%reload_ext tensorboard
%reload_ext autoreload
Flow-based Variational Autoencoders¶
import os
import time
import math
import torch
import numpy as np
import torch.nn as nn
import pytorch_lightning as pl
import torch.nn.functional as F
import torch.distributions as tdist
import torchdyn.nn.node_layers as tdnl
from enum import Enum
from joblib import dump, load
from sklearn.decomposition import PCA
from pdmtut.core import GenerativeModel
from pytorch_lightning import loggers as pl_loggers
from regilib.core.distributions import MultivariateNormal
from regilib.core.dynamics.dynamics import RegularisedDynamics
from regilib.core.dynamics.dynamical_state import DynamicalState
from regilib.core.invertible_modules import NormalisingFlow
from regilib.core.invertible_modules.bijective import ContinuousAmbientFlow
from regilib.core.invertible_modules.stochastic import VAE
store_results = True
load_models = True
Introduction¶
Implementation¶
# 9_FVAE_trainer.py was used for the training of this model
class FlowVAE(NormalisingFlow, pl.LightningModule, GenerativeModel):
class State(Enum):
"""State that the model is in."""
MANIFOLD_LEARNING = 1
DENSITY_LEARNING = 2
INFERENCE = 3
class Encoder(nn.Module):
"""Encoder q(z|x)"""
def __init__(self):
super().__init__()
self.dec1 = nn.Linear(3, 64)
self.decbn1 = nn.BatchNorm1d(num_features=64)
self.dec2 = nn.Linear(64, 128)
self.decbn2 = nn.BatchNorm1d(num_features=128)
self.dec3 = nn.Linear(128, 128)
self.decbn3 = nn.BatchNorm1d(num_features=128)
# μ
self.mu_dec4 = nn.Linear(128, 64)
self.mu_dec5 = nn.Linear(64, 2)
# log σ
self.log_var_dec4 = nn.Linear(128, 64)
self.log_var_dec5 = nn.Linear(64, 2)
def forward(self, x, sample):
x = F.elu(self.decbn1(self.dec1(x)))
x = F.elu(self.decbn2(self.dec2(x)))
x = F.elu(self.decbn3(self.dec3(x)))
# μ
mu = F.elu(self.mu_dec4(x))
mu = self.mu_dec5(mu)
# log σ
log_var = F.elu(self.log_var_dec4(x))
log_var = self.log_var_dec5(log_var)
dist = tdist.Normal(mu, torch.exp(log_var/2))
if not sample: z = mu
else: z = dist.rsample()
log_qz = dist.log_prob(z).sum(-1)
return log_qz, z
class Decoder(nn.Module):
"""Decoder p(x|z)"""
def __init__(self, noise_std):
super().__init__()
self.error_dist = MultivariateNormal(
torch.tensor([0., 0., 0.]), noise_std * torch.eye(3, 3))
self.dec1 = nn.Linear(2, 64)
self.decbn1 = nn.BatchNorm1d(num_features=64)
self.dec2 = nn.Linear(64, 128)
self.decbn2 = nn.BatchNorm1d(num_features=128)
self.dec3 = nn.Linear(128, 128)
self.decbn3 = nn.BatchNorm1d(num_features=128)
self.dec4 = nn.Linear(128, 64)
self.dec5 = nn.Linear(64, 3)
def forward(self, z, context):
x = F.elu(self.decbn1(self.dec1(z)))
x = F.elu(self.decbn2(self.dec2(x)))
x = F.elu(self.decbn3(self.dec3(x)))
x = F.elu(self.dec4(x))
x = self.dec5(x)
if context is None: return x
log_px = self.error_dist.log_prob(x - context)
return log_px, x
class FunctionDynamics(nn.Module):
def __init__(self):
super().__init__()
self._in_channels = 2
self._out_channels = 2
# expected format: N x (C * L)
# +1 for time
self.fc1 = nn.Linear(self._in_channels + 1, 128)
self.fc2 = nn.Linear(128, 256)
self.fc3 = nn.Linear(256, 256)
self.fc4 = nn.Linear(256, 128)
self.fc5 = nn.Linear(128, self._out_channels)
@property
def in_channels(self):
return self._in_channels
@property
def out_channels(self):
return self._out_channels
def forward(self, ds):
x = torch.cat([ds.state, ds.t], -1)
x = F.tanh(self.fc1(x))
x = F.tanh(self.fc2(x))
