DL-Art-School/codes/trainer/losses.py
2021-07-08 22:13:44 -06:00

588 lines
27 KiB
Python

import torch
import torch.nn as nn
from torch.cuda.amp import autocast
from trainer.loss import GANLoss
import random
import functools
import torch.nn.functional as F
from utils.util import opt_get
def create_loss(opt_loss, env):
type = opt_loss['type']
if 'teco_' in type:
from trainer.custom_training_components import create_teco_loss
return create_teco_loss(opt_loss, env)
elif 'stylegan2_' in type:
from models.stylegan import create_stylegan2_loss
return create_stylegan2_loss(opt_loss, env)
elif 'style_sr_' in type:
from models.styled_sr import create_stylesr_loss
return create_stylesr_loss(opt_loss, env)
elif 'lightweight_gan_divergence' == type:
from models.lightweight_gan import LightweightGanDivergenceLoss
return LightweightGanDivergenceLoss(opt_loss, env)
elif type == 'crossentropy':
return CrossEntropy(opt_loss, env)
elif type == 'pix':
return PixLoss(opt_loss, env)
elif type == 'sr_pix':
return SrPixLoss(opt_loss, env)
elif type == 'direct':
return DirectLoss(opt_loss, env)
elif type == 'feature':
return FeatureLoss(opt_loss, env)
elif type == 'interpreted_feature':
return InterpretedFeatureLoss(opt_loss, env)
elif type == 'generator_gan':
return GeneratorGanLoss(opt_loss, env)
elif type == 'discriminator_gan':
return DiscriminatorGanLoss(opt_loss, env)
elif type == 'geometric':
return GeometricSimilarityGeneratorLoss(opt_loss, env)
elif type == 'translational':
return TranslationInvarianceLoss(opt_loss, env)
elif type == 'recursive':
return RecursiveInvarianceLoss(opt_loss, env)
elif type == 'recurrent':
return RecurrentLoss(opt_loss, env)
elif type == 'for_element':
return ForElementLoss(opt_loss, env)
elif type == 'mixture_of_experts':
from models.switched_conv.mixture_of_experts import MixtureOfExpertsLoss
return MixtureOfExpertsLoss(opt_loss, env)
elif type == 'switch_transformer_balance':
from models.switched_conv.mixture_of_experts import SwitchTransformersLoadBalancingLoss
return SwitchTransformersLoadBalancingLoss(opt_loss, env)
elif type == 'nv_tacotron2_loss':
from models.tacotron2.loss import Tacotron2Loss
return Tacotron2Loss(opt_loss, env)
else:
raise NotImplementedError
# Converts params to a list of tensors extracted from state. Works with list/tuple params as well as scalars.
def extract_params_from_state(params: object, state: object, root: object = True) -> object:
if isinstance(params, list) or isinstance(params, tuple):
p = [extract_params_from_state(r, state, False) for r in params]
elif isinstance(params, str):
if params == 'None':
p = None
else:
p = state[params]
else:
p = params
# The root return must always be a list.
if root and not isinstance(p, list):
p = [p]
return p
class ConfigurableLoss(nn.Module):
def __init__(self, opt, env):
super(ConfigurableLoss, self).__init__()
self.opt = opt
self.env = env
self.metrics = []
# net is either a scalar network being trained or a list of networks being trained, depending on the configuration.
def forward(self, net, state):
raise NotImplementedError
def is_stateful(self) -> bool:
"""
Losses can inject into the state too. useful for when a loss computation can be used by another loss.
if this is true, the forward pass must return (loss, new_state). If false (the default), forward() only returns
the loss value.
