Growing Unsupervised Neural Cellular Automata ¶

Installation¶

You will need Python 3.11 or later, and a working JAX installation. For example, you can install JAX with:

In [ ]:

%pip install -U "jax[cuda]"

%pip install -U "jax[cuda]"

Then, install CAX from PyPi:

In [ ]:

%pip install -U "cax[examples]"

%pip install -U "cax[examples]"

Import¶

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import jax
import jax.numpy as jnp
import mediapy
import optax
import torchvision
from flax import nnx
from tqdm.auto import tqdm

from cax.core import ComplexSystem, Input, State
from cax.core.perceive import ConvPerceive, grad_kernel, identity_kernel
from cax.core.update import NCAUpdate
from cax.nn.pool import Pool
from cax.nn.vae import Encoder
from cax.utils import clip_and_uint8

import jax import jax.numpy as jnp import mediapy import optax import torchvision from flax import nnx from tqdm.auto import tqdm from cax.core import ComplexSystem, Input, State from cax.core.perceive import ConvPerceive, grad_kernel, identity_kernel from cax.core.update import NCAUpdate from cax.nn.pool import Pool from cax.nn.vae import Encoder from cax.utils import clip_and_uint8

Configuration¶

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seed = 0

spatial_dims = (28, 28)
features = (1, 32, 32)
latent_size = 8

channel_size = 32
num_kernels = 3
hidden_size = 256
cell_dropout_rate = 0.5

num_steps = 64
pool_size = 1_024
batch_size = 8
learning_rate = 1e-3

key = jax.random.key(seed)
rngs = nnx.Rngs(seed)

seed = 0 spatial_dims = (28, 28) features = (1, 32, 32) latent_size = 8 channel_size = 32 num_kernels = 3 hidden_size = 256 cell_dropout_rate = 0.5 num_steps = 64 pool_size = 1_024 batch_size = 8 learning_rate = 1e-3 key = jax.random.key(seed) rngs = nnx.Rngs(seed)

Dataset¶

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# Load MNIST dataset
ds_train = torchvision.datasets.MNIST(root="./data", train=True, download=True)
ds_test = torchvision.datasets.MNIST(root="./data", train=False, download=True)

# Convert to jax.Array
y_train = jnp.array([y.resize(spatial_dims) for y, _ in ds_train])[..., None] / 255
y_test = jnp.array([y.resize(spatial_dims) for y, _ in ds_test])[..., None] / 255

# Visualize
mediapy.show_images(y_train[:8], width=128, height=128)

# Load MNIST dataset ds_train = torchvision.datasets.MNIST(root="./data", train=True, download=True) ds_test = torchvision.datasets.MNIST(root="./data", train=False, download=True) # Convert to jax.Array y_train = jnp.array([y.resize(spatial_dims) for y, _ in ds_train])[..., None] / 255 y_test = jnp.array([y.resize(spatial_dims) for y, _ in ds_test])[..., None] / 255 # Visualize mediapy.show_images(y_train[:8], width=128, height=128)

Instantiate system¶

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class GrowingUnsupervisedNCA(ComplexSystem):
	"""Unsupervised Neural Cellular Automata class."""

	def __init__(self, *, rngs: nnx.Rngs):
		"""Initialize Unsupervised NCA.

		Args:
			rngs: rng key.

		"""
		self.perceive = ConvPerceive(
			channel_size=channel_size,
			perception_size=num_kernels * channel_size,
			feature_group_count=channel_size,
			rngs=rngs,
		)
		self.update = NCAUpdate(
			channel_size=channel_size,
			perception_size=latent_size + num_kernels * channel_size,
			hidden_layer_sizes=(hidden_size,),
			cell_dropout_rate=cell_dropout_rate,
			zeros_init=True,
			rngs=rngs,
		)
		self.encoder = Encoder(
			spatial_dims=spatial_dims,
			features=features,
			latent_size=latent_size,
			rngs=rngs,
		)

		# Initialize kernel with sobel filters
		kernel = jnp.concatenate([identity_kernel(ndim=2), grad_kernel(ndim=2)], axis=-1)
		kernel = jnp.expand_dims(jnp.concatenate([kernel] * channel_size, axis=-1), axis=-2)
		self.perceive.conv.kernel.value = kernel

	def encode(self, x):
		"""Encode image into latent space."""
		mean, logvar = self.encoder(x)
		return self.encoder.reparameterize(mean, logvar)

	def _step(self, state: State, input: Input | None = None, *, sow: bool = False) -> State:
		# Broadcast the input vector to match the state shape
		input_shape = (*state.shape[:-1], input.shape[-1])
		input = jnp.broadcast_to(input[..., None, None, :], input_shape)

