Related papers: Incorporating Symmetry into Deep Dynamics Models f…

A machine learning (ML) system must learn not only to match the output of a target function on a training set, but also to generalize to novel situations in order to yield accurate predictions at deployment. In most practical applications,…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…

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…

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter…

Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path…

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…

Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…

Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…

Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…

Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should have higher prediction accuracy and better generalization in prediction of physical dynamics. In…

Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Symmetry perception requires abstraction of long-range spatial…