"""
return False
def extra_metrics(self):
return self.metrics
def clear_metrics(self):
self.metrics = []
def get_basic_criterion_for_name(name, device):
if name == 'l1':
return nn.L1Loss().to(device)
elif name == 'l2':
return nn.MSELoss().to(device)
elif name == 'cosine':
return nn.CosineEmbeddingLoss().to(device)
else:
raise NotImplementedError
class CrossEntropy(ConfigurableLoss):
def __init__(self, opt, env):
super().__init__(opt, env)
self.opt = opt
self.ce = nn.CrossEntropyLoss()
def forward(self, _, state):
logits = state[self.opt['logits']]
labels = state[self.opt['labels']]
if self.opt['rescale']:
labels = F.interpolate(labels.type(torch.float), size=logits.shape[2:], mode="nearest").type(torch.long)
if 'mask' in self.opt.keys():
mask = state[self.opt['mask']]
if self.opt['rescale']:
mask = F.interpolate(mask, size=logits.shape[2:], mode="nearest")
logits = logits * mask
if self.opt['swap_channels']:
logits = logits.permute(0,2,3,1).contiguous()
assert labels.max()+1 <= logits.shape[-1]
return self.ce(logits.view(-1, logits.size(-1)), labels.view(-1))
class PixLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(PixLoss, self).__init__(opt, env)
self.opt = opt
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
self.real_scale = opt['real_scale'] if 'real_scale' in opt.keys() else 1
self.real_offset = opt['real_offset'] if 'real_offset' in opt.keys() else 0
self.report_metrics = opt['report_metrics'] if 'report_metrics' in opt.keys() else False
def forward(self, _, state):
real = state[self.opt['real']] * self.real_scale + float(self.real_offset)
fake = state[self.opt['fake']]
if self.report_metrics:
self.metrics.append(("real_pix_mean_histogram", torch.mean(real, dim=[1,2,3]).detach()))
self.metrics.append(("fake_pix_mean_histogram", torch.mean(fake, dim=[1,2,3]).detach()))
self.metrics.append(("real_pix_std", torch.std(real).detach()))
self.metrics.append(("fake_pix_std", torch.std(fake).detach()))
return self.criterion(fake.float(), real.float())
class SrPixLoss(ConfigurableLoss):
def __init__(self, opt, env):
super().__init__(opt, env)
self.opt = opt
self.base_loss = opt_get(opt, ['base_loss'], .2)
self.exp = opt_get(opt, ['exp'], 2)
self.scale = opt['scale']
def forward(self, _, state):
real = state[self.opt['real']]
fake = state[self.opt['fake']]
l2 = (fake - real) ** 2
self.metrics.append(("l2_loss", l2.mean()))
# Adjust loss by prioritizing reconstruction of HF details.
no_hf = F.interpolate(F.interpolate(real, scale_factor=1/self.scale, mode="area"), scale_factor=self.scale, mode="nearest")
weights = (torch.abs(real - no_hf) + self.base_loss) ** self.exp
weights = weights / weights.mean()
loss = l2*weights
# Preserve the intensity of the loss, just adjust the weighting.
loss = loss*l2.mean()/loss.mean()
return loss.mean()
# Loss defined by averaging the input tensor across all dimensions and optionally inverting it.
class DirectLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(DirectLoss, self).__init__(opt, env)
self.opt = opt
self.inverted = opt['inverted'] if 'inverted' in opt.keys() else False
self.key = opt['key']
def forward(self, _, state):
if self.inverted:
return -torch.mean(state[self.key])
else:
return torch.mean(state[self.key])
class FeatureLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(FeatureLoss, self).__init__(opt, env)
self.opt = opt
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
import trainer.networks
self.netF = trainer.networks.define_F(which_model=opt['which_model_F'],
load_path=opt['load_path'] if 'load_path' in opt.keys() else None).to(self.env['device'])
if not env['opt']['dist']:
self.netF = torch.nn.parallel.DataParallel(self.netF, device_ids=env['opt']['gpu_ids'])
def forward(self, _, state):
with autocast(enabled=self.env['opt']['fp16']):
with torch.no_grad():
logits_real = self.netF(state[self.opt['real']])
logits_fake = self.netF(state[self.opt['fake']])
if self.opt['criterion'] == 'cosine':
return self.criterion(logits_fake.float(), logits_real.float(), torch.ones(1, device=logits_fake.device))
else:
return self.criterion(logits_fake.float(), logits_real.float())
