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.
Method selects interpretable circular coordinates from data.
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path…
This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim autom…
Differentiable clustering method using perturbed spanning forests.
We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can…
We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by alter…
New algorithm for learning mixtures with mostly uniform weights, improving on previous bounds.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
New basis confirms Thurston's conjecture and reveals knot configurations.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria…
Understanding separation effects on parameter estimation in finite Gaussian mixtures
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.
New framework models complex spatial data with basis functions and graphical vectors.
Machine learning model predicts DFT total energy to complete basis set limit.
The paper explains the fair basis in bond-CDS trading during financial crises.
Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
This study tackles basis risk in weather parametric insurance using Monte Carlo simulations.
We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.
Investigates smoothness of specific algebra structures.
New basis for permutation equivariant layers reduces computation costs.
Harmonic basis vector fields on surfaces
Proves log-concavity of cluster algebra coefficients for type .
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
The study explores various localized bases and their duals for scattered data approximation.
T-Basis represents neural network tensors with fewer parameters.
Algorithm learns mixtures of Gaussians efficiently using diffusion models.
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a constrained optimization problem wherein the sum of the norm of the weights in each…
This paper optimizes PCE for efficient surrogate modeling in engineering.
In this paper we study a symmetry group of vector space. Basis manifold is a homogeneous space of a symmetry group. This concept leads us to the definition of active and passive transformations on basis manifold. Active transformation can be expressed as a transformation of vector space. Passive transformation gives ab…
A new density model using Fourier basis achieves better approximations and compression.
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties o…
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most…
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization pr…
Derives representations invariant under crystallographic groups for functions.
Given a simple algebraic group , a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a bas…
We give an explicit graded cellular basis of the -web algebra . In order to do this, we identify Kuperberg's basis for the -web space with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weigh…
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing ideals plays a critical role. However, such an approximation also gives rise to a…
The paper proposes a new algorithm for the high-dimensional financial data -- the Groupwise Interpretable Basis Selection (GIBS) algorithm, to estimate a new Adaptive Multi-Factor (AMF) asset pricing model, implied by the recently developed Generalized Arbitrage Pricing Theory, which relaxes the convention that the num…
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the bas…
Optimizes basis functions for learning dynamical systems from data.
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these co…
Study on smoothness of special algebra types.
Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squ…
Introduces tunable basis functions for Gaussian processes.
The paper approximates supply curves using a one-step basis method.