arXiv AI By Alexandre Quemy

Function Lives Where Variance Doesn't: Task-Weighted Charts of a Language Model's Computation

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The paper introduces task‑weighted charts, a method that defines low‑dimensional coordinate systems based on a chosen functional of a language model’s representation. Using these charts, the authors show that next‑token prediction requires 70–90% of the residual stream’s width to maintain perplexity, a width largely unused by variance‑based analyses. The study demonstrates that charts trained under the functional’s metric preserve predictions better than variance‑based or optimal linear compression when only a few dimensions are retained.

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