Compare ReLU, sigmoid, tanh, softmax, and other activation functions. See graphs, derivatives, and output ranges side by side.
This tool evaluates several activation functions at once against a shared input value or range, plotting each curve alongside its derivative and labeling the output range (0 to 1 for sigmoid, -1 to 1 for tanh, 0 to infinity for ReLU) so you can compare saturation and slope directly. It computes both the function and its analytic derivative rather than estimating slope numerically. The most common surprise: softmax operates on a full vector of scores and normalizes them against each other, so typing in one scalar the way you would for sigmoid or tanh does not reproduce real softmax behavior.
A concrete input and expected output from the current implementation.
Input
x = 2
Expected output
ReLU(2) = 2, ReLU'(2) = 1 | Sigmoid(2) ≈ 0.8808, Sigmoid'(2) ≈ 0.1050 | Tanh(2) ≈ 0.9640, Tanh'(2) ≈ 0.0707
Sigmoid(2) = 1/(1+e^-2) and tanh(2) = (e^4-1)/(e^4+1) are standard closed-form values; each derivative uses the function's own output (sigmoid'=s(1-s), tanh'=1-tanh^2), which is why both derivatives are already small at x=2 - both curves are heading into their flat, saturated region.
You supply a single value or a range for x, and the tool plugs it into each activation function's closed-form definition (ReLU, sigmoid, tanh, and the others it lists) to produce one curve per function on the same plot. Because all curves share the same x-axis and scale, you can see directly where one function is still responsive while another has already flattened out.
Alongside each function the tool plots its exact derivative expression - not a numerical finite-difference estimate - evaluated at the same x values. This is what lets you read off gradient magnitude at a glance, which is the practical reason to compare activations: a near-zero derivative in a saturated region is the mechanism behind vanishing gradients during backpropagation.
That depends on whether the tool's input field accepts a list rather than a single number - check the softmax panel specifically. If it only takes one x value, the number shown is not a true softmax probability, since softmax requires the full set of competing scores to normalize against.
No. It shows the textbook derivative curve for each function in isolation, which explains the mechanism, but it has no access to your model's weights, layer depth, or activations, so it can't diagnose a specific training run - use it to build intuition, then check real gradient values with your framework's own tools.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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