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arXiv research

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.

168,695 papers · 148 categories

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169338507676 · Jun 202019922001200920172026
48 results for Discrete States

New framework for discrete-state diffusion models reduces sample complexity.

problem Lack of theoretical understanding and sample complexity analysis for discrete-state diffusion models.
method Developed a principled theoretical framework, decomposing score estimation error.
result Established sample complexity bound of O~(ε2)\widetilde{\mathcal{O}}(ε^{-2}).

Deep neural network learns discrete state abstractions for efficient planning.

problem Efficient sequential decision making in large state spaces.
method Information bottleneck method for learning approximate bisimulations using deep neural encoders and action-conditioned HMM.
result Trained method efficiently plans for unseen goals in multi-goal reinforcement learning.

Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.

problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.

This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.

problem Theoretical guarantees for discrete-state diffusion models remain under-explored.
method Continuous Time Markov Chain (CTMC) framework and discrete-time sampling algorithm.
result Convergence bounds for KL divergence and TV distance are derived, showing linear dependence on dimension.

Unified framework for continuous-state discrete flow matching models.

problem Discrete generative modeling with continuous probabilities.
method Introducing αα-Flow, a family of CS-DFM models based on information geometry.
result Optimal flow matching loss for αα-flow minimizes generalized kinetic energy.

The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …

2018-07-16abs ↗pdf ↗

Bayesian inference of discrete component states in civil infrastructures using PGMs and GNNs.

problem Inferring discrete states of civil infrastructure components from measurable responses is an ill-posed inverse problem.
method The study proposes a novel Bayesian inversion paradigm based on Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs). PGMs are used to model the problem, with parameters learned from data and structural topology prior. Inference is accomplished by GNNs, and a graph property-based training strategy is developed.
result The proposed framework effectively solves the challenges of inferring the posterior PDF for discrete variables in high-dimensional problems.

This primer explains diffusion models in general state spaces.

problem Diffusion models in general state spaces are not well-introduced.
method Develops discrete-time and continuous-time views of diffusion models, deriving Fokker-Planck and master equations.
result Unified understanding of diffusion models across continuous and discrete domains.

Soft Actor-Critic is a state-of-the-art reinforcement learning algorithm for continuous action settings that is not applicable to discrete action settings. Many important settings involve discrete actions, however, and so here we derive an alternative version of the Soft Actor-Critic algorithm that is applicable to dis…

2019-10-16abs ↗pdf ↗

This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.

problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.

CADD improves generative quality by augmenting discrete diffusion with continuous latent space.

problem Loss of semantic information between denoising steps in discrete diffusion models.
method Introduces a framework that augments discrete state space with a continuous latent space, allowing for graded, informative masked tokens.
result CADD improves generative quality across text generation, image synthesis, and code modeling.

Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.

problem Challenges in understanding discrete diffusion models on combinatorial state spaces.
method Established convergence bounds for three discrete diffusion models using Euler approximations.
result Optimal non-asymptotic convergence guarantees for discrete diffusion models without boundedness assumptions.

We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in th…

2013-01-15abs ↗pdf ↗

A new method reduces high-dimensional state space for dynamic choice models.

problem Estimation of dynamic discrete choice models is computationally intensive and infeasible in high-dimensional settings.
method Recursive partitioning algorithm to reduce dimensionality of high-dimensional state space.
result Our method reduces estimation bias and makes estimation feasible.

NCDSSM models irregularly sampled time series with improved imputation and forecasting.

problem Accurate modeling of irregularly sampled time series with missing observations.
method Neural Continuous-Discrete State Space Model (NCDSSM) with amortized inference for auxiliary variables and flexible dynamic state parameterizations.
result Improved imputation and forecasting performance on multiple benchmark datasets.

The study proves a discrete version of Segre's theorem for polygonal curves.

problem Proving a discrete analog of a four-vertex theorem for spherical curves.
method Using the concept of discrete tangent indicatrix of a polygon.
result A polygon with at least four vertices and a non-self-intersecting discrete tangent indicatrix has at least four flattenings.

Discrete diffusion models improve data generation for discrete data like language and graphs.

problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.

DFMs enable flow-based models for multimodal discrete and continuous data.

problem Combining discrete and continuous data for generative models.
method Discrete Flow Models (DFMs) using Continuous Time Markov Chains.
result DFMs achieve state-of-the-art co-design performance for protein structure and sequence generation.

Study asset pricing under model uncertainty with discrete time and states.

problem Asset pricing under model uncertainty with discrete time and states.
method Novel definition of arbitrage, investigation of no-arbitrage conditions, expansion to multi-period securities model.
result Necessary and sufficient conditions for no-arbitrage asset pricing under model uncertainty.

