arXiv research

Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.

Gradient boosting with randomized trees reduces discontinuities and complexity.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

New algorithm tackles optimization problems with discontinuous gradients in finance and insurance.

This work improves SGMs' convergence guarantees for semiconvex distributions with discontinuous gradients.

New method finds optimal learning rates for neural nets.

New method estimates active subspaces for jump-discontinuous functions.

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security prici…

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…

Low-variance gradient estimation is crucial for learning directed graphical models parameterized by neural networks, where the reparameterization trick is widely used for those with continuous variables. While this technique gives low-variance gradient estimates, it has not been directly applicable to discrete variable…

We propose a simple change to existing neural network structures for better defending against gradient-based adversarial attacks. Instead of using popular activation functions (such as ReLU), we advocate the use of k-Winners-Take-All (k-WTA) activation, a C0 discontinuous function that purposely invalidates the neural …

A method for efficient approximate inference on discrete distributions.

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density functio…

Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.

New approach uses SGLD to minimize CVaR for portfolio weights.

A new algorithm learns model regimes and parameters efficiently.

New method samples from piecewise smooth distributions using Hamiltonian Monte Carlo.

Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such inverse problems, in general, are ill-posed and nonconvex, especially in cases w…

Proves nonemptyness of domains for specific group actions.

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…

Cut-DeepONet handles discontinuities and sharp transitions in neural operators.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

New domains of discontinuity found for Anosov representations.

As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…

Study the discontinuity of functions not embeddable in Euclidean space.

New framework to understand and exploit curvature in deep learning loss landscapes.

Study new symmetries in non-symmetric spaces and discontinuous groups.

SGD learns sparse parities near computational limits with discontinuous phase transitions.

Paper finds surface groups can deform in reductive symmetric spaces.

A new method for unsupervised disentanglement using axis-aligned cliffs.

Mini-batch sub-sampling in neural network training is unavoidable, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. In this study we specifically distinguish between static mini-batch sub-sampled loss functions, where mi…

TUSLA algorithm solves non-convex optimization problems with ReLU activations.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Regression trees learn gradients of differentiable functions.

Paper analyzes error in stochastic approximation for discontinuous functions.

Bayesian emulator tackles models with discontinuities efficiently.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.

Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …

Study proves rigid spectral properties of planets with metric discontinuities.

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of additional assumptions. In this paper, we provide a framework for discontinuity-based designs using Bayesian model comparison and …

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.