Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912529962237952 |
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| author | Pandey, Amit |
| author_facet | Pandey, Amit |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift Pandey, Amit Machine Learning Artificial Intelligence 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. |
| title | Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2508.06776 |