1b progress
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@ -38,4 +38,28 @@ Solved as:
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&= - sum_t (r^t - y^t) v_h x_h (1-tanh^2(ww_2 dot xx)) \
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$
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Updates:
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- $Delta v_h = eta sum_t (r^t-y^t) z^t_h$
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- $Delta w_(1,j) = eta sum_t (r^t - y^t) v_h x_h cases(0 "if" ww_1 dot xx <0, 1 "otherwise")$
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- $Delta w_(2,j) = eta sum_t (r^t - y^t) v_h x_h (1-tanh^2(ww_2 dot xx))$
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= Problem 1b
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- $E(ww,vv|XX) = - sum_t r^t log y^t + (1 - r^t) log (1 - y^t)$
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- $y^t = "sigmoid"(v_2 z_2 + v_1 z_1 + v_0)$
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- $z^t_1 = "ReLU"(w_2 x^t_2 + w_1 x^t_1 + w_0)$
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- $z^t_2 = tanh(w_2 x^t_2 + w_1 x^t_1 + w_0)$
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Updates:
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-
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Same as above:
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$Delta v_h = eta sum_t (r^t-y^t) z^t_h$
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- $
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frac(diff E, diff w_j) &= - sum_t (frac(diff E, diff y^t) frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j)) + (frac(diff E, diff y^t) frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
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&= - sum_t frac(diff E, diff y^t) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
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&= - sum_t (frac(r^t, y^t) - frac(1-r^t, 1-y^t)) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
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&= - sum_t (frac(r^t-y^t, y^t (1-y^t))) (frac(diff y^t, diff z^t_1) frac(diff z^t_1, diff w_j) + frac(diff y^t, diff z^t_2) frac(diff z^t_2, diff w_j)) \
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$
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