		# Step
		perception = self.perceive(state)
		next_state = self.update(state, perception, input)

		if sow:
			self.sow(nnx.Intermediate, "state", next_state)

		return next_state

	@nnx.jit
	def render(self, state):
		"""Render state to RGB."""
		gray = state[..., -1:]
		rgb = jnp.repeat(gray, 3, axis=-1)

		# Clip values to valid range and convert to uint8
		return clip_and_uint8(rgb)

class GrowingUnsupervisedNCA(ComplexSystem): """Unsupervised Neural Cellular Automata class.""" def __init__(self, *, rngs: nnx.Rngs): """Initialize Unsupervised NCA. Args: rngs: rng key. """ self.perceive = ConvPerceive( channel_size=channel_size, perception_size=num_kernels * channel_size, feature_group_count=channel_size, rngs=rngs, ) self.update = NCAUpdate( channel_size=channel_size, perception_size=latent_size + num_kernels * channel_size, hidden_layer_sizes=(hidden_size,), cell_dropout_rate=cell_dropout_rate, zeros_init=True, rngs=rngs, ) self.encoder = Encoder( spatial_dims=spatial_dims, features=features, latent_size=latent_size, rngs=rngs, ) # Initialize kernel with sobel filters kernel = jnp.concatenate([identity_kernel(ndim=2), grad_kernel(ndim=2)], axis=-1) kernel = jnp.expand_dims(jnp.concatenate([kernel] * channel_size, axis=-1), axis=-2) self.perceive.conv.kernel.value = kernel def encode(self, x): """Encode image into latent space.""" mean, logvar = self.encoder(x) return self.encoder.reparameterize(mean, logvar) def _step(self, state: State, input: Input | None = None, *, sow: bool = False) -> State: # Broadcast the input vector to match the state shape input_shape = (*state.shape[:-1], input.shape[-1]) input = jnp.broadcast_to(input[..., None, None, :], input_shape) # Step perception = self.perceive(state) next_state = self.update(state, perception, input) if sow: self.sow(nnx.Intermediate, "state", next_state) return next_state @nnx.jit def render(self, state): """Render state to RGB.""" gray = state[..., -1:] rgb = jnp.repeat(gray, 3, axis=-1) # Clip values to valid range and convert to uint8 return clip_and_uint8(rgb)

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cs = GrowingUnsupervisedNCA(rngs=rngs)

cs = GrowingUnsupervisedNCA(rngs=rngs)

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params = nnx.state(cs, nnx.Param)
print("Number of params:", sum(x.size for x in jax.tree.leaves(params)))

params = nnx.state(cs, nnx.Param) print("Number of params:", sum(x.size for x in jax.tree.leaves(params)))

Sample initial state¶

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def sample_state(key):
	"""Sample a state with a single alive cell."""
	# Init state
	state = jnp.zeros(spatial_dims + (channel_size,))
	mid = tuple(size // 2 for size in spatial_dims)

	# Set the center cell to alive
	state = state.at[mid[0], mid[1], -1].set(1.0)

	# Sample a random target y
	y_idx = jax.random.choice(key, y_train.shape[0])
	return state, y_idx

def sample_state(key): """Sample a state with a single alive cell.""" # Init state state = jnp.zeros(spatial_dims + (channel_size,)) mid = tuple(size // 2 for size in spatial_dims) # Set the center cell to alive state = state.at[mid[0], mid[1], -1].set(1.0) # Sample a random target y y_idx = jax.random.choice(key, y_train.shape[0]) return state, y_idx

Train¶

Pool¶

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key, subkey = jax.random.split(key)

keys = jax.random.split(subkey, pool_size)
state, y_idx = jax.vmap(lambda key: sample_state(key))(keys)

pool = Pool.create({"state": state, "y_idx": y_idx})

key, subkey = jax.random.split(key) keys = jax.random.split(subkey, pool_size) state, y_idx = jax.vmap(lambda key: sample_state(key))(keys) pool = Pool.create({"state": state, "y_idx": y_idx})

Optimizer¶

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lr_sched = optax.linear_schedule(
	init_value=learning_rate, end_value=0.1 * learning_rate, transition_steps=50_000
)

optimizer = optax.chain(
	optax.clip_by_global_norm(1.0),
	optax.adam(learning_rate=lr_sched),
)

grad_params = nnx.All(nnx.Param, nnx.Any(nnx.PathContains("update"), nnx.PathContains("encoder")))
optimizer = nnx.Optimizer(cs, optimizer, wrt=grad_params)

lr_sched = optax.linear_schedule( init_value=learning_rate, end_value=0.1 * learning_rate, transition_steps=50_000 ) optimizer = optax.chain( optax.clip_by_global_norm(1.0), optax.adam(learning_rate=lr_sched), ) grad_params = nnx.All(nnx.Param, nnx.Any(nnx.PathContains("update"), nnx.PathContains("encoder"))) optimizer = nnx.Optimizer(cs, optimizer, wrt=grad_params)

