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Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data

This is an implementation of the PAC-Bayes generalization bound optimization for stochastic neural networks, as described in the article "Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data" by Dziugaite and Roy, published in Uncertainty in AI (2017).

Requirements

Python 3.5: absl-py==0.11.0, astor==0.8.1, certifi==2020.6.20, gast==0.4.0, grpcio==1.33.2, h5py==2.10.0, importlib-metadata==2.0.0, Keras==2.2.2, Keras-Applications==1.0.4, Keras-Preprocessing==1.0.2, Markdown==3.2.2, numpy==1.14.5, protobuf==3.14.0, PyYAML==5.3.1, scipy==1.4.1, six==1.15.0, tensorboard==1.10.0, tensorflow==1.10.0, termcolor==1.1.0, Werkzeug==1.0.1, wincertstore==0.2, zipp==1.2.0

Instructions

Running the code involves 2 steps:

  1. SGD optimization, which saves initial and final network weights to snn/experiments
  2. PAC-Bayes optimization, which first loads the weights saved in the previous step, and then optimizes the PAC-Bayes bound over the weights and variances.

SGD Optimization

To run SGD on a fully connected neural network consisting of a hidden layer with 600 neurons for 20 epochs on binary MNIST, execute the following command:

python3.5 snn/experiments/run_sgd.py fc --layers 600 --sgd_epochs 20 --binary

The code will throw a FileExistsError if a checkpoint already exists. To overwrite an existing checkpoint, use the following command:

python3.5 snn/experiments/run_sgd.py fc --layers 600 --sgd_epochs 20 --overwrite --binary

PAC-Bayes Optimization

The following command can be used to run the PAC-Bayes optimization for 1000 epochs on the saved checkpoint:

python3.5 snn/experiments/run_pacb.py fc --layers 600 --sgd_epochs 20 --pacb_epochs 1000 --lr 0.001 --drop_lr 250 --lr_factor 0.1 --binary

The learning rate starts at 0.001 and is dropped to 0.0001 after 250 epochs.

Acknowledgments

The development of this code was initiated by Gintare Karolina Dziugaite and Daniel M. Roy, while they were visiting the Simons Institute for the Theory of Computing at U.C. Berkeley. During this course of this research project, GKD was supported by an EPSRC studentship; DMR was supported by an NSERC Discovery Grant, Connaught Award, and U.S. Air Force Office of Scientific Research grant #FA9550-15-1-0074.

Waseem Gharbieh (Element AI) and Gabriel Arpino (University of Toronto) contributed to improving and testing the code, and helped produce this code release.

BiBTeX

@inproceedings{DR17,
        title = {Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data},
       author = {Gintare Karolina Dziugaite and Daniel M. Roy},
         year = {2017},
    booktitle = {Proceedings of the 33rd Annual Conference on Uncertainty in Artificial Intelligence (UAI)},
archivePrefix = {arXiv},
       eprint = {1703.11008},
}

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Optimizing PAC-Bayes bounds for Stochastic Neural Networks with Gaussian weights

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