search
Search
Map of Data Science
Guest 0reps
exit_to_appLog out
Map of data science
Thanks for the thanks!
close
Outline
chevron_left Activation functions
Cancel
Post
account_circle
Profile
exit_to_app
Sign out
search
keyboard_voice
close
Searching Tips
Search for a recipe:
"Creating a table in MySQL"
Search for an API documentation: "@append"
Search for code: "!dataframe"
Apply a tag filter: "#python"
Useful Shortcuts
/ to open search panel
Esc to close search panel
to navigate between search results
d to clear all current filters
Enter to expand content preview Doc Search Code Search Beta SORRY NOTHING FOUND!
mic
Start speaking... Voice search is only supported in Safari and Chrome.
Shrink
Navigate to
A
A
brightness_medium
share
arrow_backShare Twitter Facebook
chevron_left Activation functions
check_circle
Mark as learned
thumb_up
0
thumb_down
0
chat_bubble_outline
0
auto_stories new
settings

# Comprehensive Guide on tanh

Machine Learning
chevron_right
Neural Networks
chevron_right
Activation functions
schedule Jul 1, 2022
Last updated
local_offer
Tags
expand_more
map
Check out the interactive map of data science

The $\mathrm{tanh}$ curve looks similar to the sigmoid curve in that the shape is s-like. $\mathrm{tanh}$ takes in any real value as input, and outputs a value from $-1$ to $1$.

The following is a graph of $\mathrm{tanh}$ and sigmoid function: Mathematically, we can represent $\mathrm{tanh}(x)$ like so:

$$\mathrm{tanh}(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$

# Derivative

What makes $\mathrm{tanh}$ appealing as an activation function is that the derivative of $\mathrm{tanh}$ is clean:

$$\frac{d}{dx}\mathrm{tanh}(x)=1-\mathrm{tanh}(x)^2$$

The graph of the derivative of $\mathrm{tanh}(x)$ looks like the following: # Code

The code used to generate the plot is as follows:

 import numpy as npimport matplotlib.pyplot as pltplt.style.use('seaborn-whitegrid')plt.style.use('seaborn')def sigmoid(x): return 1 / (1 + np.exp(-x))x_tanh = np.arange(-5, 5, 0.1)y_tanh = np.tanh(x)plt.figure(figsize=(5,4))plt.xlabel("x")plt.ylabel("y")plt.axhline(0, color="blue", alpha=0.2)plt.axvline(0, color="blue", alpha=0.2)x_sigmoid = np.arange(-5, 5, 0.1)y_sigmoid = sigmoid(x)plt.plot(x_sigmoid, y_sigmoid, color="red", label="Sigmoid")plt.plot(x_tanh, y_tanh, color="blue", label="tanh")plt.legend()