Related papers: HyCOP: Hybrid Composition Operators for Interpreta…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

In Transformer-based architectures, the attention mechanism is inherently permutation-invariant with respect to the input sequence's tokens. To impose sequential order, token positions are typically encoded using a scheme with either fixed…

Compositional, structured models are appealing because they explicitly decompose problems and provide interpretable intermediate outputs that give confidence that the model is not simply latching onto data artifacts. Learning these models…

Higher-order brain connectivity (HOBC), which captures interactions among three or more brain regions, provides richer organizational information than traditional pairwise functional connectivity (FC). Recent studies have begun to infer…

Sparse Mixture-of-Experts (MoE) layers route tokens through a handful of experts, and learning-free compression of these layers reduces inference cost without retraining. A subtle obstruction blocks every existing compressor in this family:…

Current inference systems for Mixture-of-Experts (MoE) models primarily employ static parallelization strategies. However, these static approaches cannot consistently achieve optimal performance across different inference scenarios, as they…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Self-supervised learning has become a central strategy for representation learning, but the majority of architectures used for encoding data have only been validated on regularly-sampled inputs such as images, audios. and videos. In many…

Motion prediction is critical for autonomous vehicles to effectively navigate complex environments and accurately anticipate the behaviors of other traffic participants. As autonomous driving continues to evolve, the need to assimilate new…

Learned PDE solvers are often trained as monolithic surrogates for a specific equation, boundary condition and discretization. This makes them difficult to reuse when mechanisms change and it can limit stability under long-horizon rollout.…

Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…

Many positional encodings (PEs) are designed to exhibit long-term decay, based on an entrenched and long-standing inductive opinion: tokens farther away from the current position carry less relevant information. We argue that long-term…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Effective generalization in robotic manipulation requires representations that capture invariant patterns of interaction across environments and tasks. We present a self-supervised framework for learning hierarchical manipulation concepts…

Recognizing unknown objects is crucial for safety-critical applications such as autonomous driving and robotics. Open-Set Panoptic Segmentation (OPS) aims to segment known thing and stuff classes while identifying valid unknown objects as…

This paper contributes to interpretable machine learning via visual knowledge discovery in parallel coordinates. The concepts of hypercubes and hyper-blocks are used as easily understandable by end-users in the visual form in parallel…

We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as…