{"ID":2884261,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06776","arxiv_id":"2508.06776","title":"Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift","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.","short_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 u...","url_abs":"https://arxiv.org/abs/2508.06776","url_pdf":"https://arxiv.org/pdf/2508.06776v1","authors":"[\"Amit Pandey\"]","published":"2025-08-09T02:05:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"stat.ML\"]","methods":"[\"Transformer\"]","has_code":false}