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.
Generic groups satisfy a chain condition for subgroups.
The paper extends Hoeffding's inequality for Markov chains using a generalized concentrability condition.
A method for learning with autoregressive chain-of-thoughts.
Generative neural samplers estimate quantum spin system properties.
A new method simulates a lazy version of a Markov chain for empirical inference.
Hidden Markov Chains and Linear-chain CRFs are equivalent.
Paper proposes semi-supervised learning with triplet Markov chains.
DCDC calculates convergence rates for Markov chains using neural networks.
In this work, we investigate a novel training procedure to learn a generative model as the transition operator of a Markov chain, such that, when applied repeatedly on an unstructured random noise sample, it will denoise it into a sample that matches the target distribution from the training set. The novel training pro…
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
Study on identifying AMP chain graph models under known and unknown component decompositions.
The paper tackles learning from non-irreducible Markov chains, proving learnability and generalization bounds.
With the help of a generalization of the Fermat principle in general relativity, we show that chains in CR geometry are geodesics of a certain Kropina metric constructed from the CR structure. We study the projective equivalence of Kropina metrics and show that if the kernel distributions of the corresponding 1-forms a…
In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities for Lipschitz functions of weakly dependent sequences proposed by Rio in 2000. We …
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
Improves multi-label classification with a new network model.
Transformers improve logical reasoning on longer proofs but struggle with length.
We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson's group . The resulting class of groups exhibits a combination of uniformity and diversity. On the one hand, a chain group either has a simple commutator subgroup or the action of the…
Study Markov chain gradient descent in Hilbert spaces for quadratic loss.
Study finds on-chain data can proxy off-chain cryptocurrency pricing.
Deep neural networks optimize inventory decisions in complex supply chains.
New Markov chains defined on simplicial complexes for understanding their topology.
The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented -manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…
The paper bounds generalization errors for deep neural networks with Markov datasets.
We prove the volume conjecture for an infinite family of links called Whitehead chains that generalizes both the Whitehead link and the Borromean rings.
We analyze a new Markov chain model for better sampling and optimization.
This work improves generalisation bounds using chaining and information theory.
The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of d…
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…
The paper proves an ascending chain condition for subgroups in hyperbolic and graph 3-manifolds.
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…
Link Floer homology is split into snake complexes and local systems.
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formal…
We explore a general framework in Markov chain Monte Carlo (MCMC) sampling where sequential proposals are tried as a candidate for the next state of the Markov chain. This sequential-proposal framework can be applied to various existing MCMC methods, including Metropolis-Hastings algorithms using random proposals and m…
Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the hypotheses, (ii) exploiting the dependence between the algorithm'…
This paper analyzes stability and generalization of Markov chain stochastic gradient methods.
New empirical PAC-Bayes bound for Markov chains with finite state space.
The Riemannian barycentre is one of the most widely used statistical descriptors for probability distributions on Riemannian manifolds. At present, existing algorithms are able to compute the Riemannian barycentre of a probability distribution, only if i.i.d. samples of this distribution are readily available. However,…
A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features. The idea of extending this chaining methodology to multi-output regression has a…
LLMs are compared to Markov chains for natural language processing.
Markov chain decoders improve generative models' ability to produce heavy-tailed data.
The paper proves inequalities for Steklov eigenvalues on finite graphs.
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star, Lie derivative, pullback and interior product. Partitions of unity exist in thi…
In this paper we describe three stochastic models based on a semi-Markov chains approach and its generalizations to study the high frequency price dynamics of traded stocks. The three models are: a simple semi-Markov chain model, an indexed semi-Markov chain model and a weighted indexed semi-Markov chain model. We show…
New MCMC method corrects bias without extra cost.
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
Langevin Dynamics fails to sample from mixture distributions efficiently.
New density estimator from Markov Chains outperforms KDE.