# Deep Minds and Shallow Probes

arXiv: https://arxiv.org/abs/2605.11448 · HTML: https://mlsanity.com/paper/2605.11448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 17 of 17)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [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)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Constitutional Classifiers: Defending against Universal Jailbreaks across Thousands of Hours of Red Teaming](https://mlsanity.com/paper/2501.18837/) (2025)
- [Large Language Models can Strategically Deceive their Users when Put Under Pressure](https://mlsanity.com/paper/2311.07590/) (2023)
- [Auditing language models for hidden objectives](https://mlsanity.com/paper/2503.10965/) (2025)
- [Eliciting Latent Knowledge from Quirky Language Models](https://mlsanity.com/paper/2312.01037/) (2023)
- [Constitutional Classifiers++: Efficient Production-Grade Defenses against Universal Jailbreaks](https://mlsanity.com/paper/2601.04603/) (2026)
- [Transferring Linear Features Across Language Models With Model Stitching](https://mlsanity.com/paper/2506.06609/) (2025)
- [When Truthful Representations Flip Under Deceptive Instructions?](https://mlsanity.com/paper/2507.22149/) (2025)
- [How not to Stitch Representations to Measure Similarity: Task Loss Matching versus Direct Matching](https://mlsanity.com/paper/2412.11299/) (2024)

## Abstract (arXiv)

Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a representation should therefore be stable under the relevant representation symmetries rather than be tied to a particular basis. We prove that, under standard nondegeneracy assumptions, behaviorally equivalent LLMs have hidden representations related by an invertible affine transformation. The resulting symmetry principle singles out a unique hierarchy of shallow coordinate-stable probes, with linear probes as its degree-1 member. We also show that a natural object for cross-model probe transfer is a shared probe-visible quotient--the representation modulo directions invisible to the probe family--rather than the full hidden state. Experiments on synthetic and real-world tasks support both predictions, showing where degree-2 probes help beyond linear ones and how quotient-based transfer enables coverage-aware monitor portability across model families. These results point toward a broader geometric representation theory of neural probing, with coverage-aware monitor transfer as a concrete operational consequence.