[SYSTEMDS-547] Implement built-in functions for max and average pooling

• Type: New Feature
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Fix Version/s: SystemML 0.10
• Component/s: Parser, Runtime
• Epic Link: Deep Learning
• Assignee: Niketan Pansare
• Reporter: Niketan Pansare
• Created: 29/Feb/16 19:28
• Updated: 27/May/16 19:45
• Resolved: 27/May/16 19:34

Description

pool2d(input, pool_size, stride_length, border_mode="valid", pool_mode="max")

Performs downscaling of the input matrix.

The arguments to this function are:
1. input is a 2-dimensional matrix.
2. pool_size is a required integer parameter.
3. stride_length is an optional Int parameter. The default value is 1.
4. border_mode is an optional String parameter. The valid values are "same" and "valid".
5. pool_mode is an optional String parameter. The valid values are "max" and "avg". We can later add additional operators here (such as sum).

For detailed documentation, see Theano's pool_2d function: https://github.com/Theano/Theano/blob/master/theano/tensor/signal/pool.py#L40

An an example, our pool2d(input=X, pool_size=2, stride_length=1, border_mode="valid", pool_mode="avg") invocation is similar to Theano's
pool_2d(X, ds=(2,2), st=(1,1), ignore_border=True, padding=(0, 0), mode="average_exc_pad")

Since padding=(0,0) is the most common padding (probably the only one most people will use), I thought of simplifying the interface by borrowing concepts from TensorFlow's functions max_pool and avg_pool. See https://www.tensorflow.org/versions/r0.7/api_docs/python/nn.html#avg_pool

The above example will translate into following TensorFlow code:
tf.nn.avg_pool(X, pool_size=(1,2,2,1), strides=(1,1,1,1), padding="VALID")

Another good reference to understanding pooling operation is http://cs231n.github.io/convolutional-networks/#pool

[e-mail], nakul02, prithvi_r_s, [e-mail]