# Mixed Precision Training¶

## Introduction¶

Traditionally, for training a neural network, we used to use FP32 for weights and activations; however computation costs for training a neural network rapidly increase over years as the success of deep learning and the growing size of a neural network. It indicates that we need to spend much more time for training a huge size of a neural network while we would like to do lots of trials before a product launch. To address this problem, companies (e.g., NVIDIA) introduced an accelerator for speeding up computation. For example, NVIDIA Volta has Tensor Cores to speed up computation.

However, it uses FP16 weights, activations, gradients, and the range of FP16 is very limited when compared to that of FP32, meaning that sometimes (or often) values of gradients overflow and/or underflow, which affects the performance of a neural network or makes it collapse during training.

Mixed precision training is one of the algorithms to circumvent that problem while maintaining the same results that we could obtain with FP32 networks. It is well-described in The Training with Mixed Precision User Guide and Mixed Precision Training.

This tutorial explains how to do the mixed precision training in NNabla step-by-step.

## Step-by-Step Instruction¶

Basically, the mixed precision training are composed of three parts.

1. Use the accelerator for computation (here we assume Tensor Cores)
2. Use loss scaling to prevent underflow
3. Use dynamic loss calling to prevent overflow/underflow

In NNabla, we can do the correspondences as follows.

### 1. Use Tensor Cores¶

ctx = get_extension_context("cudnn", type_config="half")


### 2. Use loss scaling to prevent underflow¶

loss_scale = 8
loss.backward(loss_scale)
solver.update()


### 3. Use dynamic loss scaling to prevent overflow/underflow¶

loss_scale = 8
scaling_factor = 2
counter = 0
interval = 2000
...
loss.backward(loss_scale, ...)
...
loss_scale /= scaling_factor
counter = 0
else:
solver.update()
if counter > interval:
loss_scale *= scaling_factor
counter = 0
counter += 1


Note that currently the procedures of 2nd (Use loss scaling to prevent underflow) and 3rd (Use loss scaling to prevent overflow) are experimental, and we are now trying to speed up the mixed precision training, so API might change for future use, especially 3rd.

## All-in-one Instruction¶

In the previous step-by-step example, the 3rd step is lengthy in a training loop, thus we can write a wrapper class like the following.

class DynamicLossScalingUpdater(object):
'''Dynamic Loss Scaling Updater for the mixed precision training.

Args:
solver (:obj:nnabla.solvers.Solver): Solver object. E.g., Momentum or Adam.
loss (:obj:nnabla.Variable): Loss variable from which the forward and the backward is called.
data_feeder (callable :obj:object, function, or lambda): Data feeder
scale (:obj:float): Loss scale constant. This is dynamically changing during training.
scaling_factor (:obj:float): Scaling factor for the dynamic loss scaling.
N (:obj:int): Interval, the number of iterations in training for increasing loss scale by scaling_factor.
clear_buffer (:obj:bool): Clears the no longer referenced variables during backpropagation to save memory.
accum_grad (:obj:int): Number of accumulation of gradients. Update method of the solver is called after the accum_grad number of the forward and backward is called.
weight_decay (:obj:float): Decay constant. Default is None, not applying the weight decay.
comm (:obj:nnabla.communicators.Communicator): Communicator when to do distributed training. Default is :obj:None.
grads (:obj:list of :obj:nnabla._nd_array.NdArray): The list of gradients to be exchanged when to do distributed training. Default is the empty :obj:list.

Attributes:
solver (:obj:nnabla.solvers.Solver): Solver object. E.g., Momentum or Adam.
loss (:obj:nnabla.Variable): Loss variable from which the forward and the backward is called.
data_feeder (callable :obj:object, function, lambda): Data feeder
scale (:obj:float): Loss scale constant. This is dynamically changing during training.
scaling_factor (:obj:float): Scaling factor for the dynamic loss scaling.
N (:obj:int): Interval, the number of iterations in training for increasing loss scale by scaling_factor.
clear_buffer (:obj:bool): Clears the no longer referenced variables during backpropagation to save memory.
accum_grad (:obj:int): Number of accumulation of gradients. Update method of the solver is called after the accum_grad number of the forward and backward is called.
weight_decay (:obj:float): Decay constant. Default is None, not applying the weight decay.
comm (:obj:nnabla.communicators.Communicator): Communicator when to do distributed training.
grads (:obj:list of :obj:nnabla._nd_array.NdArray): The list of gradients to be exchanged when to do distributed training.

Example:

.. code-block:: python
solver = <Solver>
loss = <Loss Variable of Network>
data_feeder = <DataFeeder>

updater = DynamicLossScalingUpdater(solver, loss, data_feeder)

# Training iteration
for itr in range(max_iter):
# Call solver.zero_grad, data_feeder, loss.forward, loss.backward
# and solver.update with the dynamic loss scaling.
updater.update()

Reference:

https://docs.nvidia.com/deeplearning/sdk/mixed-precision-training/index.html#scalefactor

'''

def __init__(self, solver, loss, data_feeder=lambda x: x,
scale=8.0, scaling_factor=2.0, N=2000, clear_buffer=True,
comm=None,
self.solver = solver
self.loss = loss
self.data_feeder = data_feeder
self.scale = scale
self.scaling_factor = scaling_factor
self.N = N
self.clear_buffer = clear_buffer
self.weight_decay = weight_decay
self.comm = comm
self._counter = 0
self._recursive_count = 0
self._max_recursive_count = 100

def update(self):
"""Monolithic update method.

This method calls the following methods with the dynamic loss scaling.

2. feed data
3. loss.forward
4. loss.backward
5. comm.all_reduce (if it is specified)
6. solver.update

"""

# Forward and backward
# feed data
self.data_feeder()

# forward

# backward with scale
self.loss.backward(self.scale, clear_buffer=self.clear_buffer)

# AllReduce
if self.comm and len(self.grads) != 0:

self.scale /= self.scaling_factor
self._counter = 0

# Recursively call udpate function until no inf nor nan.
self._recursive_count += 1
if self._recursive_count > self._max_recursive_count:
self._recursive_count = 0
return  # skip
return self.update()
self._recursive_count = 0

# Do some gradient clipping, etc.
if self.weight_decay is not None:
self.solver.weight_decay(self.weight_decay)

# Update
self.solver.update()
if self._counter > self.N:
self.scale *= self.scaling_factor
self._counter = 0
self._counter += 1


Then, call the update method in a training loop:

from nnabla.experimental.mixed_precision_training import DynamicLossScalingUpdater

solver = <Solver>
loss = <Loss Variable of Network>
data_feeder = <DataFeeder>

updater = DynamicLossScalingUpdater(solver, loss, data_feeder)

# Training iteration
for itr in range(max_iter):
# Call solver.zero_grad, data_feeder, loss.forward, loss.backward
# and solver.update with the dynamic loss scaling.
updater.update()


## Notice¶

In the mixed-precision training, the followings are premise:

1. Solver contains FP16 weights and the FP32 copy of weights. Solvers in NNabla hold FP32 weights and weight gradients and cast it to FP16 weights in forward pass and to FP16 weight gradients in backward pass if one sets type_config="half".
2. Reductions should be left in FP32, for examples, the statistics (mean and variance) computed by the batch-normalization, Mean, Sum, SoftMax, SoftMaxCrossEntropy, etc. (see The Training with Mixed Precision User Guide). In NNabla, these functions are automatically fallbacked to use FP32.