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Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…

Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…

In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar…

In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

It has been repeatedly observed that convolutional architectures when applied to image understanding tasks learn oriented bandpass filters. A standard explanation of this result is that these filters reflect the structure of the images that…

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular…

We introduce Equivariant Isomorphic Networks (EquIN) -- a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, EquIN is…

In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…

Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are…

Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

A rigid-motion scattering computes adaptive invariants along translations and rotations, with a deep convolutional network. Convolutions are calculated on the rigid-motion group, with wavelets defined on the translation and rotation…

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…

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to…

Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…

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…

Declines in cost and concerns about the environmental impact of traditional generation have boosted the penetration of renewables and non-conventional distributed energy resources into the power grid. The intermittent availability of these…