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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…
The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…
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…
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain of the data is commonly encountered manifolds such as the…
Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as…
Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…
There has been much recent interest in designing neural networks (NNs) with relaxed equivariance, which interpolate between exact equivariance and full flexibility for consistent performance gains. In a separate line of work, structured…
Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…
Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…
This work presents a quantum convolutional neural network (QCNN) for the classification of high energy physics events. The proposed model is tested using a simulated dataset from the Deep Underground Neutrino Experiment. The proposed…
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
Neural networks are a promising tool for simulating quantum many body systems. Recently, it has been shown that neural network-based models describe quantum many body systems more accurately when they are constrained to have the correct…
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by…
Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…
Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) which excel in a wide range of technical applications by explicitly encoding symmetries, such as rotations and…
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…
Group-equivariant quantum machine learning has emerged as a promising paradigm by incorporating symmetry into quantum models. However, constructing models simultaneously equivariant to both rotational and permutational symmetries in a…
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…