Paper solves POMDPs in continuous time and discrete spaces.

problem Optimal decision making in discrete state and action space systems under partial observability.
method Combining optimal filtering theory and deep learning to solve a Hamilton-Jacobi-Bellman equation.
result Derives a mathematical description and solution approach for continuous-time POMDPs.

Corrected samplers reduce discretization error in discrete flow models without additional computational cost.

problem Discretization error in samplers for discrete flow models.
method Established non-asymptotic error bounds for samplers, proposed time-corrected and location-corrected samplers.
result Location-corrected sampler has lower complexity and better generation quality.

HiPPO-Prophecy models can learn dynamical systems without fine-tuning.

problem Learning dynamical systems in context without fine-tuning parameters.
method Introduced a novel weight construction for SSMs that approximates derivatives of input signals.
result Discrete SSMs can predict the next state of any dynamical system after observing previous states.

Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach for these challenging problems. Deriving an algebraic representation allows us to…

2012-10-26abs ↗pdf ↗

A new method learns discrete representations for images and videos, improving upon previous models.

problem Learning discrete representations for images and videos to improve performance.
method Depthwise application of Vector Quantized Variational Autoencoders (VQVAE) to feature axis.
result 33% improvement in performance compared to previous discrete models.

New method reduces discrete flow transitions, improving perplexity estimation.

problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.

We study Exo-MDPs to reduce sample complexity in reinforcement learning.

problem Reducing sample complexity in reinforcement learning for structured MDPs.
method Introducing Exo-MDPs and proving structural equivalence to linear mixture MDPs, establishing regret bounds.
result Proved O(H3/2dK)O(H^{3/2}d\sqrt{K}) regret bound for Exo-MDPs, matching lower bounds.

Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete late…

2016-09-07abs ↗pdf ↗

A new model tackles language generation issues by using discrete variational attention.

problem Information under-representation and posterior collapse in variational autoencoders.
method Proposes a discrete variational attention model with categorical distribution over attention mechanism.
result Enhances latent space for language generation and avoids posterior collapse.

A new method reduces complexity in estimating dynamic choice models.

problem Estimating structural parameters in dynamic discrete choice models using behavioral data.
method Two-stage approach: inverse reinforcement learning for Q-function estimation, state selection via clustering, and maximum likelihood estimation with nested fixed-point algorithm.
result The method mitigates the curse of dimensionality and provides finite-sample bounds on estimation error.

New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.

problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.

Branching Flows generates sequences of varying lengths using binary trees.

problem Generating sequences of unknown lengths or fixed elements.
method A generative modeling framework that evolves states over binary trees, controlling sequence length.
result Branching Flows can generate sequences of varying lengths and mix different types of state spaces.

Study discrete analog of zeta-determinant maximization on triangulated surfaces.

problem Maximizing zeta-determinant for discrete Laplacian on triangulated surfaces.
method Analogous to Osgood, Phillips, and Sarnak's theorem, study stationary points of determinants for discrete cotan-Laplacian.
result Discrete metrics of constant discrete Gaussian curvature are stationary points of the determinant, suggesting minima.

GDM models time series with smoother transitions and interpretable states.

problem Capturing smooth, variable-speed transitions and stochastic mixtures of states.
method Introduces a continuous relaxation of discrete states and a Gumbel noise model.
result Models real-world datasets more faithfully with smoother dynamics and interpretable states.

Rewiring networks using discrete geometry improves GNN training accuracy and reduces runtime.

problem Inefficient information propagation between distant nodes in graph neural networks.
method Discrete analogues of classical geometric curvature to model and rewire networks.
result Classical geometric notions achieve state-of-the-art GNN training accuracy and significantly reduce runtime.

Proposes a new method for two-dimensional data discretization.

problem Discretization of multi-dimensional data, especially when dimensions are dependent.
method PALM algorithm, which alternately partitions and merges regions using the MDL principle.
result PALM accurately reveals ground truth partitions and approximates well outside the model class.

GraphBSI generates graphs by refining a belief in continuous space, outperforming existing models.

problem Generating discrete, unordered graph data is challenging for traditional models.
method GraphBSI uses Bayesian Sample Inference (BSI) to iteratively refine a belief over graph distribution parameters.
result GraphBSI outperforms existing one-shot graph generative models on molecular and synthetic graph generation benchmarks.

Quantum method generates unbiased samples from discrete graphical models.

problem Sampling from discrete graphical models is challenging and intractable in high dimensions.
method Embedding graphical models into unitary operators and using quantum circuits.
result Provably generates unbiased and independent samples from general discrete factor models.