Matrix Compression Library

This document describes an experimental API that facilitates matrix compression of a neural network's weight tensors. The API helps inject the necessary tensorflow operations into the training graph so the model can be compressed while it is being trained.

Full documentation can be found here.

Table of contents

1. Library Overview
2. Model creation
3. Hyperparameters for compression
   • Smoothed compression
4. Adding compression ops to the training graph
5. Example

Library overview

1. MatrixCompressorInterface - used to implement any matrix compression algorithm in the method
2. CompressionOpInterface - used to create a tensorflow operator-like object that injects any matrix compression method dynamically into a tensorflow layer.
3. ApplyCompression - convenience wrapper class that can be used directly or extended for novel compression operator types; used to repeatedly invoke the compression operator to different layers in a model.
4. CompressionWrapper - wrapper module used to create the proper ApplyCompression implementation for the compression_option (method) of choice.

Model creation

The first step involves creating an ApplyCompression object, with the desired compression parameters. This object then is used to compress the model weights and use these compressed weights during the forward execution of the graph. Matrices are compressed to the rank specified in the compression parameters, provided at the start. To apply the compression, the weight tensor of the layer should be wrapped with the compression object's 'apply_compression' method, provided in compression_op.py.For an example, see the section below.

Hyperparameters for compression

The pruning library allows for specification of the following hyper parameters:

Compression Methods & Algorithms (compression_option param)

1. Low Rank Approximation
2. Simhash
3. Dictionary Learning
4. Kmeans Quantization

Decomposed Matrix Dimensions

The hyperparameter rank (r) is used to compute the new ranks as such: (rank of A) * (100 / r) + 1. For simhash compression, the value r provided should be the ratio value you would like divided by 8 (i.e. 300 / 8 -> same as using r = 300 in the equation above). This is because simhash compression represents values as bits (rather than bytes) therefore the true rank is the size of the array divided by 8.

Computing Compression Ratio

If the original weights were m-by-n and the compressed decomposition B*C is (m-by-k)*(k-by-n), then the compression ratio is (m*k + k*n) / (m*n).

Smoothed compression

A gradually increasing alpha value is used to smooth the compression from start_step to end_step. This way the model gradually moves from the full weights matrix to a compressed one. For example, in the low-rank approximation scheme, the weight matrix that is used in the training process is W = (alpha) * A + (1 - alpha) * BC. This alpha value is decremented over time from alpha = 1 to alpha = 0, using the alpha_decrement_value at intervals of compression_frequency.

Adding compression ops to the training graph

# Parse compression hyperparameters
compression_hparams = compression.CompressionOp.get_default_hparams().parse(
      hparams)

# Create a compression object using the compression hyperparameters
compression_obj = compression_wrapper.get_apply_compression(
    compression_hparams, global_step=global_step)

# somewhere in the model, compute the compressed weights
local = tf.nn.relu(
         tf.matmul(reshape, compression_obj.apply_compression(weights, scope)) +
         biases,
         name=scope.name)

all_update_op = [apply_gradient_op, ...] # all existing model updates
# Run compression update steps with all the other updates. Example below is
# assuming update_option=0.
all_update_op.append(compression_obj.all_update_op())

with tf.control_dependencies(all_update_op):
  train_op = tf.no_op(name='train')

Ensure that global_step is being incremented, otherwise compression will not work!

Example Usage

As an example, the cifar10 model provided in Tensorflow’s Advanced Convolutional Neural Networks (see page for more details) has been modified to incorporate the compression library:

• cifar10_compression.py creates the deep CNN and adds the weight compression to the fully-connected layers.
• cifar10_train.py creates the compression object and provides it to the training graph (described above) to use.

To train the compression version of cifar10 (make sure you're working in a properly configured virtualenv - as setup using the run.sh script):

$ python cifar10_train.py --compression_hparams=name=cifar10_compression,alpha_decrement_value=0.005,begin_compression_step=40000,end_compression_step=100000,compression_frequency=100,compression_option=1,use_tpu=True,update_option=0,rank=200 --max_steps 120000

Eval:

$ python cifar10_eval.py --compression_hparams=name=cifar10_compression,alpha_decrement_value=0.005,begin_compression_step=40000,end_compression_step=100000,compression_frequency=100,compression_option=1,use_tpu=True,update_option=0,rank=200 --run_once

Eager execution example.

An eager execution example is provided at compression_lib/examples/mnist_eager_mode/mnist_compression.py. To train the model, run:

$python mnist_compression.py

Authors: Rina Panigrahy (corresponding author -- email: rinap@google.com), Lucine Oganesian, Sudeshna Roy, Xin Wang, with support from: Badih Ghazi for helpful contributions, Rasmus Pagh (pagh@google.com, doc) for the simhash code, Zoya Svitkina for code reviews, and Suyog Gupta for consultations.