The thesis investigates practical optimization techniques used in modern machine learning, such as submodel training, gradient clipping, and layer-wise non‑Euclidean directions, by analyzing their actual objectives, assumptions, updates, and computations rather than simplified proxies. It demonstrates that Independent Subnetwork Training can converge to a shifted fixed point due to sketching bias, while Model‑Agnostic Sparsified Training incorporates the sketch distribution to achieve unbiased gradients and convergence guarantees. The work also explores private optimization, showing that adaptive quantile clipping retains bias unless a suitable schedule is used, and combines smoothed normalization with error compensation to obtain distributed private convergence without bounded gradient assumptions. Additionally, it develops a layer‑wise generalized smoothness model for optimizers based on linear minimization oracles, validates it through the Gluon framework, and highlights the importance of precise orthogonalization in Muon‑style methods.
Modern machine learning relies on practical optimization methods that often differ from the algorithms studied in classical analyses: they train submodels, clip or normalize gradients, use layer-wise...
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
arXiv:2608.09523v2 Announce Type: replace Abstract: Stochastic gradient descent (SGD) and its variants train deep neural networks (DNNs) effectively in practice, yet classical optimization theory doe...
arXiv:2610.32465v1 Announce Type: new Abstract: Adversarial sharpness penalty per iteration of a base optimizer, known as sharpness-aware minimization (SAM), is an accepted technique to improve gener...
The paper introduces a data‑driven criterion that dynamically selects optimal Linear Minimization Oracle (LMO) geometries for each layer of a deep neural network, bridging the gap between SGD and Muon updates. By deriving the criterion from gradient and activation statistics via a single‑step random feature regression surrogate, the authors enable a design space that interpolates between existing optimizers, including SGD, Muon, Adam, and MuAdam. The adaptive approach incurs only about a 3% runtime overhead and demonstrates competitive or superior performance compared to the best static optimizer across three training scenarios.
arXiv:2606. 05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators.
arXiv:2606. 01521v1 Announce Type: new Abstract: A central problem in machine learning is that models can achieve near-perfect training performance while generalizing substantially less well to unseen examples.
arXiv:2505. 22988v3 Announce Type: replace-cross Abstract: The goal of quantization is to produce a compressed model whose output distribution is as close to the original model's as possible.
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
arXiv:2606. 08783v1 Announce Type: cross Abstract: Orthogonalized momentum updates, as used in Muon-style optimizers, have recently shown strong empirical stability in large-scale deep learning.
The paper introduces Batched SGD, a variant that groups online samples into epochs and performs a single update per epoch using a low‑variance gradient estimate. This batching approach allows a straightforward high‑probability analysis without restrictive assumptions or auxiliary sequences, yielding near‑optimal rates for both strongly convex and non‑convex objectives under standard smoothness and sub‑Gaussian noise conditions. The authors also extend the method to federated learning, providing the first high‑probability guarantees with logarithmic communication complexity, linear speedup in the number of agents, and robustness to data heterogeneity.