vector_quantize_pytorch.py

import torch
from torch import nn, einsum
import torch.nn.functional as F
import torch.distributed as distributed
from torch.cuda.amp import autocast

from einops import rearrange, repeat
from contextlib import contextmanager

def exists(val):
    return val is not None

def default(val, d):
    return val if exists(val) else d

def noop(*args, **kwargs):
    pass

def l2norm(t):
    return F.normalize(t, p = 2, dim = -1)

def log(t, eps = 1e-20):
    return torch.log(t.clamp(min = eps))

def uniform_init(*shape):
    t = torch.empty(shape)
    nn.init.kaiming_uniform_(t)
    return t

def gumbel_noise(t):
    noise = torch.zeros_like(t).uniform_(0, 1)
    return -log(-log(noise))

def gumbel_sample(t, temperature = 1., dim = -1):
    if temperature == 0:
        return t.argmax(dim = dim)

    return ((t / temperature) + gumbel_noise(t)).argmax(dim = dim)

def ema_inplace(moving_avg, new, decay):
    moving_avg.data.mul_(decay).add_(new, alpha = (1 - decay))

def laplace_smoothing(x, n_categories, eps = 1e-5):
    return (x + eps) / (x.sum() + n_categories * eps)

def sample_vectors(samples, num):
    num_samples, device = samples.shape[0], samples.device
    if num_samples >= num:
        indices = torch.randperm(num_samples, device = device)[:num]
    else:
        indices = torch.randint(0, num_samples, (num,), device = device)

    return samples[indices]

def batched_sample_vectors(samples, num):
    return torch.stack([sample_vectors(sample, num) for sample in samples.unbind(dim = 0)], dim = 0)

def pad_shape(shape, size, dim = 0):
    return [size if i == dim else s for i, s in enumerate(shape)]

def sample_multinomial(total_count, probs):
    device = probs.device
    probs = probs.cpu()

    total_count = probs.new_full((), total_count)
    remainder = probs.new_ones(())
    sample = torch.empty_like(probs, dtype = torch.long)

    for i, p in enumerate(probs):
        s = torch.binomial(total_count, p / remainder)
        sample[i] = s
        total_count -= s
        remainder -= p

    return sample.to(device)

def all_gather_sizes(x, dim):
    size = torch.tensor(x.shape[dim], dtype = torch.long, device = x.device)
    all_sizes = [torch.empty_like(size) for _ in range(distributed.get_world_size())]
    distributed.all_gather(all_sizes, size)

    return torch.stack(all_sizes)

def all_gather_variably_sized(x, sizes, dim = 0):
    rank = distributed.get_rank()
    all_x = []

    for i, size in enumerate(sizes):
        t = x if i == rank else x.new_empty(pad_shape(x.shape, size, dim))
        distributed.broadcast(t, src = i, async_op = True)
        all_x.append(t)

    distributed.barrier()
    return all_x

def sample_vectors_distributed(local_samples, num):
    rank = distributed.get_rank()
    all_num_samples = all_gather_sizes(local_samples, dim = 0)

    if rank == 0:
        samples_per_rank = sample_multinomial(num, all_num_samples / all_num_samples.sum())
    else:
        samples_per_rank = torch.empty_like(all_num_samples)

    distributed.broadcast(samples_per_rank, src = 0)
    samples_per_rank = samples_per_rank.tolist()

    local_samples = batched_sample_vectors(local_samples, samples_per_rank[rank])
    all_samples = all_gather_variably_sized(local_samples, samples_per_rank, dim = 0)
    return torch.cat(all_samples, dim = 0)

def batched_bincount(x, *, minlength):
    batch, dtype, device = x.shape[0], x.dtype, x.device
    target = torch.zeros(batch, minlength, dtype = dtype, device = device)
    values = torch.ones_like(x)
    target.scatter_add_(-1, x, values)
    return target

def kmeans(
    samples,
    num_clusters,
    num_iters = 10,
    use_cosine_sim = False,
    sample_fn = batched_sample_vectors,
    all_reduce_fn = noop
):
    num_codebooks, dim, dtype, device = samples.shape[0], samples.shape[-1], samples.dtype, samples.device

    means = sample_fn(samples, num_clusters)

    for _ in range(num_iters):
        if use_cosine_sim:
            dists = samples @ rearrange(means, 'h n d -> h d n')
        else:
            dists = -torch.cdist(samples, means, p = 2)

