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139. Activation function tanh
GeneralImplement the tanh activation function for a layer output, which squashes real-valued inputs into the range ((-1, 1)). This is a common deep-learning basic used to add non-linearity to neural networks.
The activation is defined as:
Requirements
Implement the function
Rules:
- Compute for every element in the input array
x. - Return a NumPy array of the same shape as
x. - Do not use any prebuilt tanh activation helpers (e.g.,
np.tanh,torch.tanh,jax.numpy.tanh). - Use vectorized NumPy operations (e.g.
np.exp) for efficiency. - Keep the implementation numerically reasonable (e.g., avoid obvious overflow patterns when possible).
Example
Output:
| Argument | Type |
|---|---|
| x | np.ndarray |
| Return Name | Type |
|---|---|
| value | np.ndarray |
Constraints
Input/output must be NumPy array.
No built-in tanh helpers (np.tanh/torch.tanh).
Avoid overflow; use stable exp-based formula.
Hint 1
Implement tanh element-wise using vectorized NumPy operations.
Hint 2
Avoid torch.tanh/np.tanh; use np.exp and the identity tanh(x) = (e^x - e^{-x})/(e^x + e^{-x}) (or an equivalent form).
Hint 3
For numerical stability, avoid computing both exp(x) and exp(-x) for large |x|. Use a stable rewrite with np.where: e.g. for x>=0: (1-exp(-2x))/(1+exp(-2x)), and for x<0 mirror it with exp(2x).
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Python Editor