Neural Network Forward Pass in NumPy

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Problem

Implement a simple neural network forward pass in NumPy.

Use fully connected layers, apply ReLU after every hidden layer, and apply numerically stable softmax to the final logits. The function receives X as a batch matrix, weights as matrices shaped (input_dim, output_dim), and biases as vectors. Return the output probabilities as a nested Python list with one row per input example.

Example: X = [[0, 0]], one zero-weight layer produces [[0.5, 0.5]]. A network with negative hidden activations must apply ReLU before the next layer.

Constraints

1 <= number of input examples <= 1000
1 <= number of layers <= 10
Each weight matrix has shape (previous_layer_width, current_layer_width)
Each bias vector has length equal to its layer's output width
The input and every layer contain at least one feature
All values are finite real numbers

Function Signature

def neural_network_forward(X, weights, biases):

Your solutionPython 3

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