# Spectral Geometry of LoRA Adapters Encodes Training Objective and Predicts Harmful Compliance

arXiv: https://arxiv.org/abs/2604.08844 · HTML: https://mlsanity.com/paper/2604.08844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Safety alignment and jailbreak attacks, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Safety alignment and jailbreak attacks](https://mlsanity.com/alignment/safety-alignment-and-jailbreak-attacks/)

## Builds on (most cited first, 11 of 11)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [Watch the Weights: Unsupervised monitoring and control of fine-tuned LLMs](https://mlsanity.com/paper/2508.00161/) (2025)

## Built on by (most cited first, 1 of 1)

- [Harmful SFT Leaves a Continuous Trace in LLM Checkpoint Updates](https://mlsanity.com/paper/2610.07518/) (2026)

## Abstract (arXiv)

We study whether low-rank spectral summaries of LoRA weight deltas can identify which fine-tuning objective was applied to a language model, and whether that geometric signal predicts downstream behavioral harm. In a pre-registered experiment on textttLlama-3.2-3B-Instruct, we manufacture 38 LoRA adapters across four categories: healthy SFT baselines, DPO on inverted harmlessness preferences, DPO on inverted helpfulness preferences, and activation-steering-derived adapters, and extract per-layer spectral features (norms, stable rank, singular-value entropy, effective rank, and singular-vector cosine alignment to a healthy centroid). Within a single training method (DPO), a logistic regression classifier achieves AUC~1.00 on binary drift detection, all six pairwise objective comparisons, and near-perfect ordinal severity ranking (ρ ≥ 0.956). Principal component analysis on flattened weight deltas reveals that training objective is PC1 (AUC~1.00 for objective separation), orthogonal to training duration on PC2. Query-projection weights detect that drift occurred; value-projection weights identify which objective. Cross-method generalization fails completely: a DPO-trained classifier assigns every steering adapter a lower drift score than every DPO adapter (AUC~0.00). In a behavioral evaluation phase, DPO-inverted-harmlessness adapters show elevated harmful compliance on HEx-PHI prompts (mean ASR 0.266 vs. healthy 0.112, Delta = +0.154), with near-perfect dose--response (ρ = 0.986). The geometry-to-behavior rank correlation is ρ = 0.72 across 24 non-steered adapters. These results establish that within a controlled manufacturing regime, LoRA weight-space geometry carries objective identity, intensity ordering, and a coarse link to harmful compliance, and that cross-method monitoring requires per-method calibration.