New network learns non-parametric invariances from data.
problem Modeling non-parametric invariances in data.
method Introduces PRC-NPTN networks with permanent random connectomes.
result Improves generalization and outperforms existing methods.
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arXiv research
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.
168,742 papers · 148 categories
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7 results for “parametrization-invariant”
New method for comparing curves with flexible matching constraints.
problem Comparing plane curves with general elastic metrics.
method Combining transform for elastic metrics with parametrization-invariant fidelity metrics.
result Simple optimization problem for discretized curves.
We give a condition for a function to produce a Möbius invariant weighted inner product on the tangent space of the space of knots, and show that some kind of Möbius invariant knot energies can produce Möbius invariant and parametrization invariant weighted inner products. They would give a natural way to study the evo…
We consider the results of combining two approaches developed for the design of Riemannian metrics on curves and surfaces, namely parametrization-invariant metrics of the Sobolev type on spaces of immersions, and metrics derived through Riemannian submersions from right-invariant Sobolev metrics on groups of diffeomorp…
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
problem The dependence of maximum a posteriori estimates on parametrization.
method Assuming a Riemannian manifold with Fisher metric, the paper reinterprets priors and posteriors as distributions over probability distributions, making estimates independent of parametrization.
result A maximum a posteriori estimate independent of parametrization is defined.
Researchers find conditions for autoparallels to be Finsler geodesics.
problem Existence of a Finsler Lagrangian metrizing autoparallels in metric-affine geometry.
method Determined necessary and sufficient conditions for Finsler metrizability of torsion-free affine connections.
result A broad class of connections is Finsler metrizable, making their autoparallels Finsler geodesics.
New framework for equivariant neural networks using Lie group decompositions.
problem Limitations of existing equivariant neural network methods for Lie groups.
method Lie group structure and geometry, decomposition into subgroups and submanifolds.
result Equivariant neural networks for affine transformations outperform previous methods.