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"""
Module containing all vae losses.
"""
import abc
import math
import torch
import torch.nn as nn
from torch.nn import functional as F
from torch import optim
from .discriminator import Discriminator
from disvae.utils.math import (log_density_gaussian, log_importance_weight_matrix,
matrix_log_density_gaussian)
LOSSES = ["VAE", "betaH", "betaB", "factor", "btcvae"]
RECON_DIST = ["bernoulli", "laplace", "gaussian"]
# TO-DO: clean n_data and device
def get_loss_f(loss_name, **kwargs_parse):
"""Return the correct loss function given the argparse arguments."""
kwargs_all = dict(rec_dist=kwargs_parse["rec_dist"],
steps_anneal=kwargs_parse["reg_anneal"])
if loss_name == "betaH":
return BetaHLoss(beta=kwargs_parse["betaH_B"], **kwargs_all)
elif loss_name == "VAE":
return BetaHLoss(beta=1, **kwargs_all)
elif loss_name == "betaB":
return BetaBLoss(C_init=kwargs_parse["betaB_initC"],
C_fin=kwargs_parse["betaB_finC"],
gamma=kwargs_parse["betaB_G"],
**kwargs_all)
elif loss_name == "factor":
return FactorKLoss(kwargs_parse["device"],
gamma=kwargs_parse["factor_G"],
disc_kwargs=dict(latent_dim=kwargs_parse["latent_dim"]),
optim_kwargs=dict(lr=kwargs_parse["lr_disc"], betas=(0.5, 0.9)),
**kwargs_all)
elif loss_name == "btcvae":
return BtcvaeLoss(kwargs_parse["n_data"],
alpha=kwargs_parse["btcvae_A"],
beta=kwargs_parse["btcvae_B"],
gamma=kwargs_parse["btcvae_G"],
**kwargs_all)
else:
assert loss_name not in LOSSES
raise ValueError("Uknown loss : {}".format(loss_name))
class BaseLoss(abc.ABC):
"""
Base class for losses.
Parameters
----------
record_loss_every: int, optional
Every how many steps to recorsd the loss.
rec_dist: {"bernoulli", "gaussian", "laplace"}, optional
Reconstruction distribution istribution of the likelihood on the each pixel.
Implicitely defines the reconstruction loss. Bernoulli corresponds to a
binary cross entropy (bse), Gaussian corresponds to MSE, Laplace
corresponds to L1.
steps_anneal: nool, optional
Number of annealing steps where gradually adding the regularisation.
"""
def __init__(self, record_loss_every=50, rec_dist="bernoulli", steps_anneal=0):
self.n_train_steps = 0
self.record_loss_every = record_loss_every
self.rec_dist = rec_dist
self.steps_anneal = steps_anneal
@abc.abstractmethod
def __call__(self, data, recon_data, latent_dist, is_train, storer, **kwargs):
"""
Calculates loss for a batch of data.
Parameters
----------
data : torch.Tensor
Input data (e.g. batch of images). Shape : (batch_size, n_chan,
height, width).
recon_data : torch.Tensor
Reconstructed data. Shape : (batch_size, n_chan, height, width).
latent_dist : tuple of torch.tensor
sufficient statistics of the latent dimension. E.g. for gaussian
(mean, log_var) each of shape : (batch_size, latent_dim).
is_train : bool
Whether currently in train mode.
storer : dict
Dictionary in which to store important variables for vizualisation.
kwargs:
Loss specific arguments
"""
def _pre_call(self, is_train, storer):
if is_train:
self.n_train_steps += 1
if not is_train or self.n_train_steps % self.record_loss_every == 1:
storer = storer
else:
storer = None
return storer
class BetaHLoss(BaseLoss):
"""
Compute the Beta-VAE loss as in [1]
Parameters
----------
beta : float, optional
Weight of the kl divergence.
kwargs:
Additional arguments for `BaseLoss`, e.g. rec_dist`.
References
----------
[1] Higgins, Irina, et al. "beta-vae: Learning basic visual concepts with
a constrained variational framework." (2016).
