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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.

168,738 papers · 148 categories

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1122 · Jul 202519922001200920172026
14 results for curvature-aware

ManifoldMind uses adaptive-curvature probabilistic spheres for trustworthy recommendations in semantic hierarchies.

problem Sparse and abstract recommendation domains where users explore diverse conceptual paths.
method Adaptive-curvature probabilistic spheres, soft multi-hop inference, and curvature-aware semantic kernel.
result Superior NDCG, calibration, and diversity compared to baselines on public benchmarks.

This work improves data reconstruction methods by ensuring unique solutions and refining optimization.

problem Ensuring unique solutions and optimizing reconstruction from KKT conditions.
method Discussion of sufficient conditions for unique solutions and introduction of sample splitting for optimization.
result Sample splitting improves reconstruction performance across various methods.

EpiMer merges models by solving Fréchet mean on a Riemannian manifold.

problem Integrating knowledge from multiple models without retraining.
method EpiMer casts model merging as solving the Fréchet mean on a Riemannian manifold, restricting computation to a low-rank subspace.
result EpiMer outperforms flat-geometry methods on image classification tasks.

New method discovers mean and variance causal graphs from heteroscedastic data.

problem Understanding causal relationships in data with varying variance.
method Bayesian, moment-driven approach inferring separate mean and variance causal graphs.
result Accurately recovers mean and variance structures from heteroscedastic data.

This paper analyzes tokenized U.S. Treasuries, revealing patterns and roles in blockchain transactions.

problem Limited empirical analysis of transaction-level behaviors in tokenized U.S. Treasuries.
method Quantitative dissection of U.S. Treasury-backed RWA tokens across multiple chains, introducing a curvature-aware representation learning model for address-level economic role inference.
result Decoded transaction-level patterns reveal the degree of retail participation and distinguish roles in Web3 finance.

The paper refines classical covariance asymptotics using geometric information geometry.

problem Deviation of finite-sample behavior from classical predictions in curved models.
method Develops a curvature-aware refinement by viewing parametric families as Riemannian manifolds with Fisher-Rao metric.
result Derives an \(n^{-2}\) correction to the leading \(n^{-1}I(θ)^{-1}\) covariance term for score-root estimators.

A lightweight framework improves convergence and stability of PINNs for complex PDEs.

problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.

Study shows how to balance memory and learning efficiency in continual learning.

problem Balancing memory and learning efficiency in continual learning.
method Structural regularization with Hessian-based regularization.
result Structural regularization improves statistical performance at the cost of increased memory complexity.

The Gauss-Newton method is analyzed for neural networks using Riemannian optimization techniques.

problem Training neural networks with smooth activations and convergence rates.
method Riemannian optimization perspective, analyzing the Gauss-Newton method in both underparameterized and overparameterized regimes.
result Geometric convergence rates independent of conditioning and eigenvalues, demonstrating accelerated convergence.

Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.

problem Improving estimator efficiency in non-asymptotic settings.
method Incorporates curvature-aware corrections based on extrinsic geometry of statistical model manifold.
result Meaningful tightening of estimator variance bounds.

The paper introduces heterogeneous manifolds for better graph embeddings.

problem Graph embeddings in Euclidean spaces often fail to capture the curvature of real-world graphs.
method The authors propose heterogeneous rotationally-symmetric manifolds with a radial dimension to account for varying curvature.
result The method improves graph embeddings by better preserving high-order structures and heterogeneous random graphs.