Accelerated SGD

Accelerated SGD

import torch

from fastAIcourse.datasets import *
from fastAIcourse.conv import *
from fastAIcourse.learner import *
from fastAIcourse.activations import *
from fastAIcourse.init import *

import pickle,gzip,math,os,time,shutil,torch,matplotlib as mpl,numpy as np,matplotlib.pyplot as plt
import fastcore.all as fc
from collections.abc import Mapping
from pathlib import Path
from operator import attrgetter,itemgetter
from functools import partial
from copy import copy
from contextlib import contextmanager

import torchvision.transforms.functional as TF,torch.nn.functional as F
from torch import tensor,nn,optim
from torch.utils.data import DataLoader,default_collate
from torch.nn import init
from torch.optim import lr_scheduler
from torcheval.metrics import MulticlassAccuracy
from datasets import load_dataset,load_dataset_builder

from fastcore.test import test_close

torch.set_printoptions(precision=2, linewidth=140, sci_mode=False)
torch.manual_seed(1)

import logging
logging.disable(logging.WARNING)

set_seed(42)

xl,yl = 'image','label'
name = "fashion_mnist"
dsd = load_dataset(name)

bs = 1024
xmean,xstd = 0.28, 0.35

@inplace
def transformi(b): b[xl] = [(TF.to_tensor(o)-xmean)/xstd for o in b[xl]]

tds = dsd.with_transform(transformi)
dls = DataLoaders.from_dd(tds, bs, num_workers=4)

metrics = MetricsCB(accuracy=MulticlassAccuracy())
astats = ActivationStats(fc.risinstance(GeneralRelu))
cbs = [DeviceCB(), metrics, ProgressCB(plot=True), astats]
act_gr = partial(GeneralRelu, leak=0.1, sub=0.4)
iw = partial(init_weights, leaky=0.1)
lrf_cbs = [DeviceCB(), LRFinderCB()]

Optimizers

SGD

class SGD:
    def __init__(self, params, lr, wd=0.):
        params = list(params)
        fc.store_attr()
        self.i = 0

    def step(self):
        with torch.no_grad():
            for p in self.params:
                self.reg_step(p)
                self.opt_step(p)
        self.i +=1

    def opt_step(self, p): p -= p.grad * self.lr
    def reg_step(self, p):
        if self.wd != 0: p *= 1 - self.lr*self.wd

    def zero_grad(self):
        for p in self.params: p.grad.data.zero_()

set_seed(42)
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
learn = TrainLearner(model, dls, F.cross_entropy, lr=0.4, cbs=cbs, opt_func=SGD)

learn.fit(3)

accuracy	loss	epoch	train
0.772	0.640	0	train
0.824	0.477	0	eval
0.845	0.424	1	train
0.849	0.419	1	eval
0.865	0.373	2	train
0.851	0.403	2	eval

Consider the difference between weight decay and L2 regularization:

weight -= lr*wd*weight

…vs…

weight.grad += wd*weight

Momentum

xs = torch.linspace(-4, 4, 100)
ys = 1 - (xs/3) ** 2 + torch.randn(100) * 0.1

_,axs = plt.subplots(2,2, figsize=(12,8))
betas = [0.5,0.7,0.9,0.99]
for beta,ax in zip(betas, axs.flatten()):
    ax.scatter(xs,ys)
    avg,res = 0,[]
    for yi in ys:
        avg = beta*avg + (1-beta)*yi
        res.append(avg)
    ax.plot(xs,np.array(res), color='red');
    ax.set_title(f'beta={beta}')

class Momentum(SGD):
    def __init__(self, params, lr, wd=0., mom=0.9):
        super().__init__(params, lr=lr, wd=wd)
        self.mom=mom

    def opt_step(self, p):
        if not hasattr(p, 'grad_avg'): p.grad_avg = torch.zeros_like(p.grad)
        p.grad_avg = p.grad_avg*self.mom + p.grad*(1-self.mom)
        p -= self.lr * p.grad_avg

set_seed(42)
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
learn = TrainLearner(model, dls, F.cross_entropy, lr=1.5, cbs=cbs, opt_func=Momentum)

learn.fit(3)

accuracy	loss	epoch	train
0.787	0.597	0	train
0.848	0.417	0	eval
0.869	0.360	1	train
0.861	0.368	1	eval
0.885	0.315	2	train
0.871	0.360	2	eval

astats.color_dim()

