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Deep Minds and Shallow Probes

NeurIPS 2026 · Architectures and efficiency › RNNs and normalization · approach: Symmetry and equivariance in loss landscapes · 0 citations (OpenAlex)

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Shows that behaviorally equivalent readouts imply affine-related hidden coordinates, derives a polynomial probe hierarchy (degree-1 linear, degree-2 CP), and proposes transferring probes via a probe-visible quotient, tested on synthetic tasks, Pythia agreement probes, and Qwen-to-Mistral safety monitor transfer.

Problem

Probe families are chosen ad hoc, and probe success can reflect probe capacity rather than structure in the representation; cross-model probe transfer needs a coordinate-free target. The paper asks which probe families are stable under the symmetries of neural representations.

Approach

Behavioral equivalence of final readouts forces hidden states to be related by an affine map; requiring a finite-dimensional, affine-invariant scalar probe space then forces polynomial spaces of bounded degree, and cross-model transfer should use the probe-visible quotient H/K(V) rather than the full hidden state.

Key results

• On subject-verb agreement across Pythia-70m/160m/410m, CP rank-1 probes beat linear heads by 16.8-20.0pp AUROC.
• Zero-label quotient transfer from Qwen-2.5-7B to Mistral-7B reaches AUROC 0.67-0.97 across five safety concepts, while a random-initialization control is near chance on four of five.
• Synthetic quotient transfer keeps in-span balanced accuracy around 0.99 under nuisance growth to 56 dims, while rejecting out-of-span concepts at chance; full-state OLS transfers them at 0.989.

Surprising findings

• Full-state OLS transfers held-out low-ISF concepts at 0.77-0.95 AUROC, whereas the quotient correctly drops to 0.67-0.77, showing full-state alignment can mask coverage failures.
• Under affine reparameterization, a sparse top-50 monomial probe collapses to R^2 = -18.3, while analytically transported full quadratics remain exact.

Limitations

• Symmetry result is exact only for the final readout layer; deeper-layer symmetries may be only approximate.
• Cross-architecture transfer is heterogeneous; some concepts such as Qwen-7B to Mistral jailbreaking transfer weakly (0.669).

Experimental setup

Datasets: Universal Dependencies English-EWT BeaverTails

Benchmarks: BeaverTails Universal Dependencies English-EWT synthetic circular N-parity synthetic quotient transfer

Metrics: AUROC balanced accuracy silent-failure rate harmful compliance rate benign false-refusal rate

Baselines: linear probe full quadratic probe PCA projection random projection full-state OLS

Builds on: model stitching structural probing

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