        buckets = torch.argmax(dists, dim = -1)
        bins = batched_bincount(buckets, minlength = num_clusters)
        all_reduce_fn(bins)

        zero_mask = bins == 0
        bins_min_clamped = bins.masked_fill(zero_mask, 1)

        new_means = buckets.new_zeros(num_codebooks, num_clusters, dim, dtype = dtype)

        new_means.scatter_add_(1, repeat(buckets, 'h n -> h n d', d = dim), samples)
        new_means = new_means / rearrange(bins_min_clamped, '... -> ... 1')
        all_reduce_fn(new_means)

        if use_cosine_sim:
            new_means = l2norm(new_means)

        means = torch.where(
            rearrange(zero_mask, '... -> ... 1'),
            means,
            new_means
        )

    return means, bins

def batched_embedding(indices, embeds):
    batch, dim = indices.shape[1], embeds.shape[-1]
    indices = repeat(indices, 'h b n -> h b n d', d = dim)
    embeds = repeat(embeds, 'h c d -> h b c d', b = batch)
    return embeds.gather(2, indices)

# regularization losses

def orthogonal_loss_fn(t):
    # eq (2) from https://arxiv.org/abs/2112.00384
    h, n = t.shape[:2]
    normed_codes = l2norm(t)
    identity = repeat(torch.eye(n, device = t.device), 'i j -> h i j', h = h)
    cosine_sim = einsum('h i d, h j d -> h i j', normed_codes, normed_codes)
    return ((cosine_sim - identity) ** 2).sum() / (h * n ** 2)

# distance types

class EuclideanCodebook(nn.Module):
    def __init__(
        self,
        dim,
        codebook_size,
        num_codebooks = 1,
        kmeans_init = False,
        kmeans_iters = 10,
        decay = 0.8,
        eps = 1e-5,
        threshold_ema_dead_code = 2,
        use_ddp = False,
        learnable_codebook = False,
        sample_codebook_temp = 0
    ):
        super().__init__()
        self.decay = decay
        init_fn = uniform_init if not kmeans_init else torch.zeros
        embed = init_fn(num_codebooks, codebook_size, dim)

        self.codebook_size = codebook_size
        self.num_codebooks = num_codebooks

        self.kmeans_iters = kmeans_iters
        self.eps = eps
        self.threshold_ema_dead_code = threshold_ema_dead_code
        self.sample_codebook_temp = sample_codebook_temp

        self.sample_fn = sample_vectors_distributed if use_ddp else batched_sample_vectors
        self.all_reduce_fn = distributed.all_reduce if use_ddp else noop

        self.register_buffer('initted', torch.Tensor([not kmeans_init]))
        self.register_buffer('cluster_size', torch.zeros(num_codebooks, codebook_size))
        self.register_buffer('embed_avg', embed.clone())

        self.learnable_codebook = learnable_codebook
        if learnable_codebook:
            self.embed = nn.Parameter(embed)
        else:
            self.register_buffer('embed', embed)

    @torch.jit.ignore
    def init_embed_(self, data):
        if self.initted:
            return

        embed, cluster_size = kmeans(
            data,
            self.codebook_size,
            self.kmeans_iters,
            sample_fn = self.sample_fn,
            all_reduce_fn = self.all_reduce_fn
        )

        self.embed.data.copy_(embed)
        self.embed_avg.data.copy_(embed.clone())
        self.cluster_size.data.copy_(cluster_size)
        self.initted.data.copy_(torch.Tensor([True]))

    def replace(self, batch_samples, batch_mask):
        batch_samples = l2norm(batch_samples)

        for ind, (samples, mask) in enumerate(zip(batch_samples.unbind(dim = 0), batch_mask.unbind(dim = 0))):
            if not torch.any(mask):
                continue

            sampled = self.sample_fn(rearrange(samples, '... -> 1 ...'), mask.sum().item())
            self.embed.data[ind][mask] = rearrange(sampled, '1 ... -> ...')

    def expire_codes_(self, batch_samples):
        if self.threshold_ema_dead_code == 0:
            return

        expired_codes = self.cluster_size < self.threshold_ema_dead_code

        if not torch.any(expired_codes):
            return

        batch_samples = rearrange(batch_samples, 'h ... d -> h (...) d')
        self.replace(batch_samples, batch_mask = expired_codes)