RMSProp

class RMSProp(SGD):
    def __init__(self, params, lr, wd=0., sqr_mom=0.99, eps=1e-5):
        super().__init__(params, lr=lr, wd=wd)
        self.sqr_mom,self.eps = sqr_mom,eps

    def opt_step(self, p):
        if not hasattr(p, 'sqr_avg'): p.sqr_avg = p.grad**2
        p.sqr_avg = p.sqr_avg*self.sqr_mom + p.grad**2*(1-self.sqr_mom)
        p -= self.lr * p.grad/(p.sqr_avg.sqrt() + self.eps)

set_seed(42)
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
learn = TrainLearner(model, dls, F.cross_entropy, lr=3e-3, cbs=cbs, opt_func=RMSProp)
learn.fit(3)

accuracy	loss	epoch	train
0.766	0.664	0	train
0.821	0.482	0	eval
0.848	0.416	1	train
0.846	0.424	1	eval
0.866	0.367	2	train
0.851	0.404	2	eval

astats.color_dim()

Adam

class Adam(SGD):
    def __init__(self, params, lr, wd=0., beta1=0.9, beta2=0.99, eps=1e-5):
        super().__init__(params, lr=lr, wd=wd)
        self.beta1,self.beta2,self.eps = beta1,beta2,eps

    def opt_step(self, p):
        if not hasattr(p, 'avg'): p.avg = torch.zeros_like(p.grad.data)
        if not hasattr(p, 'sqr_avg'): p.sqr_avg = torch.zeros_like(p.grad.data)
        p.avg = self.beta1*p.avg + (1-self.beta1)*p.grad
        unbias_avg = p.avg / (1 - (self.beta1**(self.i+1)))
        p.sqr_avg = self.beta2*p.sqr_avg + (1-self.beta2)*(p.grad**2)
        unbias_sqr_avg = p.sqr_avg / (1 - (self.beta2**(self.i+1)))
        p -= self.lr * unbias_avg / (unbias_sqr_avg + self.eps).sqrt()

set_seed(42)
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
learn = TrainLearner(model, dls, F.cross_entropy, lr=6e-3, cbs=cbs, opt_func=Adam)
learn.fit(3)

accuracy	loss	epoch	train
0.791	0.583	0	train
0.839	0.428	0	eval
0.870	0.359	1	train
0.859	0.379	1	eval
0.886	0.312	2	train
0.874	0.345	2	eval

Schedulers

We’ve already seen how we can easily write a custom LR-adjusting callback or Learner, or can use the predefined PyTorch schedulers. We’ll use the predefined ones for now since there’s nothing new to learn in implementing them ourselves.

dir(lr_scheduler)

['ChainedScheduler',
 'ConstantLR',
 'CosineAnnealingLR',
 'CosineAnnealingWarmRestarts',
 'Counter',
 'CyclicLR',
 'EPOCH_DEPRECATION_WARNING',
 'ExponentialLR',
 'LRScheduler',
 'LambdaLR',
 'LinearLR',
 'MultiStepLR',
 'MultiplicativeLR',
 'OneCycleLR',
 'Optimizer',
 'PolynomialLR',
 'ReduceLROnPlateau',
 'SequentialLR',
 'StepLR',
 '_LRScheduler',
 '__all__',
 '__builtins__',
 '__cached__',
 '__doc__',
 '__file__',
 '__loader__',
 '__name__',
 '__package__',
 '__spec__',
 '_enable_get_lr_call',
 'bisect_right',
 'inf',
 'math',
 'types',
 'warnings',
 'weakref',
 'wraps']

' '.join(o for o in dir(lr_scheduler) if o[0].isupper() and o[1].islower())

'ChainedScheduler ConstantLR CosineAnnealingLR CosineAnnealingWarmRestarts Counter CyclicLR ExponentialLR LambdaLR LinearLR MultiStepLR MultiplicativeLR OneCycleLR Optimizer PolynomialLR ReduceLROnPlateau SequentialLR StepLR'

' '.join(filter(lambda x: x[0].isupper() and x[1].islower(), dir(lr_scheduler)))

