---
title: "Vector-Jacobian product mathematical notation"
description: "Vector-Jacobian product is a recurring research-paper notation family. Multiplies an output-side vector by a Jacobian to propagate sensitivity backward…"
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/vector-jacobian-product"
md_url: "https://fanout.sh/labs/math-decoder/symbol/vector-jacobian-product.md"
last_updated: "2026-08-09"
access: "public"
---

# Vector-Jacobian product mathematical notation

Vector-Jacobian product is a recurring research-paper notation family. Multiplies an output-side vector by a Jacobian to propagate sensitivity backward…

## Public overview

Vector-Jacobian product is a recurring research-paper notation family. Multiplies an output-side vector by a Jacobian to propagate sensitivity backward without constructing the full matrix.

Vector-Jacobian product: Multiplies an output-side vector by a Jacobian to propagate sensitivity backward without constructing the full matrix. Example: Pull output sensitivity backward to the input coordinates.

---
This representation contains public Fanout content only. Protected Pro lessons, account data, billing, checkout, and pricing are not included.

Browse the public content map: https://fanout.sh/sitemap.md