arXiv cs.CL· Anshul Kumar, Neha Prasad, Manoj Kumar, Barnab\'as P\'oczos, Deeksha Varshney·· 10 小时前AI 评分31
从线性探针到贝叶斯流形：大语言模型算术能力的几何结构
Linear Probes to Bayesian Manifolds: Geometry of Arithmetic in Large Language Models
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研究提出四阶段贝叶斯流程，将线性探针结论拆分为可解码性、形状、归属与因果使用四项主张分别检验，并在 GPT-J 6B、Llama 3.1 8B 和 Pythia 6.9B 的两位数加法与乘法上验证。
正文 · 原文
Abstract:Linear probes are a standard method to study geometric structures, such as helices and circles, from the activations of large language models (LLMs), and such structure is often taken as evidence that the model computes with it. Probe accuracy alone cannot establish this, because it conflates four separate claims. These are (1) that the concept is decodable from the activations, (2) that they form a specific shape, (3) that the shape belongs to the probed concept rather than to a related concept the model also represents, and (4) that the output of the model depends on the shape. We call these claims decodability, shape, ownership, and causal use, and we test them separately with a four-stage Bayesian pipeline. Stage 2 compares candidate shapes and selects the best one only when its evidence passes a predefined threshold. Stage 3 removes a set of related concepts, specified in advance, and tests whether the shape is owned or inherited. Stage 4 intervenes on the shape to test whether the output of the model depends on it. We apply the pipeline to two-digit addition and multiplication in GPT-J 6B, Llama 3.1 8B, and Pythia 6.9B. Nearly every concept is decodable, but the decoded directions overlap substantially across concepts. Every strongly supported comparison selects a ribbon, which is a helix whose radius changes with the value, or a torus. Of 1,330 cells with an ownership verdict, 19% of shapes are owned and 81% are inherited. Owned and inherited shapes move the output about equally often. Intervening on the shape retains approximately 61% of the effect of intervening on the full probe while using at most five dimensions, against a median of nine for the probe. Our results indicate that a probe verdict alone overstates what a model computes with, and we propose that probe results be reported as verdicts on all four claims rather than as a single accuracy.
| Comments: | 26 pages, 4 figures, 20 tables. Under review at ICLR 2027 |
| Subjects: | Machine Learning (cs.LG); Computation and Language (cs.CL) |
| Cite as: | arXiv:2611.12998 [cs.LG] |
| (or arXiv:2611.12998v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.12998 arXiv-issued DOI via DataCite |
Submission history
From: Anshul Kumar [view email]
[v1]
Sun, 8 Nov 2026 14:13:26 UTC (785 KB)
来源：arXiv cs.CL · arxiv.org