# 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. | |

- | + | === Finetuning with Backpropagation === | |

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For your convenience, the summary of the backpropagation algorithm using element wise notation is below: | For your convenience, the summary of the backpropagation algorithm using element wise notation is below: | ||

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::<math>\begin{align} | ::<math>\begin{align} | ||

\delta^{(n_l)} | \delta^{(n_l)} | ||

- | = - ( | + | = - (\nabla_{a^{n_l}}J) \bullet f'(z^{(n_l)}) |

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

+ | ::(When using softmax regression, the softmax layer has <math>\nabla J = \theta^T(I-P)</math> where <math>I</math> is the input labels and <math>P</math> is the vector of conditional probabilities.) | ||

: 3. For <math>\textstyle l = n_l-1, n_l-2, n_l-3, \ldots, 2</math> | : 3. For <math>\textstyle l = n_l-1, n_l-2, n_l-3, \ldots, 2</math> | ||

::Set | ::Set | ||

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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 (in Step 2) are computed using <math>\delta^{(n_l)} = - (\nabla_{a^{n_l}}J) \bullet f'(z^{(n_l)})</math>, where <math>\nabla J = \theta^T(I-P)</math>. | ||

+ | }} | ||

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+ | {{CNN}} | ||

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+ | {{Languages|微调多层自编码算法|中文}} |