x = F.tanh(self.fc3(x))
x = F.tanh(self.fc4(x))
x = self.fc5(x)
return x
def __init__(self, noise_std, input_dimensions=3):
super().__init__(
base_distribution=MultivariateNormal(torch.zeros(2), torch.eye(2)))
self.input_dimensions = input_dimensions
# state=[l, e, n | state]
self.vae1 = VAE(FlowVAE.Encoder(), FlowVAE.Decoder(noise_std=noise_std))
self.aug1 = tdnl.Augmenter(augment_dims=3)
self.af1 = ContinuousAmbientFlow(
dynamics=RegularisedDynamics(fdyn=FlowVAE.FunctionDynamics()),
sensitivity='autograd', default_n_steps=5
)
self.state = FlowVAE.State.INFERENCE
# Region NormalisingFlow
def forward(self, x, ds_context=None, af_estimate=True, vae_sample=False):
ds = x.clone() if isinstance(x, DynamicalState) else DynamicalState(state=x)
ds = super().forward(ds)
# TODO: check how we can compute the log prob in forward direction
ds = self.af1.dynamics.update_ds(ds, self.aug1(ds['state']))
ds = self.af1.forward(ds, estimate_trace=af_estimate)
ds = self.vae1.forward(ds, sample=vae_sample)
return ds
def inverse(self, x, af_estimate=True, vae_sample=False):
ds = x.clone() if isinstance(x, DynamicalState) else DynamicalState(state=x)
ds = self.vae1.inverse(ds, sample=vae_sample)
ds = self.af1.dynamics.update_ds(ds, self.aug1(ds['state']))
ds = self.af1.inverse(ds, estimate_trace=af_estimate)
ds = super().inverse(ds)
return ds
# Region GenerativeModel
def encode(self, X):
ds = self.inverse(X)
return ds['state'].cpu().detach()
def decode(self, z):
ds = self.forward(z)
return ds['state'].cpu().detach()
def save(self, path):
torch.save(self, os.path.join(path, 'model.pt'))
def load(path):
return torch.load(os.path.join(path, 'model.pt'))
def save_exists(path):
return (
os.path.isfile(os.path.join(path, 'model.pt')))
def log_likelihood(self, x, n_mc_samples):
# TODO: do this more efficiently
# draw MC samples
log_probs = []
for i in range(n_mc_samples):
ds = x.clone() if isinstance(x, DynamicalState) else DynamicalState(state=x)
# log(p(x|z)/q(z|x))
ds = self.vae1.inverse(ds, sample=True)
# log |det J(z)|
ds = self.af1.dynamics.update_ds(ds, self.aug1(ds['state']))
ds = self.af1.inverse(ds, estimate_trace=False)
# log p(z)
ds = super().inverse(ds)
# ELBO ≈ log p(z) + log |det J(z)| + log(p(x|z)/q(z|x)), with z ~ q(z|x)
log_probs.append(ds.log_prob.cpu().detach())
log_prob = torch.stack(log_probs).mean(0)
return log_prob
def sample_posterior(self, n_samples):
ds = super().sample_posterior(n_samples)
return ds['state'].detach().cpu()
def fit_model(self, X, X_val=None, path=None):
start_time = time.time()
if path is None:
tb_logger = False
checkpoint_callback=False
#MANIFOLD PHASE
self.state = FlowVAE.State.MANIFOLD_LEARNING
self.vae1.freeze(False); self.af1.freeze(True)
if path is not None:
tb_logger = pl_loggers.TensorBoardLogger(
os.path.join(path, 'mp'), version=0)
checkpoint_callback=True
trainer = pl.Trainer(
max_epochs=5000, gpus=1, logger=tb_logger,
checkpoint_callback=checkpoint_callback
)
trainer.fit(
self, train_dataloaders=X, val_dataloaders=X_val)
# DENSITY PHASE
self.state = FlowVAE.State.DENSITY_LEARNING
self.vae1.freeze(True); self.af1.freeze(False)
if path is not None:
tb_logger = pl_loggers.TensorBoardLogger(
os.path.join(path, 'dp/'), version=0)
checkpoint_callback=True
trainer = pl.Trainer(
max_epochs=8000, gpus=1, logger=tb_logger,
checkpoint_callback=checkpoint_callback
)
trainer.fit(
self, train_dataloaders=X, val_dataloaders=X_val)
