# The Geometric Canary: Predicting Steerability and Detecting Drift via Representational Stability

arXiv: https://arxiv.org/abs/2604.17698 · HTML: https://mlsanity.com/paper/2604.17698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [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)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [Inspecting and Editing Knowledge Representations in Language Models](https://mlsanity.com/paper/2304.00740/) (2023)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO](https://mlsanity.com/paper/2405.00662/) (2024)
- [Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes](https://mlsanity.com/paper/1801.01990/) (2018)
- [On the Predictive Power of Representation Dispersion in Language Models](https://mlsanity.com/paper/2506.24106/) (2025)
- [The Geometry of Alignment Collapse: When Fine-Tuning Breaks Safety](https://mlsanity.com/paper/2602.15799/) (2026)
- [Geometric Stability: The Missing Axis of Representations](https://mlsanity.com/paper/2601.09173/) (2026)

## Abstract (arXiv)

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ = 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ = 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρ ≈ 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2× greater geometric change than CKA during post-training alignment (up to 5.23× in Llama) while providing earlier warning in 73% of models and maintaining a 6× lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.