Related papers: GeoSeq2Seq: Information Geometric Sequence-to-Sequ…

Textual network embeddings aim to learn a low-dimensional representation for every node in the network so that both the structural and textual information from the networks can be well preserved in the representations. Traditionally, the…

In hierarchal order of molecular geometry, we compare the performances of Geometric Quantum Machine Learning models. Two molecular datasets are considered: the simplistic linear shaped LiH-molecule and the trigonal pyramidal molecule NH3.…

When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…

Recent advances in machine learning research have produced powerful neural graph embedding methods, which learn useful, low-dimensional vector representations of network data. These neural methods for graph embedding excel in graph machine…

One important task in the study of information cascade is to predict the future recipients of a message given its past spreading trajectory. While the network structure serves as the backbone of the spreading, an accurate prediction can…

This work presents a two-stage neural architecture for learning and refining structural correspondences between graphs. First, we use localized node embeddings computed by a graph neural network to obtain an initial ranking of soft…

Fisher's linear discriminant analysis is a classical method for classification, yet it is limited to capturing linear features only. Kernel discriminant analysis as an extension is known to successfully alleviate the limitation through a…

Neural state-of-the-art sequence-to-sequence (seq2seq) models often do not perform well for small training sets. We address paradigm completion, the morphological task of, given a partial paradigm, generating all missing forms. We propose…

In recent years, knowledge graph embedding becomes a pretty hot research topic of artificial intelligence and plays increasingly vital roles in various downstream applications, such as recommendation and question answering. However,…

This paper proposes a method for learning joint embeddings of images and text using a two-branch neural network with multiple layers of linear projections followed by nonlinearities. The network is trained using a large margin objective…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

We introduce a new generative approach for synthesizing 3D geometry and images from single-view collections. Most existing approaches predict volumetric density to render multi-view consistent images. By employing volumetric rendering using…

We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder phi is evaluated by U(phi) = I(phi(X); Y) - beta * C(phi), where…

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean…

We introduce tf_geometric, an efficient and friendly library for graph deep learning, which is compatible with both TensorFlow 1.x and 2.x. tf_geometric provides kernel libraries for building Graph Neural Networks (GNNs) as well as…

This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on…

We provide quantitative bounds measuring the $L^2$ difference in function space between the trajectory of a finite-width network trained on finitely many samples from the idealized kernel dynamics of infinite width and infinite data. An…

Diffusion models often degrade when trained in latent spaces (e.g., VAEs), yet the formal causes remain poorly understood. We quantify latent-space diffusability through the rate of change of the Minimum Mean Squared Error (MMSE) along the…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…