---
title: "Self-Normalized Inference from Riemannian Stochastic Gradient Paths"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.01035v1"
permalink: "https://feed.astralor.com/items/itm_1739773fd3ed5d703124f534"
published: "2026-10-31T15:23:17.000Z"
score: 52
channel: "tech"
tags: ["推理效率","RAG","Self-Normalized Inference","Riemannian Stochastic Gradient","Paths Riemannian","Hessian","Riemannian","Their"]
---

# Self-Normalized Inference from Riemannian Stochastic Gradient Paths

## At a glance

Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance. We develop self-normalized inference from one path by ex…

## Key points

- Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance.
- We develop self-normalized inference from one path by expressing retained iterates in a common random tangent space.
- Their average and centered partial sums share an unknown covariance factor that cancels in a Brownian bridge pivot.

## Full text

Riemannian stochastic gradient paths estimate constrained parameters, but confidence regions usually require estimating the Hessian and gradient-noise covariance. We develop self-normalized inference from one path by expressing retained iterates in a common random tangent space. Their average and centered partial sums share an unknown covariance factor that cancels in a Brownian bridge pivot. Under suitable regularity conditions, a joint expansion of the averaged estimator and integrated path controls nonlinear coordinate errors using conditional second moments. The procedure uses fixed-dimensional memory and extends to nondegenerate smooth functionals and alternative local coordinates. Numerical studies show competitive coverage relative to plug-in Wald inference while avoiding Hessian and residual-density estimation.

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