About Softplus Function Calculator
This softplus calculator plots ln(1 + e^x) and its derivative and evaluates them at any x. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Softplus is a smooth approximation of ReLU. For large positive x it is almost exactly x; for large negative x it approaches 0 from above but never reaches it; at x = 0 it equals ln 2, about 0.693. It is always positive and differentiable everywhere, with no corner.
Its derivative is the sigmoid, which gives a tidy link between the functions on this page: the slope of softplus is the probability-like curve of sigmoid. Softplus is useful where an output must be strictly positive, such as a variance or a rate.
How to use Softplus Function Calculator
- Choose a function from the menu, or "Compare all" to overlay the curves.
- For leaky ReLU, ELU and swish, set the extra parameter (alpha or beta) if you want something other than the default.
- Type an x to see f(x) and f'(x), and read the table of values.
- Zoom, pan and trace the plot to read the curve. Double-tap resets the view.
- For softmax, enter your scores separated by commas, set the temperature and read the probabilities and the steps.
- Read the strengths and weaknesses under the plot to compare the functions.
Features
- Nine activation functions with formulas and derivatives rendered in LaTeX.
- Interactive plot of the function and its derivative, with zoom, pan, trace and PNG download.
- A compare view of eight functions on one plot.
- Parameters for leaky ReLU (alpha), ELU (alpha) and swish (beta).
- GELU computed exactly with the error function, not the tanh approximation.
- Softmax with temperature and a worked, numerically stable calculation.
- A value table, range, and plain-language strengths and weaknesses for each function.
Softplus
The derivative of softplus is the logistic sigmoid.
softplus(x) = ln(1 + e^x)
softplus'(x) = 1 / (1 + e^-x)Worked examples
x = -3, -1, 0, 1, 3 gives -3: 0.0486, -1: 0.3133, 0: 0.6931, 1: 1.3133, 3: 3.0486
Softplus(0) is 0.6931 = ln 2.
Privacy: how it works
- All calculations and plots run in your browser tab. Nothing is sent to Ulkaa or anyone else.
Tips
- Compare the derivative curves: where one is flat near zero, learning is slow in that region of input.
- Try a leaky ReLU with a large alpha such as 0.3 to see how the negative side tilts, and a swish beta of 5 to see it approach ReLU.
- For softmax, add 100 to every score: the probabilities do not change, because only the differences matter.
- Scores with one very large value give a probability close to 1 for that class, whatever the others are.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your inputs are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your inputs are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is softplus?
The function ln(1 + e^x), a smooth, always positive version of ReLU.
What is the derivative of softplus?
The sigmoid function, 1 / (1 + e^-x).
More Activation Function Plotter pages
- Activation Function PlotterPlot any activation function and its derivative, evaluate it at a point, or turn scores into softmax probabilities.
- Sigmoid Function CalculatorEvaluate the logistic sigmoid and its derivative at any x, and plot both.
- Tanh Function CalculatorEvaluate tanh and its derivative at any x, and plot both.
- ReLU Activation FunctionPlot max(0, x) and its derivative and evaluate them at any input.
- Leaky ReLU CalculatorSet the negative slope alpha and see how leaky ReLU differs from ReLU.
- ELU Activation FunctionPlot the exponential linear unit and its derivative for any alpha.
- GELU Activation FunctionPlot the Gaussian error linear unit and its derivative, and evaluate it at any x.
- Swish (SiLU) Activation FunctionPlot x times sigmoid(beta x) and its derivative, and change beta.
- Softmax CalculatorTurn a list of scores into probabilities, with the working shown.