Backpropagation Algorithm
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Finally, we can also re-write the algorithm using matrix-vectorial notation. We will use "<math>\textstyle \bullet</math>" to denote the element-wise product operator (denoted "<tt>.*</tt>" in Matlab or Octave, and also called the Hadamard product), so that if <math>\textstyle a = b \bullet c</math>, then <math>\textstyle a_i = b_ic_i</math>. Similar to how we extended the definition of <math>\textstyle f(\cdot)</math> to apply element-wise to vectors, we also do the same for <math>\textstyle f'(\cdot)</math> (so that <math>\textstyle f'([z_1, z_2, z_3]) = | Finally, we can also re-write the algorithm using matrix-vectorial notation. We will use "<math>\textstyle \bullet</math>" to denote the element-wise product operator (denoted "<tt>.*</tt>" in Matlab or Octave, and also called the Hadamard product), so that if <math>\textstyle a = b \bullet c</math>, then <math>\textstyle a_i = b_ic_i</math>. Similar to how we extended the definition of <math>\textstyle f(\cdot)</math> to apply element-wise to vectors, we also do the same for <math>\textstyle f'(\cdot)</math> (so that <math>\textstyle f'([z_1, z_2, z_3]) = | ||
- | [ | + | [f'(z_1), |
- | + | f'(z_2), | |
- | + | f'(z_3)]</math>). | |
The algorithm can then be written: | The algorithm can then be written: |