A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper tackles division difficulty, proposing new methods to improve accuracy.
Study on geodesics and dihedral groups in lattices.
Study geodesics entering a fixed cusp neighborhood multiple times.
The paper models social networks with varying levels of reciprocity.
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …
The study examines the growth of reciprocal classes in Hecke groups, proving an asymptotic formula.
Classifies reciprocal elements in Hecke groups, generalizing Sarnak's work.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
Estimates growth of reciprocal classes in Hecke groups.
The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.
M3E2 neural network estimates multiple treatment effects.
Formulates Hilbert reciprocity law on 3-manifolds.
Minimal spectral radii found for specific matrix types.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…
The paper models reciprocity in interbank markets using a statistical null model.
Reciprocal learning unifies various machine learning algorithms.
New method reconstructs interbank networks enforcing reciprocity to improve stability and risk prediction.
Growth rates of geodesics on modular orbifolds are studied.
The paper proves generalization bounds and stopping rules for self-selected data in reciprocal learning.
The abstract discusses conjectures about Chern-Simons invariants of 3-manifolds.
Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for …
Reciprocity laws for line bundles on circle fibrations over complex manifolds.
Transformers use ReLUs to approximate softmax efficiently.
This paper presents a novel model for multimodal learning based on gated neural networks. The Gated Multimodal Unit (GMU) model is intended to be used as an internal unit in a neural network architecture whose purpose is to find an intermediate representation based on a combination of data from different modalities. Th…
We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientat…
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series…
We prove a reciprocity formula between Gauss sums that is used in the computation of certain quantum invariants of 3-manifolds. Our proof uses the discriminant construction applied to the tensor product of lattices.
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…
This paper gives a new definition of the Contou-Carrere symbol in terms of an exponential of a Chen iterated integral and proves the corresponding reciprocity law.
The paper models and analyzes faults in TPU-based neural networks.
We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. This leads either to an inefficient distribution of computational resources or an extensive increase in the comput…
Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative…
Dropout is a regularisation technique in neural network training where unit activations are randomly set to zero with a given probability \emph{independently}. In this work, we propose a generalisation of dropout and other multiplicative noise injection schemes for shallow and deep neural networks, where the random noi…
The determinants of the velocity of money have been examined based on life-cycle hypothesis. The velocity of money can be expressed by reciprocal of the average value of holding time which is defined as interval between participating exchanges for one unit of money. This expression indicates that the velocity is govern…
In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evalu…
Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. However, this leads to an extensive increase in the computational complexity of the training procedure. We present…
Deep nets solve MDPs without high dimensions.
In this work, we propose a novel recurrent neural network (RNN) architecture. The proposed RNN, gated-feedback RNN (GF-RNN), extends the existing approach of stacking multiple recurrent layers by allowing and controlling signals flowing from upper recurrent layers to lower layers using a global gating unit for each pai…
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut stochastic gradient descent (SGD) learning in networks composed of multiple lay…
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …
In this paper, we construct an asymptotically hyperbolic metric with scalar curvature -6 on unit ball , which contains multiple horizons.
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels us…
Parameters in deep neural networks which are trained on large-scale databases can generalize across multiple domains, which is referred as "transferability". Unfortunately, the transferability is usually defined as discrete states and it differs with domains and network architectures. Existing works usually heuristical…
Neural operators solve families of 2BSDEs efficiently.
Optimizes neural networks by removing unnecessary layers, improving performance and speed.
A fast ML method solves complex combinatorial auction problems.
New model accounts for scale variation and noise in pairwise comparisons.