EBMs trained on discrete data using heat equations on graph structures.
problem Training EBMs on discrete or mixed data.
method Heat equations on graph structures for data perturbation.
result Efficacy demonstrated in various applications.
On-device research index
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.
168,742 papers · 148 categories
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48 results for “discrete model structures”
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 .
Proposes a differentiable structure learning framework for general binary data.
problem Limitations of existing methods in discrete data structure learning.
method Formulates a differentiable optimization task for arbitrary dependencies in general discrete models.
result Establishes identifiability of complete set of compatible parameters and structures under mild assumptions.
This text explores strategies for learning discrete latent structures in neural networks.
problem Learning discrete latent structures in neural networks is challenging.
method Continuous relaxation, surrogate gradients, and probabilistic estimation.
result Many latent structure learning strategies use the same fundamental building blocks but apply them differently.
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
problem Formulating discrete mechanics with constraints.
method Developed -discrete Dirac structures and induced Dirac structures.
result Discrete Lagrange--Dirac systems are equivalent to -discrete Lagrange--d'Alembert equations.
Lecture notes on crystallography and discrete surfaces.
problem Mathematical modeling of crystal structures.
method Variational principle and discrete surface theory.
result Most symmetric crystal structures identified.
Novel SVAE learns interpretable discrete data representations from deep learning.
problem Learning interpretable discrete data representations from deep learning.
method Structured variational autoencoder (SVAE) with novel optimization algorithms.
result First competitive comparisons with state-of-the-art time series models.
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.
Extends rigidity and existence results for discrete conformal structures on surfaces with boundary.
problem Rigidity and existence of discrete conformal structures on surfaces with boundary.
method Axiomatic framework and classification of discrete conformal structures.
result Extends results by Guo-Luo and Guo to a general context.
A framework for discrete structure recovery using iterative algorithms.
problem Recovering various discrete structures from data.
method General iterative algorithm for discrete structure recovery.
result Linear convergence of the proposed algorithm under certain conditions.
This paper completes the classification of discrete conformal structures on surfaces.
problem Classifying discrete conformal structures on surfaces.
method Axiomatic approach and study of existing structures.
result Find new classes of discrete conformal structures, including generalized circle packing metrics.
A new method trains discrete EBMs without sampling.
problem Training EBMs on discrete spaces is hard.
method Energy Discrepancy (ED), a contrastive loss.
result ED offers theoretical guarantees for various perturbation types.
NES optimizes discrete structured VAEs effectively without gradient propagation.
problem Learning high-dimensional discrete latent spaces in generative models.
method Natural Evolution Strategies (NES) for gradient-free optimization of discrete structures.
result NES effectively optimizes discrete structured VAEs, comparable to gradient-based methods.
FLOP algorithm speeds up causal structure learning for linear models.
problem Efficiently learning causal structures from discrete data.
method FLOP algorithm combines fast parent selection and iterative score updates.
result FLOP finds highly accurate causal structures with near-perfect recovery.
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…
Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. Howe…
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
problem Discretization issues and complex statistical dependencies in discrete data.
method Continuous normalizing flows on factorizing discrete measures, geodesic flow matching.
result Efficient training and broad applicability demonstrated through experiments.
Paper tackles goal-directed generation of discrete structures using conditional generative models.
problem Challenges in generating structured discrete data, especially for problems like program synthesis and materials design.
method Investigates conditional generative models to directly model the distribution of discrete structures given properties of interest. Introduces a novel approach to optimize a reinforcement learning objective.
result Improvements over maximum likelihood estimation and other baselines in generating molecules and identifying short python expressions.
CANDI solves the gap between continuous and discrete diffusion models for text generation.
problem Underperformance of continuous diffusion models in discrete data domains.
method Introduces token identifiability and a hybrid framework (CANDI) to decouple discrete and continuous corruption.
result CANDI successfully avoids temporal dissonance, enabling continuous diffusion benefits for discrete spaces.
Study on deforming discrete conformal structures on surfaces with boundaries.
problem Deforming discrete conformal structures on surfaces with boundaries.
method Introduce combinatorial Ricci flow and combinatorial Calabi flow, establish longtime existence and global convergence of solutions.
result Effective algorithms for finding discrete hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths.
Develops TCD maps to relate discrete differential geometry and cluster algebras.
problem Capturing constraints and dynamics in discrete differential geometry.
method Triple crossing diagram maps (TCD maps) and geometric operations.
result Establishes a hierarchy of cluster structures on TCD maps.
Deep generative models have been successfully used to learn representations for high-dimensional discrete spaces by representing discrete objects as sequences and employing powerful sequence-based deep models. Unfortunately, these sequence-based models often produce invalid sequences: sequences which do not represent a…
Spatio-temporal Lie-Poisson discretization for incompressible magnetohydrodynamics on the spheremath.NA
New method preserves MHD equations on sphere without costly matrix exponentials.
problem Discretizing MHD equations on sphere for numerical simulations.
method Lie-Poisson discretization, geometric quantization, semi-direct product Lie algebras.
result Preserves Lie-Poisson structure and Casimir functions.
New method fine-tunes discrete diffusion models for RLHF tasks.
problem Fine-tuning discrete diffusion models with policy gradient methods is challenging.
method Proposed SEPO algorithm for efficient fine-tuning over non-differentiable rewards.
result Numerical experiments show scalability and efficiency of SEPO.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
Proposes a VAE with a discrete bottleneck for better text generation.
problem VAEs struggle with latent variable auto-regressive decoding in text generation.
method Introduces a discretized bottleneck to enforce latent feature matching in a compact space.
result Demonstrates improved text generation capabilities across various tasks.
