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vocabulary_size = len(tokenizer.word_index) + 1
). This addition accounts for the fact that word indices typically start at 1 (with 0 reserved for padding), ensuring that every word has a unique index. This size defines the dimensions of both the embedding layer (input_dim) and the output layer of the network.
L = -Σ (y_true * log(y_pred))
, to measure the divergence between the predicted probability distribution (from the softmax layer) and the true distribution.
L = -Σ y_truei * log(y_predi)
for each word in the vocabulary. This formulation penalizes predictions that diverge from the one-hot true label, effectively training the model to assign a higher probability to the correct next word.
zₜ = σ(Wzxₜ + Uzhₜ₋₁)
(update gate) and rₜ = σ(Wrxₜ + Urhₜ₋₁)
(reset gate). Then, the candidate activation is computed as h̃ₜ = tanh(Wxₜ + U(rₜ ⊙ hₜ₋₁))
, and the new hidden state is hₜ = (1 - zₜ) ⊙ hₜ₋₁ + zₜ ⊙ h̃ₜ
.
iₜ = σ(Wixₜ + Uihₜ₋₁)
, fₜ = σ(Wfxₜ + Ufhₜ₋₁)
, and oₜ = σ(Woxₜ + Uohₜ₋₁)
control the input, forgetting, and output of information respectively, while the cell state is updated as cₜ = fₜ ⊙ cₜ₋₁ + iₜ ⊙ tanh(Wc xₜ + Uc hₜ₋₁)
. These mathematical formulations allow LSTM to better capture long-range dependencies.
L = -∑ (ytrue * log(ypred))
w ← w - η * ∂L/∂w