arXiv research

Generalizes soft noncommutative schemes to flag varieties.

Constructs noncommutative spaces for D-branes on complex algebraic spaces.

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in…

Enhances RL performance with a population-guided parallel learning scheme.

Voice activity detection (VAD), which classifies frames as speech or non-speech, is an important module in many speech applications including speaker verification. In this paper, we propose a novel method, called self-adaptive soft VAD, to incorporate a deep neural network (DNN)-based VAD into a deep speaker embedding …

Develops noncommutative Cowen-Douglas theory for noncommuting operators.

MODULE solves LfO problem with high sample efficiency and stability.

D-branes on noncommutative spaces mimic string theory, offering new insights into mirror symmetry.

Promotes spectral functionals to noncommutative fields and proves a theorem.

Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions can be expressed as a system of partial differential equations relating the metri…

Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL objective and thus generally converges to a policy different from the optimal gree…

Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.

The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.

A general question behind this paper is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80s. It has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori. In this paper, we exte…

In this article, we propose a novel ensemble technique with a multi-scheme weighting based on a technique called coopetitive soft gating. This technique combines both, ensemble member competition and cooperation, in order to maximize the overall forecasting accuracy of the ensemble. The proposed algorithm combines the …

Defines and proves generalized noncommutative residue theorems for specific dimensions.

The paper explores noncommutative geometry of frame bundles using C*-algebras.

In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and gauge transformations. Two different approaches to noncommutative geometry are co…

Develops Riemannian geometry for noncommutative super surfaces.

Our understanding of the notion of curvature in a noncommutative setting has progressed substantially in the past ten years. This new episode in noncommutative geometry started when a Gauss-Bonnet theorem was proved by Connes and Tretkoff for a curved noncommutative two torus. Ideas from spectral geometry and heat kern…

This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential g…

In this work, we introduce a deep learning-based polar code construction algorithm. The core idea is to represent the information/frozen bit indices of a polar code as a binary vector which can be interpreted as trainable weights of a neural network (NN). For this, we demonstrate how this binary vector can be relaxed t…

Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now,…

This paper augments the reward received by a reinforcement learning agent with potential functions in order to help the agent learn (possibly stochastic) optimal policies. We show that a potential-based reward shaping scheme is able to preserve optimality of stochastic policies, and demonstrate that the ability of an a…

Noncritical soft-faults and model deviations are a challenge for Fault Detection and Diagnosis (FDD) of resident Autonomous Underwater Vehicles (AUVs). Such systems may have a faster performance degradation due to the permanent exposure to the marine environment, and constant monitoring of component conditions is requi…

We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.

Intrinsic formulation of noncommutative geometry for quantum gravity.

The paper constructs a noncommutative bracket on surface groups and proves it's Hamiltonian.

We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being compatible with standard theories of physics. We focus on noncommutative deformat…

Derives Atiyah sequence for noncommutative bundles.

First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a noncommutative algebra associated with a transversely symplectic foliation and co…

Review of instantons in noncommutative gauge theories across 4, 6, and 8 dimensions.

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further…

In this paper we prove a version of Connes' trace theorem for noncommutative tori of any dimension~$n\geq 2$. This allows us to recover and improve earlier versions of this result in dimension $n=2$ and $n=4$ by Fathizadeh-Khalkhali. We also recover the Connes integration formula for flat noncommutative tori of McDonal…

The paper extends Lie bracket to noncommutative geometry using differential operators.

The paper derives spectral (0,4)-tensor functionals using the noncommutative residue.

A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,α)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $α:\mathbb{T}^n\rightarrow\Aut(A)$, which induces a (smooth) continuous action of $\mathbb{T}^n$ on $A$. In this…

End-to-end text-to-speech (TTS) synthesis is a method that directly converts input text to output acoustic features using a single network. A recent advance of end-to-end TTS is due to a key technique called attention mechanisms, and all successful methods proposed so far have been based on soft attention mechanisms. H…

We show that Calabi-Yau manifolds are emergent from the commutative limit of six-dimensional noncommutative Hermitian U(1) instantons. Therefore we argue that the noncommutative Hermitian U(1) instantons correspond to quantized Calabi-Yau manifolds.

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997. In the published version, an epilogue of recent developments and many ne…

A neural architecture learns and refines graph correspondences.

We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…

New bridge between diffeology and noncommutative geometry.

The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.

New spectral functionals related to noncommutative residue and torsion Dirac operators.

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capt…

Motivated by recently published methods using frequency decompositions of convolutions (e.g. Octave Convolutions), we propose a novel convolution scheme to stabilize the training and reduce the likelihood of a mode collapse. The basic idea of our approach is to split convolutional filters into additive high and low fre…

Noncommutatively deformed geometries, such as the noncommutative torus, do not exist generically. I showed in a previous paper that the existence of such a deformation implies compatibility conditions between the classical metric and the Poisson bivector (which characterizes the noncommutativity). Here I present anothe…