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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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2 results for “neuromanifolds”

Deterministic Bounds and Random Estimates of Metric Tensors on Neuromanifoldscs.LG

Estimates metric tensor on neuromanifolds using Fisher information and random methods.

problem Computing the metric tensor on high-dimensional neuromanifolds efficiently and accurately.

method Deterministic bounds and unbiased random estimators based on Hutchinson's trace method.

result An efficient random estimator with bounded standard deviation.

neuromanifolds metric tensors Fisher information random estimation Hutchinson's trace

2025-05-19abs ↗pdf ↗

Geometry of Polynomial Neural Networksmath.AG

Study the expressivity and training complexity of polynomial neural networks.

problem Understanding the expressivity and training complexity of polynomial neural networks.

method Use algebraic geometry to describe neuromanifolds and neurovarieties, analyzing their dimension and learning degree.

result Characterized the dimension and learning degree of neuromanifolds, providing geometric and complexity measures.

polynomial neural networks algebraic geometry neuromanifolds neurovarieties expressivity

2024-02-01abs ↗pdf ↗