More Machine Learning

But first, a detour

Procedural Generation

Algorithmically making "content"

Similar in distribution of "features" 

Generate Similar Output Based on a Single Input

https://github.com/mxgmn/WaveFunctionCollapse

Wave Function Collapse

https://github.com/mxgmn/WaveFunctionCollapse

Wave Function Collapse

Input:

  • A set of \(t\) "tiles"
  • Their probability w.r.t the entire
  • Adjacency rules
  • (optional) Additional symmetry
  • Output size \(w\) and \(h\)

Algorithm:

  1. Initialize states (a grid of \(w\times h \times t\) booleans)
  2. Choose minimum entropy cell, and "collapse" to a valid state (if no such cell, finish)
  3. Propogate constraints 
  4. Goto 2

https://github.com/mxgmn/WaveFunctionCollapse

"Overlapping Model"

Catalog the frequency of appearance, and the compatibility with neighbours of each tile

https://github.com/mxgmn/WaveFunctionCollapse

Wave Function Collapse

https://github.com/mxgmn/WaveFunctionCollapse

Return to PyTorch

Last week we talked about tensors, operations on tensors and autograd

Let's talk about some higher level functionality now

Modules

A Module is the "Base class for all neural network modules"

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

They provide a bit of "magic" behind the scenes (registration of parameters)

An Example Network

Generator from DC-GAN (Deep Convolutional GAN)

https://pytorch.org/tutorials/beginner/dcgan_faces_tutorial.html

Loss Functions

https://pytorch.org/docs/stable/nn.html#loss-functions

Loss functions model the problem you're trying to solve

import torch.nn as nn
import torch.nn.functional as F


model = Model(...)

predicted = model(inputs)

loss = LossFunc(predicted, expected)

loss.backwards()

Network contains computed gradient after \(backwards\) call.

Optimizers

https://pytorch.org/docs/stable/optim.html

Optimizers optimize....

import torch.nn as nn
import torch.nn.functional as F

optimizer = torch.optim.SGD({model_parameters}, {optim_parameters})

... code to compute loss ...

loss.backwards()
optimizer.step()

These handle all the heavy lifting for optimization, you setup the gradient, the optimizer adjusts the parameters

A More Complete Example

Can we reproduce WFC quality results with a generative network?

Generator

Convolutional: 128 -> (64, 64, 95) 

95 Unique tiles

Flowers

Discriminator

Convolutional: 128 -> (64, 64, 3) 

Reverse of Generator

Reverse of Generator

Dense 

Dense 

Generated 10,000 examples  in both formats.

DC-GAN


# Initialize generator and discriminator
generator = Generator()
discriminator = Discriminator()

generator.cuda()
discriminator.cuda()

lr = .0001
b1 = 0.5
b2 = .999

# Optimizers
optimizer_G = torch.optim.Adam(generator.parameters(), lr=lr, betas=(b1, b2))
optimizer_D = torch.optim.Adam(discriminator.parameters(), lr=lr, betas=(b1, b2))

# Loss function
loss_fn = nn.BCELoss()

An Example Network

Generator from DC-GAN (Deep Convolutional GAN)

An Example Network

Discriminator from DC-GAN (Deep Convolutional GAN)

Training Loop


for epoch in range(epochs):
    for i, data in enumerate(dataloader, 0):
        real_imgs = data[0].float().to(0)
        
        # Train generator
        optimizer_G.zero_grad()

        # Sample noise as generator input
        z = Variable(Tensor(np.random.normal(0, 1, (real_imgs.shape[0], latent_dim))))

        real_labels = torch.ones((real_imgs.shape[0],), requires_grad=False).to(0) 
        fake_labels = torch.zeros((real_imgs.shape[0],), requires_grad=False).to(0) 

        # Generate a batch of images
        gen_imgs = generator(z)

        # Loss measures generator's ability to fool the discriminator
        g_loss = loss_fn(discriminator(gen_imgs).view(-1), real_labels)
        g_loss.backward()
        
        optimizer_G.step()

        # ...

Training Loop


for epoch in range(epochs):
    for i, data in enumerate(dataloader, 0):
        # ... previous slide, train generator
        
        # Train Discriminator
        optimizer_D.zero_grad()

        # Measure discriminator's ability to classify real from generated samples
        real_loss = loss_fn(discriminator(real_imgs).view(-1), real_labels)
        fake_loss = loss_fn(discriminator(gen_imgs.detach()).view(-1), fake_labels)
        d_loss = (real_loss + fake_loss) / 2

        d_loss.backward()
        optimizer_D.step()

Wave Function Collapse (RGB) 

Wave Function Collapse (RGB) 

Wave Function Collapse (1-hot state) 

Wave Function Collapse (1-hot state) 

Definitely worse...

Wave Function Collapse (Dense WGAN) 

Wave Function Collapse (Dense WGAN) 

Wave-function Collapse

By Joshua Horacsek

Wave-function Collapse

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