Loss¶

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def mse(state, y):
	"""Mean Squared Error."""
	return jnp.mean(jnp.square(state[..., -1:] - y))

def mse(state, y): """Mean Squared Error.""" return jnp.mean(jnp.square(state[..., -1:] - y))

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@nnx.jit
def loss_fn(cs, state, y, key):
	"""Loss function."""
	z = cs.encode(y)

	state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None})
	nnx.split_rngs(splits=batch_size)(
		nnx.vmap(
			lambda cs, state, z: cs(state, z, num_steps=num_steps, sow=True),
			in_axes=(state_axes, 0, 0),
		)
	)(cs, state, z)

	# Get intermediate states
	intermediates = nnx.pop(cs, nnx.Intermediate)
	state = intermediates.state.value[0]

	idx = jax.random.randint(key, (batch_size,), num_steps // 2, num_steps)
	state = state[jnp.arange(batch_size), idx]

	loss = mse(state, y)
	return loss, state

@nnx.jit def loss_fn(cs, state, y, key): """Loss function.""" z = cs.encode(y) state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None}) nnx.split_rngs(splits=batch_size)( nnx.vmap( lambda cs, state, z: cs(state, z, num_steps=num_steps, sow=True), in_axes=(state_axes, 0, 0), ) )(cs, state, z) # Get intermediate states intermediates = nnx.pop(cs, nnx.Intermediate) state = intermediates.state.value[0] idx = jax.random.randint(key, (batch_size,), num_steps // 2, num_steps) state = state[jnp.arange(batch_size), idx] loss = mse(state, y) return loss, state

Train step¶

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@nnx.jit
def train_step(cs, optimizer, pool, key):
	"""Train step."""
	sample_key, sample_state_key, loss_key = jax.random.split(key, 3)

	# Sample from pool
	pool_idx, batch = pool.sample(sample_key, batch_size=batch_size)
	current_state = batch["state"]
	current_y_idx = batch["y_idx"]
	current_y = y_train[current_y_idx]

	# Sort by descending loss
	sort_idx = jnp.argsort(jax.vmap(mse)(current_state, current_y), descending=True)
	pool_idx = pool_idx[sort_idx]
	current_state = current_state[sort_idx]
	current_y_idx = current_y_idx[sort_idx]

	# Sample a new state to replace the worst
	new_state, new_y_idx = sample_state(sample_state_key)
	current_state = current_state.at[0].set(new_state)
	current_y_idx = current_y_idx.at[0].set(new_y_idx)
	current_y = y_train[current_y_idx]

	(loss, current_state), grad = nnx.value_and_grad(
		loss_fn, has_aux=True, argnums=nnx.DiffState(0, grad_params)
	)(cs, current_state, current_y, loss_key)
	optimizer.update(cs, grad)

	pool = pool.update(pool_idx, {"state": current_state, "y_idx": current_y_idx})
	return loss, pool

@nnx.jit def train_step(cs, optimizer, pool, key): """Train step.""" sample_key, sample_state_key, loss_key = jax.random.split(key, 3) # Sample from pool pool_idx, batch = pool.sample(sample_key, batch_size=batch_size) current_state = batch["state"] current_y_idx = batch["y_idx"] current_y = y_train[current_y_idx] # Sort by descending loss sort_idx = jnp.argsort(jax.vmap(mse)(current_state, current_y), descending=True) pool_idx = pool_idx[sort_idx] current_state = current_state[sort_idx] current_y_idx = current_y_idx[sort_idx] # Sample a new state to replace the worst new_state, new_y_idx = sample_state(sample_state_key) current_state = current_state.at[0].set(new_state) current_y_idx = current_y_idx.at[0].set(new_y_idx) current_y = y_train[current_y_idx] (loss, current_state), grad = nnx.value_and_grad( loss_fn, has_aux=True, argnums=nnx.DiffState(0, grad_params) )(cs, current_state, current_y, loss_key) optimizer.update(cs, grad) pool = pool.update(pool_idx, {"state": current_state, "y_idx": current_y_idx}) return loss, pool

