Related papers: Narrowing the Gap between Combinatorial and Hyperb…
Temporal link prediction, aiming to predict future edges between paired nodes in a dynamic graph, is of vital importance in diverse applications. However, existing methods are mainly built upon uniform Euclidean space, which has been found…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…
High-precision atomic structure calculations require accurate modelling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy method, one can find explicit constructions and counterexamples to several open conjectures in extremal combinatorics and graph theory. Amongst the…
Learning Ising or Potts models from data has become an important topic in statistical physics and computational biology, with applications to predictions of structural contacts in proteins and other areas of biological data analysis. The…
Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…
Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic…
This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…
Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a…
This paper focuses on the study of recognizing discontiguous entities. Motivated by a previous work, we propose to use a novel hypergraph representation to jointly encode discontiguous entities of unbounded length, which can overlap with…
A recent paper by Davies et al (2021) describes how deep learning (DL) technology was used to find plausible hypotheses that have led to two original mathematical results: one in knot theory, one in representation theory. I argue here that…
The aim of this work is to enable inference of deep networks that retain high accuracy for the least possible model complexity, with the latter deduced from the data during inference. To this end, we revisit deep networks that comprise…
Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…
Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…