'ChainedScheduler ConstantLR CosineAnnealingLR CosineAnnealingWarmRestarts Counter CyclicLR ExponentialLR LambdaLR LinearLR MultiStepLR MultiplicativeLR OneCycleLR Optimizer PolynomialLR ReduceLROnPlateau SequentialLR StepLR'

learn = TrainLearner(get_model(), dls, F.cross_entropy, lr=6e-3, cbs=[DeviceCB(), SingleBatchCB()])
learn.fit(1)

opt = learn.opt
' '.join(o for o in dir(opt) if o[0]!='_')

'add_param_group defaults load_state_dict param_groups profile_hook_step register_step_post_hook register_step_pre_hook state state_dict step zero_grad'

opt

SGD (
Parameter Group 0
    dampening: 0
    differentiable: False
    foreach: None
    lr: 0.006
    maximize: False
    momentum: 0
    nesterov: False
    weight_decay: 0
)

param = next(iter(learn.model.parameters()))
st = opt.state[param]

st

{'momentum_buffer': None}

len(opt.param_groups)

1

pg = opt.param_groups[0]

list(pg)

['params',
 'lr',
 'momentum',
 'dampening',
 'weight_decay',
 'nesterov',
 'maximize',
 'foreach',
 'differentiable']

sched = lr_scheduler.CosineAnnealingLR(opt, 100)

sched.base_lrs

[0.006]

sched.get_last_lr()

[0.006]

def sched_lrs(sched, steps):
    lrs = [sched.get_last_lr()]
    for i in range(steps):
        sched.optimizer.step()
        sched.step()
        lrs.append(sched.get_last_lr())
    plt.plot(lrs)

sched_lrs(sched, 110)

Scheduler callbacks

def _lr(cb): return cb.pg['lr']

len(dls.train)

59

tmax = 3 * len(dls.train)
sched = partial(lr_scheduler.CosineAnnealingLR, T_max=tmax)

set_seed(42)
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
rec = RecorderCB(lr=_lr)
xtra = [BatchSchedCB(sched),rec]
learn = TrainLearner(model, dls, F.cross_entropy, lr=2e-2, cbs=cbs+xtra, opt_func=optim.AdamW)
learn.fit(3)

accuracy	loss	epoch	train
0.806	0.525	0	train
0.848	0.415	0	eval
0.878	0.331	1	train
0.879	0.330	1	eval
0.897	0.282	2	train
0.881	0.318	2	eval

rec.plot()

class EpochSchedCB(BaseSchedCB):
    def after_epoch(self, learn): self._step(learn)

sched = partial(lr_scheduler.CosineAnnealingLR, T_max=3)
set_seed(42)
xtra = [EpochSchedCB(sched),rec]
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
learn = TrainLearner(model, dls, F.cross_entropy, lr=2e-2, cbs=cbs+xtra, opt_func=optim.AdamW)
learn.fit(3)

accuracy	loss	epoch	train
0.806	0.524	0	train
0.857	0.382	0	eval
0.879	0.328	1	train
0.874	0.336	1	eval
0.898	0.275	2	train
0.883	0.309	2	eval

rec.plot()

1cycle training

Paper by Leslie Smith.

def _beta1(cb): return cb.pg['betas'][0]
rec = RecorderCB(lr=_lr, mom=_beta1)

set_seed(42)
lr,epochs = 6e-2,5
model = get_model(act_gr, norm=nn.BatchNorm2d).apply(iw)
tmax = epochs * len(dls.train)
sched = partial(lr_scheduler.OneCycleLR, max_lr=lr, total_steps=tmax)
xtra = [BatchSchedCB(sched), rec]
learn = TrainLearner(model, dls, F.cross_entropy, lr=lr, cbs=cbs+xtra, opt_func=optim.AdamW)
learn.fit(epochs)

accuracy	loss	epoch	train
0.767	0.660	0	train
0.842	0.462	0	eval
0.855	0.391	1	train
0.859	0.396	1	eval
0.884	0.312	2	train
0.881	0.327	2	eval
0.906	0.254	3	train
0.895	0.284	3	eval
0.920	0.215	4	train
0.900	0.271	4	eval

rec.plot()