    @autocast(enabled = False)
    def forward(self, x):
        needs_codebook_dim = x.ndim < 4

        x = x.float()

        if needs_codebook_dim:
            x = rearrange(x, '... -> 1 ...')

        shape, dtype = x.shape, x.dtype
        flatten = rearrange(x, 'h ... d -> h (...) d')

        self.init_embed_(flatten)

        embed = self.embed if not self.learnable_codebook else self.embed.detach()

        dist = -torch.cdist(flatten, embed, p = 2)

        embed_ind = gumbel_sample(dist, dim = -1, temperature = self.sample_codebook_temp)
        embed_onehot = F.one_hot(embed_ind, self.codebook_size).type(dtype)
        embed_ind = embed_ind.view(*shape[:-1])

        quantize = batched_embedding(embed_ind, self.embed)

        if self.training:
            cluster_size = embed_onehot.sum(dim = 1)

            self.all_reduce_fn(cluster_size)
            ema_inplace(self.cluster_size, cluster_size, self.decay)

            embed_sum = einsum('h n d, h n c -> h c d', flatten, embed_onehot)
            self.all_reduce_fn(embed_sum)

            cluster_size = laplace_smoothing(self.cluster_size, self.codebook_size, self.eps) * self.cluster_size.sum()

            embed_normalized = self.embed_avg / rearrange(cluster_size, '... -> ... 1')
            self.embed.data.copy_(embed_normalized)
            self.expire_codes_(x)

        if needs_codebook_dim:
            quantize, embed_ind = map(lambda t: rearrange(t, '1 ... -> ...'), (quantize, embed_ind))

        return quantize, embed_ind

class CosineSimCodebook(nn.Module):
    def __init__(
        self,
        dim,
        codebook_size,
        num_codebooks = 1,
        kmeans_init = False,
        kmeans_iters = 10,
        decay = 0.8,
        eps = 1e-5,
        threshold_ema_dead_code = 2,
        use_ddp = False,
        learnable_codebook = False,
        sample_codebook_temp = 0.
    ):
        super().__init__()
        self.decay = decay

        if not kmeans_init:
            embed = l2norm(uniform_init(num_codebooks, codebook_size, dim))
        else:
            embed = torch.zeros(num_codebooks, codebook_size, dim)

        self.codebook_size = codebook_size
        self.num_codebooks = num_codebooks

        self.kmeans_iters = kmeans_iters
        self.eps = eps
        self.threshold_ema_dead_code = threshold_ema_dead_code
        self.sample_codebook_temp = sample_codebook_temp

        self.sample_fn = sample_vectors_distributed if use_ddp else batched_sample_vectors
        self.all_reduce_fn = distributed.all_reduce if use_ddp else noop

        self.register_buffer('initted', torch.Tensor([not kmeans_init]))
        self.register_buffer('cluster_size', torch.zeros(num_codebooks, codebook_size))

        self.learnable_codebook = learnable_codebook
        if learnable_codebook:
            self.embed = nn.Parameter(embed)
        else:
            self.register_buffer('embed', embed)

    @torch.jit.ignore
    def init_embed_(self, data):
        if self.initted:
            return

        embed, cluster_size = kmeans(
            data,
            self.codebook_size,
            self.kmeans_iters,
            use_cosine_sim = True,
            sample_fn = self.sample_fn,
            all_reduce_fn = self.all_reduce_fn
        )

        self.embed.data.copy_(embed)
        self.cluster_size.data.copy_(cluster_size)
        self.initted.data.copy_(torch.Tensor([True]))

    def replace(self, batch_samples, batch_mask):
        batch_samples = l2norm(batch_samples)

        for ind, (samples, mask) in enumerate(zip(batch_samples.unbind(dim = 0), batch_mask.unbind(dim = 0))):
            if not torch.any(mask):
                continue

            sampled = self.sample_fn(rearrange(samples, '... -> 1 ...'), mask.sum().item())
            self.embed.data[ind][mask] = rearrange(sampled, '1 ... -> ...')

    def expire_codes_(self, batch_samples):
        if self.threshold_ema_dead_code == 0:
            return

        expired_codes = self.cluster_size < self.threshold_ema_dead_code

        if not torch.any(expired_codes):
            return

        batch_samples = rearrange(batch_samples, 'h ... d -> h (...) d')
        self.replace(batch_samples, batch_mask = expired_codes)

