Deep Minds and Shallow Probes

Abstract: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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2605.11448 [cs.LG]

(or arXiv:2605.11448v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.11448 Focus to learn more arXiv-issued DOI via DataCite

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