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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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0111 · Dec 201519922001200920172026
7 results for geometry-adaptive

New method improves counterfactual distribution learning for high-dimensional outcomes.

problem Counterfactual distribution learning for high-dimensional outcomes with concentrated structure.
method Geometry-adaptive diffusion-guided smoothing estimators combining causal nuisance adjustment and local outcome geometry.
result Geometry-adaptive methods show steeper error decay in semi-synthetic experiments.

We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kaehler manifold gives rise to a c-projective structure and this is one…

2015-12-14abs ↗pdf ↗

Diffusion models adapt to data geometry through log-domain smoothing.

problem Understanding why diffusion models generalize well across diverse domains.
method Investigating the role of score matching and log-domain smoothing in diffusion models.
result Log-domain smoothing adapts the diffusion model to the data manifold.

Adaptive sampling improves graph diffusion models by maintaining uniform information speed.

problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.

CWGD measures gradient diversity weighted by curvature, improving SGD convergence.

problem Gradient noise in high-curvature directions is underestimated by standard methods.
method CWGD weights gradient diversity by the inverse square root of the Hessian.
result CWGD-Cosine reduces optimization error by up to 20% compared to standard cosine annealing.

GABI learns geometry from diverse systems to improve Bayesian inference.

problem Bayesian inversion of physical systems with varying geometries.
method Geometric Autoencoders for Bayesian Inversion (GABI) learns geometry-aware priors from large datasets.
result GABI yields comparable predictive accuracy to deterministic methods and well-calibrated uncertainty quantification.

This research explains why SGD generalizes better than ADAM in deep learning.

problem Understanding the generalization gap between SGD and ADAM in deep learning.
method Analyzing local convergence behaviors through Levy-driven stochastic differential equations (SDEs).
result SGD is more locally unstable and better escapes from sharp minima to flatter ones, leading to better generalization.