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Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…

Convolutional neural networks have shown remarkable performance in recent years on various computer vision problems. However, the traditional convolutional neural network architecture lacks a critical property: shift equivariance and…

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…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

Neural Processes (NPs) are a popular class of approaches for meta-learning. Similar to Gaussian Processes (GPs), NPs define distributions over functions and can estimate uncertainty in their predictions. However, unlike GPs, NPs and their…

Group symmetries provide a powerful inductive bias for reinforcement learning (RL), enabling efficient generalization across symmetric states and actions via group-invariant Markov Decision Processes (MDPs). However, real-world environments…

Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an…

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging…

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for…

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…

Incorporating inductive biases is a promising approach for tackling challenging robot learning domains with sample-efficient solutions. This paper identifies partially observable domains where symmetries can be a useful inductive bias for…

In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group $G$. We then leverage this theory in the context of deep neural networks with group symmetries in order to obtain novel…

Incorporating geometric invariance into neural networks enhances parameter efficiency but typically increases computational costs. This paper introduces new equivariant neural networks that preserve symmetry while maintaining a comparable…

At the core of self-supervised learning for vision is the idea of learning invariant or equivariant representations with respect to a set of data transformations. This approach, however, introduces strong inductive biases, which can render…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…

Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces discontinuities that can affect stability during training,…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…