Package: deep-ei
deep-eiThis code accompanies the paper"Examining the Causal Structures of Artificial Neural Networks Using Information Theory"by Simon Mattsson,Eric J. Michaud, andErik HoelWhat's here?This repository contains all the code used in the paper (notebooks for creating figures, experiment scripts, etc) in theexperimentsdirectory, but most importantly holds the open-sourcedeep-eimodule. We encourage people to installdeep-eiand perform their own experiments on new datasets, neural network architectures, etc. There are so many experiments we'd like to do, but haven't had time to yet! If you'd like to contribute to code, just submit a pull request! (note that all the code is currently structured as a single module, but may eventually be restructured as a package if that makes sense).Installation:The simplest way to install thedeep_eimodule is with:pip install deep-eiBecauespytorchcan be fragile, it is recommended that you install and testpytorchbefore installingdeep-ei(such as withconda install pytorch -c pytorch). To installdeep-eidirectly from this repository:git clone https://github.com/EI-research-group/deep-ei.git
cd deep-ei
pip install .Basic tests can be executed with:python setup.py testNote that we have also provided an anaconda environment file. You can use it to create a new environment withdeep-eiand all its dependencies:conda env create --file environment.ymlExperimentsCode from the paper has been grouped into two directories:experiments/
├── notebooks
└── runsWherenotebookscontains notebooks for making the figures andrunscontains the code and resulting data from the experiments.Note that all these files use a version of deep-ei before 0.7.0. So to run any of them yourself, install version 0.6.4 from commit 7d37642649594d14bc02590dc4edb5a1f858f501. Note also that you will have to change the path to the experiment data in many of these notebooks.Usingdeep-eiDetailed documentation can be found atreadthedocs.io, but here are some basic examples:importtorchimporttorch.nnasnnfromdeep_eiimporttopology_of,ei,ei_parts,sensitivitydevice=torch.device('cuda'iftorch.cuda.is_available()else'cpu')dtype=torch.float32torch.set_default_dtype(dtype)network=nn.Linear(5,5,bias=False).to(device)top=topology_of(network,input=torch.zeros((1,5)).to(device))EI=ei(network,top,samples=int(1e5),batch_size=100,in_range=(0,1),in_bins=8,out_range=(0,1),out_bins=8,activation=nn.Sigmoid(),device=device)This will compute the EI of the5 -> 5dense layernetworkusing a sigmoid activation and 100000 samples.The functiontopology_ofcreates anetworkxgraph representing the connectivity of the network.eican infer argument values using this graph, such as the ranges of the inputs and outputs of the layer and its activation function:network=nn.Sequential(nn.Linear(20,10,bias=False),nn.Sigmoid(),nn.Linear(10,5,bias=False),nn.Tanh())top=topology_of(network,input=torch.zeros((1,20)).to(device))layer1,_,layer2,_=networkEI_layer1=ei(layer1,top,samples=int(1e5),batch_size=100,in_range=(0,1),in_bins=8,out_bins=8,device=device)EI_layer2=ei(layer2,top,samples=int(1e5),batch_size=100,in_bins=8,out_bins=8,device=device)Which will use an activation ofnn.Sigmoidand anout_rangeof(0, 1)for the first layer and an activation ofnn.Tanhand anout_rangeof(-1, 1)for the second layer. Note that we have to specify anin_rangefor the first layer.EI_parts can be computed similarly:device=torch.device('cuda'iftorch.cuda.is_available()else'cpu')dtype=torch.float32torch.set_default_dtype(dtype)network=nn.Linear(5,5,bias=False).to(device)top=topology_of(network,input=torch.zeros((1,5)).to(device))EI_parts=ei_parts(network,top,samples=int(1e5),batch_size=100,in_range=(0,1),in_bins=8,out_range=(0,1),out_bins=8,activation=nn.Sigmoid(),device=device)Withei_parts, you can specify athresholdinstead of setting a manual number ofsamples(indeed this is the default behavior ofei_parts, with default threshold of 0.05). The function will increase the number of samples it uses until EI_parts levels off (characterized by whether EI_parts will change by less thanthresholdof its current value even if we doubled the number of samples):network=nn.Linear(10,10,bias=False).to(device)top=topology_of(network,input=torch.zeros((1,10)).to(device))EI=ei_parts(network,top,threshold=0.05,batch_size=100,in_range=(0,1),in_bins=64,out_range=(0,1),out_bins=64,activation=nn.Sigmoid(),device=device)You can also measure the sensitivity of a layer like so:network=nn.Linear(10,10,bias=False).to(device)top=topology_of(network,input=torch.zeros((1,10)).to(device))sensitivity=sensitivity(network,top,samples=1000,batch_size=100,in_range=(0,1),in_bins=64,out_range=(0,1),out_bins=64,activation=nn.Sigmoid(),device=device)If you want to compute the EI of each edge in a layer (giving you each term that is summed to get EI_parts), use theei_parts_matrixfunction:network=nn.Linear(20,10,bias=False).to(device)top=topology_of(network,input=torch.zeros((1,20)).to(device))EI=ei_parts_matrix(network,top,samles=50000,batch_size=100,in_range=(0,1),in_bins=64,out_range=(0,1),out_bins=64,activation=nn.Sigmoid(),device=device)Which will return a20 x 10matrix where the rows correspond with in-neurons and the columns correspond with out-neurons.Ideas for future experimentsWe'd love for people to use and expand on this code to make new discoveries. Here are some questions we haven't looked into yet:How does dropout effect the EI of a layer? In otherwise identical networks, does dropout increase or decrease the EI of the network layers?What can EI tell us about generalization? Does EI evolve in the causal plane in different ways when a network is memorizing a dataset vs generalizing? To test this, train networks on some dataset as you would normally, but then randomize the labels in the training dataset and train new networks. This label randomization will force the network to memorize the dataset.On harder tasks, where deep networks are required (in MNIST and Iris, which we studied, it is unnecessary that networks be deep for them to achieve good acuracy), do the hidden layers differentiate in the causal plane?Can EI be measured in recurrent networks? How would this work?Contributing & Questions:We'd welcome feedback and contributions! Feel free to email me ateric.michaud99@gmail.comif you have questions about the code.