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.
The study finds new infinite dilogarithm identities related to number sequences and continued fractions.
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an …
Develops correlation number for specific potentials and Hitchin representations.
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient s…
NSR enables neural networks to reason with continuous numbers and extrapolate.
A rational link may be represented by any of the (infinitely) many link diagrams corresponding to various continued fraction expansions of the same rational number. The continued fraction expansion of the rational number in which all signs are the same is called a {\em nonalternating form} and the diagram corresponding…
Topic models are probabilistic models for discovering topical themes in collections of documents. In real world applications, these models provide us with the means of organizing what would otherwise be unstructured collections. They can help us cluster a huge collection into different topics or find a subset of the co…
The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.
We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating Bayesian belief updates into long-term expected return. However, computing an e…
This paper explores how rational numbers on the Stern-Brocot diagram map to lines when terms are extended.
Paper characterizes relation numbers for parabolic two-generator groups.
A graph's winding numbers around two non-adjacent vertices differ by ±1.
New methods for calculating curvature in graph theory.
Introduces injective category number for continuous maps, linking classical and contemporary research.
Study of skateboard flips as continuous curves in group.
Finite number of eigenvalues found in cylindrical surface.
The study calculates average crosscap numbers for 2-bridge knots.
xVal tokenizes numbers continuously for better scientific model training.
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a m…
Study shows how to balance memory and learning efficiency in continual learning.
New algorithm reduces regret in online learning for piecewise continuous functions.
Geometrically, twist numbers on punctured tori are dense and non-continuous.
PSRL extension for continuing environments reduces regret.
This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an orbifold with another triangulation. This method is used to show that eventually p…
DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
Study on neural networks forgetting in continual learning.
A new method optimizes in nonstationary environments with many arms efficiently.
New NN design for nonlinear systems control with guarantees.
A Bayesian nonparametric approach for continual learning using neural networks.
ContinuousNet generalizes ResNets to continuous dynamical systems.
Paper defines benchmarks for learning new tasks sequentially.
George Cybenko's landmark 1989 paper showed that there exists a feedforward neural network, with exactly one hidden layer (and a finite number of neurons), that can arbitrarily approximate a given continuous function on the unit hypercube. The paper did not address how to find the weight/parameters of such a networ…
We consider a continuous family , of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant (or equivalently the sum of the affine Milnor number and the Milnor number at infinity $μ(s)+λ…
Continuous epimorphisms between certain mapping class groups are induced by homeomorphisms.
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
Develops a statistical learning framework for personalized asset allocation.
The paper designs neural networks with assurance for controlling nonlinear systems.
Continuous-time analysis shows SGD with noise prefers flat minima.
We study the Gibbs sampling algorithm for continuous determinantal point processes. We show that, given a warm start, the Gibbs sampler generates a random sample from a continuous -DPP defined on a -dimensional domain by only taking number of steps. As an application, we design an algorithm to ge…
Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By appl…
This article deals with a continuous closed 1-form defined on a CW-complex. In particular, we show Lusternik-Schnirelmann type theory on continuous closed 1-forms which is related to gradient-like flows. M.Farber defined a continuous closed 1-form and a category with a respect to a cohomology class and constructed a Lu…
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice of a random number generator. The aim of this paper is to provide the tools for…
We present a new method of learning a continuous occupancy field for use in robot navigation. Occupancy grid maps, or variants of, are possibly the most widely used and accepted method of building a map of a robot's environment. Various methods have been developed to learn continuous occupancy maps and have successfull…
Simple neural networks approximate any continuous function with fixed neurons.
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets…
For any two continuous maps between two solvmanifolds of same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.
We propose a method for tackling catastrophic forgetting in deep reinforcement learning that is \textit{agnostic} to the timescale of changes in the distribution of experiences, does not require knowledge of task boundaries, and can adapt in \textit{continuously} changing environments. In our \textit{policy consolidati…