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May 2026

Guest Editorial for Part 2 of the Special Issue on the Mathematics of Deep Learning [From the Guest Editors]

Deep learning (DL) is a field of study within machine learning and signal processing that has been around for nearly 40 years. In the last 10 years, its progress on problems including speech-to-text, image recognition, image generation, and language generation has been phenomenal. This exponential progress has been driven by exciting engineering and algorithmic developments.

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Spectral Graph Theory: The mathematics of self-supervised learning [Special Issue on the Mathematics of Deep Learning]

Possessing a manipulable representation of the world is a requirement for intelligent machines to plan, reason, and act in the world. Endowing computational systems, e.g., deep networks (DNs), with artificial intelligence (AI) capabilities is the goal of self-supervised learning (SSL). Immense optimism, fueled by early successes, funneled vast resources into SSL, which led to fast-paced but fragmented early developments. 

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On the Convergence, Implicit Bias, and Edge of Stability of Gradient Descent in Deep Learning: Reviewing recent progress [Special Issue on the Mathematics of Deep Learning]

Deep neural networks (DNNs) trained via gradient descent (GD) with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. To theoretically understand this puzzling phenomenon, many works on convergence analysis for GD algorithms on NNs have been developed over the last half-decade. 

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