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In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant…
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…
Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality…
In the task of Object Recognition, there exists a dichotomy between the categorization of objects and estimating object pose, where the former necessitates a view-invariant representation, while the latter requires a representation capable…
Learning 3D point sets with rotational invariance is an important and challenging problem in machine learning. Through rotational invariant architectures, 3D point cloud neural networks are relieved from requiring a canonical global pose…
Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…
Convolutional Neural Networks (CNN) possess many positive qualities when it comes to spatial raster data. Translation invariance enables CNNs to detect features regardless of their position in the scene. However, in some domains, like…
Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input…
LiDAR-based place recognition plays a crucial role in Simultaneous Localization and Mapping (SLAM) and LiDAR localization. Despite the emergence of various deep learning-based and hand-crafting-based methods, rotation-induced place…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of…
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…
The neural network and quantum computing are both significant and appealing fields, with their interactive disciplines promising for large-scale computing tasks that are untackled by conventional computers. However, both developments are…
Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentially-growing computational cost.…
Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a…
There is a great need for accurate and autonomous spectral classification methods in astrophysics. This thesis is about training a convolutional neural network (ConvNet) to recognize an object class (quasar, star or galaxy) from…
Equivariant networks have been adopted in many 3-D learning areas. Here we identify a fundamental limitation of these networks: their ambiguity to symmetries. Equivariant networks cannot complete symmetry-dependent tasks like segmenting a…
The widespread success of convolutional neural networks may largely be attributed to their intrinsic property of translation equivariance. However, convolutions are not equivariant to variations in scale and fail to generalize to objects of…