"""
def __init__(self, beta=4, **kwargs):
super().__init__(**kwargs)
self.beta = beta
def __call__(self, data, recon_data, latent_dist, is_train, storer, **kwargs):
storer = self._pre_call(is_train, storer)
rec_loss = _reconstruction_loss(data, recon_data,
storer=storer,
distribution=self.rec_dist)
kl_loss = _kl_normal_loss(*latent_dist, storer)
anneal_reg = (linear_annealing(0, 1, self.n_train_steps, self.steps_anneal)
if is_train else 1)
loss = rec_loss + anneal_reg * (self.beta * kl_loss)
if storer is not None:
storer['loss'].append(loss.item())
return loss
class BetaBLoss(BaseLoss):
"""
Compute the Beta-VAE loss as in [1]
Parameters
----------
C_init : float, optional
Starting annealed capacity C.
C_fin : float, optional
Final annealed capacity C.
gamma : float, optional
Weight of the KL divergence term.
kwargs:
Additional arguments for `BaseLoss`, e.g. rec_dist`.
References
----------
[1] Burgess, Christopher P., et al. "Understanding disentangling in
$\beta$-VAE." arXiv preprint arXiv:1804.03599 (2018).
"""
def __init__(self, C_init=0., C_fin=20., gamma=100., **kwargs):
super().__init__(**kwargs)
self.gamma = gamma
self.C_init = C_init
self.C_fin = C_fin
def __call__(self, data, recon_data, latent_dist, is_train, storer, **kwargs):
storer = self._pre_call(is_train, storer)
rec_loss = _reconstruction_loss(data, recon_data,
storer=storer,
distribution=self.rec_dist)
kl_loss = _kl_normal_loss(*latent_dist, storer)
C = (linear_annealing(self.C_init, self.C_fin, self.n_train_steps, self.steps_anneal)
if is_train else self.C_fin)
loss = rec_loss + self.gamma * (kl_loss - C).abs()
if storer is not None:
storer['loss'].append(loss.item())
return loss
class FactorKLoss(BaseLoss):
"""
Compute the Factor-VAE loss as per Algorithm 2 of [1]
Parameters
----------
device : torch.device
gamma : float, optional
Weight of the TC loss term. `gamma` in the paper.
discriminator : disvae.discriminator.Discriminator
optimizer_d : torch.optim
kwargs:
Additional arguments for `BaseLoss`, e.g. rec_dist`.
References
----------
[1] Kim, Hyunjik, and Andriy Mnih. "Disentangling by factorising."
arXiv preprint arXiv:1802.05983 (2018).
"""
def __init__(self, device,
gamma=10.,
disc_kwargs={},
optim_kwargs=dict(lr=5e-5, betas=(0.5, 0.9)),
**kwargs):
super().__init__(**kwargs)
self.gamma = gamma
self.device = device
self.discriminator = Discriminator(**disc_kwargs).to(self.device)
self.optimizer_d = optim.Adam(self.discriminator.parameters(), **optim_kwargs)
def __call__(self, *args, **kwargs):
raise ValueError("Use `call_optimize` to also train the discriminator")
def call_optimize(self, data, model, optimizer, storer):
storer = self._pre_call(model.training, storer)
# factor-vae split data into two batches. In the paper they sample 2 batches
batch_size = data.size(dim=0)
half_batch_size = batch_size // 2
data = data.split(half_batch_size)
data1 = data[0]
data2 = data[1]
# Factor VAE Loss
recon_batch, latent_dist, latent_sample1 = model(data1)
rec_loss = _reconstruction_loss(data1, recon_batch,
storer=storer,
distribution=self.rec_dist)
kl_loss = _kl_normal_loss(*latent_dist, storer)
d_z = self.discriminator(latent_sample1)
# We want log(p_true/p_false). If not using logisitc regression but softmax
# then p_true = exp(logit_true) / Z; p_false = exp(logit_false) / Z
# so log(p_true/p_false) = logit_true - logit_false
tc_loss = (d_z[:, 0] - d_z[:, 1]).mean()
# with sigmoid (not good results) should be `tc_loss = (2 * d_z.flatten()).mean()`
anneal_reg = (linear_annealing(0, 1, self.n_train_steps, self.steps_anneal)
if model.training else 1)
vae_loss = rec_loss + kl_loss + anneal_reg * self.gamma * tc_loss
if storer is not None:
storer['loss'].append(vae_loss.item())
storer['tc_loss'].append(tc_loss.item())
if not model.training:
# don't backprop if evaluating
return vae_loss
# Compute VAE gradients
optimizer.zero_grad()
vae_loss.backward(retain_graph=True)
# Discriminator Loss
# Get second sample of latent distribution
latent_sample2 = model.sample_latent(data2)
z_perm = _permute_dims(latent_sample2).detach()
d_z_perm = self.discriminator(z_perm)
# Calculate total correlation loss
# for cross entropy the target is the index => need to be long and says
# that it's first output for d_z and second for perm
ones = torch.ones(half_batch_size, dtype=torch.long, device=self.device)
zeros = torch.zeros_like(ones)
d_tc_loss = 0.5 * (F.cross_entropy(d_z, zeros) + F.cross_entropy(d_z_perm, ones))
