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240. Batch normalization forward pass
medium
Generalsenior
Implement the forward pass of Batch Normalization for a mini-batch, a core building block in deep learning that stabilizes activations during training. You’ll compute per-feature mean/variance over the batch, normalize, then apply learnable scale and shift.
Requirements
Implement the function
python
Rules:
- Normalize each feature (column) using batch mean and batch variance, then apply (Y = \gamma \odot \hat{X} + \beta).
- Use the variance definition (\mathrm{var} = \frac{1}{m}\sum_{i=1}^{m}(x_i-\mu)^2) (no Bessel correction).
- Keep everything vectorized with NumPy (no per-element Python loops over
m*d). - Do not use any prebuilt batch norm utilities (e.g., from PyTorch/TensorFlow).
- Return a NumPy array.
Example
python
Output:
python
Input Signature
| Argument | Type |
|---|---|
| X | np.ndarray |
| eps | float |
| beta | np.ndarray |
| gamma | np.ndarray |
Output Signature
| Return Name | Type |
|---|---|
| value | np.ndarray |
Constraints
Use NumPy vectorization; no elementwise Python loops
Variance uses 1/m (no Bessel correction)
Return NumPy array
Hint 1
Use axis=0 to compute mean and variance per feature.
Hint 2
Variance must be no Bessel correction: var = np.mean((x - mu)**2, axis=0); then normalize with np.sqrt(var + eps).
Hint 3
Use broadcasting for the affine step: y = gamma * x_hat + beta.
Roles
ML Engineer
AI Engineer
Companies
GeneralLevels
senior
entry
Tags
batch-normalization
numpy-broadcasting
vectorization
numerical-stability
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