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With the prosperity of mobile devices, the distributed learning approach enabling model training with decentralized data has attracted wide research. However, the lack of training capability for edge devices significantly limits the energy…

We propose an energy stable network (EStable-Net) for solving gradient flow equations. The EStable-Net enables decreasing of a discrete energy along the neural network, which is consistent with the property of the gradient flow equation.…

We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…

Evidence-based decision-making entails collecting (costly) observations about an underlying phenomenon of interest, and subsequently committing to an (informed) decision on the basis of accumulated evidence. In this setting, active sensing…

In scientific machine learning, models are routinely deployed with parameter values or boundary conditions far from those used in training. This paper studies the learning-where-to-learn problem of designing a training data distribution…

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…

We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…

Continual learning is the problem of learning and retaining knowledge through time over multiple tasks and environments. Research has primarily focused on the incremental classification setting, where new tasks/classes are added at discrete…

While deep learning-based classification is generally tackled using standardized approaches, a wide variety of techniques are employed for regression. In computer vision, one particularly popular such technique is that of confidence-based…

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models…

In computational neuroscience, fixed points of recurrent neural networks are commonly used to model neural responses to static or slowly changing stimuli. These applications raise the question of how to train the weights in a recurrent…

Coarse graining techniques play an essential role in accelerating molecular simulations of systems with large length and time scales. Theoretically grounded bottom-up models are appealing due to their thermodynamic consistency with the…

A distribution system can flexibly adjust its substation-level power output by aggregating its local distributed energy resources (DERs). Due to DER and network constraints, characterizing the exact feasible power output region is…

The onset of life is often framed around membrane bound compartments and encoded metabolism, leaving unresolved how spatial organization arose before stable boundaries. In this context, environmental gradients are usually treated as…

Despite their growing popularity, data-driven models of real-world dynamical systems require lots of data. However, due to sensing limitations as well as privacy concerns, this data is not always available, especially in domains such as…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…

Localized receptive fields -- neurons that are selective for certain contiguous spatiotemporal features of their input -- populate early sensory regions of the mammalian brain. Unsupervised learning algorithms that optimize explicit…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…