Related papers: Gauge-invariant representation holonomy

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{invariant representations} of the data. These are representations of the covariates such that…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…

Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local…

A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both…

Most invariance-based self-supervised methods rely on single object-centric images (e.g., ImageNet images) for pretraining, learning features that invariant to geometric transformation. However, when images are not object-centric, the…

Internal noise in deep networks is usually inherited from heuristics such as dropout, hard masking, or additive perturbation. We ask two questions: what correlation geometry should internal noise have, and is the implemented perturbation…

Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the…

Representation learning algorithms offer the opportunity to learn invariant representations of the input data with regard to nuisance factors. Many authors have leveraged such strategies to learn fair representations, i.e., vectors where…

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems. Recent work has proposed adding biologically-inspired components to…

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…

In the loop quantum gravity framework, spin network states carry entanglement between quantum excitations of the geometry at different space points. This intertwiner entanglement is gauge-invariant and comes from quantum superposition of…

Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…

We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained…

In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…