# with sigmoid would be :
# d_tc_loss = 0.5 * (self.bce(d_z.flatten(), ones) + self.bce(d_z_perm.flatten(), 1 - ones))
# TO-DO: check ifshould also anneals discriminator if not becomes too good ???
#d_tc_loss = anneal_reg * d_tc_loss
# Compute discriminator gradients
self.optimizer_d.zero_grad()
d_tc_loss.backward()
# Update at the end (since pytorch 1.5. complains if update before)
optimizer.step()
self.optimizer_d.step()
if storer is not None:
storer['discrim_loss'].append(d_tc_loss.item())
return vae_loss
class BtcvaeLoss(BaseLoss):
"""
Compute the decomposed KL loss with either minibatch weighted sampling or
minibatch stratified sampling according to [1]
Parameters
----------
n_data: int
Number of data in the training set
alpha : float
Weight of the mutual information term.
beta : float
Weight of the total correlation term.
gamma : float
Weight of the dimension-wise KL term.
is_mss : bool
Whether to use minibatch stratified sampling instead of minibatch
weighted sampling.
kwargs:
Additional arguments for `BaseLoss`, e.g. rec_dist`.
References
----------
[1] Chen, Tian Qi, et al. "Isolating sources of disentanglement in variational
autoencoders." Advances in Neural Information Processing Systems. 2018.
"""
def __init__(self, n_data, alpha=1., beta=6., gamma=1., is_mss=True, **kwargs):
super().__init__(**kwargs)
self.n_data = n_data
self.beta = beta
self.alpha = alpha
self.gamma = gamma
self.is_mss = is_mss # minibatch stratified sampling
def __call__(self, data, recon_batch, latent_dist, is_train, storer,
latent_sample=None):
storer = self._pre_call(is_train, storer)
batch_size, latent_dim = latent_sample.shape
rec_loss = _reconstruction_loss(data, recon_batch,
storer=storer,
distribution=self.rec_dist)
log_pz, log_qz, log_prod_qzi, log_q_zCx = _get_log_pz_qz_prodzi_qzCx(latent_sample,
latent_dist,
self.n_data,
is_mss=self.is_mss)
# I[z;x] = KL[q(z,x)||q(x)q(z)] = E_x[KL[q(z|x)||q(z)]]
mi_loss = (log_q_zCx - log_qz).mean()
# TC[z] = KL[q(z)||\prod_i z_i]
tc_loss = (log_qz - log_prod_qzi).mean()
# dw_kl_loss is KL[q(z)||p(z)] instead of usual KL[q(z|x)||p(z))]
dw_kl_loss = (log_prod_qzi - log_pz).mean()
anneal_reg = (linear_annealing(0, 1, self.n_train_steps, self.steps_anneal)
if is_train else 1)
# total loss
loss = rec_loss + (self.alpha * mi_loss +
self.beta * tc_loss +
anneal_reg * self.gamma * dw_kl_loss)
if storer is not None:
storer['loss'].append(loss.item())
storer['mi_loss'].append(mi_loss.item())
storer['tc_loss'].append(tc_loss.item())
storer['dw_kl_loss'].append(dw_kl_loss.item())
# computing this for storing and comparaison purposes
_ = _kl_normal_loss(*latent_dist, storer)
return loss
def _reconstruction_loss(data, recon_data, distribution="bernoulli", storer=None):
"""
Calculates the per image reconstruction loss for a batch of data. I.e. negative
log likelihood.
Parameters
----------
data : torch.Tensor
Input data (e.g. batch of images). Shape : (batch_size, n_chan,
height, width).
recon_data : torch.Tensor
Reconstructed data. Shape : (batch_size, n_chan, height, width).
distribution : {"bernoulli", "gaussian", "laplace"}
Distribution of the likelihood on the each pixel. Implicitely defines the
loss Bernoulli corresponds to a binary cross entropy (bse) loss and is the
most commonly used. It has the issue that it doesn't penalize the same
way (0.1,0.2) and (0.4,0.5), which might not be optimal. Gaussian
distribution corresponds to MSE, and is sometimes used, but hard to train
ecause it ends up focusing only a few pixels that are very wrong. Laplace
distribution corresponds to L1 solves partially the issue of MSE.
storer : dict
Dictionary in which to store important variables for vizualisation.
