Pearcey Kernel Basis:
Beyond Second Order Differential Equations

There is a well-known connection between orthogonal polynomials, second-order Sturm-Liouville differential equations, random matrices, and orthogonal projectors in \( L_2 \). This post explores an extension of this topic. We have identified a basis for the Pearcey Kernel, initially introduced by Brezin and Hikami . To achieve this, we move beyond the traditional approach of second-order differential equations and orthogonal polynomials, employing third-order equations and biorthogonal bases instead.

published 8.04.2021, last update 24.06.2024

Batch size vs Momentum

Imagine we've pinpointed the optimal learning rate and other hyperparameters for a gradient descent method and a specific model. The natural progression is to train this model on more powerful hardware, equipped with additional GPU units and RAM, enabling larger batch sizes. But how do we adjust the gradient descent hyperparameters to scale up effectively without disrupting the current settings?

In this article, we explore this question along with some related ones. Our main thesis: changing the batch size is roughly equivalent to adjusting the learning rate and momentum.

published 8.04.2021, last update 24.06.2024