# Back-propagation Through Time

What is the meaning of "partitions " in this paragraph “… the first few words of The Time Machine : randomized truncation partitions the text into segments of varying length …”?
What is the meaning of the arrow expression?
Thanks

Hi @ernie55ernie, “partition” means to “divide a sentence into parts” . You can think of each arrow as the position to divide the sentence.

Equation 8.7.3: Isn’t it supposed to be - g(h_t, w_o) instead of g(h_t, w_h)?

Truncate the sum after \tau steps…The approximation error is thus given by ∂_hf(x_t,h_{t−1},w)∂w_h_{t−1}∂_hf(x_t,h_{t−1},w)∂w_h_{t−1} (multiplied by a product of gradients involving ∂hf).

Isn’t the subscript t-1 supposed to be: t-\tau?

Assume h has dimension (n, 1), then ∂ht / ∂𝐖ℎℎ in (8.7.16) should be a 3 dimensional jacobian matrix with shape (n, n, n) right?

For first line of the equation 8.7.16, isn’t it supposed to be h_{j-1} instead of h_j ? Because when we differentiate h_t we will never actually have h_t as the equation is actually depending on h_{t-1}.

I think the second line is good though as h_t is depending on X_t