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X-WR-CALNAME:CMM
X-WR-CALDESC:Centro de Modelamiento Matemático
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DTSTART:20260624T011822
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DTSTART;TZID=America/Santiago:20260624T150000
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DTSTAMP:20260622T121220Z
CREATED:20260622
LAST-MODIFIED:20260622
PRIORITY:5
SEQUENCE:1
TRANSP:OPAQUE
SUMMARY:Seminario Math&AI: “Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model”
DESCRIPTION:Abstract:  We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination of latent compositional features whose weights decrease as a power law. We show that a layer-wise spectral algorithm adapted to this compositional structure achieves improved scaling relative to shallow, non-adaptive methods, and recovers the latent directions sequentially: strong features become detectable at small sample sizes, while weaker features require more data. \nWe prove sharp feature-wise recovery thresholds and show that aggregating these transitions yields an explicit power-law decay of the prediction error. Technically, the analysis relies on random matrix methods and a resolvent-based perturbation argument, which gives matching upper and lower bounds for individual eigenvector recovery beyond what standard gap-based perturbation bounds provide. \nNumerical experiments confirm the predicted sequential recovery, finite-size smoothing of the thresholds, and separation from non-hierarchical kernel baselines. Together, these results show how smooth scaling laws can emerge from a cascade of sharp feature-learning transitions.                                         \nSpeaker: Arie Wortsman Zurich, Center for Data Science, ENS Paris\n
URL:https://www.cmm.uchile.cl/events/seminario-mathai-scaling-laws-from-sequential-feature-recovery-a-solvable-hierarchical-model/
ORGANIZER;CN=CMM:MAILTO:
CATEGORIES:Seminarios
LOCATION:Sala Maryam Mirzakhani - 6to piso CMM
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