---
title: "Hyperbolic tangent mathematical notation"
description: "Hyperbolic tangent is a recurring research-paper notation family. Maps real inputs smoothly into the interval from negative one to one with an odd,…"
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/hyperbolic-tangent"
md_url: "https://fanout.sh/labs/math-decoder/symbol/hyperbolic-tangent.md"
last_updated: "2026-08-09"
access: "public"
---

# Hyperbolic tangent mathematical notation

Hyperbolic tangent is a recurring research-paper notation family. Maps real inputs smoothly into the interval from negative one to one with an odd,…

## Public overview

Hyperbolic tangent is a recurring research-paper notation family. Maps real inputs smoothly into the interval from negative one to one with an odd, zero-centered S-shaped curve.

Hyperbolic tangent: Maps real inputs smoothly into the interval from negative one to one with an odd, zero-centered S-shaped curve. Example: A zero pre-activation remains zero after tanh.

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