arXiv research

New homological results for bordered Floer algebras derived from hypertoric categories.

Automates standards design through machine learning.

Adversarial training has been successfully applied to build robust models at a certain cost. While the robustness of a model increases, the standard classification accuracy declines. This phenomenon is suggested to be an inherent trade-off. We propose a model that employs feature prioritization by a nonlinear attention…

We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. We define homological operators and we show that they actually provide a representation for an integral version for $U_q \mathfrak{sl}(2)$. We suggest an isomorp…

We propose a new point of view on quantum cohomology, strongly motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is the D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. A stand…

This paper introduces the probabilistic module interface, which allows encapsulation of complex probabilistic models with latent variables alongside custom stochastic approximate inference machinery, and provides a platform-agnostic abstraction barrier separating the model internals from the host probabilistic inferenc…

Python module for RL trading in limit order books.

Differentiable Window improves attention modules by enabling more focused attentions.

A standard technique for understanding underlying dependency structures among a set of variables posits a shared conditional probability distribution for the variables measured on individuals within a group. This approach is often referred to as module networks, where individuals are represented by nodes in a network, …

A framework evaluates the impact of different modules in graph contrastive learning.

NFM improves deep learning by selectively processing hidden states.

In arXiv:1308.3152, the author proved that the Khovanov-Rozansky homology $\mathcal{H}_N$ with potential $ax^{N+1}$ is an invariant for transverse links in the standard contact $3$-sphere. In the current paper, we study the $\mathbb{Z}_2 \oplus \mathbb{Z}^{\oplus 3}$-graded $\mathbb{Q}[a]$-module structure of $\mathcal…

New STDP rule for spiking neurons solves discrete action reinforcement learning tasks.

Study bounds variance modulation function for K-spider distributions.

Study of Markov-modulated affine processes for richer models in finance.

We construct an action of the free group $F_n$ on the homotopy category of projective modules over a finite dimensional zigzag algebra. The main theorem in the paper is that this action is faithful. We describe the relationship between homotopy classes of paths in the punctured disc and complexes of projective zigzag m…

The category of finite dimensional module over the quantum superalgebra U_q(sl(2|1)) is not semi-simple and the quantum dimension of a generic U_q(sl(2|1))-module vanishes. This vanishing happens for any value of q (even when q is not a root of unity). These properties make it difficult to create a fusion or modular ca…

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Ou…

The study of neurocognitive tasks requiring accurate localisation of activity often rely on functional Magnetic Resonance Imaging, a widely adopted technique that makes use of a pipeline of data processing modules, each involving a variety of parameters. These parameters are frequently set according to the local goal o…

This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing "messages" based only on the representation of the source of each edge. In GNN-FiLM, the representation of the target node of an…

Paper analyzes why deeper layers of ViTs perform worse on out-of-distribution tasks.

Given a null-homologous knot $K$ in a rational homology 3-sphere $M$, and the standard infinite cyclic covering $\tilde{X}$ of $(M,K)$, we define an invariant of triples of curves in $\tilde{X}$, by means of equivariant triple intersections of surfaces. We prove that this invariant provides a map $φ$ on $\Al^{\otimes 3…

The present paper is a short survey on the mathematical basics of Classical Field Theory including the Serre-Swan' theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin^C-structures, Dirac operators, exterior algebra bundles and Connes' differential algebras in the commutative case…

The paper studies combinatorics of injective words in the context of Temperley-Lieb algebras.

SuTaT creates dialogue summaries for tete-a-tetes without labeled data.

A core aspect of human intelligence is the ability to learn new tasks quickly and switch between them flexibly. Here, we describe a modular continual reinforcement learning paradigm inspired by these abilities. We first introduce a visual interaction environment that allows many types of tasks to be unified in a single…

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning bas…

We introduce and study the problem of Online Continual Compression, where one attempts to simultaneously learn to compress and store a representative dataset from a non i.i.d data stream, while only observing each sample once. A naive application of auto-encoders in this setting encounters a major challenge: representa…

Paper investigates Lipschitz constants of self-attention modules in neural networks.

We introduce a general-purpose conditioning method for neural networks called FiLM: Feature-wise Linear Modulation. FiLM layers influence neural network computation via a simple, feature-wise affine transformation based on conditioning information. We show that FiLM layers are highly effective for visual reasoning - an…

Khovanov defined graded homology groups for links L in R^3 and showed that their polynomial Euler characteristic is the Jones polynomial of L. Khovanov's construction does not extend in a straightforward way to links in I-bundles M over surfaces F not D^2 (except for the homology with Z/2 coefficients only). Hence, the…

We compute the equivariant bordism of free oriented $(\mathbb{Z}/p)^n$-manifolds as a module over $Ω_*^{SO}$, when $p$ is an odd prime. We show, among others, that this module is canonically isomorphic to a direct sum of suspensions of multiple tensor products of $Ω^{SO}_*(B \mathbb{Z}/p)$, and that it is generated by …

New CNN architecture improves pediatric image segmentation by homogenizing pose and size.

In this note we define a lifting of a local torus action modeled on the standard representation (we call it a local torus action for simplicity) to a principal torus bundle, and show that there is an obstruction class for the existence of liftings in the first cohomology of the fundamental group of the orbit space with…

Timely detection of Hardware Trojans (HTs) has become a major challenge for secure integrated circuits. We present a run-time methodology for HT detection that employs a multi-parameter statistical traffic modeling of the communication channel in a given System-on-Chip (SoC), named as SIMCom. The main idea is to model …

AaSP improves audio self-supervised learning by addressing aliasing issues.

Enhances multi-modular models by directing information flow between components.

In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard do…

V-HMN integrates memory mechanisms for improved image recognition.

Motivation: Identifying interaction clusters of large gene regulatory networks (GRNs) is critical for its further investigation, while this task is very challenging, attributed to data noise in experiment data, large scale of GRNs, and inconsistency between gene expression profiles and function modules, etc. It is prom…

Achieving machine intelligence requires a smooth integration of perception and reasoning, yet models developed to date tend to specialize in one or the other; sophisticated manipulation of symbols acquired from rich perceptual spaces has so far proved elusive. Consider a visual arithmetic task, where the goal is to car…

In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant Einstein metric which is not naturally reductive except …

Neural responses are highly variable, and some portion of this variability arises from fluctuations in modulatory factors that alter their gain, such as adaptation, attention, arousal, expected or actual reward, emotion, and local metabolic resource availability. Regardless of their origin, fluctuations in these signal…

In \cite{GZ}, Gilmer and Zhong established the existence of an invariant for links in $S^1\times S^2$ which is a rational function in variables $a$ and $s$ and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT ske…

Classifies modules of surface-knots in terms of their properties.

Variance-Calibrated Modulation (VCM) addresses the likelihood trap in LLMs by reshaping the probability distribution before truncation.

The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables (or events) by modeling them as a renewal process and inferring a probability dens…

Proves finiteness and holonomicity of skein modules for 3-manifolds.