Growing Unsupervised Neural Cellular Automata ¶

Installation¶

You will need Python 3.12 or later, and a working JAX installation. For example, you can install JAX with:

In [1]:

%pip install -U "jax[cuda]"

%pip install -U "jax[cuda]"

/home/faldor_google_com/dev/cax/.venv/bin/python3: No module named pip

Note: you may need to restart the kernel to use updated packages.

Then, install CAX from PyPi:

In [2]:

%pip install -U "cax[examples]"

%pip install -U "cax[examples]"

/home/faldor_google_com/dev/cax/.venv/bin/python3: No module named pip

Note: you may need to restart the kernel to use updated packages.

Import¶

In [3]:

import time

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

from cax.core import ComplexSystem
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 time import jax import jax.numpy as jnp import mediapy import optax import torchvision from flax import nnx from jax import Array from cax.core import ComplexSystem 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¶

In [4]:

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¶

In [5]:

# 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].repeat(4, axis=-3).repeat(4, axis=-2))

# 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].repeat(4, axis=-3).repeat(4, axis=-2))

Instantiate system¶

In [6]:

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(num_dims=2), grad_kernel(num_dims=2)], axis=-1
        )
        kernel = jnp.expand_dims(
            jnp.concatenate([kernel] * channel_size, axis=-1), axis=-2
        )
        self.perceive.conv.kernel[...] = 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: Array, input: Array | None = None) -> Array:
        # 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)

        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(num_dims=2), grad_kernel(num_dims=2)], axis=-1 ) kernel = jnp.expand_dims( jnp.concatenate([kernel] * channel_size, axis=-1), axis=-2 ) self.perceive.conv.kernel[...] = 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: Array, input: Array | None = None) -> Array: # 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) 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)

In [7]:

cs = GrowingUnsupervisedNCA(rngs=rngs)

cs = GrowingUnsupervisedNCA(rngs=rngs)

In [8]:

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)))

Number of params: 2530832

Sample initial state¶

In [9]:

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, with hidden channels at one
    state = state.at[mid[0], mid[1], -1].set(1.0)
    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, with hidden channels at one state = state.at[mid[0], mid[1], -1].set(1.0) 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¶

In [10]:

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¶

In [11]:

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¶

In [12]:

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))

In [13]:

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

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

    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, ...: None}) _, state = nnx.split_rngs(splits=batch_size)( nnx.vmap( lambda cs, state, z: cs(state, z, num_steps=num_steps, return_states=True), in_axes=(state_axes, 0, 0), ) )(cs, state, z) 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¶

In [14]:

@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, replace=False)
    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, replace=False) 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¶

In [15]:

num_train_steps = 8_192
print_interval = 128

losses = []
start = time.perf_counter()
for i in range(num_train_steps):
    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:])
        elapsed = time.perf_counter() - start
        print(f"Step {i:>4}/{num_train_steps} | {elapsed:6.1f}s | Loss {avg_loss:.3e}")

print(f"✨ Trained for {num_train_steps} steps in {time.perf_counter() - start:.0f}s")

num_train_steps = 8_192 print_interval = 128 losses = [] start = time.perf_counter() for i in range(num_train_steps): 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:]) elapsed = time.perf_counter() - start print(f"Step {i:>4}/{num_train_steps} | {elapsed:6.1f}s | Loss {avg_loss:.3e}") print(f"✨ Trained for {num_train_steps} steps in {time.perf_counter() - start:.0f}s")

