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Vicente Opazo

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#machine learning Preprint Aug 2026

Three Tokens Force Exponential Feature Rank in Nonnegative Kernel Attention

How much feature rank does comparison require in kernel attention? On Min-IP over $m$-bit tokens, rank one solves every sequence of length at most two exactly. At length three, the minimum feature rank of one normalized nonnegative kernel-attention head is $2^{\Theta(m)}$ for error strictly below $1/2$ on every input,...

Vicente Opazo · 0 citations
#machine learning Preprint Sep 2026

When a Flatness Proxy Is Not a Function: Robustness Certificates and Training Interventions

A valid curvature upper bound need not justify either a robustness certificate or an intervention on an intrinsic predictor property. We demonstrate this distinction for a last-layer relative-flatness proxy used in both settings. First, empirical-risk stationarity does not eliminate pointwise first-order loss terms: at...

Vicente Opazo, Jose Calatayud-Mateu, Cristóbal Rojas et al. · 0 citations

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