Related papers: Efficient Generalized Spherical CNNs
Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…
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…
An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…
Deep learning using Convolutional Neural Networks (CNNs) has been shown to significantly out-performed many conventional vision algorithms. Despite efforts to increase the CNN efficiency both algorithmically and with specialized hardware,…
Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…
We present a novel rotation invariant architecture operating directly on point cloud data. We demonstrate how rotation invariance can be injected into a recently proposed point-based PCNN architecture, at all layers of the network,…
Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the…
Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
Normalizing flows are an essential alternative to GANs for generative modelling, which can be optimized directly on the maximum likelihood of the dataset. They also allow computation of the exact latent vector corresponding to an image…
It has recently been demonstrated that spatial resolution adaptation can be integrated within video compression to improve overall coding performance by spatially down-sampling before encoding and super-resolving at the decoder. Significant…
Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field…
Histology images are inherently symmetric under rotation, where each orientation is equally as likely to appear. However, this rotational symmetry is not widely utilised as prior knowledge in modern Convolutional Neural Networks (CNNs),…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a…
Convolutional Neural Networks (CNNs) require large image corpora to be trained on classification tasks. The variation in image resolutions, sizes of objects and patterns depicted, and image scales, hampers CNN training and performance,…
In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely,…
Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…
This work introduces a lean CNN (convolutional neural network) framework, with a drastically reduced number of fittable parameters (<81K) compared to the benchmarks in current literature, to capture the underlying low-computational cost…
A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L…