This repository contains scripts for reproducing the experiments in the paper Inductive Bias of Deep Convolutional Networks through Pooling Geometry.

Due to inherent randomness in the experiments, obtained results might differ slightly from those reported in the paper. Qualitatively however, full compliance with the paper is expected.

The repository includes as a submodule the Caffe fork of the SimNets Architecture. To clone the repository along with the submodule, call git clone with its --recursive flag:

git clone --recursive https://github.com/HUJI-Deep/inductive-pooling.git

After cloning, make sure to install the Python package versions listed in requirements.txt:

pip install -r requirements.txt

Finally, go to the SimNets submodule in deps/simnets and follow its installation instructions.

The experiments in the paper are based on a synthetic classification benchmark consisting of images displaying random shapes ('blobs'). Two labels are assigned to images, ranking properties of the displayed blob:

• closure: how morphologically closed the blob is
• symmetry: how left-right symmetric the blob is about its center

Convolutional networks with two pooling geometries are evaluated:

• square: standard contiguous square windows
• mirror: pooling windows join together nodes with their spatial reflections

It is shown that different pooling geometries lead to superior performance in different tasks. Specifically, square pooling outperforms mirror on the task of closure ranking, whereas the opposite occurs when ranking symmetry.

Scripts for running the experiments are under exp/blob. generate_blob.py can be called directly to generate the dataset, though this is not necessary (running a convolutional network will generate the dataset automatically in case it is missing).

The folder exp/blob/cac contains scripts for evaluating convolutional arithmetic circuits (convolutional networks with linear activation and product pooling):

• net.prototmp: template for prototxt specifying network architecture and training scheme
• train_plan.json: list of values for the unspecified parameters in net.prototmp
• train.py: substitutes the values in train_plan.json into net.prototmp and trains the network, measuring its train and test accuracies along the way

By default, calling train.py initiates 4 runs, corresponding to the different combinations of closure/symmetry task and square/mirror pooling. The gaps in performance (square pooling better than mirror for closure, opposite for symmetry) should be evident.

To evaluate convolutional rectifier networks (convolutional networks with ReLU activation and max or average pooling), go to exp/blob/crn. This folder contains the exact same files as exp/blob/cac, implementing the exact same functionalities. The only difference (from the user's perspective) is that calling train.py initiates 8 runs instead of 4, corresponding to the fact that every setting is run twice -- once with average pooling, and once with max pooling.

You are welcome to alter the architectural and optimization parameters of the networks. In particular, network breadth (number of channels in hidden layers) can be configured in train_plan.json, and network depth can be set by modifying net.prototmp.

Please do not move any of the scripts mentioned above, as they all rely on their original path relative to the root of the repository.