arXiv research

Study examines infinite limits of transformer dynamics, identifying key parameterizations.

Study on infinite neural networks for generalization.

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spa…

This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian non…

New approach finds optimal hidden paths in large models, scaling to high dimensions.

Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.

Infinite-dimensional contact geometry explored.

The paper discusses the importance of infinite-mean models in finance and risk management.

This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponential-Blurring-Mean-Sh…

Infinite-dimensional diffusion models tackle generative tasks for complex data.

Study evaluates initialization strategies for infinite hidden Markov models.

This research develops approximation theory for OOMs of infinite-dimensional processes.

Project infinite time series graphs to finite marginal models using number theory.

This paper conditions non-linear infinite-dimensional diffusion processes.

Develops robust methods for infinite-dimensional stochastic processes.

The grand arc graph's asymptotic dimension is shown to be infinite.

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In th…

Paper introduces infinite-dimensional generative models using Doob's h-transform.

Infinite-dimensional SBDMs improve image generation across multiple resolutions.

Probabilistic model for exhaustion in infinite-genus curve complexes.

We extend rectified flow to infinite-dimensional Hilbert space.

Study improves kernel quadrature for infinitely wide models with faster approximation and estimation rates.

New framework for understanding infinite-width neural networks.

Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.

Two new algorithms improve model-free RL for infinite-horizon MDPs.

We present the Infinite Latent Events Model, a nonparametric hierarchical Bayesian distribution over infinite dimensional Dynamic Bayesian Networks with binary state representations and noisy-OR-like transitions. The distribution can be used to learn structure in discrete timeseries data by simultaneously inferring a s…

Solves infinite horizon portfolio problem with path-dependent labor income.

Improves deep generative models to generate images of any size.

Lectures on deep learning properties in infinite and large-width networks.

New method for Bayesian inference in infinite dimensions using SDMs.

Bayesian neural networks approximate Student-t processes in the infinite-width limit.

New method handles infinite models with rigorous $L^1$-constraint.

Existence of balanced embedding proved for complex manifold into infinite-dimensional space.

Study shows how Poisson brackets factor on infinite dimensional manifolds.

This work investigates training infinite mixtures with maximum likelihood for improved uncertainty quantification.

Unified asymptotic theory and tests for ACD models reveal infinite-mean durations in cryptocurrency trading.

Paper constructs infinitely many tangent functors on diffeological spaces.

We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds under submersions and pre-images under mappings whose differentials have dense im…

Develops infinite-dimensional Kempf-Ness theory for complexification-free groups.

We construct a new infinite family of models of exotic 7-spheres. These models are direct generalizations of the Gromoll-Meyer sphere. From their symmetries, geodesics and submanifolds half of them are closer to the standard 7-sphere than any other known model for an exotic 7-sphere.

Deep neural networks' infinite-width behavior approximated by Gaussian models.

FDPs generalize diffusion models to function spaces, enabling efficient image generation.

Veech groups uniformize Teichmüller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite ends. We further show that examples exist for which each direction of an infinite end …

Most existing approaches to clustering gene expression time course data treat the different time points as independent dimensions and are invariant to permutations, such as reversal, of the experimental time course. Approaches utilizing HMMs have been shown to be helpful in this regard, but are hampered by having to ch…

UDN adapts depth to data complexity, outperforming standard neural networks.

Innovative PGMs match neural networks, revealing precise approximations during forward propagation.

Proposes an algorithm for infinite-dimensional sparse learning in system identification.

Study pricing options on forward contracts using infinite-dimensional affine models.