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.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
New framework explains normalizing flows' power and limitations.
New invertible transformations improve flow-based generative models.
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…
CF-INNs can approximate any invertible function, resolving a long-standing problem.
Unified geometric flows improve deep learning efficiency and simplify neural network topologies.
A new method for optimal transport using neural ODEs that preserves marginal constraints.
In this paper, we present a new approach to interpret deep learning models. By coupling mutual information with network science, we explore how information flows through feedforward networks. We show that efficiently approximating mutual information allows us to create an information measure that quantifies how much in…
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not str…
New proof shows coupling-based flows converge linearly to diagonalize data covariance.
Bounds on Hessian of heat equation coupled with Ricci flow.
The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed f…
Let be a solution to the Ricci flow coupled with the heat equation for a scalar field . We show that a complete, -noncollapsed solution to this coupled Ricci flow with a Type I singularity at time will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base po…
This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.
CPFM integrates dimensionality reduction and reconstruction with flow networks.
A one-parameter family of coupled flows depending on a parameter is introduced which reduces when to the coupled flow of a metric with a -form due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for , estimates for derivatives of all orders would follow from…
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we…
Incorporates matrix exponential into generative flows for improved performance.
Study mean curvature flow into evolving manifold with coupled flows.
We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive coupling constant alpha. This system can be interpreted as the gradient flow of an ene…
Triangular flows ensure statistical consistency and fast rates in generative modeling.
We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of point-wise charges. This coupling constrains the motion when the curve matches a picture placed as backgrou…
CFIL uses coupled flows to model state distributions for imitation learning.
Developed MF-PINNs to solve coupled Stokes-Darcy equations more accurately.
We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate that one natural geometric context for the flow is a special case of the locally …
In this note we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang's work, we extend some results of Zhang and Bamler-Zhang including distance distortion estimates and a backward pseudolocality theorem for Ricci flow on compact ma…
Steerable neural ODEs on homogeneous spaces for equivariant feature dynamics.
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this …
Alternative construction of quasi-Fuchsian flows using vortex equations.
Improved NPE with conditional diffusions and summary networks.
Large Sinkhorn couplings improve flow models in data generation tasks.
A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based models are slow to invert, making either density estimation or sample generation sl…
Improved flow-based models capture dependencies better with multi-scale autoregressive priors.
Normalizing flows are shown to be equivalent to Bayesian networks, revealing new insights.
Covariance shrinkage via stochastic interpolation
We review coupled -structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of flows of -structures with respect to the coupled condition.
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for…
Augmented bridge matching preserves coupling information between distributions.
OptIMIS method improves SRAM yield estimation efficiency and accuracy.
The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they…
New method learns PDE solutions from low-fidelity data.
The paper studies geometric constants under modified Ricci flows with variable parameters.
Analyzed geometric and diffusion properties of a coupled system.
We investigate Bartnik's static metric extension conjecture under the additional assumption of axisymmetry of both the given Bartnik data and the desired static extensions. To do so, we suggest a geometric flow approach, coupled to the Weyl-Papapetrou formalism for axisymmetric static solutions to the Einstein vacuum e…
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…
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…