Main loop¶

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num_train_steps = 8_192
print_interval = 128

pbar = tqdm(range(num_train_steps), desc="Training", unit="train_step")
losses = []
for i in pbar:
	key, subkey = jax.random.split(key)
	loss, pool = train_step(cs, optimizer, pool, subkey)
	losses.append(loss)

	if i % print_interval == 0 or i == num_train_steps - 1:
		avg_loss = sum(losses[-print_interval:]) / len(losses[-print_interval:])
		pbar.set_postfix({"Average Loss": f"{avg_loss:.3e}"})

num_train_steps = 8_192 print_interval = 128 pbar = tqdm(range(num_train_steps), desc="Training", unit="train_step") losses = [] for i in pbar: key, subkey = jax.random.split(key) loss, pool = train_step(cs, optimizer, pool, subkey) losses.append(loss) if i % print_interval == 0 or i == num_train_steps - 1: avg_loss = sum(losses[-print_interval:]) / len(losses[-print_interval:]) pbar.set_postfix({"Average Loss": f"{avg_loss:.3e}"})

Run¶

In [ ]:

num_examples = 8

key, subkey = jax.random.split(key)
keys = jax.random.split(subkey, num_examples)
state_init, y_idx = jax.vmap(sample_state)(keys)

y = y_train[y_idx]
z = cs.encode(y)

state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None})
state_final = nnx.split_rngs(splits=num_examples)(
	nnx.vmap(
		lambda cs, state, z: cs(state, z, num_steps=2 * num_steps, sow=True),
		in_axes=(state_axes, 0, 0),
	)
)(cs, state_init, z)

num_examples = 8 key, subkey = jax.random.split(key) keys = jax.random.split(subkey, num_examples) state_init, y_idx = jax.vmap(sample_state)(keys) y = y_train[y_idx] z = cs.encode(y) state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None}) state_final = nnx.split_rngs(splits=num_examples)( nnx.vmap( lambda cs, state, z: cs(state, z, num_steps=2 * num_steps, sow=True), in_axes=(state_axes, 0, 0), ) )(cs, state_init, z)

Visualize¶

In [ ]:

intermediates = nnx.pop(cs, nnx.Intermediate)
states = intermediates.state.value[0]

intermediates = nnx.pop(cs, nnx.Intermediate) states = intermediates.state.value[0]

In [ ]:

states = jnp.concatenate([state_init[:, None], states], axis=1)
frames = nnx.vmap(
	lambda cs, state: cs.render(state),
	in_axes=(None, 0),
)(cs, states)

mediapy.show_images(y, width=128, height=128)
mediapy.show_videos(frames, width=128, height=128, codec="gif")

states = jnp.concatenate([state_init[:, None], states], axis=1) frames = nnx.vmap( lambda cs, state: cs.render(state), in_axes=(None, 0), )(cs, states) mediapy.show_images(y, width=128, height=128) mediapy.show_videos(frames, width=128, height=128, codec="gif")

Interpolation¶

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# Sample two random images
key, subkey = jax.random.split(key)
y_idx = jax.random.choice(subkey, y_train.shape[0], shape=(2,))
y = y_train[y_idx]

# Compute latent encodings
z = cs.encode(y)

# Interpolate between the two latent encodings
num_interpolations = 8
alphas = jnp.linspace(0.0, 1.0, num_interpolations)
z = jnp.array([alpha * z[0] + (1 - alpha) * z[1] for alpha in alphas])

# Sample initial state
key, subkey = jax.random.split(key)
keys = jax.random.split(subkey, num_interpolations)
state_init, _ = jax.vmap(sample_state)(keys)

# Run
state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None})
state_final = nnx.split_rngs(splits=num_interpolations)(
	nnx.vmap(
		lambda cs, state, z: cs(state, z, num_steps=num_steps),
		in_axes=(state_axes, 0, 0),
	)
)(cs, state_init, z)

# Sample two random images key, subkey = jax.random.split(key) y_idx = jax.random.choice(subkey, y_train.shape[0], shape=(2,)) y = y_train[y_idx] # Compute latent encodings z = cs.encode(y) # Interpolate between the two latent encodings num_interpolations = 8 alphas = jnp.linspace(0.0, 1.0, num_interpolations) z = jnp.array([alpha * z[0] + (1 - alpha) * z[1] for alpha in alphas]) # Sample initial state key, subkey = jax.random.split(key) keys = jax.random.split(subkey, num_interpolations) state_init, _ = jax.vmap(sample_state)(keys) # Run state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None}) state_final = nnx.split_rngs(splits=num_interpolations)( nnx.vmap( lambda cs, state, z: cs(state, z, num_steps=num_steps), in_axes=(state_axes, 0, 0), ) )(cs, state_init, z)

In [ ]:

frames = nnx.vmap(
	lambda cs, state: cs.render(state),
	in_axes=(None, 0),
)(cs, state_final)

mediapy.show_images(frames, width=128, height=128)

frames = nnx.vmap( lambda cs, state: cs.render(state), in_axes=(None, 0), )(cs, state_final) mediapy.show_images(frames, width=128, height=128)