# Special form of feature loss which first computes the feature embedding for the truth space, then uses a second
# network which was trained to replicate that embedding on an altered input space (for example, LR or greyscale) to
# compute the embedding in the generated space. Useful for weakening the influence of the feature network in controlled
# ways.
class InterpretedFeatureLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(InterpretedFeatureLoss, self).__init__(opt, env)
self.opt = opt
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
import trainer.networks
self.netF_real = trainer.networks.define_F(which_model=opt['which_model_F']).to(self.env['device'])
self.netF_gen = trainer.networks.define_F(which_model=opt['which_model_F'], load_path=opt['load_path']).to(self.env['device'])
if not env['opt']['dist']:
self.netF_real = torch.nn.parallel.DataParallel(self.netF_real)
self.netF_gen = torch.nn.parallel.DataParallel(self.netF_gen)
def forward(self, _, state):
logits_real = self.netF_real(state[self.opt['real']])
logits_fake = self.netF_gen(state[self.opt['fake']])
return self.criterion(logits_fake.float(), logits_real.float())
class GeneratorGanLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(GeneratorGanLoss, self).__init__(opt, env)
self.opt = opt
self.criterion = GANLoss(opt['gan_type'], 1.0, 0.0).to(env['device'])
self.noise = None if 'noise' not in opt.keys() else opt['noise']
self.detach_real = opt['detach_real'] if 'detach_real' in opt.keys() else True
# This is a mechanism to prevent backpropagation for a GAN loss if it goes too low. This can be used to balance
# generators and discriminators by essentially having them skip steps while their counterparts "catch up".
self.min_loss = opt['min_loss'] if 'min_loss' in opt.keys() else 0
if self.min_loss != 0:
self.loss_rotating_buffer = torch.zeros(10, requires_grad=False)
self.rb_ptr = 0
self.losses_computed = 0
def forward(self, _, state):
netD = self.env['discriminators'][self.opt['discriminator']]
real = extract_params_from_state(self.opt['real'], state)
fake = extract_params_from_state(self.opt['fake'], state)
if self.noise:
nreal = []
nfake = []
for i, t in enumerate(real):
if isinstance(t, torch.Tensor):
nreal.append(t + torch.rand_like(t) * self.noise)
nfake.append(fake[i] + torch.rand_like(t) * self.noise)
else:
nreal.append(t)
nfake.append(fake[i])
real = nreal
fake = nfake
with autocast(enabled=self.env['opt']['fp16']):
if self.opt['gan_type'] in ['gan', 'pixgan', 'pixgan_fea']:
pred_g_fake = netD(*fake)
loss = self.criterion(pred_g_fake, True)
elif self.opt['gan_type'] == 'ragan':
pred_d_real = netD(*real)
if self.detach_real:
pred_d_real = pred_d_real.detach()
pred_g_fake = netD(*fake)
d_fake_diff = pred_g_fake - torch.mean(pred_d_real)
self.metrics.append(("d_fake", torch.mean(pred_g_fake)))
self.metrics.append(("d_fake_diff", torch.mean(d_fake_diff)))
loss = (self.criterion(pred_d_real - torch.mean(pred_g_fake), False) +
self.criterion(d_fake_diff, True)) / 2
else:
raise NotImplementedError
if self.min_loss != 0:
self.loss_rotating_buffer[self.rb_ptr] = loss.item()
self.rb_ptr = (self.rb_ptr + 1) % self.loss_rotating_buffer.shape[0]
if torch.mean(self.loss_rotating_buffer) < self.min_loss:
return 0
self.losses_computed += 1
self.metrics.append(("loss_counter", self.losses_computed))
return loss
class DiscriminatorGanLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(DiscriminatorGanLoss, self).__init__(opt, env)
self.opt = opt
self.criterion = GANLoss(opt['gan_type'], 1.0, 0.0).to(env['device'])
self.noise = None if 'noise' not in opt.keys() else opt['noise']
# This is a mechanism to prevent backpropagation for a GAN loss if it goes too low. This can be used to balance
# generators and discriminators by essentially having them skip steps while their counterparts "catch up".
self.min_loss = opt['min_loss'] if 'min_loss' in opt.keys() else 0
self.gradient_penalty = opt['gradient_penalty'] if 'gradient_penalty' in opt.keys() else False
if self.min_loss != 0:
assert not self.env['dist'] # distributed training does not support 'min_loss' - it can result in backward() desync by design.
