Related papers: An Equivariance Toolbox for Learning Dynamics

Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in…

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…

The interpretation of deep learning as a dynamical system has gained a considerable attention in recent years as it provides a promising framework. It allows for the use of existing ideas from established fields of mathematics for studying…

Neural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In line with such efforts, a deep learning model for one-dimensional consolidation where the governing equation…

Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly…

Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…

Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental. We undertake a systematic study of the role that symmetry plays. In particular, we…

Domain adaptation techniques address the problem of reducing the sensitivity of machine learning methods to the so-called domain shift, namely the difference between source (training) and target (test) data distributions. In particular,…

Particle physics classification often assumes flat geometry, ignoring the curved statistical structure of collision data. We present a geometric framework for Vector Boson Fusion Higgs classification that combines physics-inspired…

Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

Harnessing the local topography of the loss landscape is a central challenge in advanced optimization tasks. By accounting for the effect of potential parameter changes, we can alter the model more efficiently. Contrary to standard…

Most state-of-the-art works in trajectory forecasting for automotive target predicting the pose and orientation of the agents in the scene. This represents a particularly useful problem, for instance in autonomous driving, but it does not…

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…

Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…

The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…

This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…