# INFERENCE PHASE
self.state = FlowVAE.State.INFERENCE
elapsed_time = time.time() - start_time
if path is not None:
with open(os.path.join(path, 'training_time.txt'), 'w') as f:
f.write(str(elapsed_time))
def train_step_g(self, x):
# ML
ds = x.clone() if isinstance(
x, DynamicalState) else DynamicalState(state=x)
ds = self.vae1.inverse(ds, sample=True)
ds = super().inverse(ds)
loss = -ds.log_prob.sum() / (x.shape[0]*x.shape[1])
return loss
def train_step_h(self, x):
# DE
lambda_e, lambda_n = 0.01, 0.01
ds_z = self.inverse(x, af_estimate=True, vae_sample=False)
# minimise negative log likelihood and energy
loss = (-ds_z.log_prob + lambda_e * ds_z.e[:, 0] + lambda_n * ds_z.n[:, 0]
).sum() / (x.shape[0]*x.shape[1])
return loss
def training_step(self, batch, batch_idx):
x = batch[0]
if self.state is FlowVAE.State.MANIFOLD_LEARNING:
loss = self.train_step_g(x)
if self.state is FlowVAE.State.DENSITY_LEARNING:
loss = self.train_step_h(x)
self.log('train_loss', loss)
return {'loss': loss}
def validation_step(self, batch, batch_idx):
x = batch[0]
if self.state is FlowVAE.State.MANIFOLD_LEARNING:
loss = self.train_step_g(x)
if self.state is FlowVAE.State.DENSITY_LEARNING:
loss = self.train_step_h(x)
self.log('validation_loss', loss)
return {'val_loss': loss}
def configure_optimizers(self):
if self.state is FlowVAE.State.MANIFOLD_LEARNING:
optimizer = torch.optim.Adam(self.parameters(), lr=1e-2)
return {
'optimizer': optimizer,
'lr_scheduler':
torch.optim.lr_scheduler.ReduceLROnPlateau(
optimizer, min_lr=1e-8, factor=0.5, verbose=True,
patience=500
), 'monitor': 'train_loss'
}
if self.state is FlowVAE.State.DENSITY_LEARNING:
return torch.optim.Adam(self.parameters(), lr=9e-5)
def __str__(self):
return 'fvae'
Experiment 1: swiss roll¶
import pyvista as pv
from pdmtut.datasets import SwissRoll
pv.set_plot_theme("document")
model_save_path = '../results/swiss_roll/fvae'
if store_results:
result_save_path = '../results/swiss_roll/fvae'
pv.set_jupyter_backend('None')
else:
pv.set_jupyter_backend('ipygany')
result_save_path = None
dataset = SwissRoll(n_samples=100**2, seed=11)
if load_models and FlowVAE.save_exists(model_save_path):
model = FlowVAE.load(model_save_path)
else:
model = FlowVAE(noise_std=1e-2)
model.fit_model(
X=dataset.train_loader(batch_size=512),
X_val=dataset.validation_loader(batch_size=512),
path=result_save_path)
if store_results:
model.save(model_save_path)
model = model.eval()
%tensorboard --logdir ../results/swiss_roll/fvae
Reusing TensorBoard on port 6008 (pid 112026), started 0:09:19 ago. (Use '!kill 112026' to kill it.)
Input Representation¶
from pdmtut.vis import plot_representation
z = model.encode(dataset.X)
z_extremes = model.encode(dataset.y_extremes)
z_extremes = torch.cat([z_extremes, z_extremes[[1,2]]])
/home/bawaw/.conda/envs/pdm_tutorial/lib/python3.8/site-packages/torch/nn/functional.py:1795: UserWarning: nn.functional.tanh is deprecated. Use torch.tanh instead.
warnings.warn("nn.functional.tanh is deprecated. Use torch.tanh instead.")
plot_representation(z.numpy(), index_colors=dataset.index_colors, z_extremes=z_extremes, interpolate_background=True, root=result_save_path)
Input Reconstruction¶
from pdmtut.vis import plot_reconstruction
z = model.encode(dataset.X)
x = model.decode(z)
/home/bawaw/.conda/envs/pdm_tutorial/lib/python3.8/site-packages/torch/nn/functional.py:1795: UserWarning: nn.functional.tanh is deprecated. Use torch.tanh instead.