self.loss_rotating_buffer = torch.zeros(10, requires_grad=False)
self.rb_ptr = 0
self.losses_computed = 0
def forward(self, net, state):
real = extract_params_from_state(self.opt['real'], state)
real = [r.detach() for r in real]
if self.gradient_penalty:
[r.requires_grad_() for r in real]
fake = extract_params_from_state(self.opt['fake'], state)
new_state = {}
fake = [f.detach() for f in fake]
new_state = {}
if self.noise:
nreal = []
nfake = []
for i, t in enumerate(real):
if isinstance(t, torch.Tensor):
nreal.append(t + torch.rand_like(t) * self.noise)
nfake.append(fake[i] + torch.rand_like(t) * self.noise)
else:
nreal.append(t)
nfake.append(fake[i])
real = nreal
fake = nfake
with autocast(enabled=self.env['opt']['fp16']):
d_real = net(*real)
d_fake = net(*fake)
if self.opt['gan_type'] in ['gan', 'pixgan']:
self.metrics.append(("d_fake", torch.mean(d_fake)))
self.metrics.append(("d_real", torch.mean(d_real)))
l_real = self.criterion(d_real, True)
l_fake = self.criterion(d_fake, False)
l_total = l_real + l_fake
loss = l_total
elif self.opt['gan_type'] == 'ragan' or self.opt['gan_type'] == 'max_spread':
d_fake_diff = d_fake - torch.mean(d_real)
self.metrics.append(("d_fake_diff", torch.mean(d_fake_diff)))
loss = (self.criterion(d_real - torch.mean(d_fake), True) +
self.criterion(d_fake_diff, False))
else:
raise NotImplementedError
if self.min_loss != 0:
self.loss_rotating_buffer[self.rb_ptr] = loss.item()
self.rb_ptr = (self.rb_ptr + 1) % self.loss_rotating_buffer.shape[0]
self.metrics.append(("loss_counter", self.losses_computed))
if torch.mean(self.loss_rotating_buffer) < self.min_loss:
return 0
self.losses_computed += 1
if self.gradient_penalty:
# Apply gradient penalty. TODO: migrate this elsewhere.
from models.stylegan.stylegan2_lucidrains import gradient_penalty
assert len(real) == 1 # Grad penalty doesn't currently support multi-input discriminators.
gp, gp_structure = gradient_penalty(real[0], d_real, return_structured_grads=True)
self.metrics.append(("gradient_penalty", gp.clone().detach()))
loss = loss + gp
self.metrics.append(("gradient_penalty", gp))
# The gp_structure is a useful visual debugging tool to see what areas of the generated image the disc is paying attention to.
gpimg = (gp_structure / (torch.std(gp_structure, dim=(-1, -2), keepdim=True) * 2)) \
- torch.mean(gp_structure, dim=(-1, -2), keepdim=True) + .5
new_state['%s_%s_gp_structure_img' % (self.opt['fake'], self.opt['real'])] = gpimg
return loss, new_state
# This loss is stateful because it injects a debugging result from the GP term when enabled.
def is_stateful(self) -> bool:
