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We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the…
We propose Alternating Phase-Field Fourier Neural Networks (APF-FNNs) as a unified and physics-based framework for topology optimization. The approach decouples the design problem by representing the state, adjoint, and topology fields with…
Muon and related normalized optimizers decouple the choice of update direction from the choice of step scale, but their practical performance remains sensitive to the scale of the normalized step. We study adaptive scaling rules for Muon in…
Energy efficiency and reliability have long been crucial factors for ensuring cost-effective and safe missions in autonomous systems computers. With the rapid evolution of industries such as space robotics and advanced air mobility, the…
Fine-tuning pretrained models is a standard and effective workflow in modern machine learning. However, robust fine-tuning (RFT), which aims to simultaneously achieve adaptation to a downstream task and robustness to adversarial examples,…
Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in finite horizon scenarios, where input lengths are finite,…
The training of diffusion models is often absent in the evaluation of new optimization techniques. In this work, we benchmark recent optimization algorithms for training a diffusion model for denoising flow trajectories. We observe that…
Recent developments in deep learning optimization have brought about radically new algorithms based on the Linear Minimization Oracle (LMO) framework, such as $\sf Muon$ and $\sf Scion$. After over a decade of $\sf Adam$'s dominance, these…
Large-batch training has been essential in leveraging large-scale datasets and models in deep learning. While it is computationally beneficial to use large batch sizes, it often requires a specially designed learning rate (LR) schedule to…
Slimmable networks are a family of neural networks that can instantly adjust the runtime width. The width can be chosen from a predefined widths set to adaptively optimize accuracy-efficiency trade-offs at runtime. In this work, we propose…
In the endeavor to make autonomous robots take actions, task planning is a major challenge that requires translating high-level task descriptions to long-horizon action sequences. Despite recent advances in language model agents, they…
In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full…
How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows…
The concept of learning to optimize involves utilizing a trainable optimization strategy rather than relying on manually defined full gradient estimations such as ADAM. We present a framework that jointly trains the full gradient estimator…
Gating mechanisms are ubiquitous, yet a complementary question in feed-forward networks remains under-explored: how to introduce frequency-rich expressivity without sacrificing stability and scalability? This tension is exposed by…
Recently many first and second order variants of SGD have been proposed to facilitate training of Deep Neural Networks (DNNs). A common limitation of these works stem from the fact that they use the same learning rate across all instances…
Adaptive optimizers with decoupled weight decay, such as AdamW, are the de facto standard for pre-training large transformer-based generative models. Yet the quadratic nature of the $\ell_2$ penalty embedded in weight decay drives all…
As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…
Convolutional Neural Networks (CNNs) achieved great cognitive performance at the expense of considerable computation load. To relieve the computation load, many optimization works are developed to reduce the model redundancy by identifying…
Efficiently post-training large language models remains a challenging task due to the vast computational resources required. We present Spectrum, a method that accelerates LLM training by selectively targeting layer modules based on their…