mlsanity.com/paper/2410.12299/) (2024)
- [DeAL: Decoding-time Alignment for Large Language Models](https://mlsanity.com/paper/2402.06147/) (2024)
- [Fishing for Magikarp: Automatically Detecting Under-trained Tokens in Large Language Models](https://mlsanity.com/paper/2405.05417/) (2024)
- [Extracting Prompts by Inverting LLM Outputs](https://mlsanity.com/paper/2405.15012/) (2024)
- [Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens](https://mlsanity.com/paper/2602.13517/) (2026)
- [Spherical Steering: Geometry-Aware Activation Rotation for Language Models](https://mlsanity.com/paper/2602.08169/) (2026)

## Abstract (arXiv)

Alignment does not eliminate behavioral errors in language models. Models may still refuse benign requests, call unnecessary tools, or yield to false user claims. Current methods mitigate such errors as a computation problem, and rarely explore if the desired behavior is already encoded in the model's representation. Motivated by the observation that behavior-relevant information remains linearly decodable from the final hidden state even when the resulting logits produce the undesired behavior, we introduce HeadEdit, a gradient-free method that calibrates model behavior through the unembedding matrix. HeadEdit extracts a low-rank behavioral subspace from paired completions and uses each prompt's coordinates within it to generate a vocabulary-wide correction, thereby implementing implicitly adaptive steering without manually specified target tokens or parameter updates. HeadEdit improves all nine experimental settings across three tasks and three model families, with negligible inference overhead and no systematic loss of general capabilities. It also reveals a connection to gradient-based alignment. HeadEdit's low-dimensional representation partly predicts how preference tuning changes output logits on unseen prompts. The subspace learned from the model can also be reused after tuning, improving performance without re-extracting or retuning. These results show that HeadEdit provides a practical, lightweight, and interpretable way to calibrate model behavior through the unembedding matrix.