return True
# Computes a loss created by comparing the output of a generator to the output from the same generator when fed an
# input that has been altered randomly by rotation or flip.
# The "real" parameter to this loss is the actual output of the generator (from an injection point)
# The "fake" parameter is the LR input that produced the "real" parameter when fed through the generator.
class GeometricSimilarityGeneratorLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(GeometricSimilarityGeneratorLoss, self).__init__(opt, env)
self.opt = opt
self.generator = opt['generator']
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
self.gen_input_for_alteration = opt['input_alteration_index'] if 'input_alteration_index' in opt.keys() else 0
self.gen_output_to_use = opt['generator_output_index'] if 'generator_output_index' in opt.keys() else None
self.detach_fake = opt['detach_fake'] if 'detach_fake' in opt.keys() else False
# Returns a random alteration and its counterpart (that undoes the alteration)
def random_alteration(self):
return random.choice([(functools.partial(torch.flip, dims=(2,)), functools.partial(torch.flip, dims=(2,))),
(functools.partial(torch.flip, dims=(3,)), functools.partial(torch.flip, dims=(3,))),
(functools.partial(torch.rot90, k=1, dims=[2,3]), functools.partial(torch.rot90, k=3, dims=[2,3])),
(functools.partial(torch.rot90, k=2, dims=[2,3]), functools.partial(torch.rot90, k=2, dims=[2,3])),
(functools.partial(torch.rot90, k=3, dims=[2,3]), functools.partial(torch.rot90, k=1, dims=[2,3]))])
def forward(self, net, state):
net = self.env['generators'][self.generator] # Get the network from an explicit parameter.
# The <net> parameter is not reliable for generator losses since often they are combined with many networks.
fake = extract_params_from_state(self.opt['fake'], state)
alteration, undo_fn = self.random_alteration()
altered = []
for i, t in enumerate(fake):
if i == self.gen_input_for_alteration:
altered.append(alteration(t))
else:
altered.append(t)
with autocast(enabled=self.env['opt']['fp16']):
if self.detach_fake:
with torch.no_grad():
upsampled_altered = net(*altered)
else:
upsampled_altered = net(*altered)
if self.gen_output_to_use is not None:
upsampled_altered = upsampled_altered[self.gen_output_to_use]
# Undo alteration on HR image
upsampled_altered = undo_fn(upsampled_altered)
if self.opt['criterion'] == 'cosine':
return self.criterion(state[self.opt['real']], upsampled_altered, torch.ones(1, device=upsampled_altered.device))
else:
return self.criterion(state[self.opt['real']].float(), upsampled_altered.float())
# Computes a loss created by comparing the output of a generator to the output from the same generator when fed an
# input that has been translated in a random direction.
# The "real" parameter to this loss is the actual output of the generator on the top left image patch.
# The "fake" parameter is the output base fed into a ImagePatchInjector.
class TranslationInvarianceLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(TranslationInvarianceLoss, self).__init__(opt, env)
self.opt = opt
self.generator = opt['generator']
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
self.gen_input_for_alteration = opt['input_alteration_index'] if 'input_alteration_index' in opt.keys() else 0
self.gen_output_to_use = opt['generator_output_index'] if 'generator_output_index' in opt.keys() else None
self.patch_size = opt['patch_size']
self.overlap = opt['overlap'] # For maximum overlap, can be calculated as 2*patch_size-image_size
self.detach_fake = opt['detach_fake']
assert(self.patch_size > self.overlap)
def forward(self, net, state):
net = self.env['generators'][self.generator] # Get the network from an explicit parameter.
# The <net> parameter is not reliable for generator losses since often they are combined with many networks.
border_sz = self.patch_size - self.overlap
translation = random.choice([("top_right", border_sz, border_sz+self.overlap, 0, self.overlap),
("bottom_left", 0, self.overlap, border_sz, border_sz+self.overlap),
("bottom_right", 0, self.overlap, 0, self.overlap)])
trans_name, hl, hh, wl, wh = translation
# Change the "fake" input name that we are translating to one that specifies the random translation.
fake = self.opt['fake'].copy()
fake[self.gen_input_for_alteration] = "%s_%s" % (fake[self.gen_input_for_alteration], trans_name)
input = extract_params_from_state(fake, state)
with autocast(enabled=self.env['opt']['fp16']):
if self.detach_fake:
with torch.no_grad():
trans_output = net(*input)
else:
trans_output = net(*input)
if not isinstance(trans_output, list) and not isinstance(trans_output, tuple):
trans_output = [trans_output]
if self.gen_output_to_use is not None:
fake_shared_output = trans_output[self.gen_output_to_use][:, :, hl:hh, wl:wh]
else:
fake_shared_output = trans_output[:, :, hl:hh, wl:wh]
# The "real" input is assumed to always come from the top left tile.
gen_output = state[self.opt['real']]
real_shared_output = gen_output[:, :, border_sz:border_sz+self.overlap, border_sz:border_sz+self.overlap]
if self.opt['criterion'] == 'cosine':
return self.criterion(fake_shared_output, real_shared_output, torch.ones(1, device=real_shared_output.device))
else:
return self.criterion(fake_shared_output.float(), real_shared_output.float())
