arXiv research

Gem theory helps estimate trisection genus of 4-manifolds.

Review of gem theory's interactions with Kirby diagrams and trisections.

The paper extends trisection theory to non-orientable 4-manifolds using colored triangulations.

Within crystallization theory, two interesting PL invariants for $d$-manifolds have been introduced and studied, namely {\it gem-complexity} and {\it regular genus}. In the present paper we prove that, for any closed connected PL $4$-manifold $M$, its gem-complexity $\mathit{k}(M)$ and its regular genus $ \mathcal G(M)…

The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM) algorithm in the context of Gaussian mixture models, where the maximization step in t…

Classifies semi-equivelar gems on surfaces with Euler characteristic -1.

The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove …

GEM-T generates synthetic tabular data by fitting moments, outperforming neural networks.

This paper classifies semi-equivelar gems on a double torus.

In lifelong learning, the learner is presented with a sequence of tasks, incrementally building a data-driven prior which may be leveraged to speed up learning of a new task. In this work, we investigate the efficiency of current lifelong approaches, in terms of sample complexity, computational and memory cost. Towards…

The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard dia…

Factorization machine (FM) is an effective model for feature-based recommendation which utilizes inner product to capture second-order feature interactions. However, one of the major drawbacks of FM is that it couldn't capture complex high-order interaction signals. A common solution is to change the interaction functi…

Current deep neural networks can achieve remarkable performance on a single task. However, when the deep neural network is continually trained on a sequence of tasks, it seems to gradually forget the previous learned knowledge. This phenomenon is referred to as \textit{catastrophic forgetting} and motivates the field c…

Given an special type of triangulation $T$ for an oriented closed 3-manifold $M^3$ we produce a framed link in $S^3$ which induces the same $M^3$ by an algorithm of complexity $O(n^2)$ where $n$ is the number of tetrahedra in $T$ . The special class is formed by the duals of the {\em solvable gems}. These are in practi…

Lower bounds for PL 4-manifolds with boundary are improved.

GEM learns a manifold for cross-modal data, capturing structure without modality dependence.

We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in a wide subset of interesting cases, the isomorphism conditions for Lins-Mandel g…

We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogu…

The paper studies special crystallizations of 4-manifolds to minimize certain PL-invariants.

New model solves complex SDEs with high-dimensional spatial and stochastic spaces.

The idea of studying trisections of closed smooth $4$-manifolds via (singular) triangulations, endowed with a suitable vertex-labelling by three colors, is due to Bell, Hass, Rubinstein and Tillmann, and has been applied by Spreer and Tillmann to colored triangulations associated to the so called simple crystallization…

Graph Energy Matching improves generation quality for molecular graphs.

This is part 2 of a 3-part article where we provide an $O(n^2)$-algorithm to produce a surgery presentation of a 3-manifold induced by a gem with a resolution. In this part we produce a sequence of colored simplicial 2-complexes which are inverses and dual to the sequence of gems produced in the first part. The refinem…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address concerns about the external validity of a model. The GA of a model estimated on a sampl…

Generative neural network models, including Generative Adversarial Network (GAN) and Auto-Encoders (AE), are among the most popular neural network models to generate adversarial data. The GAN model is composed of a generator that produces synthetic data and of a discriminator that discriminates between the generator's …

We extend to dimension $n \geq 3$ the concept of $ρ$-pair in a coloured graph and we prove the existence theorem for minimal rigid crystallizations of handle-free, closed $n$-manifolds.

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling th…

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling th…

HeMPPCAT improves PCA for data with varying noise.

Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous SGD under the lens of Lagrangian mechanics. Using this description, we introduce …

Let $(Γ,γ)$ be a crystallization of connected compact 3-manifold $M$ with $h$ boundary components. Let $\mathcal{G}(M)$ and $\mathit k (M)$ be the regular genus and gem-complexity of $M$ respectively, and let $\mathcal{G}(\partial M)$ be the regular genus of $\partial M$. We prove that $$\mathit k (M)\geq 3 (\mathcal{G…

From a pseudo-triangulation with $n$ tetrahedra $T$ of an arbitrary closed orientable connected 3-manifold (for short, {\em a 3D-space}) $M^3$, we present a gem $J '$, inducing $\IS^3$, with the following characteristics: (a) its number of vertices is O(n); (b) it has a set of $p$ pairwise disjoint couples of vertices …

New PL-invariants defined for 4-manifolds with boundary.

Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL $4$-manifold $M$ admitting a simple crystallization admits a special hand…

In this article, we construct a crystallization of the mapping torus of some (PL) homeomorphisms $f:M \to M$ for a certain class of PL-manifolds $M$. These yield upper bounds for gem-complexity and regular genus of a large class of PL-manifolds. The bound for the regular genus is sharp for the mapping torus of some (PL…

The thesis models financial returns using mixtures of generalized normal distributions.

We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Differ…

One of the most important problems of data processing in high energy and nuclear physics is the event reconstruction. Its main part is the track reconstruction procedure which consists in looking for all tracks that elementary particles leave when they pass through a detector among a huge number of points, so-called hi…

This paper introduces a new learning rule for probabilistic SNNs that improves log-likelihood, accuracy, and calibration.

A {\it blink} is a plane graph with its edges being red or green. A {\it 3D-space} or, simply, a {\it space} is a connected, closed and oriented 3-manifold. In this work we explore in details, for the first time, the fact that every blink induces a space and any space is induced by some blink (actually infinitely many …

We present, GEM, the first heterogeneous graph neural network approach for detecting malicious accounts at Alipay, one of the world's leading mobile cashless payment platform. Our approach, inspired from a connected subgraph approach, adaptively learns discriminative embeddings from heterogeneous account-device graphs …

Developed deep learning models to predict crop yields across diverse environments.

We first pose the Unsupervised Progressive Learning (UPL) problem: an online representation learning problem in which the learner observes a non-stationary and unlabeled data stream, learning a growing number of features that persist over time even though the data is not stored or replayed. To solve the UPL problem we …

The paper connects Kirby diagrams and 5-colored graphs to represent 4-manifolds.

In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained machine learning decision rules, based on their response to the variability of the i…

Proposes a CL technique to improve accuracy and reduce forgetting.

CLOPS improves deep learning for continuous physiological data.

Study compact PL 4-manifolds with special handle decompositions.