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.
Generative model for discrete objects using Markov chains with valid transitions.
In this work we present Discrete Attend Infer Repeat (Discrete-AIR), a Recurrent Auto-Encoder with structured latent distributions containing discrete categorical distributions, continuous attribute distributions, and factorised spatial attention. While inspired by the original AIR model andretaining AIR model's capabi…
Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we introduce a subdivision method by applying the Goldberg-Coxeter subdivision and…
New discrete cobordism category for nested manifolds and relations to algebraic structures.
In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in LP_d. We introdu…
Develops combinatorial theory of vector bundles on simplicial complexes.
Study improves sampling efficiency of diffusion models using RL and PDEs.
Deep learning techniques have been hugely successful for traditional supervised and unsupervised machine learning problems. In large part, these techniques solve continuous optimization problems. Recently however, discrete generative deep learning models have been successfully used to efficiently search high-dimensiona…
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
This work extends reduction processes for nonholonomic discrete mechanical systems.
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, namely stochastic gradient descent and its variants, to such d…
New mechanics on non-associative octonions discovered.
FLDD improves discrete diffusion models by learning a non-Markovian noising process.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
TVO tightens variational inference bounds for deep models.
LSB is a new MCMC method for discrete spaces that reduces target evaluations.
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of qu…
Bayesian optimization tackles expensive discrete and mixed parameter spaces.
Survey on discrete curvature concepts for polygons and polyhedral surfaces.
A new algorithm for minimizing functions on Wasserstein space.
Algorithm identifies Pareto optimal designs efficiently for noisy, multi-objective functions.
A new method for training generative models with sparse supervision.
In this paper we study a new reinforcement learning setting where the environment is non-rewarding, contains several possibly related objects of various controllability, and where an apt agent Bob acts independently, with non-observable intentions. We argue that this setting defines a realistic scenario and we present …
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…
DD-VAE uses deterministic decoding for better latent code utilization in discrete data.
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…
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…
Develop contact Tulczyjew formalism for dissipative dynamics on skew algebroids.
We explore non-acyclic GFlowNets in discrete settings.
Direct policy gradients optimize policies in discrete action spaces using sampling.
ANT learns sparse embeddings for large vocabularies efficiently.
Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches general…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but also discrete vector fields and the operators acting on these objects. This allow…
Generative Adversarial Networks (GAN) have limitations when the goal is to generate sequences of discrete elements. The reason for this is that samples from a distribution on discrete objects such as the multinomial are not differentiable with respect to the distribution parameters. This problem can be avoided by using…
Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under leveraged. In this paper, we show that such models are more amenable to training whe…
Simplified masked diffusion models improve discrete data generation.
Multilayer switch networks are proposed as artificial generators of high-dimensional discrete data (e.g., binary vectors, categorical data, natural language, network log files, and discrete-valued time series). Unlike deconvolution networks which generate continuous-valued data and which consist of upsampling filters a…
The paper proposes a method to learn structured representations from unlabeled data using mutual information maximization.
Skew parallelogram nets factorize, encompassing discrete differential geometry.
Unified discrete diffusion for categorical data simplifies training and sampling.
We propose a natural discretisation scheme for classical projective minimal surfaces. We follow the classical geometric characterisation and classification of projective minimal surfaces and introduce at each step canonical discrete models of the associated geometric notions and objects. Thus, we introduce discrete ana…
A new method for categorical variational inference using discrete normalizing flows.
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk patterns by optimizing an objective function, which turns out to be intimately …
Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an operation and is non-dif…
Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts certain types of lattice paths. We define continuous versions of binomials and multinomials, and describe some identities and partial differe…
We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning machine learning hyperparameters, optimization via simulation, and sequential des…
Quantum algorithm finds extrema in discrete optimisation problems.
Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models f…