MorphNet: Fast & Simple Resource-Constrained Learning of Deep Network Structure

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What is MorphNet?

MorphNet is a method for learning deep network structure during training. The
key principle is continuous relaxation of the network-structure learning
problem. Specifically, activation sparsity is induced by adding regularizers
that target the consumption of specific resources such as FLOPs or model size.
When the regularizer loss is added to the training loss and their sum is
minimized via stochastic gradient descent or a similar optimizer, the learning
problem becomes a constrained optimization of the structure of the network,
under the constraint represented by the regularizer. The method was first
introduced in our CVPR 2018, paper "MorphNet: Fast & Simple Resource-Constrained Learning of
Deep Network Structure". A overview of the
approach as well as new device-specific latency regularizers were prestend in
GTC 2019

[slides, recording: YouTube, GTC on-demand].

In short, the MorphNet regularizer pushes weights down, and once they are small
enough, the corresponding output channels are marked for removal from the
network.

Usage

Suppose you have a working convolutional neural network for image classification
but want to shrink the model to satisfy some constraints (e.g., memory,
latency). Given an existing model (the “seed network”) and a target criterion,
MorphNet will propose a new model by adjusting the number of output channels in
each convolution layer.

Note that MorphNet does not change the topology of the network -- the proposed
model will have the same number of layers and connectivity pattern as the seed
network.

To use MorphNet, you must:

1. Choose a regularizer from morphnet.network_regularizers. The choice is
   based on

   • your target cost (e.g., FLOPs, latency)
   • your network architecture: use Gamma regularizer if the seed network
     has BatchNorm; use GroupLasso otherwise.

   Note: If you use BatchNorm, you must enable the scale parameters (“gamma
   variables”), i.e., by setting scale=True if you are using
   tf.keras.layers.BatchNormalization.

2. Initialize the regularizer with a threshold and the output boundary ops and
   (optionally) the input boundary ops of your model.

   MorphNet regularizer crawls your graph starting from the output boundary,
   and applies regularization to some of the ops it encounters. When it
   encounters any of the input boundary ops, it does not crawl past them (the
   ops in the input boundary are not regularized). The threshold determines
   which output channels can be eliminated.

3. Add the regularization term to your loss.

   As always, regularization loss must be scaled. We recommend to search for
   the scaling hyperparameter (regularization strength) along a logarithmic
   scale spanning a few orders of magnitude around 1/(initial cost). For
   example, if the seed network starts with 1e9 FLOPs, explore regularization
   strength around 1e-9.

   Note: MorphNet does not currently add the regularization loss to the
   tf.GraphKeys.REGULARIZATION_LOSSES collection; this choice is subject to
   revision.

   Note: Do not confuse get_regularization_term() (the loss you should add to
   your training) with get_cost() (the estimated cost of the network if the
   proposed structure is applied).

4. Train the model.

   Note: We recommend using a fixed learning rate (no decay) for this step,
   though this is not strictly necessary.

5. Save the proposed model structure with the StructureExporter.

   The exported files are in JSON format. Note that as the training progresses,
   the proposed model structure will change. There are no specific guidelines
   on the stopping time, although you would likely want to wait for the
   regularization loss (reported via summaries) to stabilize.

6. (Optional) Create summary ops to monitor the training progress through
   TensorBoard.

7. Modify your model using the StructureExporter output.

8. Retrain the model from scratch without the MorphNet regularizer.

   Note: Use the standard values for all hyperparameters (such as the learning
   rate schedule).

9. (Optional) Uniformly expand the network to adjust the accuracy vs. cost
   trade-off as desired. Alternatively, this step can be performed before
   the structure learning step.

We refer to the first round of training as structure learning and the second
round as retraining.

To summarize, the key hyperparameters for MorphNet are:

• Regularization strength
• Alive threshold

Note that the regularizer type is not a hyperparameter because it's uniquely
determined by the metric of interest (FLOPs, latency) and the presence of
BatchNorm.

Regularizer Types

Regularizer classes can be found under network_regularizers/ directory. They
are named by the algorithm they use and the target cost they attempt to
minimize. For example, GammaFlopsRegularizer uses the batch norm gamma in
order to regularize the FLOP cost.

Regularizer Algorithms

• GroupLasso is designed for models without batch norm.
• Gamma is designed for
  models with batch norm; it requires that batch norm scale is enabled.

Regularizer Target Costs

• Flops targets the FLOP count of the inference network.
• Model Size targets the number of weights of the network.
• Latency optimizes for the estimated inference latency of the network, based
  on the specific hardware characteristics.

Examples

Adding a FLOPs Regularizer

The example below demonstrates how to use MorphNet to reduce the number of FLOPs
in your model. In this example, the regularizer will traverse the graph
starting with logits, and will not go past any op whose name matches the regex
/images.*; this allows to specify the subgraph for MorphNet to optimize.

from morph_net.network_regularizers import flop_regularizer
from morph_net.tools import structure_exporter

inputs, labels = preprocessor()
logits = build_model(inputs, labels, ...)

network_regularizer = flop_regularizer.GammaFlopsRegularizer(
    output_boundary=[logits.op],
    input_boundary=[inputs.op, labels.op],
    gamma_threshold=1e-3
)
regularization_strength = 1e-10
regularizer_loss = (network_regularizer.get_regularization_term() * regularization_strength)

model_loss = tf.nn.sparse_softmax_cross_entropy_with_logits(labels, logits)

optimizer = tf.train.MomentumOptimizer(learning_rate=0.01, momentum=0.9)

train_op = optimizer.minimize(model_loss + regularizer_loss)

You should monitor the progress of structure learning training via Tensorboard.
In particular, you should consider adding a summary that computes the current
MorphNet regularization loss and the cost if the currently proposed structure is
adopted.

tf.summary.scalar('RegularizationLoss', regularizer_loss)
tf.summary.scalar(network_regularizer.cost_name, network_regularizer.get_cost())

Larger values of regularization_strength will converge to smaller effective
FLOP count. If regularization_strength is large enough, the FLOP count will
collapse to zero. Conversely, if it is small enough, the FLOP count will remain
at its initial value and the network structure will not vary. The
regularization_strength parameter is your knob to control where you want to be
on the price-performance curve. The gamma_threshold parameter is used for
determining when an activation is alive.

Extracting the Architecture Learned by MorphNet

During training, you should save a JSON file that contains the learned structure
of the network, that is the count of activations in a given layer kept alive (as
opposed to removed) by MorphNet.

exporter = structure_exporter.StructureExporter(
    network_regularizer.op_regularizer_manager)

with tf.Session() as sess:
  tf.global_variables_initializer().run()
  for step in range(max_steps):
    _, structure_exporter_tensors = sess.run([train_op, exporter.tensors])
    if (step % 1000 == 0):
      exporter.populate_tensor_values(structure_exporter_tensors)
      exporter.create_file_and_save_alive_counts(train_dir, step)

Misc

Contact: morphnet@google.com

Maintainers

• Elad Eban, github: eladeban
• Andrew Poon, github: ayp-google
• Yair Movshovitz-Attias, github: yairmov
• Max Moroz, github: pkch

Contributors

• Ariel Gordon, github: gariel-google.