Calculator Inputs
Model Recommendation
Formula Used
The calculator evaluates the selected activation function for every input. It also computes analytical and numerical derivatives. Stable formulas reduce exponential overflow and underflow.
| Function | Formula | Typical Range | Key Property |
|---|---|---|---|
| Sigmoid | 1 / (1 + e−x) | 0 to 1 | Probability output |
| Tanh | tanh(x) | −1 to 1 | Zero-centred |
| ReLU | max(0, x) | 0 to ∞ | Sparse activations |
| Leaky ReLU | x or αx | −∞ to ∞ | Negative gradient retained |
| GELU | 0.5x[1 + erf(x/√2)] | Approximately −0.17 to ∞ | Smooth gating |
| Softmax | exᵢ / Σexⱼ | 0 to 1 | Class probabilities |
How to Use
- Select an activation function and model use case.
- Enter one number, a vector, or a batch of values.
- Adjust function parameters and graph settings when needed.
- Choose comparison functions and derivative options.
- Submit the form, review warnings, then export results.
Example Data
| Example | Input | Suggested Function | Purpose |
|---|---|---|---|
| Centred values | −3, −2, −1, 0, 1, 2, 3 | ReLU or Tanh | Inspect negative and positive behaviour |
| Binary logit | 1.4 | Sigmoid | Convert one logit into probability |
| Class logits | 2.1, 0.3, −1.2 | Softmax | Generate multiclass probabilities |
| Large magnitudes | −100, 0, 100 | Sigmoid | Test numerical stability |
Activation Function Comparison
| Function | Zero-centred | Saturation | Sparse Output | Complexity | Common Use |
|---|---|---|---|---|---|
| Sigmoid | No | High | No | Medium | Binary output |
| Tanh | Yes | High | No | Medium | Recurrent states |
| ReLU | No | Negative region | Yes | Low | Hidden layers |
| Leaky ReLU | Near | Low | Limited | Low | Deep networks |
| GELU | No | Low | No | High | Transformers |
| Swish | No | Low | No | High | Deep models |
| Softmax | No | Possible | No | Medium | Multiclass output |
Frequently Asked Questions
What is an activation function?
It transforms a neuron's weighted input into an output. Nonlinear functions let neural networks learn complex relationships. Different functions suit different layers and tasks.
Why compare analytical and numerical derivatives?
The comparison helps verify derivative implementations. Large differences may reveal discontinuities or numerical issues. Small differences increase confidence in gradient calculations.
What causes vanishing gradients?
Very small derivatives reduce parameter updates during backpropagation. Saturated Sigmoid and Tanh regions often cause this. ReLU-family functions usually reduce that risk.
What is a dead ReLU?
A dead ReLU outputs zero for every observed input. Its derivative also stays zero there. Leaky ReLU can preserve a small gradient.
Why use stable Softmax?
Exponentials can overflow for large logits. Subtracting the maximum logit preserves identical probabilities. It also improves numerical reliability during training.
What does Softmax temperature change?
Lower temperatures create sharper probability distributions. Higher temperatures create softer, more uniform distributions. Temperature must remain greater than zero.
Which function suits hidden layers?
ReLU is a strong general default. GELU and Swish provide smoother alternatives. Leaky ReLU helps when dead neurons appear.
Which function suits regression outputs?
Linear activation supports unrestricted numeric predictions. Softplus restricts outputs to positive values. Tanh can enforce a bounded signed range.
Is the second derivative always meaningful?
Piecewise functions may be nondifferentiable at boundary points. Numerical estimates near boundaries can vary. Smooth functions provide more stable curvature information.
Can this calculator replace model testing?
No single activation works best everywhere. Use this calculator for analysis and education. Validate choices with training and evaluation experiments.