## Introduction * [Link to Paper](http://arxiv.org/pdf/1412.6071v4.pdf) * Spatial pooling layers are building blocks for Convolutional Neural Networks (CNNs). * Input to pooling operation is a $N_{in}$ x $N_{in}$ matrix and output is a smaller matrix $N_{out}$ x $N_{out}$. * Pooling operation divides $N_{in}$ x $N_{in}$ square into $N^2_{out}$ pooling regions $P_{i, j}$. * $P_{i, j}$ ⊂ $\{1, 2, . . . , N_{in}\}$ $\forall$ $(i, j) \in \{1, . . . , N_{out} \}^2$ ## MP2 * Refers to 2x2 maxpooling layer. * Popular choice for maxpooling operation. ### Advantages of MP2 * Fast. * Quickly reduces the size of the hidden layer. * Encodes a degree of invariance with respect to translations and elastic distortions. ### Issues with MP2 * Disjoint nature of pooling regions. * Since size decreases rapidly, stacks of backtoback CNNs are needed to build deep networks. ## FMP * Reduces the spatial size of the image by a factor of *α*, where *α ∈ (1, 2)*. * Introduces randomness in terms of choice of pooling region. * Pooling regions can be chosen in a *random* or *pseudorandom* manner. * Pooling regions can be *disjoint* or *overlapping*. ## Generating Pooling Regions * Let $a_i$ and $b_i$ be 2 increasing sequences of integers, starting at 1 and ending at $N_{in}$. * Increments are either 1 or 2. * For *disjoint regions, $P = [a_{i−1}, a_{i − 1}] × [b_{j−1}, b_{j − 1}]$ * For *overlapping regions, $P = [a_{i−1}, a_i] × [b_{j−1}, b_j 1]$ * Pooling regions can be generated *randomly* by choosing the increment randomly at each step. * To generate pooling regions in a *peusdorandom* manner, choose $a_i$ = ceil($\alpha  (i+u))$, where $\alpha \in (1, 2)$ with some $u \in (0, 1)$. * Each FMP layer uses a different pair of sequence. * An FMP network can be thought of as an ensemble of similar networks, with each different poolingregion configuration defining a different member of the ensemble. ## Observations * *Random* FMP is good on its own but may underfit when combined with dropout or training data augmentation. * *Pseudorandom* approach generates more stable pooling regions. * *Overlapping* FMP performs better than *disjoint* FMP. ## Weakness * No justification is provided for the observations mentioned above. * It needs to be seen how performance is affected if the pooling layer in architectures like GoogLeNet.
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