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Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…
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…
The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
While Transformer architectures have show remarkable success, they are bound to the computation of all pairwise interactions of input element and thus suffer from limited scalability. Recent work has been successful by avoiding the…
Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…
Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance…
Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations…
Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…
The global attention mechanism is one of the keys to the success of transformer architecture, but it incurs quadratic computational costs in relation to the number of tokens. On the other hand, equivariant models, which leverage the…
Why are state-of-the-art Vision Transformers (ViTs) not designed to exploit natural geometric symmetries such as 90-degree rotations and reflections? In this paper, we argue that there is no fundamental reason, and what has been missing is…
Humans perceive and interact with the world with the awareness of equivariance, facilitating us in manipulating different objects in diverse poses. For robotic manipulation, such equivariance also exists in many scenarios. For example, no…
Equivariance is a powerful prior for learning physical dynamics, yet exact group equivariance can degrade performance if the symmetries are broken. We propose object-centric world models built with geometric algebra neural networks,…
Convolutional neural networks revolutionized computer vision and natrual language processing. Their efficiency, as compared to fully connected neural networks, has its origin in the architecture, where convolutions reflect the translation…
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…
We introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group $\mathrm{SE}(d)$. We propose an equivariant attention mechanism that operates on features…
Pixelizations of Platonic solids such as the cube and icosahedron have been widely used to represent spherical data, from climate records to Cosmic Microwave Background maps. Platonic solids have well-known global symmetries. Once we…
Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…
Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…