arXiv research

New tools connect CP to GF inference for better probabilistic prediction.

Geometrical flows (GF) play an important role in modern mathematics and physics. In this letter we have considered some integrable isotropic GF -- Ricci flows (RF) and mean curvature flows (MCF) -- which are related with integrable Heisenberg ferromagnets. In 2+1 dimensions, these GF have a singularity at $t=t_{0}$.

Two-parameter models can learn high-dimensional targets via gradient flow.

Gradient flow on ReLU networks converges to a simple model with few regions.

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…

GD monotonically decreases GFS sharpness in neural networks and scalar models.

Gradient descent and SGD achieve low test error in specific network weight regimes.

Let $M$ be a compact and connected smooth manifold endowed with a smooth action of a finite group $Γ$, and let $f$ be a $Γ$-invariant Morse function on $M$. We prove that the space of $Γ$-invariant Riemannian metrics on $M$ contains a residual subset ${\mathcal Met}_f$ with the following property. Let $g\in{\mathcal Me…

Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for complex distributions. However, the standard SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable. In this work, we develop a gradient-free variant …

Filtering is a general name for inferring the states of a dynamical system given observations. The most common filtering approach is Gaussian Filtering (GF) where the distribution of the inferred states is a Gaussian whose mean is an affine function of the observations. There are two restrictions in this model: Gaussia…

Wide neural networks converge linearly to zero loss with feature learning.

Let N^h be a hyperbolic 3-manifold of bounded geometry corresponding to a hyperbolic structure on a pared manifold (M,P). Further, suppose that (\partial{M} - P) is incompressible, i.e. the boundary of M is incompressible away from cusps. Further, suppose that M_{gf} is a geometrically finite hyperbolic structure on (M…

Gradient descent converges to a global minimum in nonlinear ReLU implicit networks with linear width.

The paper studies SDP feasibility and sos ranks for specific polynomials.

Graph neural networks (GNNs) have been shown to replicate convolutional neural networks' (CNNs) superior performance in many problems involving graphs. By replacing regular convolutions with linear shift-invariant graph filters (LSI-GFs), GNNs take into account the (irregular) structure of the graph and provide meaning…

Develops a new framework to analyze gradient flow regimes and derive explicit solutions.

With the great success of graph embedding model on both academic and industry area, the robustness of graph embedding against adversarial attack inevitably becomes a central problem in graph learning domain. Regardless of the fruitful progress, most of the current works perform the attack in a white-box fashion: they n…

We derive bounds on the path length $ζ$ of gradient descent (GD) and gradient flow (GF) curves for various classes of smooth convex and nonconvex functions. Among other results, we prove that: (a) if the iterates are linearly convergent with factor $(1-c)$, then $ζ$ is at most $\mathcal{O}(1/c)$; (b) under the Polyak-K…

ReLU networks implicitly favor low-rank solutions, but not as strongly as linear networks.

GF-Net learns Green's functions for linear reaction-diffusion equations.

Derives EoM for DNNs to describe GD dynamics precisely.

We found a way to code meanders and show they are idempotent.

The paper is divided in 2 parts. The first part is the original paper of the second and third authors arXiv:1202.5442v2. The second part is an erratum/addendum written in english and concatenated at the end of the former paper. In the erratum/addentum, we amend Theorems 1.3 and 1.11 of arXiv:1202.5442v2: Finitude géomé…

Proposes a method to improve surrogate modeling and design optimization using latent variables.

Rainfall ensemble forecasts have to be skillful for both low precipitation and extreme events. We present statistical post-processing methods based on Quantile Regression Forests (QRF) and Gradient Forests (GF) with a parametric extension for heavy-tailed distributions. Our goal is to improve ensemble quality for all t…

Despite the advantages of all-weather and all-day high-resolution imaging, SAR remote sensing images are much less viewed and used by general people because human vision is not adapted to microwave scattering phenomenon. However, expert interpreters can be trained by compare side-by-side SAR and optical images to learn…

Two-dimensional Riemannian manifolds uniquely determined by boundary data.

Funar algebra $K_\infty=K_\infty(α,β;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $σ_1^3-ασ_1^2+βσ_1-1=0$ and another one which involves $σ_1$ and $σ_2$. The universal Markov trace on $K_\infty$ is the quotient map $t$ of $K_\infty(α,β,k[u,v])$ to its qu…

Method solves Calderón problem for surfaces near disks.

We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $Λ_μ=\mathbb{Z}[t_1^{\pm1},\dots,t_μ^{\pm1}]$. If $D$ is a diagram of a link $L$ with $μ$ components, then the colorings of $D$ with values in $M$ form a $Λ_μ$-module…

Reconstructing a planar domain from its Dirichlet-to-Neumann data

New concept of attitude towards probability introduced in risk sharing problems.

Non-trivialization probability of arc system in 3D space

There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability forms. The biggest obstacle of the probability model is the probability distribu…

Identifies conditions for multiple invariant probabilities in Markov kernels.

NT probability measures knotting in 3D arc systems.

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be …

This work improves deep neural network probability estimation methods.

This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which…

A new method for adapting to label shifts using class probability matching.

Study classifies submanifolds in probability simplex.

Study generalizes property elicitation to imprecise probabilities.

Study on the probability of immunity and its bounds.

This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The accuracy of the predicted probability can be improved by measuring more probability es…

The paper addresses probability calibration for incomplete sequences.

Investigates statistical properties of perturb-softmax and perturb-argmax distributions.

Categorical d-separation criterion simplifies probability graph analysis.

Paper constructs unfaithful probability distributions in binary causal graphs.