Related papers: Optimal Symmetries in Binary Classification
A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants…
The multi-group learning model formalizes the learning scenario in which a single predictor must generalize well on multiple, possibly overlapping subgroups of interest. We extend the study of multi-group learning to the natural case where…
This paper characterizes optimal classification when individuals adjust their behavior in response to the classification rule. We model the interaction between a designer and a population as a Stackelberg game: the designer selects a…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…
In robotic tasks, changes in reference frames typically do not influence the underlying physical properties of the system, which has been known as invariance of physical laws.These changes, which preserve distance, encompass isometric…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning…
Algorithmic fairness has become a central concern in modern machine learning and AI applications. However, two pressing challenges remain: (1) The fairness guarantees of existing methods often rely on specific data distributional…
We investigate the generalization error of group-invariant neural networks within the Barron framework. Our analysis shows that incorporating group-invariant structures introduces a group-dependent factor $\delta_{G,\Gamma,\sigma} \le 1$…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…
Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…
In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest.…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
In this work, we aim to calibrate the score outputs of an estimator for the binary classification problem by finding an 'optimal' mapping to class probabilities, where the 'optimal' mapping is in the sense that minimizes the classification…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…