Auditing Neural Thickets with Low-Rank Routes

Miroslav Lžičař

Keywords: weight-space geometry; low-rank adaptation; optimization

TL;DR: Strict accounting turns learned low-rank thicket search into a control-dominated selector-sensitivity audit.

Abstract: Neural thickets suggest that many task experts lie dense around pretrained weights, but density alone does not imply that such experts are easy to discover. We audit whether those experts can be found through much smaller learned low-rank routes under deployable selection and matched total query budgets. Here, ``rank'' denotes the dimension of a linear search basis inside an $8$-dimensional master perturbation span. On a four-window Countdown audit with Qwen2.5-7B-Instruct, strict selected-before-test accounting gives a mixed and selector-sensitive picture: fixed low-rank controls beat selected dense in two windows and fall below it in two others, while exact-test-oracle diagnostics are stronger but non-deployable. Independent-noise and one-window random-abundance checks preserve the same caution. The result is negative for a unique reward-learned core or one-shot query-efficiency claim, but positive for low-rank routes as probes of compressible, degenerate, and selector-sensitive neighborhoods around frozen checkpoints.

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Submission Number: 29