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.
Statistical field theory aids in understanding deep learning complexities.
Simplified neural network EFTs reveal a single critical condition.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
Renormalization in neural networks linked to quantum field theory.
Develops a dynamic mean field theory for reinforcement learning.
Extreme value theory enhances statistical learning extrapolation for rare events.
New algebraic geometry and statistical manifold connections proven.
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message pas…
This work uses statistical mechanics to explain AI learning.
The paper derives Einstein tensors for a family of α-connections on quasi-statistical manifolds.
Study on kernel methods in large-scale machine learning problems.
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. Thi…
High-dimensional statistics advances in complex data domains.
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this rapidly growing field. The notes are the basis of lectures given at the conference…
Revises mean-field theory of Santa Fe model using kinetic theory.
The paper develops a new algorithm for RBMs using dynamical mean-field theory.
Machine learning should incorporate maximum likelihood for better estimation.
The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…
Counting the number of clusters, when these clusters overlap significantly is a challenging problem in machine learning. We argue that a purely mathematical quantum theory, formulated using the path integral technique, when applied to non-physics modeling leads to non-physics quantum theories that are statistical in na…
Paper connects RL and non-equilibrium statistical mechanics for entropy-regularized RL.
Paper explores the Jones polynomial and its impact on knot theory and related fields.
Study finds Calabi-Yau models' operator spectra match random matrix theory.
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way using methods from statistical field theory. Here I describe new results that allo…
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…
Study on Alexander polynomials in braids, linking number theory and topology.
Global EQG sums boundary states over manifold diffeomorphism classes.
Unified theory for deep and recurrent networks using Gaussian processes.
New theory predicts deep neural networks can operate in an extended critical regime without fine-tuning.
Paper uses SLT to improve model selection for SHM.
Sharp statistical theory for conditional diffusion models.
In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be corrected by using neural network-based MCMC or importance sampling which leads to a…
Explains how geometry and statistics intertwine, focusing on information geometry.
Paper reviews algebraic research in machine learning theory.
The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely …
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped st…
Model financial time series using φ^4 quantum field theory.
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
Statistical learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations. A statistical learning machine (SLM) is the algorithm, function, model, or rule, that learns such a process; and machine learning (ML) is the conventional name of this…
The simplest field theory description of the multivariate statistics of forward rate variations over time and maturities, involves a quadratic action containing a gradient squared rigidity term. However, this choice leads to a spurious kink (infinite curvature) of the normalized correlation function for coinciding matu…
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulatio…
Study loop corrections in random feature models affecting training and test errors.
Theory proposes neural networks can be initialized for optimal information transmission.
Proves equations for high-dimensional gradient-based methods from Gaussian data.
Improves survey sampling with unbiased machine learning methods.
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and vector spaces in the edges, called tensor network. Such tensor networks have been …
Paper characterizes gradient descent in high-dimensional learning problems.