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cs.LG2021
Effective dimension of machine learning models
Amira Abbas, David Sutter, Alessio Figalli +1
Making statements about the performance of trained models on tasks involving new data is one of the primary goals of machine learning, i.e., to understand the generalization power…
math.AP2021
Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations
Alessio Figalli, Yi Ru-Ya Zhang
We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well-known that: - For , there exist Morse index solu…
math.AP2021
The singular set in the Stefan problem
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
In this paper we analyze the singular set in the Stefan problem and prove the following results: - The singular set has parabolic Hausdorff dimension at most . - The solution…