A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified method for CNNs to approximate equivariant maps across various groups.
L-CNNs preserve gauge symmetry in neural networks.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
Group-equivariant subsampling layers improve CNNs' equivariance.
L-CNNs preserve gauge symmetry in lattice simulations.
Equivariant CNNs improve RL performance in symmetric environments.
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant maps between spaces of fields. The theory enables a systematic cla…
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of s…
L-CNNs learn gauge invariant quantities on lattices.
Proposes a new CNN for meshes that can handle orientation.
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST-equivariant) CNN with joint convolutions across th…
We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a …
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 imaging problems that exhibit symmetries. Here we show how this principle can be exte…
DeepSphere improves spherical CNNs by balancing efficiency and rotation equivariance.
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these net…
Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typic…
Geometric models improve feature extraction and equivariance in image generation.
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional filters over joint steerable bases across the space and the group …
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution la…
GNNs generalize CNNs for graph data, showing equivariance and stability.
Group convolutional neural networks (G-CNNs) can be used to improve classical CNNs by equipping them with the geometric structure of groups. Central in the success of G-CNNs is the lifting of feature maps to higher dimensional disentangled representations, in which data characteristics are effectively learned, geometri…
The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various t…
We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysi…
Measures equivariance in vision models using Lie derivative.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as equivarification. We further show that group convolutional neural networks (G-CNN…
It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and flexible class of equivariant convolutional networks. We show that steerable CNNs …
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
Group equivariant neural networks simplify complex tasks with group representation theory.
New framework uses symmetry-based matrices for efficient, flexible NNs.
Coordinate-independent convolutions on manifolds avoid reference frame ambiguity.
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant M…
Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than spherical convolutions. As equivariance is desired to exploit rotational symmet…
Generalizes CNNs for Lie group equivariance across various data types.
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 transformations. The group equivariant CNN framework is extended for segmentation by introdu…
Study on geodesic distances on SE(3)/SO(2) in machine learning.
Equivariant neural network simplifies particle physics models.
In this proceeding we give an overview of the idea of covariance (or equivariance) featured in the recent development of convolutional neural networks (CNNs). We study the similarities and differences between the use of covariance in theoretical physics and in the CNN context. Additionally, we demonstrate that the simp…
This work relaxes GNN symmetries to approximate automorphisms, improving model performance.
Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding…
New approximative kernels improve PDE-G-CNNs for geometric deep learning.
The paper introduces MDP homomorphic networks for faster reinforcement learning.
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions b…
Classical models describe primary visual cortex (V1) as a filter bank of orientation-selective linear-nonlinear (LN) or energy models, but these models fail to predict neural responses to natural stimuli accurately. Recent work shows that models based on convolutional neural networks (CNNs) lead to much more accurate p…
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, mo…
In this paper, we propose Generative Adversarial Network (GAN) architectures that use Capsule Networks for image-synthesis. Based on the principal of positional-equivariance of features, Capsule Network's ability to encode spatial relationships between the features of the image helps it become a more powerful critic in…
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 scheme using the magnitude response of the 2D-discrete-Fourier transform (2D-DFT)…