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.
This paper uses linear rational splines for invertible modeling, offering a simpler inverse and similar costs.
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general…
This study compares different types of normalizing flows for generating complex distributions.
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…
Sig-Splines model uses signatures and splines for time series data, achieving universality and convexity.
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing need for spline interpolation on curved, non-Euclidean space. The generalization…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given pr…
Improves BN graph learning with splines for scalability.
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the success of deep networks. In this article we take another route by comparing the expre…
A new spline method for manifold learning using Hessian-based curvature penalties.
This paper develops a new method for constructing splines on Lie groups using Poisson equation solutions.
New framework explains deep neural networks using variational spline theory.
Temporal Functional Circuits explain KAN forecasts with interpretable edge functions.
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…
Dropout improves regularization in flexible models for rare features.
We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a general representer theorem for deep neural networks that makes a direct connectio…
A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based models are slow to invert, making either density estimation or sample generation sl…
A new modeling framework CSN simplifies and interprets machine learning models.
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been…
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distribu…
Improves MARS for nonparametric multivariate regression with dimension reduction.
Paper finds maximum curvature of Bézier-spline curves.
T-KAN improves HFT LOB forecasting with learnable splines.
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
Revisits stochastic collocation with exponential splines for option pricing.
Researchers found new functions for spherical clothoids using special functions.
Approximates nonlocal curvature of curves using splines.
New method adds interactions to interpretable models for large-scale data.
New knots show linear independence in slice concordance.
Paper proves regularity and existence of Riemannian splines.
We prove a negative result for the approximation of functions defined on compact subsets of (where ) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to…
Unified analysis of multi-task functional linear regression with manifold and composite penalties.
Improves spline quality and accuracy in computational microscopy.
Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochast…
KAN-PCA improves asset return analysis by capturing more variance than classical PCA during market crises.
Improved classification model for high-cardinality categorical predictors.
Neural networks with rectified linear unit activations are essentially multivariate linear splines. As such, one of many ways to measure the "complexity" or "expressivity" of a neural network is to count the number of knots in the spline model. We study the number of knots in fully-connected feedforward neural networks…
We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the condi…
A new method combines machine learning with mixed-effects models for better repeated measurement analysis.
A wide variety of activation functions have been proposed for neural networks. The Rectified Linear Unit (ReLU) is especially popular today. There are many practical reasons that motivate the use of the ReLU. This paper provides new theoretical characterizations that support the use of the ReLU, its variants such as th…
Sinh-acceleration speeds up B-spline option pricing.
Combines spline interpolation and ARIMA for stock market forecasting.
A new method evolves point clouds using B-splines for smooth surfaces.
Kronecker trend filtering improves lattice data smoothing.
Represents neural networks as solutions to inverse problems in Banach spaces.
A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the …