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Month: March 2025

Unraveling spectral properties of kernel matrices – II

Posted on March 24, 2025March 24, 2025 by Francis Bach

This month, we pursue our exploration of spectral properties of kernel matrices. As mentioned in a previous post, understanding how eigenvalues decay is not only fun but also key to understanding algorithmic and statistical properties of many learning methods (see, e.g., chapter 7 of my book “Learning Theory from First Principles“). This month, we look…

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Recent Posts

  • Closed-form dynamics beyond quadratics
  • Beyond Power Laws: Scaling Laws for Next-Token Prediction
  • Revisiting scaling laws via the z-transform
  • Unraveling spectral properties of kernel matrices – II
  • My book is (at last) out!

About

I am Francis Bach, a researcher at INRIA in the Computer Science department of Ecole Normale Supérieure, in Paris, France. I have been working on machine learning since 2000, with a focus on algorithmic and theoretical contributions, in particular in optimization. All of my papers can be downloaded from my web page or my Google Scholar page. I also have a Twitter account. I recently published a book “Learning Theory from First Principles“.

Recent Posts

  • Closed-form dynamics beyond quadratics
  • Beyond Power Laws: Scaling Laws for Next-Token Prediction
  • Revisiting scaling laws via the z-transform
  • Unraveling spectral properties of kernel matrices – II
  • My book is (at last) out!

Recent Comments

  • Francis Bach on Beyond Power Laws: Scaling Laws for Next-Token Prediction
  • Akshay on Beyond Power Laws: Scaling Laws for Next-Token Prediction
  • Francis Bach on My book is (at last) out!
  • Sidd on My book is (at last) out!
  • Francis Bach on Sums-of-squares for dummies: a view from the Fourier domain

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