---
title: "Gradient-descent parameter update"
description: "Updates parameters by taking a learning-rate-sized step opposite the local loss gradient."
canonical_url: "https://fanout.sh/labs/math-decoder/formula/gradient-descent-parameter-update"
md_url: "https://fanout.sh/labs/math-decoder/formula/gradient-descent-parameter-update.md"
last_updated: "2026-08-09"
access: "public"
---

# Gradient-descent parameter update

Updates parameters by taking a learning-rate-sized step opposite the local loss gradient.

## Public overview

Theta at time t plus one equals theta at time t minus eta times the gradient with respect to theta of the loss at theta t.

Measure which way makes loss rise fastest, then move a controlled distance the other way.

The equals sign defines an iterative update, while subtraction reverses the gradient's uphill direction.

This is an update rule rather than the optimization objective itself; optimizers such as momentum and Adam modify the direction or scaling.

---
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