---
title: "Riemannian Newton Methods with Statistical Inference"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.00949v1"
permalink: "https://feed.astralor.com/items/itm_4140652fd2c5b73cf78dab3a"
published: "2026-10-31T13:53:14.000Z"
score: 53
channel: "tech"
tags: ["推理效率","RAG","Riemannian Newton Methods","Statistical Inference","Polyak-Ruppert","Newton","Riemannian"]
---

# Riemannian Newton Methods with Statistical Inference

## 速览

We develop online statistical inference for Polyak-Ruppert averages of inexact Newton iterates on Riemannian manifolds. A local asymptotic representation separates observation noise, solver randomization, and accumulate…

## 关键点

- We develop online statistical inference for Polyak-Ruppert averages of inexact Newton iterates on Riemannian manifolds.
- A local asymptotic representation separates observation noise, solver randomization, and accumulated implementation bias, and yields one-pass covariance estimators and asymptotically valid Wald regions under local regul…
- Independent fresh solves add a positive semidefinite term to the score-sandwich covariance; averaging solver replicas reduces this term in inverse proportion to their number.

## 全文

We develop online statistical inference for Polyak-Ruppert averages of inexact Newton iterates on Riemannian manifolds. A local asymptotic representation separates observation noise, solver randomization, and accumulated implementation bias, and yields one-pass covariance estimators and asymptotically valid Wald regions under local regularity and centering conditions. Independent fresh solves add a positive semidefinite term to the score-sandwich covariance; averaging solver replicas reduces this term in inverse proportion to their number. Slowly varying predictable gains instead cancel from the first order law. Product torus simulations show how Newton scaling shortens an ill-conditioned transient and how retaining solver variation restores coverage. Intrinsic means and principal subspaces provide geometric applications, with a streaming data illustration.

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