RNN Forward Pass

mediumPROSequence ProcessingNLP 2: Applications

Implement a simple RNN forward pass (Elman RNN) using NumPy.

At each time step t, the RNN computes: $h_t = \tanh(W_{xh} \cdot x_t + W_{hh} \cdot h_{t-1} + b_h)$

Where:

$x_t$ is the input at time step t
$h_{t-1}$ is the previous hidden state
$W_{xh}$ is the input-to-hidden weight matrix
$W_{hh}$ is the hidden-to-hidden weight matrix
$b_h$ is the hidden bias

Input format:

Line 1: input_size hidden_size seq_length (space-separated ints)
Next input_size lines: W_xh matrix (hidden_size columns per line)
Next hidden_size lines: W_hh matrix (hidden_size columns per line)
Next line: b_h (hidden_size values)
Next seq_length lines: one input vector per time step (input_size values)
Next line: h_0 initial hidden state (hidden_size values)

Output: The final hidden state as a list, rounded to 4 decimal places.

Example

Input

2 3 2
0.1 0.2 0.3
0.4 0.5 0.6
0.1 0.0 0.1
0.0 0.1 0.0
0.1 0.0 0.1
0.01 0.02 0.03
1.0 0.5
0.5 1.0
0.0 0.0 0.0

Output

[0.2729, 0.1567, 0.3878]

Reasoning

Time step 1: x=[1.0, 0.5] W_xh @ x = [0.11+0.40.5, 0.21+0.50.5, 0.31+0.60.5] = [0.3, 0.45, 0.6] W_hh @ h_0 = [0, 0, 0] (h_0 is zeros) h_1 = tanh([0.3+0+0.01, 0.45+0+0.02, 0.6+0+0.03]) = tanh([0.31, 0.47, 0.63]) h_1 = [0.3004, 0.4382, 0.5581]

Time step 2: x=[0.5, 1.0] Similarly compute W_xh @ x + W_hh @ h_1 + b_h, then tanh. Final h_2 = [0.2729, 0.1567, 0.3878]

Constraints

Use numpy for matrix operations
Use np.tanh for activation
Initial hidden state h_0 is provided
Round final hidden state to 4 decimal places

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Python 3.13

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RNN Forward Pass

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