The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
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24 results for “reparametrisation”
This work connects SAM to variational inference and evaluates its performance.
problem Improving generalization of gradient-based learning by finding flat minima.
method Establishes connections between SAM and Mean-Field Variational Inference (MFVI), and evaluates variational algorithms combining or interpolating between SAM and MFVI.
result SAM-like updates can be used as a drop-in replacement for the reparametrisation trick.
AISLE framework improves on IWAE by directly optimising proposal distribution.
problem IWAE's multi-sample objective leads to inference-network gradients that break down with increasing samples.
method Introduces AISLE framework, which optimises proposal distribution directly.
result AISLE admits IWAE-STL and IWAE-DREG as special cases, avoiding breakdown.
Study of foliations' geometric and topological structures.
problem Analyzing the geometric and topological properties of transversely affine foliations.
method Attach holonomy group and quotient stack, identify reparametrisations, classify them, and study the Kato-Nakayama space.
result Holonomy group controls the geometric part, while the Kato-Nakayama space captures the topological and dynamical aspects.
Wide Bayesian neural networks have a simple weight posterior: theory and accelerated samplingstat.ML
Wide Bayesian neural networks have a simpler weight posterior, leading to faster MCMC sampling.
problem Sampling from the posterior of wide Bayesian neural networks is challenging.
method Introducing repriorisation, a data-dependent reparameterisation that simplifies the posterior distribution.
result The repriorisation map accelerates MCMC sampling, achieving up to 50x higher effective sample size.
The paper explores efficient sampling for Bayesian wide neural networks.
problem Sampling from posterior distributions of wide neural networks.
method Preconditioned Crank-Nicolson and Langevin algorithms for reparametrised posterior distributions.
result The preconditioned Crank-Nicolson algorithm improves sampling efficiency in wide networks.
Minimal tori that are linearly full in the 3-sphere possess a natural invariant g called their spectral genus, which was introduced by Hitchin. We show that for each g>0, there are countably many real g-dimensional families of minimally immersed tori with spectral genus g (two of these dimensions are just reparametrisa…
Gradient flow of curve length on Sobolev metrics preserves convexity.
problem Optimal low-regularity gradient flow of curve length.
method Explicit gradient formula, Picard-Lindelöf theorem, time-reparametrisation.
result Exponential decay of length and preservation of convexity.
We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which ove…
Solves Lie's 3D metric problem for projective vector fields.
problem Describing 3D Levi-Civita metrics with non-trivial projective vector fields.
method Analyzes Riemannian and Levi-Civita metrics of arbitrary signature.
result Solves the analog of Lie's problem in 3D.
This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending t…
Describes geodesic scattering on hyperboloids using quadrics results.
problem Understanding geodesic scattering on hyperboloids.
method Uses results from Moser and Knörrer on quadrics and Neumann system.
result Extends Knörrer's map to the projective closure of hyperboloids.
Scheme minimizes -elastic energy of curves over time.
problem Minimizing -elastic energy of curves over time.
method Minimizing movement scheme with approximate normal graphs.
result Short-time existence and lower bound on solution's lifetime.
We study a time reparametrisation of the Newton type equations on Riemannian manifolds slightly modifying the Chaplygin multiplier method, allowing us to consider the Chaplygin method and the Maupertuis principle within a unified framework. As an example, the reduced nonholonomic problem of rolling without slipping and…
We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian -manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow induced by the Hilbert metric on the quotient surface of divisible convex sets. We …
A new differentiable resampling method for Monte Carlo simulations.
problem Improving the efficiency and differentiability of resampling in Monte Carlo simulations.
method Proposes a diffusion model surrogate for resampling, proving consistency and outperforming existing methods.
result The proposed method outperforms state-of-the-art differentiable resampling methods on various benchmarks.
Study on curve diffusion flows with scale-critical curvature term.
problem Analyzing stability of curve diffusion flows with scale-critical curvature.
method Introduced and studied a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term. Analyzed dynamical stability of homothetic circles using variational methods.
result Established that any small perturbation of an -fold circle monotonically approaches the unit -circle after rescaling, translation, and reparametrisation.
Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian neural networks; several extensions ensued. We show that the log-uniform prior us…
Funk functions and projective deformations of sprays and Finsler spaces of scalar flag curvaturemath.DG
In 2001, Zhongmin Shen asked if it is possible for two projectively related Finsler metrics to have the same Riemann curvature tensor, [14, page 184]. In this paper, we provide an answer to this question, within the class of Finsler metrics of scalar flag curvature. In Theorem 3.1, we show that the answer is negative, …
Study on flows of G2-structures on contact Calabi-Yau 7-manifolds.
problem Analyzing the behavior of G2-structures under Laplacian and Hitchin flows.
method Investigation of Laplacian and Hitchin flows on contact Calabi-Yau 7-manifolds.
result Ancient solutions of the Laplacian flow with finite time Type I singularity and immortal solutions of the Laplacian coflow with infinite time Type IIb singularity.
A new method detects anomalies in multivariate streams without unit dependence.
problem Detect anomalies in multivariate streams without unit dependence.
method Proposes SigMahaKNN combining variance norm and path signature.
result SigMahaKNN detects anomalies better than existing methods.
A new neural network approach reduces tracking error in index replication.
problem Efficiently replicating an index with cardinality constraints.
method Reparametrisation and stochastic neural networks for optimisation.
result Our model achieves the lowest tracking error compared to benchmarks.
Deep model predicts shapes of curves with multiple covariates.
problem Predicting shapes of planar curves with various covariates.
method Deep learning model using complex-valued functions, conditional covariance smoother with modality-specific encoders.
result Model accurately predicts shapes of curves with multimodal covariates.
Clarifies EM algorithm and variational Bayesian inference concepts.
problem Gaps in AI literature understanding of EM and variational concepts.
method Tutorial presentation of EM algorithm, variational Bayesian inference, and autoencoded variational Bayes.
result Establishes clear links between EM and variational methods.