math.OC · 2026-06-16 · No. 25

Optimization and Control, 2026-06-16.

2 new papers in math.OC. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Exploding and vanishing gradients in deep neural networks: the effect of residual connections

    Vivek S Borkar

    math.OC · cs.LG

    The well known phenomenon of exploding and vanishing gradients in deep neural networks is analyzed using multiplicative ergodic theory. The effect of adding a residual connection is explained in this context. Specifically, a characterization of Liapunov exponents due to Furstenberg and Kifer is exploited in order to make a precise statement about the Liapunov spectrum and the effect of residual connections on it.

    arxiv.org/abs/2606.17013 · PDF

  2. 02

    Functional Gradient Descent with Adaptive Representations

    Daniel Csillag, Rodrigo Schuller, Pedro Dall'Antonia, Leonidas Guibas, Luiz Velho, Tiago Novello

    math.OC · cs.LG · stat.ML

    Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis. An interesting alternative is functional gradient descent (FGD), that is, gradient descent directly in function space, which benefits from strong convergence results and admits a clean theory. However, FGD is...

    arxiv.org/abs/2606.16926 · PDF

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