arXiv research

The paper analyzes finite-time singularities in Spin(7)-structure flows using Shi-type estimates.

Flow IV uses IVs to infer counterfactuals in complex models.

Shapley Flow interprets model predictions using a graph-based approach to feature importance.

In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called lambda-bar. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non-positive. On the other hand, the Perelman invariant just equals + i…

In 2011 Enders, Müller and Topping showed that any blow up sequence of a Type I Ricci flow near a singular point converges to a non-trivial gradient Ricci soliton, leading them to conclude that for such flows all reasonable definitions of singular points agree with each other. We prove the analogous result for the harm…

Physically-based overland flow models are computationally demanding, hindering their use for real-time applications. Therefore, the development of fast (and reasonably accurate) overland flow models is needed if they are to be used to support flood mitigation decision making. In this study, we investigate the potential…

In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from $C^0$…

We present a particle flow realization of Bayes' rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to re…

We consider Ricci flow on a closed surface with cone points. The main result is: given a (nonsmooth) cone metric g_0 over a closed surface there is a smooth Ricci flow g(t) defined for (0,T], with curvature unbounded above, such that g(t) tends to g_0 as t tends to 0. This result means that Ricci flow provides a way fo…

New model reconstructs flow from sparse data with uncertainty quantification.

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, con…

Protein Thoughts interprets protein interactions with clear reasoning, improving prediction accuracy.

Researchers extend Chen, Erchenko, and Gogolev's result to more cases.

This paper improves normalizing flows by combining MLE and sliced-Wasserstein distance for better data fidelity.

Study on subgroups' evolution in 3D Lie groups using mean curvature flow.

Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.

In this paper we consider a class of weighted-volume preserving curvature flows acting on hypersurfaces that are trapped within two parallel hyperplanes and satisfy an orthogonal boundary condition. In the author's thesis the stability of cylinders under the flows was considered; it was found that they are stable provi…

Causal normalizing flows recover causal models from observational data.

Cascading flows improve variational inference in structured programs.

Proposes a Coulomb-like model for international trade flows, fitting real-world data.

A new method uses Gaussian Processes to solve power flow problems with uncertain renewable and load inputs.

This paper provides a mathematical foundation for deep neural networks solving PDEs.

The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.

Improved Markov models learn from their mistakes and adapt to problem complexity.

CFIL uses coupled flows to model state distributions for imitation learning.

MAGIC-Flow generates and classifies medical images with interpretability.

SeqRF straightens generative model flows to speed up sampling.

TD-Flow improves long-term predictions in agent learning.

DoFlow models time series data for causal forecasting and anomaly detection.

We consider the Hele-Shaw flow that arises from injection of two-dimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin \cite{HS} and obtain essen…

Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and automated reasoning. Computing the underlying structure and dynamics of such complex systems is extrem…

We recall the construction of the Kontsevich graph orientation morphism $γ\mapsto {\rm O\vec{r}}(γ)$ which maps cocycles $γ$ in the non-oriented graph complex to infinitesimal symmetries $\dot{\mathcal{P}} = {\rm O\vec{r}}(γ)(\mathcal{P})$ of Poisson bi-vectors on affine manifolds. We reveal in particular why there alw…

In this short note, we prove that the space of all admissible piecewise linear metrics parameterized by length square on a triangulated manifolds is a convex cone. We further study Regge's Einstein-Hilbert action and give a much more reasonable definition of discrete Einstein metric than our former version in \cite{G}.…

EXOC framework uses auxiliary variables for counterfactual fairness in machine learning.

Study reveals how initialization scale affects training accuracy in linear networks.

LiveTradeBench evaluates LLMs in live trading environments.

The paper develops a new theory to understand deep learning optimization.

New framework learns nonlinear cyclic causal models from data.

The paper develops a multi-unit soft sensing model for virtual flow meters that improves few-shot learning.

ALPODS AI diagnoses high-dimensional biomedical data with human-understandable explanations.

This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.

Neural networks predict flow and elastic stresses in viscoelastic turbulence.

Paper proves short-time existence for network flow, providing detailed insights.

Study shows price impact increases with order-flow imbalance, using machine learning.

Enhances RJMCMC efficiency with non-linear transport-based proposals.

The quest for biologically plausible deep learning is driven, not just by the desire to explain experimentally-observed properties of biological neural networks, but also by the hope of discovering more efficient methods for training artificial networks. In this paper, we propose a new algorithm named Variational Proba…

Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.

We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market dynamics which we study both empirically and theoretically. We demonstrate that th…