# Computes a loss repeatedly feeding the generator downsampled inputs created from its outputs. The expectation is
# that the generator's outputs do not change on repeated forward passes.
# The "real" parameter to this loss is the actual output of the generator.
# The "fake" parameter is the expected inputs that should be fed into the generator. 'input_alteration_index' is changed
# so that it feeds the recursive input.
class RecursiveInvarianceLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(RecursiveInvarianceLoss, self).__init__(opt, env)
self.opt = opt
self.generator = opt['generator']
self.criterion = get_basic_criterion_for_name(opt['criterion'], env['device'])
self.gen_input_for_alteration = opt['input_alteration_index'] if 'input_alteration_index' in opt.keys() else 0
self.gen_output_to_use = opt['generator_output_index'] if 'generator_output_index' in opt.keys() else None
self.recursive_depth = opt['recursive_depth'] # How many times to recursively feed the output of the generator back into itself
self.downsample_factor = opt['downsample_factor'] # Just 1/opt['scale']. Necessary since this loss doesnt have access to opt['scale'].
assert(self.recursive_depth > 0)
def forward(self, net, state):
net = self.env['generators'][self.generator] # Get the network from an explicit parameter.
# The <net> parameter is not reliable for generator losses since they can be combined with many networks.
gen_output = state[self.opt['real']]
recurrent_gen_output = gen_output
fake = self.opt['fake'].copy()
input = extract_params_from_state(fake, state)
for i in range(self.recursive_depth):
input[self.gen_input_for_alteration] = torch.nn.functional.interpolate(recurrent_gen_output, scale_factor=self.downsample_factor, mode="nearest")
with autocast(enabled=self.env['opt']['fp16']):
recurrent_gen_output = net(*input)[self.gen_output_to_use]
compare_real = gen_output
compare_fake = recurrent_gen_output
if self.opt['criterion'] == 'cosine':
return self.criterion(compare_real, compare_fake, torch.ones(1, device=compare_real.device))
else:
return self.criterion(compare_real.float(), compare_fake.float())
# Loss that pulls tensors from dim 1 of the input and repeatedly feeds them into the
# 'subtype' loss.
class RecurrentLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(RecurrentLoss, self).__init__(opt, env)
o = opt.copy()
o['type'] = opt['subtype']
o['fake'] = '_fake'
o['real'] = '_real'
self.loss = create_loss(o, self.env)
# Use this option to specify a differential weighting scheme for losses inside of the recurrent construct. For
# example, if later recurrent outputs should contribute more to the loss than earlier ones. When specified,
# must be a list of weights that exactly aligns with the recurrent list fed to forward().
self.recurrent_weights = opt['recurrent_weights'] if 'recurrent_weights' in opt.keys() else 1
def forward(self, net, state):
total_loss = 0
st = state.copy()
real = state[self.opt['real']]
for i in range(real.shape[1]):
st['_real'] = real[:, i]
st['_fake'] = state[self.opt['fake']][:, i]
subloss = self.loss(net, st)
if isinstance(self.recurrent_weights, list):
subloss = subloss * self.recurrent_weights[i]
total_loss += subloss
return total_loss
def extra_metrics(self):
return self.loss.extra_metrics()
def clear_metrics(self):
self.loss.clear_metrics()
# Loss that pulls a tensor from dim 1 of the input and feeds it into a "sub" loss.
class ForElementLoss(ConfigurableLoss):
def __init__(self, opt, env):
super(ForElementLoss, self).__init__(opt, env)
o = opt.copy()
o['type'] = opt['subtype']
self.index = opt['index']
o['fake'] = '_fake'
o['real'] = '_real'
self.loss = create_loss(o, self.env)
def forward(self, net, state):
st = state.copy()
st['_real'] = state[self.opt['real']][:, self.index]
st['_fake'] = state[self.opt['fake']][:, self.index]
return self.loss(net, st)
def extra_metrics(self):
return self.loss.extra_metrics()
def clear_metrics(self):
self.loss.clear_metrics()