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.
Proves a tree of shapes for n-D images in optimal time.
The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the …
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorit…
AI mirrors modern math's autonomous development, raising interpretive challenges.
Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance imaging, interior tomography, and sparse-view computed tomography, where deep lea…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous…
GANs as priors improve uncertainty quantification in complex fields.
Develops statistical guarantees for image-to-image regression models.
GeoTop resolves topological ambiguity in diagnostic imaging using geometric-topological analysis.
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine emission imaging. The derivation of the classical inversion formula is through the re…
Paper defines mathematical framework for neural network explainability.
New algebraic structures called cyclic Lie-Rinehart algebras are defined.
Study finds CNNs perform better with financial ratio data than fundamental data.
New method tackles inexact bilevel optimization for faster parameter learning.
This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different patterns of an image, we are inspired by a method called "PCANet" in "PCANet: A Simple …
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very…
We introduce a general method of performing Residual Network inference and learning in the JPEG transform domain that allows the network to consume compressed images as input. Our formulation leverages the linearity of the JPEG transform to redefine convolution and batch normalization with a tune-able numerical approxi…
Wavelet SGM accelerates generative modeling with linear time complexity.
The Burau representation is a fundamental bridge between the braid group and diverse other topics in mathematics. A 1974 question of Birman asks for a description of the image; in this paper we give a "strong approximation" to the answer. Since a 1984 paper of Squier it has been known that the Burau representation pres…
Deep neural networks have been proved efficient for medical image denoising. Current training methods require both noisy and clean images. However, clean images cannot be acquired for many practical medical applications due to naturally noisy signal, such as dynamic imaging, spectral computed tomography, arterial spin …
Bayesian Scattering offers a simple baseline for image data uncertainty.
ChronoMID builds on the success of cross-modal convolutional neural networks (X-CNNs), making the novel application of the technique to medical imaging data. Specifically, this paper presents and compares alternative approaches - timestamps and difference images - to incorporate temporal information for the classificat…
Paper proposes TBSD for efficient anomaly detection in textured images.
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function approximators (neural networks), and can be trained with stochastic gradient descent. VAEs …
New method uses topological data analysis to study stock market crashes.
Adds a precortical module to CNNs for improved robustness to light variations.
The instance segmentation problem intends to precisely detect and delineate objects in images. Most of the current solutions rely on deep convolutional neural networks but despite this fact proposed solutions are very diverse. Some solutions approach the problem as a network problem, where they use several networks or …
Bayesian approach improves image captioning quality metrics.
PAC-Bayesian method improves deep learning generalization in medical imaging.
Automatically designs normalization and activation layers together.
We outline new approaches to incorporate ideas from deep learning into wave-based least-squares imaging. The aim, and main contribution of this work, is the combination of handcrafted constraints with deep convolutional neural networks, as a way to harness their remarkable ease of generating natural images. The mathema…
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is c…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional T…
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be o…
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical …
From linear classifiers to neural networks, image classification has been a widely explored topic in mathematics, and many algorithms have proven to be effective classifiers. However, the most accurate classifiers typically have significantly high storage costs, or require complicated procedures that may be computation…
Paper calculates KL divergence for isotropic Gaussian-Markov fields.
Paper shows equivalence between MM and PH for n-D Morse functions.
In this paper, we explore creative image generation constrained by small data. To partially automate the creation of cartoon sketches consistent with a specific designer's style, where acquiring a very large original image set is impossible or cost prohibitive, we exploit domain specific knowledge for a huge reduction …
Improved text-to-image and multimodal understanding through adaptive generation order optimization.
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets, factored RBMs, mcRBMs, convolutional RBMs, sparse autoencoders and several othe…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing (NLP) and Image Classification (IC). However, scientific and engineering problems …
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine learning algorithms. We describe a generic mathematical model to leverage quantum…
Review of diffusion priors for solving imaging inverse problems.
CLIP controls neural network stability by bounding Lipschitz constants.
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models…
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this property of NMF on three applications, in image processing, text mining and hyperspe…
New method reconstructs 3D shapes from 2D images using Kendall's shape space.