Study preserves symplectic structure in forced discrete mechanical systems.
problem Preserving symplectic structure in forced discrete mechanical systems.
method Analyzes a specific type of forced discrete mechanical system , preserving a symplectic structure on .
result The preserved symplectic structure can be seen as Marsden-Weinstein reduction of the canonical symplectic structure.
Alternative discrete Dirac mechanics using Dirac structures.
problem Developing a new framework for discrete mechanics.
method Introducing 'continuous Dirac system' and proposing a definition of 'discrete Dirac system'.
result It is possible to recover discrete Lagrangian and Hamiltonian systems.
A novel symmetry in nanocarbons: pre-constant discrete principal curvature structurecond-mat.mtrl-sci
Novel symmetry found in nanocarbons' discrete principal curvature structure.
problem Identifying novel symmetries in nanocarbons' geometric structures.
method First-principles calculations and discrete geometry analysis.
result Discovery of a novel symmetry (pre-constant discrete principal curvature) in nanocarbons.
New theorem proves convergence of various discrete conformal structures to conformal maps.
problem Proving convergence of discrete conformal structures to conformal maps.
method General theorem using piecewise linear discrete conformal mappings and Riemannian barycentric coordinates.
result Discrete conformal mappings converge to conformal maps under certain conditions.
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…
This paper classifies discrete conformal structures on surfaces with boundary.
problem Classifying discrete conformal structures on surfaces with boundary.
method Axiomatic approach ensuring good geometric structure, classification based on triangulation and axioms.
result Unified and generalized existing discrete conformal structures on surfaces with boundary.
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the…
Paper analyzes pricing model for bonds with early redemption.
problem Analyzing pricing of bonds with early redemption features.
method Structural approach for mathematical modeling of bond prices.
result Existence and uniqueness of default and early redemption boundaries proved.
Extends Zeitlin's model to 3-D axisymmetric Euler equations.
problem Preserving geometric structure in 3-D Euler equations.
method Axisymmetric discretization of 3-D Euler equations on the 3-sphere.
result First discretization of 3-D Euler equations preserving geometric structure.
GFlowNet-EM learns complex latent variable models with discrete structures.
problem Challenges in modeling posteriors over discrete compositional latents with expectation-maximization.
method Uses GFlowNets to learn stochastic policies for sampling from complex posterior distributions.
result GFlowNet-EM enables training expressive LVMs with discrete compositional latents.
SOM-VQ tokenizes discrete models with semantic structure and navigable topology.
problem Lack of semantic structure in vector quantized representations limits interpretable human control.
method Combines vector quantization with Self-Organizing Maps to learn discrete codebooks with explicit topology.
result SOM-VQ produces more learnable token sequences and provides an explicit navigable geometry in code space.
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and sho…
Discretization of Dirac systems and port-Hamiltonian systems: the role of the constraint algorithmmath.NA
Study discretizes Dirac and port-Hamiltonian systems using manifolds.
problem Discretization of Dirac and port-Hamiltonian systems.
method Retraction and discretization maps on manifolds for Dirac structures, applied to port-Hamiltonian systems.
result Numerical integrators for port-Hamiltonian systems derived from discretization techniques.
We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold , endowed with a flat, symmetric connection . The metric deter…
New method for efficient marginalization of discrete latent variables in neural networks.
problem Computational challenges in training models with discrete latent variables.
method Parameterizing discrete distributions using sparse mappings (sparsemax and structured variants) to reduce support and enable efficient marginalization.
result Achieved good performance in various tasks with efficient and practical training.
New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.
problem Creating new discrete conformal structures on surfaces with boundary.
method Introducing new discrete conformal structures, proving global rigidity using variational principles, and introducing combinatorial curvature flows.
result Global rigidity of new discrete conformal structures and effective algorithms for constructing hyperbolic metrics.
The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.
problem Finding piecewise constant curvature metrics on surfaces with prescribed combinatorial curvatures.
method Combinatorial curvature flows, including Ricci flow and Calabi flow, are applied to deform Glickenstein's discrete conformal structures.
result The solution of the combinatorial Ricci flow can be uniquely extended and converges exponentially fast for any initial value under certain conditions.
SDE automatically recovers interpretable discrete distributions.
problem Limited interpretable discrete probability laws.
method Unsupervised framework using symbolic density estimation.
result Accurately recovers interpretable discrete distributions.
Unsupervised framework captures acquisition variability in structural connectomes.
problem Acquisition differences across sites, scanners, and protocols complicate structural connectome analysis.
method An unsupervised framework using architectural annealing to balance discrete and continuous latent variables.
result Architectural annealing produces stronger site learning than baseline models.
DCRL learns causal relationships from mixed-type discrete data.
problem Challenges in learning causal relationships from discrete, mixed-type data.
method Generative framework modeling directed acyclic graph and sparse bipartite graph, flexible measurement models for different types of data.
result Consistent recovery of latent causal structure from observed data distribution.
The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.
problem Discrete conformal structures on polyhedral surfaces and their rigidity.
method Parameterized combinatorial curvature, combinatorial α-Ricci flow, and flow extension through singularities.
result Existence and convergence of combinatorial α-Ricci flow for solving the Yamabe problem.