About Leaky ReLU Calculator
This leaky ReLU calculator plots the function and its derivative for a negative slope alpha that you can change, and evaluates both at any x. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Leaky ReLU returns x for positive inputs and alpha times x for negative inputs, with alpha usually 0.01. The small slope means a unit with a negative input still receives a little gradient, so it can recover instead of dying as a plain ReLU unit can. The derivative is 1 on the right and alpha on the left.
Set alpha to 0.3 to see an obvious tilt on the left, to 0 to recover ReLU, and to 1 to get a straight line. Parametric ReLU (PReLU) is the same function with alpha learned during training.
How to use Leaky ReLU 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.
Leaky ReLU
Alpha is the slope for negative inputs.
f(x) = x if x > 0
f(x) = alpha x if x <= 0
f'(x) = 1 or alphaWorked examples
alpha = 0.01 at x = -4, -2, 0, 2 gives -4: -0.04, -2: -0.02, 0: 0, 2: 2
With alpha = 0.1, f(-4) is -0.4.
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 alpha should I use for leaky ReLU?
0.01 is the common default, and values up to about 0.3 are used. PReLU learns alpha instead.
How is leaky ReLU different from ReLU?
It keeps a small non-zero slope for negative inputs, so the gradient is never exactly zero.
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.
- 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.
- Softplus Function CalculatorPlot softplus and its derivative, which is exactly the sigmoid.
- Softmax CalculatorTurn a list of scores into probabilities, with the working shown.