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arXiv · 2508.06776

Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift

Amit Pandey
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Abstract

We present Zero-Direction Probing (ZDP), a theory-only framework for detecting model drift from null directions of transformer activations without task labels or output evaluations. Under assumptions A1--A6, we prove: (i) the Variance--Leak Theorem, (ii) Fisher Null-Conservation, (iii) a Rank--Leak bound for low-rank updates, and (iv) a logarithmic-regret guarantee for online null-space trackers. We derive a Spectral Null-Leakage (SNL) metric with non-asymptotic tail bounds and a concentration inequality, yielding a-priori thresholds for drift under a Gaussian null model. These results show that monitoring right/left null spaces of layer activations and their Fisher geometry provides concrete, testable guarantees on representational change.

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Amit Pandey. 2025-08-09. Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift. https://arxiv.org/abs/2508.06776

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