# Fine-tuning Stacked AEs

### From Ufldl

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=== General Strategy === | === General Strategy === | ||

- | + | Fortunately, we already have all the tools necessary to implement fine tuning for stacked autoencoders! In order to compute the gradients for all the layers of the stacked autoencoder in each iteration, we use the [[Backpropagation Algorithm]], as discussed in the sparse autoencoder section. As the backpropagation algorithm can be extended to apply for an arbitrary number of layers, we can actually use this algorithm on a stacked autoencoder of arbitrary depth. | |

Note: most stacked autoencoders don't go past five layers. | Note: most stacked autoencoders don't go past five layers. | ||

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&= \left[ \frac{1}{m} \sum_{i=1}^m J(W,b;x^{(i)},y^{(i)}) \right] | &= \left[ \frac{1}{m} \sum_{i=1}^m J(W,b;x^{(i)},y^{(i)}) \right] | ||

\end{align}</math> | \end{align}</math> | ||

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+ | {{Quote| | ||

+ | Note: While one could consider the softmax classifier as an additional layer, the derivation above does not. Specifically, we consider the "last layer" of the network to be the features that goes into the softmax classifier. Therefore, the derivatives are computed using <math>\delta^{(n_l)} = - (\nabla_{a^{n_l}}J) \bullet f'(z^{(n_l)})</math>. | ||

+ | }} |