Growing 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:

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%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 PIL
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.utils import clip_and_uint8, get_emoji, rgba_to_rgb

import jax import jax.numpy as jnp import mediapy import optax import PIL 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.utils import clip_and_uint8, get_emoji, rgba_to_rgb

Configuration¶

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seed = 0

channel_size = 16
num_kernels = 3
hidden_size = 128
cell_dropout_rate = 0.5

num_steps = 128
pool_size = 1_024
batch_size = 8
learning_rate = 2e-3

emoji = "🦎"
size = 40
pad_width = 16

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

seed = 0 channel_size = 16 num_kernels = 3 hidden_size = 128 cell_dropout_rate = 0.5 num_steps = 128 pool_size = 1_024 batch_size = 8 learning_rate = 2e-3 emoji = "🦎" size = 40 pad_width = 16 key = jax.random.key(seed) rngs = nnx.Rngs(seed)

Dataset¶

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def get_y_from_emoji(emoji: str) -> jax.Array:
	"""Get target y from an emoji."""
	emoji_pil = get_emoji(emoji)
	emoji_pil = emoji_pil.resize((size, size), resample=PIL.Image.Resampling.LANCZOS)

	y = jnp.array(emoji_pil, dtype=jnp.float32) / 255.0
	y = jnp.pad(y, ((pad_width, pad_width), (pad_width, pad_width), (0, 0)))

	return y


y = get_y_from_emoji(emoji)

mediapy.show_image(y)

def get_y_from_emoji(emoji: str) -> jax.Array: """Get target y from an emoji.""" emoji_pil = get_emoji(emoji) emoji_pil = emoji_pil.resize((size, size), resample=PIL.Image.Resampling.LANCZOS) y = jnp.array(emoji_pil, dtype=jnp.float32) / 255.0 y = jnp.pad(y, ((pad_width, pad_width), (pad_width, pad_width), (0, 0))) return y y = get_y_from_emoji(emoji) mediapy.show_image(y)

Instantiate system¶

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class GrowingNCA(ComplexSystem):
	"""Growing Neural Cellular Automata class."""

	def __init__(self, *, rngs: nnx.Rngs):
		"""Initialize Growing 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=num_kernels * channel_size,
			hidden_layer_sizes=(hidden_size,),
			cell_dropout_rate=cell_dropout_rate,
			zeros_init=True,
			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 _step(self, state: State, input: Input | None = None, *, sow: bool = False) -> State:
		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."""
		rgba = state[..., -4:]
		rgb = rgba_to_rgb(rgba)

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

	@nnx.jit
	def render_rgba(self, state):
		"""Render state to RGBA."""
		rgba = state[..., -4:]

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

class GrowingNCA(ComplexSystem): """Growing Neural Cellular Automata class.""" def __init__(self, *, rngs: nnx.Rngs): """Initialize Growing 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=num_kernels * channel_size, hidden_layer_sizes=(hidden_size,), cell_dropout_rate=cell_dropout_rate, zeros_init=True, 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 _step(self, state: State, input: Input | None = None, *, sow: bool = False) -> State: 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.""" rgba = state[..., -4:] rgb = rgba_to_rgb(rgba) # Clip values to valid range and convert to uint8 return clip_and_uint8(rgb) @nnx.jit def render_rgba(self, state): """Render state to RGBA.""" rgba = state[..., -4:] # Clip values to valid range and convert to uint8 return clip_and_uint8(rgba)

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cs = GrowingNCA(rngs=rngs)

cs = GrowingNCA(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():
	"""Sample a state with a single alive cell."""
	spatial_dims = y.shape[:2]

	# Init state
	state = jnp.zeros(spatial_dims + (channel_size,))

	# Set the center cell to alive
	mid = tuple(size // 2 for size in spatial_dims)
	return state.at[mid[0], mid[1], -1].set(1.0)

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

Train¶

Pool¶

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state = jax.vmap(lambda _: sample_state())(jnp.zeros(pool_size))

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

state = jax.vmap(lambda _: sample_state())(jnp.zeros(pool_size)) pool = Pool.create({"state": state})

Optimizer¶

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lr_sched = optax.linear_schedule(
	init_value=learning_rate, end_value=0.1 * learning_rate, transition_steps=2_000
)

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

update_params = nnx.All(nnx.Param, nnx.PathContains("update"))
optimizer = nnx.Optimizer(cs, optimizer, wrt=update_params)

lr_sched = optax.linear_schedule( init_value=learning_rate, end_value=0.1 * learning_rate, transition_steps=2_000 ) optimizer = optax.chain( optax.clip_by_global_norm(1.0), optax.adam(learning_rate=lr_sched), ) update_params = nnx.All(nnx.Param, nnx.PathContains("update")) optimizer = nnx.Optimizer(cs, optimizer, wrt=update_params)

Loss¶

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def mse(state):
	"""Mean Squared Error."""
	return jnp.mean(jnp.square(state[..., -4:] - y))

def mse(state): """Mean Squared Error.""" return jnp.mean(jnp.square(state[..., -4:] - y))

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@nnx.jit
def loss_fn(cs, state, key):
	"""Loss function."""
	state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None})
	nnx.split_rngs(splits=batch_size)(
		nnx.vmap(
			lambda cs, state: cs(state, num_steps=num_steps, sow=True),
			in_axes=(state_axes, 0),
		)
	)(cs, state)

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

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

	loss = mse(state)
	return loss, state

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

Train step¶

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

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

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

	# Sample a new state to replace the worst
	new_state = sample_state()
	current_state = current_state.at[0].set(new_state)

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

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

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

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num_examples = 8

state_init = jax.vmap(lambda _: sample_state())(jnp.zeros(num_examples))

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

num_examples = 8 state_init = jax.vmap(lambda _: sample_state())(jnp.zeros(num_examples)) state_axes = nnx.StateAxes({nnx.RngState: 0, nnx.Intermediate: 0, ...: None}) state_final = nnx.split_rngs(splits=num_examples)( nnx.vmap( lambda cs, state_init: cs(state_init, num_steps=2 * num_steps, sow=True), in_axes=(state_axes, 0), ) )(cs, state_init)

Visualize¶

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

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

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

frames_final_rgba = nnx.vmap(
	lambda cs, state: cs.render_rgba(state),
	in_axes=(None, 0),
)(cs, state_final)

mediapy.show_images(frames_final, width=128, height=128)
mediapy.show_images(frames_final_rgba, width=128, height=128)

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

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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_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_videos(frames, width=128, height=128, codec="gif")