研究：维度缩放中的结构——通过维度缩放探测神经对称性

View PDF HTML (experimental)

Abstract:How much of a neural population's measured dimensionality is the code, and how much is the act of measuring it? The slope of the participation ratio against subsample size is reported for cortical populations and for the layers of language models as a number that belongs to the system. It does not. One patch of eleven thousand mouse V1 neurons returns three slopes, 0.25 along random stimulus subsets, 0.31 along drift direction, 0.35 along neuron count, and only the middle one carries structure; the other two are the sampling floor.
We split every exponent into that floor and a shift earned along a declared axis, and read the shift against two nulls: permuting the labels, and permuting them only among samples that share a nuisance. On V1 the direction-aligned shift clears the label null in eight of eight grating recordings, is positive in 32 of 32 animals in a second laboratory, and reads both sectors of the code's O(2) symmetry. The even sector sets how the ladder starts: it decides which order of adding classes climbs faster, predicts the opposite order in an equivariant network, and flows under coarse-graining by a closed-form factor that says what orientation columns do to mesoscale signals. The odd sector, carried by the direction-selective neurons, keeps the ladder climbing past half the classes. On language models the same split separates content inherited from the tokens from construction built with depth, on five architectures, and the second null shows that a grammaticality signal of twenty standard deviations is entirely carrier composition. With a floor and a declared axis, dimensionality scaling is an axis-resolved measurement, and where the axis follows a known symmetry it resolves the sector content of the code. The instrument, rung, trains no probe and reads any array or any Hugging Face model layer by layer (this https URL).

Submission history

From: Adil Amin [view email]
[v1] Wed, 16 Sep 2026 03:08:01 UTC (2,708 KB)