Function Lives Where Variance Doesn't: Task-Weighted Charts of a Language Model's Computation
How many dimensions does a language model's computation actually use? The question is ill-posed until one names a functional. Task-weighted charts make it well-posed: low-dimensional coordinate systems fit against a chosen functional of the representation, under the functional's own metric, turning distillation into plain least squares. Across six models from three families, spanning 70m to 7B parameters, next-token prediction needs 70--90% of the residual stream's width to stay within 5% of intact perplexity, a width consumed by the rare tail of language, and the variance profile predicts none of it: two directions carry 90% of GPT-2's activation variance and almost none of its function....
| Authors | Alexandre Quemy |
|---|---|
| Primary category | cs.AI |
| Published | 12 August 2026 |
| Last updated at source | 12 August 2026 |
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