LSTM gates forward - ML & AI Coding

270. LSTM gates forward

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General

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Implement the forward pass of the gates in a single LSTM cell, which controls how information is forgotten, added, and exposed at each timestep in a sequence model. Given an input vector and the previous hidden/cell states, you’ll compute the new hidden and cell states for one step.

\begin{aligned} f_t &= \sigma(W_f x_t + U_f h_{t-1} + b_f) \\ i_t &= \sigma(W_i x_t + U_i h_{t-1} + b_i) \\ \tilde{c}_t &= \tanh(W_c x_t + U_c h_{t-1} + b_c) \\ c_t &= f_t \odot c_{t-1} + i_t \odot \tilde{c}_t \\ o_t &= \sigma(W_o x_t + U_o h_{t-1} + b_o) \\ h_t &= o_t \odot \tanh(c_t) \end{aligned}

Requirements

Implement the function:

python

Rules:

Compute the 4 gates f_t, i_t, o_t and candidate state c_tilde using the formulas above.
Use sigmoid for gates and tanh for candidate/hidden activation.
Use elementwise multiplication for \odot.
Use only NumPy and Python built-in libraries (no deep learning frameworks).
Return h_t and c_t as NumPy arrays.

Example

python

Output:

python

Input Signature

Argument	Type
x_t	np.ndarray
c_prev	np.ndarray
h_prev	np.ndarray
params	dict

Output Signature

Return Name	Type
value	tuple

Constraints

Use NumPy only; no deep learning frameworks.
Ensure shapes: W(hid,in), U(hid,hid), b(hid).
Return NumPy arrays.

Hint 1

Ensure inputs are NumPy arrays for @ matrix multiplication.

Hint 2

Implement sigmoid(z)=1/(1+exp(-z)); use np.tanh for candidate/hidden.

Hint 3

Compute gates: f,i,o = sigmoid(W@x + U@h + b); then c=f*c_prev+i*c_tilde, h=o*tanh(c); return NumPy arrays.

Roles

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AI Engineer

Companies

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Levels

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senior

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Input Arguments

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