arXiv research

A new method for 3D surface registration using dynamic programming.

We classify compact Kähler surfaces with nonconstant Killing potentials such that all integral curves of their gradients are reparametrized geodesics.

Improved VI with Price's gradient estimator for target log-density.

Monge SAM improves deep learning by making sharpness-aware minimization invariant to reparametrizations.

Quantized Variational Inference improves ELBO optimization with fast convergence.

Efficiently infers latent SDEs with scalable memory and time costs.

Proposes spred for solving $L_1$ penalty with SGD.

A vector field on a Riemannian manifold is called geodesic if its integral curves are reparametrized geodesics. We classify compact Kähler manifolds admitting nontrivial real-holomorphic geodesic gradient vector fields that satisfy an additional integrability condition. They are all biholomorphic to bundles of complex …

BBVI converges nearly dimensionally independent for log-concave targets.

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the weight normalization (WN) method [Salimans and Kingma, 2016] and a variant call…

Develop gradient boosting for estimating covariate-dependent GP distributions in insurance.

This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our var…

We introduce Natural Neural Networks, a novel family of algorithms that speed up convergence by adapting their internal representation during training to improve conditioning of the Fisher matrix. In particular, we show a specific example that employs a simple and efficient reparametrization of the neural network weigh…

Study on how reparametrization affects neural nets' parameter spaces from a geometric perspective.

DualVDT improves time-series forecasting with a novel dual reparametrized structure.

Two new proofs of Gromov's non-squeezing theorem using curve reparametrization and gradient bounds.

Gradient flow in parameters equals linear interpolation in outputs.

Evolution Strategies (ES) are a powerful class of blackbox optimization techniques that recently became a competitive alternative to state-of-the-art policy gradient (PG) algorithms for reinforcement learning (RL). We propose a new method for improving accuracy of the ES algorithms, that as opposed to recent approaches…

Improved diffusion bridge sampling with rKL-LD loss.

We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov chain Monte Carlo operation and a deterministic transformation that can be optimized…

New findings show a balance between data fit and complexity in kernel hyperparameters.

We prove an optimal control on the time-dependent measure of a measurable set under a reparametrized Lagrangian mean curvature flow of almost calibrated submanifolds in a Calabi-Yau manifold. Moreover we give a classification of those Lagrangian translating solitons in $\mathbb{C}^m$ that evolve by this reparametrized …

We consider pairs of a non-empty compact connected and locally connected Hausdorff space and a real-valued continuous function. Our aim is to measure the difference between this kind of the pairs. In this notes we introduce new pseudodistances between pairs associated with reparametrization invariant seminorms. We fini…

We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by generalizing the gradient computation in stochastic backpropagation via a reparametriza…

Paper proves trajectories of Chaplygin systems are reparametrized geodesics.

Completeness of surface metrics established for Sobolev spaces.

A new numerical framework simplifies elastic surface matching and comparison.

We simplify SVI volatility smile constraints for three sub-SVIs without numerical methods.

Motivated by Demailly's strategy towards the Kobayashi hyperbolicity conjecture, we study the action on the k-jets of germs of holomorphic discs in a complex manifold X of the reparametrization group of k-jets of germs of biholomorphisms of the source. This reparametrization group is a subgroup of the general linear gr…

New approach uses SPG for semantic communication without a known channel model.

The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [3], provides a way of representing immersed surfaces in $\mathbb R^3$, and equipping the set of these immersions with a "distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under…

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 $\arg \max$ operation and is non-dif…

We analyze a notion of multiple valued sections of a vector bundle over an abstract smooth Riemannian manifold, which was suggested by W. Allard in the unpublished note "Some useful techniques for dealing with multiple valued functions" and generalizes Almgren's $Q$-valued functions. We study some relevant properties o…

A new variational method improves deep neural network inference.

The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge without any reparametrization, and a new proof of this fact is given. The semi-stable and unstable cases are new, and it is shown that the flow …

We reparametrize ReLU NNs as splines to understand their learning dynamics.

In this article we investigate a first order reparametrization-invariant Sobolev metric on the space of immersed curves. Motivated by applications in shape analysis where discretizations of this infinite-dimensional space are needed, we extend this metric to the space of Lipschitz curves, establish the wellposedness of…

This study compares two methods for sampling with transport maps, finding flow-based proposals work better for multimodal distributions.

In this paper we study the shape space of curves with values in a homogeneous space $M = G/K$, where $G$ is a Lie group and $K$ is a compact Lie subgroup. We generalize the square root velocity framework to obtain a reparametrization invariant metric on the space of curves in $M$. By identifying curves in $M$ with thei…

Study on completeness of Sobolev metrics on manifold-valued curves.

The space of all immersed closed curves of rotation degree 0 in the plane modulo reparametrizations has the same homotopy groups as the circle times the 2-sphere.

Research shows deep generative models' likelihoods are unreliable for anomaly detection.

The chapter reviews metrics for comparing curves, focusing on quotient elastic and square root velocity metrics.

Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. If certain parameters of the loss function such as smoothness or strong convexity constants are known, theoretical learning rate schedules can be applied. However, in practice, such …

MetFlow combines MCMC and VI efficiently for better inference.

Study disproves conjecture about metric completion of curve spaces.

Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and dynamic programming.

New connections share geodesics with superintegrable systems.