Related papers: Integrating Symmetry into Differentiable Planning …
Deep belief networks are used extensively for unsupervised stochastic learning on large datasets. Compared to other deep learning approaches their layer-by-layer learning makes them highly scalable. Unfortunately, the principles by which…
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…
Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The…
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…
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…
The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and…
Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes…
Analyzing volumetric data with rotational invariance or equivariance is an active topic in current research. Existing deep-learning approaches utilize either group convolutional networks limited to discrete rotations or steerable…
The notion of group invariance helps neural networks in recognizing patterns and features under geometric transformations. Group convolutional neural networks enhance traditional convolutional neural networks by incorporating group-based…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…
Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…
Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to…
We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry…
Equivariant diffusion policies (EDPs) combine the generative expressivity of diffusion models with the strong generalization and sample efficiency afforded by geometric symmetries. While steering these policies with reinforcement learning…
Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and…
Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is…
Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…