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PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…

We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…

Flow $Q$-learning has recently been introduced to integrate learning from expert demonstrations into an actor-critic structure. Central to this innovation is the ``the one-step policy'' network, which is optimized through a $Q$-function…

In this paper, we propose a unified method to jointly learn optical flow and stereo matching. Our first intuition is stereo matching can be modeled as a special case of optical flow, and we can leverage 3D geometry behind stereoscopic…

We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve…

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…

A method to control results of gradient descent unsupervised learning in a deep neural network by using evolutionary algorithm is proposed. To process crossover of unsupervisedly trained models, the algorithm evaluates pointwise fitness of…

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…

The autoencoder model uses an encoder to map data samples to a lower dimensional latent space and then a decoder to map the latent space representations back to the data space. Implicitly, it relies on the encoder to approximate the inverse…

Many model-based Visual Odometry (VO) algorithms have been proposed in the past decade, often restricted to the type of camera optics, or the underlying motion manifold observed. We envision robots to be able to learn and perform these…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

The rise of test-time scaling has remarkably boosted the reasoning and agentic proficiency of Large Language Models (LLMs). Yet, standard Transformers struggle to scale inference-time compute efficiently, as conventional looping strategies…

Spatiotemporal modeling is critical for understanding complex systems across various scientific and engineering disciplines, but governing equations are often not fully known or computationally intractable due to inherent system complexity.…

Real-time object detectors like YOLO achieve exceptional performance when trained on large datasets for multiple epochs. However, in real-world scenarios where data arrives incrementally, neural networks suffer from catastrophic forgetting,…

Learning multiple tasks sequentially without forgetting previous knowledge, called Continual Learning(CL), remains a long-standing challenge for neural networks. Most existing methods rely on additional network capacity or data replay. In…

When interacting with highly dynamic environments, scene flow allows autonomous systems to reason about the non-rigid motion of multiple independent objects. This is of particular interest in the field of autonomous driving, in which many…

Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, popular methods such as masked autoencoders (MAEs) rely on reconstructing inputs from a fixed, predetermined masking ratio. Instead…

A comprehensive methodology for establishing the existence of gradient flows for cross-diffusion systems with respect to suitable energies is proposed. The approach is based on the construction of piecewise-in-time constant approximations…

We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…