Difference between revisions of "Thread:Talk:Rolling Averages/Rolling Average vs Softmax & Cross Entropy"
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: q<sub>i</sub> - 1, if bin is hit | : q<sub>i</sub> - 1, if bin is hit | ||
: q<sub>i</sub>, otherwise | : q<sub>i</sub>, otherwise | ||
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+ | Where q<sub>i</sub> is the output of the i<sup>th</sup> unit after Softmax (estimated probability) | ||
If gradient is not applied on logits as normal, but instead applied on q<sub>i</sub> itself, then: | If gradient is not applied on logits as normal, but instead applied on q<sub>i</sub> itself, then: |
Revision as of 06:03, 27 July 2021
If each Guess Factor bin is considered an output unit before Softmax (logit), and loss is Cross Entropy, then the gradient of each logit is then:
- qi - 1, if bin is hit
- qi, otherwise
Where qi is the output of the ith unit after Softmax (estimated probability)
If gradient is not applied on logits as normal, but instead applied on qi itself, then:
- qi := qi - eta * (qi - 1) = (1 - eta) * qi + eta * 1, if bin i hit
- qi := qi - eta * qi = (1 - eta) * qi + eta * 0, otherwise
Which is essentially rolling average, where eta (learning rate) equals to the alpha (decay rate) in exponential moving average.
Anyway this analog isn't how rolling average works, as logit doesn't equal to qi at all. But what if we replace rolling average with gradient descent? I suppose it could learn even faster, as the outputs farther from real value get higher decay rate...