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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.
From Coordination to Execution: Positioning the IEEE Signal Processing Society at the Core of IEEE’s Artificial Intelligence Ecosystem [From the Editor]
Artificial intelligence (AI) is transforming our technical priorities and the way our community organizes, collaborates, and delivers impact. In this environment, coordination alone is insufficient. We require structured execution, clearly defined roles and responsibilities, and assessable outcomes.
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.
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.
March 2026
The Nasreddin Hodja Principle and the Mathematics of Deep Learning [From the Editor]
You may have noticed that our magazine covers have been venturing beyond the customary look of a technical publication. I hope this shift has been enjoyable for you to see. I confess that I’ve been enjoying it myself, particularly the process of selecting the images and shaping the final composition. It has been an engaging experience exploring the possibilities and connections between the ideas we wish to highlight and images drawn from the natural world.
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