Related papers: Efficient Model-Agnostic Multi-Group Equivariant N…

Motivated by the recent developments in artificial intelligence, we introduce linear quadratic deep structured teams in this paper. Two notions of equivariant and partially equivariant systems are defined, and it is shown that such systems…

Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…

Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentially-growing computational cost.…

Deep neural networks (DNNs) has shown great promise in computer vision tasks. However, machine vision achieved by DNNs cannot be as robust as human perception. Adversarial attacks and data distribution shifts have been known as two major…

We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of…

Equivariance has gained strong interest as a desirable network property that inherently ensures robust generalization. However, when dealing with complex systems such as articulated objects or multi-object scenes, effectively capturing…

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…

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very…

I present IGAN (Inferent Generative Adversarial Networks), a neural architecture that learns both a generative and an inference model on a complex high dimensional data distribution, i.e. a bidirectional mapping between data samples and a…

Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory…

We propose a new volumetric grasp model that is equivariant to rotations around the vertical axis, leading to a significant improvement in sampling efficiency. Our model employs a tri-plane volumetric feature representation -- i.e., the…

The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations.…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the…

Convolutional Neural Networks (CNNs) have advanced existing medical systems for automatic disease diagnosis. However, there are still concerns about the reliability of deep medical diagnosis systems against the potential threats of…

Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and…

Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in…

Deep networks were recently suggested to face the odds between accuracy (on clean natural images) and robustness (on adversarially perturbed images) (Tsipras et al., 2019). Such a dilemma is shown to be rooted in the inherently higher…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve…