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Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…

Sequential deep learning models such as RNN, causal CNN and attention mechanism do not readily consume continuous-time information. Discretizing the temporal data, as we show, causes inconsistency even for simple continuous-time processes.…

Task sequencing (TS) is one of the core open problems in Deep Learning, arising in a plethora of real-world domains, from robotic assembly lines to autonomous driving. Unfortunately, prior work has not convincingly demonstrated the…

Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…

Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

Off-policy learning ability is an important feature of reinforcement learning (RL) for practical applications. However, even one of the most elementary RL algorithms, temporal-difference (TD) learning, is known to suffer form divergence…

In this paper, we study the Temporal Difference (TD) learning with linear value function approximation. It is well known that most TD learning algorithms are unstable with linear function approximation and off-policy learning. Recent…

Real-world visual data rarely presents as isolated, static instances. Instead, it often evolves gradually over time through variations in pose, lighting, object state, or scene context. However, conventional classifiers are typically…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…

Sequential modelling of high-dimensional data is an important problem that appears in many domains including model-based reinforcement learning and dynamics identification for control. Latent variable models applied to sequential data…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Semantic segmentation models classify pixels into a set of known (``in-distribution'') visual classes. When deployed in an open world, the reliability of these models depends on their ability not only to classify in-distribution pixels but…

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…