warnings.warn("nn.functional.tanh is deprecated. Use torch.tanh instead.")
mse = (dataset.unnormalise_scale(dataset.X) - dataset.unnormalise_scale(x)).pow(2).sum(-1).mean()
if result_save_path is not None:
with open(os.path.join(result_save_path, 'reconstruction.txt'), 'w') as f:
f.write(str(mse.item()))
mse
tensor(0.9598)
plot_reconstruction(dataset.unnormalise_scale(x).numpy(), dataset.index_colors, root=result_save_path)
Density Estimation¶
from pdmtut.vis import plot_density
from regilib.core.invertible_modules.bijective import AffineTransform
# compute log_likelihood in [-1, 1]^3 space
log_likelihood = model.log_likelihood(dataset.X, 20)
# unnormalise the data and compute the change in density
un_normalise = AffineTransform(dataset._mean, 1/dataset._std)
data = un_normalise.forward(DynamicalState(state=dataset.X.clone().requires_grad_(True), log_prob=log_likelihood.clone()))
/home/bawaw/.conda/envs/pdm_tutorial/lib/python3.8/site-packages/torch/nn/functional.py:1795: UserWarning: nn.functional.tanh is deprecated. Use torch.tanh instead.
warnings.warn("nn.functional.tanh is deprecated. Use torch.tanh instead.")
data_log_likelihood = data.log_prob.mean()
if result_save_path is not None:
with open(os.path.join(result_save_path, 'density.txt'), 'w') as f:
f.write(str(data_log_likelihood.item()))
data_log_likelihood
tensor(-8.8009)
plot_density(data.state.detach().numpy(), data.log_prob.detach().numpy(), root=result_save_path)
Generate Samples¶
from pdmtut.vis import plot_generated_samples
from regilib.core.invertible_modules.bijective import AffineTransform
generated_samples = model.sample_posterior(100**2)
generated_samples_log_likelihood = model.log_likelihood(generated_samples, 20)
# unnormalise the data and compute the change in density
un_normalise = AffineTransform(dataset._mean, 1/dataset._std)
data = un_normalise.forward(DynamicalState(state=generated_samples.clone().requires_grad_(True), log_prob=generated_samples_log_likelihood.clone()))
plot_generated_samples(data.state.detach().numpy(), data.log_prob.detach().numpy(), root=result_save_path)
Interpolation¶
from pdmtut.vis import plot_interpolation
from scipy.interpolate import interp1d
z_extremes = model.encode(dataset.y_extremes)
uniform_state, uniform_log_prob, _ = dataset.sample_points_uniformly(n_samples=100**2, seed=11)
linfit1 = interp1d([1,20], z_extremes[:2].numpy(), axis=0)
linfit2 = interp1d([1,20], z_extremes[2:].numpy(), axis=0)
linfit3 = interp1d([1,20], z_extremes[[1,2]].numpy(), axis=0)
interpolated_points_1 = model.decode(torch.Tensor(linfit1(np.arange(1,21))))
interpolated_points_2 = model.decode(torch.Tensor(linfit2(np.arange(1,21))))
interpolated_points_3 = model.decode(torch.Tensor(linfit3(np.arange(1,21))))
/home/bawaw/.conda/envs/pdm_tutorial/lib/python3.8/site-packages/torch/functional.py:445: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at /opt/conda/conda-bld/pytorch_1639180588308/work/aten/src/ATen/native/TensorShape.cpp:2157.)
return _VF.meshgrid(tensors, **kwargs) # type: ignore[attr-defined]
plot_interpolation(
dataset.unnormalise_scale(interpolated_points_1).numpy(),
dataset.unnormalise_scale(interpolated_points_2).numpy(),
dataset.unnormalise_scale(interpolated_points_3).numpy(),
uniform_state.detach().view(100, 100, 3).permute(2, 0, 1).numpy(),
uniform_log_prob.numpy(), root=result_save_path
)
Extra¶
from matplotlib import pyplot as plt
from pdmtut.vis import plot_representation
ds = DynamicalState(state=dataset.X)
ds = model.vae1.inverse(ds, sample=False)
fig = plt.figure()
plot_representation(ds.state.detach().numpy(), index_colors=dataset.index_colors, axis=fig)
plt.savefig(os.path.join(result_save_path, 'vae_base_representation.png'))
<Figure size 432x288 with 0 Axes>
