arXiv research

New KWS neural networks improve accuracy and power efficiency.

Paper defines curvature equivalence for Legendre curves in a plane.

The study examines Bertrand Legendre curves in the unit tangent bundle over Euclidean plane.

This paper classifies Legendre singularities of sub-Riemannian geodesics on surfaces.

Characterizes special curves on surface tangent bundles.

We obtain the explicit representation of Legendre surfaces in the unit $5$-sphere with harmonic mean curvature vector field, under the condition that the mean curvature function is constant along a certain special direction.

Study forecasts aortic pressure with deep learning models.

In this paper, Legendre curves on unit tangent bundle are given using rotation minimizing (RM) vector fields. Ruled surfaces corresponding to these curves are represented. Singularities of these ruled surfaces are also analyzed and classifed.

Let $(\mathbb{M}_{1}^{2},g)$ be a Minkowski surface and $(T_1\mathbb{M}_1^2, g_1)$ its unit tangent bundle endowed with the pseudo-Riemannian induced Sasaki metric. We extend in this paper the study of the N-Legendre and N-slant curves which the inner product of normal vector and Reeb vector is zero and nonzero constan…

HiPPO framework optimizes memory compression for sequential data.

We obtain the parametric equations of all biharmonic Legendre curves and Hopf cylinders in the 3-dimensional unit sphere endowed with the modified Sasakian structure defined by Tanno.

Faster training of neural ODEs using Gauß-Legendre quadrature.

Study of contact whirl curves in Sasakian Lorentzian 3-manifolds.

The study examines vertices in curves with singular points in the Euclidean plane.

In this paper, we present Gamma-LSTM, an enhanced long short term memory (LSTM) unit, to enable learning of hierarchical representations through multiple stages of temporal abstractions. Gamma memory, a hierarchical memory unit, forms the central memory of Gamma-LSTM with gates to regulate the information flow into var…

A geometrization of Schmidt-Legendre transformation of the second order Lagrangians is proposed by building a proper Tulczyjew's triplet. The symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre transformations is obtained. Several examples are presented.

Legendre transformations link related integrable hierarchies.

FiLM improves deep learning for long-term time series forecasting.

The paper characterizes Legendre curves on trans-S-manifolds.

We classify the biharmonic Legendre curves in a Sasakian space form, and obtain their explicit parametric equations in the $(2n+1)$-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. Then, composing with the flow of the Reeb vector field, we transform a biharmonic inte…

Characterizes the Legendre involution on generic frontals.

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

Introduces Legendre bundle for dually flat manifolds and quantum field theories.

Sequential learning of tasks using gradient descent leads to an unremitting decline in the accuracy of tasks for which training data is no longer available, termed catastrophic forgetting. Generative models have been explored as a means to approximate the distribution of old tasks and bypass storage of real data. Here …

Tautness of submanifolds in spheres is preserved under Lie sphere transformations.

We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory Units (Tree-SMU) to enable strong compositional generalization. Tree-SMU is a recurs…

The report analyzes Legendre decomposition for tensor data.

The paper studies a flow of Legendre curves, generalizing the inverse curvature flow of regular curves.

A new family of conformal test martingales based on Legendre polynomials for online exchangeability testing.

MEMGAN uses memory to improve anomaly detection by isolating abnormal data.

We introduce complex generalizations of the classical Legendre transform, operating on Kähler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of Kähler metrics around any real analytic Kähler metric, answering a question origi…

Paper solves recovery of parametrizations from Legendre data.

Legendre curves are smooth plane curves which may have singular points, but still have a well defined smooth normal (and corresponding tangent) vector field. Because of the existence of singular points, the usual curvature concept for regular curves cannot be straightforwardly extended to these curves. However, Fukunag…

Severe constraints on memory and computation characterizing the Internet-of-Things (IoT) units may prevent the execution of Deep Learning (DL)-based solutions, which typically demand large memory and high processing load. In order to support a real-time execution of the considered DL model at the IoT unit level, DL sol…

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central Processing Unit (CPU) and Graphical Processing Unit (GPU). While alternating least squar…

SliceOut speeds up deep learning training without sacrificing accuracy.

Improved SNNs with quantized activations outperform traditional networks.

Following Burstall and Hertrich-Jeromin we study the Ribaucour transformation of Legendre submanifolds in Lie sphere geometry. We give an explicit parametrization of the resulted Legendre submanifold $\hat{F}$ of a Ribaucour transformation, via a single real function $τ$ which represents the regular Ribaucour sphere co…

We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant $φ$-sectional curvature.

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…

In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (ρ,η)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented. Using that, a Legendre description of Lagrangian Mechanics and Hamiltonian Mechanics is d…

The concepts of unitary evolution matrices and associative memory have boosted the field of Recurrent Neural Networks (RNN) to state-of-the-art performance in a variety of sequential tasks. However, RNN still have a limited capacity to manipulate long-term memory. To bypass this weakness the most successful application…

Learning and adapting to new distributions or learning new tasks sequentially without forgetting the previously learned knowledge is a challenging phenomenon in continual learning models. Most of the conventional deep learning models are not capable of learning new tasks sequentially in one model without forgetting the…

The general framework of Legendre transformation is extended to the case of symplectic groupoids, using an appropriate generalization of the notion of generating function (of a Lagrangian submanifold).

The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.

New method reconstructs Black-Scholes option prices from current profiles.

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we compute the average density for a field in half-space with Dirichlet boundary c…

The paper studies area-preserving and length-preserving inverse curvature flow for planar curves with singularities.