arXiv research

Unified framework for continuous-state discrete flow matching models.

Exact guidance for discrete data improves posterior sampling efficiency.

Proposes DAM for optimizing discrete generative models.

Novel framework combines tree-based discretization and ILP matching for causal inference.

New method reduces discrete flow transitions, improving perplexity estimation.

New method distills discrete diffusion models, maintaining quality and diversity.

New method boosts performance of diffusion models on discrete data like natural language.

Paper proposes a new generative model for discrete distributions using flows on submanifolds.

A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.

Graph Energy Matching improves generation quality for molecular graphs.

The paper characterizes discrete Morse functions on knot diagrams and generalizes a clock theorem.

Unified error analysis for discrete flow models.

Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds, through a reduction to the erasability problem. Here, we refine the stu…

Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.

The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an op…

Branching Flows generates sequences of varying lengths using binary trees.

We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based tensors, with an improved sample complexity. Moreover, we reuse standard ICA techni…

Optimal SQ bounds for learning binary product distributions and Ising models.

Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however, despite several recent improvements, the training of discrete latent variable m…

RFM uses tangent vector fields to match data on manifolds, analyzing TV convergence for Euler discretization.

Improved language models using ratio-matching and KL divergence.

The paper explores a new method for landmark matching using sub-Riemannian geometry and neural networks.

Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been completely resolved for score matching. First, we provide a formal link between maxim…

Simplified analysis of diffusion models using discrete random variables.

Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations of $C$ can be efficiently computed, in particular its homology or Morse-Smale d…

SFM matches flows on statistical manifolds for better discrete generation.

DFM models are analyzed for generating distributions with provable convergence.

We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis …

This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be appli…

The paper models market dynamics using a limit order book system to explain slippage and inefficiency.

DTM improves dLLM fine-tuning stability and performance.

New technique connects graph matching complexes to Morse theory for better topology understanding.

A new method for generative modeling of discrete data using geometric latent subspaces.

Simplifies denoising score matching for manifold learning.

Study asset price bubbles using random matching and stochastic factors.

In the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that any Euler structure on a smooth oriented closed 3-manifold has a particular rea…

This paper compares VaR estimation methods under tail misspecification, finding importance sampling underestimates VaR.

Proximal Diffusion Models improve generative model efficiency.

Develop contact Tulczyjew formalism for dissipative dynamics on skew algebroids.

Bayesian rating system for large competitions improves prediction and efficiency.

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of…

Improved bounds for estimating discrete distributions in KL divergence.

SIGMA model improves graph matching across various applications.

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new estimators designed specifically to overcome this intractability, but virtually nothing i…

Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.

Paper studies matching of samples from two distributions with a Gibbs probability weight.

Discrete noise improves graph generation quality and speed.

We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching contexts. We emphasize that the discrete optimal transport plays the role of a varia…