Step    0/8192 |    7.1s | Loss 1.053e-01

Step  128/8192 |    8.9s | Loss 1.340e-01

Step  256/8192 |   10.7s | Loss 8.107e-02

Step  384/8192 |   12.6s | Loss 7.069e-02

Step  512/8192 |   14.4s | Loss 5.714e-02

Step  640/8192 |   16.2s | Loss 5.008e-02

Step  768/8192 |   18.0s | Loss 4.437e-02

Step  896/8192 |   19.8s | Loss 3.966e-02

Step 1024/8192 |   21.6s | Loss 3.680e-02

Step 1152/8192 |   23.4s | Loss 3.403e-02

Step 1280/8192 |   25.2s | Loss 3.305e-02

Step 1408/8192 |   27.1s | Loss 2.968e-02

Step 1536/8192 |   28.9s | Loss 2.963e-02

Step 1664/8192 |   30.7s | Loss 2.807e-02

Step 1792/8192 |   32.5s | Loss 2.635e-02

Step 1920/8192 |   34.3s | Loss 2.607e-02

Step 2048/8192 |   36.1s | Loss 2.536e-02

Step 2176/8192 |   37.9s | Loss 2.425e-02

Step 2304/8192 |   39.8s | Loss 2.394e-02

Step 2432/8192 |   41.6s | Loss 2.306e-02

Step 2560/8192 |   43.4s | Loss 2.220e-02

Step 2688/8192 |   45.2s | Loss 2.133e-02

Step 2816/8192 |   47.0s | Loss 2.026e-02

Step 2944/8192 |   48.8s | Loss 2.029e-02

Step 3072/8192 |   50.6s | Loss 1.966e-02

Step 3200/8192 |   52.4s | Loss 1.919e-02

Step 3328/8192 |   54.3s | Loss 1.909e-02

Step 3456/8192 |   56.1s | Loss 1.888e-02

Step 3584/8192 |   57.9s | Loss 1.825e-02

Step 3712/8192 |   59.7s | Loss 1.831e-02

Step 3840/8192 |   61.5s | Loss 1.763e-02

Step 3968/8192 |   63.3s | Loss 1.729e-02

Step 4096/8192 |   65.1s | Loss 1.674e-02

Step 4224/8192 |   67.0s | Loss 1.595e-02

Step 4352/8192 |   68.8s | Loss 1.594e-02

Step 4480/8192 |   70.6s | Loss 1.644e-02

Step 4608/8192 |   72.4s | Loss 1.554e-02

Step 4736/8192 |   74.2s | Loss 1.569e-02

Step 4864/8192 |   76.0s | Loss 1.573e-02

Step 4992/8192 |   77.8s | Loss 1.522e-02

Step 5120/8192 |   79.7s | Loss 1.463e-02

Step 5248/8192 |   81.5s | Loss 1.561e-02

Step 5376/8192 |   83.3s | Loss 1.469e-02

Step 5504/8192 |   85.1s | Loss 1.410e-02

Step 5632/8192 |   86.9s | Loss 1.487e-02

Step 5760/8192 |   88.7s | Loss 1.487e-02

Step 5888/8192 |   90.5s | Loss 1.386e-02

Step 6016/8192 |   92.4s | Loss 1.385e-02

Step 6144/8192 |   94.2s | Loss 1.321e-02

Step 6272/8192 |   96.0s | Loss 1.399e-02

Step 6400/8192 |   97.8s | Loss 1.374e-02

Step 6528/8192 |   99.6s | Loss 1.317e-02

Step 6656/8192 |  101.4s | Loss 1.314e-02

Step 6784/8192 |  103.2s | Loss 1.311e-02

Step 6912/8192 |  105.1s | Loss 1.307e-02

Step 7040/8192 |  106.9s | Loss 1.318e-02

Step 7168/8192 |  108.7s | Loss 1.231e-02

Step 7296/8192 |  110.5s | Loss 1.289e-02

Step 7424/8192 |  112.3s | Loss 1.230e-02

Step 7552/8192 |  114.1s | Loss 1.253e-02

Step 7680/8192 |  115.9s | Loss 1.297e-02

Step 7808/8192 |  117.8s | Loss 1.218e-02

Step 7936/8192 |  119.6s | Loss 1.226e-02

Step 8064/8192 |  121.4s | Loss 1.289e-02

Step 8191/8192 |  123.2s | Loss 1.245e-02
✨ Trained for 8192 steps in 123s

Run¶

In [16]:

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, ...: None})
state_final, states = nnx.split_rngs(splits=num_examples)(
    nnx.vmap(
        lambda cs, state, z: cs(state, z, num_steps=2 * num_steps, return_states=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, ...: None}) state_final, states = nnx.split_rngs(splits=num_examples)( nnx.vmap( lambda cs, state, z: cs(state, z, num_steps=2 * num_steps, return_states=True), in_axes=(state_axes, 0, 0), ) )(cs, state_init, z)

Visualize¶

In [17]:

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.repeat(4, axis=-3).repeat(4, axis=-2))
mediapy.show_videos(frames.repeat(4, axis=-3).repeat(4, axis=-2))

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.repeat(4, axis=-3).repeat(4, axis=-2)) mediapy.show_videos(frames.repeat(4, axis=-3).repeat(4, axis=-2))

Interpolation¶

In [18]:

# 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, ...: 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, ...: 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 [19]:

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

mediapy.show_images(frames.repeat(4, axis=-3).repeat(4, axis=-2))

frames = nnx.vmap( lambda cs, state: cs.render(state), in_axes=(None, 0), )(cs, state_final) mediapy.show_images(frames.repeat(4, axis=-3).repeat(4, axis=-2))