Returns
-------
loss : torch.Tensor
Per image cross entropy (i.e. normalized per batch but not pixel and
channel)
"""
batch_size, n_chan, height, width = recon_data.size()
is_colored = n_chan == 3
if distribution == "bernoulli":
loss = F.binary_cross_entropy(recon_data, data, reduction="sum")
elif distribution == "gaussian":
# loss in [0,255] space but normalized by 255 to not be too big
loss = F.mse_loss(recon_data * 255, data * 255, reduction="sum") / 255
elif distribution == "laplace":
# loss in [0,255] space but normalized by 255 to not be too big but
# multiply by 255 and divide 255, is the same as not doing anything for L1
loss = F.l1_loss(recon_data, data, reduction="sum")
loss = loss * 3 # emperical value to give similar values than bernoulli => use same hyperparam
loss = loss * (loss != 0) # masking to avoid nan
else:
assert distribution not in RECON_DIST
raise ValueError("Unkown distribution: {}".format(distribution))
loss = loss / batch_size
if storer is not None:
storer['recon_loss'].append(loss.item())
return loss
def _kl_normal_loss(mean, logvar, storer=None):
"""
Calculates the KL divergence between a normal distribution
with diagonal covariance and a unit normal distribution.
Parameters
----------
mean : torch.Tensor
Mean of the normal distribution. Shape (batch_size, latent_dim) where
D is dimension of distribution.
logvar : torch.Tensor
Diagonal log variance of the normal distribution. Shape (batch_size,
latent_dim)
storer : dict
Dictionary in which to store important variables for vizualisation.
"""
latent_dim = mean.size(1)
# batch mean of kl for each latent dimension
latent_kl = 0.5 * (-1 - logvar + mean.pow(2) + logvar.exp()).mean(dim=0)
total_kl = latent_kl.sum()
if storer is not None:
storer['kl_loss'].append(total_kl.item())
for i in range(latent_dim):
storer['kl_loss_' + str(i)].append(latent_kl[i].item())
return total_kl
def _permute_dims(latent_sample):
"""
Implementation of Algorithm 1 in ref [1]. Randomly permutes the sample from
q(z) (latent_dist) across the batch for each of the latent dimensions (mean
and log_var).
Parameters
----------
latent_sample: torch.Tensor
sample from the latent dimension using the reparameterisation trick
shape : (batch_size, latent_dim).
References
----------
[1] Kim, Hyunjik, and Andriy Mnih. "Disentangling by factorising."
arXiv preprint arXiv:1802.05983 (2018).
"""
perm = torch.zeros_like(latent_sample)
batch_size, dim_z = perm.size()
for z in range(dim_z):
pi = torch.randperm(batch_size).to(latent_sample.device)
perm[:, z] = latent_sample[pi, z]
return perm
def linear_annealing(init, fin, step, annealing_steps):
"""Linear annealing of a parameter."""
if annealing_steps == 0:
return fin
assert fin > init
delta = fin - init
annealed = min(init + delta * step / annealing_steps, fin)
return annealed
# Batch TC specific
# TO-DO: test if mss is better!
def _get_log_pz_qz_prodzi_qzCx(latent_sample, latent_dist, n_data, is_mss=True):
batch_size, hidden_dim = latent_sample.shape
# calculate log q(z|x)
log_q_zCx = log_density_gaussian(latent_sample, *latent_dist).sum(dim=1)
# calculate log p(z)
# mean and log var is 0
zeros = torch.zeros_like(latent_sample)
log_pz = log_density_gaussian(latent_sample, zeros, zeros).sum(1)
mat_log_qz = matrix_log_density_gaussian(latent_sample, *latent_dist)
if is_mss:
# use stratification
log_iw_mat = log_importance_weight_matrix(batch_size, n_data).to(latent_sample.device)
mat_log_qz = mat_log_qz + log_iw_mat.view(batch_size, batch_size, 1)
log_qz = torch.logsumexp(mat_log_qz.sum(2), dim=1, keepdim=False)
log_prod_qzi = torch.logsumexp(mat_log_qz, dim=1, keepdim=False).sum(1)
return log_pz, log_qz, log_prod_qzi, log_q_zCx
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