    @autocast(enabled = False)
    def forward(self, x):
        needs_codebook_dim = x.ndim < 4

        x = x.float()

        if needs_codebook_dim:
            x = rearrange(x, '... -> 1 ...')

        shape, dtype = x.shape, x.dtype

        flatten = rearrange(x, 'h ... d -> h (...) d')
        flatten = l2norm(flatten)

        self.init_embed_(flatten)

        embed = self.embed if not self.learnable_codebook else self.embed.detach()
        embed = l2norm(embed)

        dist = einsum('h n d, h c d -> h n c', flatten, embed)
        embed_ind = gumbel_sample(dist, dim = -1, temperature = self.sample_codebook_temp)
        embed_onehot = F.one_hot(embed_ind, self.codebook_size).type(dtype)
        embed_ind = embed_ind.view(*shape[:-1])

        quantize = batched_embedding(embed_ind, self.embed)

        if self.training:
            bins = embed_onehot.sum(dim = 1)
            self.all_reduce_fn(bins)

            ema_inplace(self.cluster_size, bins, self.decay)

            zero_mask = (bins == 0)
            bins = bins.masked_fill(zero_mask, 1.)

            embed_sum = einsum('h n d, h n c -> h c d', flatten, embed_onehot)
            self.all_reduce_fn(embed_sum)

            embed_normalized = embed_sum / rearrange(bins, '... -> ... 1')
            embed_normalized = l2norm(embed_normalized)

            embed_normalized = torch.where(
                rearrange(zero_mask, '... -> ... 1'),
                embed,
                embed_normalized
            )

            ema_inplace(self.embed, embed_normalized, self.decay)
            self.expire_codes_(x)

        if needs_codebook_dim:
            quantize, embed_ind = map(lambda t: rearrange(t, '1 ... -> ...'), (quantize, embed_ind))

        return quantize, embed_ind

# main class

class VectorQuantize(nn.Module):
    def __init__(
        self,
        dim,
        codebook_size,
        codebook_dim = None,
        heads = 1,
        separate_codebook_per_head = False,
        decay = 0.8,
        eps = 1e-5,
        kmeans_init = False,
        kmeans_iters = 10,
        use_cosine_sim = False,
        threshold_ema_dead_code = 0,
        channel_last = True,
        accept_image_fmap = False,
        commitment_weight = 1.,
        orthogonal_reg_weight = 0.,
        orthogonal_reg_active_codes_only = False,
        orthogonal_reg_max_codes = None,
        sample_codebook_temp = 0.,
        sync_codebook = False
    ):
        super().__init__()
        self.heads = heads
        self.separate_codebook_per_head = separate_codebook_per_head

        codebook_dim = default(codebook_dim, dim)
        codebook_input_dim = codebook_dim * heads

        requires_projection = codebook_input_dim != dim
        self.project_in = nn.Linear(dim, codebook_input_dim) if requires_projection else nn.Identity()
        self.project_out = nn.Linear(codebook_input_dim, dim) if requires_projection else nn.Identity()

        self.eps = eps
        self.commitment_weight = commitment_weight

        has_codebook_orthogonal_loss = orthogonal_reg_weight > 0
        self.orthogonal_reg_weight = orthogonal_reg_weight
        self.orthogonal_reg_active_codes_only = orthogonal_reg_active_codes_only
        self.orthogonal_reg_max_codes = orthogonal_reg_max_codes

        codebook_class = EuclideanCodebook if not use_cosine_sim else CosineSimCodebook

        self._codebook = codebook_class(
            dim = codebook_dim,
            num_codebooks = heads if separate_codebook_per_head else 1,
            codebook_size = codebook_size,
            kmeans_init = kmeans_init,
            kmeans_iters = kmeans_iters,
            decay = decay,
            eps = eps,
            threshold_ema_dead_code = threshold_ema_dead_code,
            use_ddp = sync_codebook,
            learnable_codebook = has_codebook_orthogonal_loss,
            sample_codebook_temp = sample_codebook_temp
        )

        self.codebook_size = codebook_size

        self.accept_image_fmap = accept_image_fmap
        self.channel_last = channel_last

    @property
    def codebook(self):
        codebook = self._codebook.embed
        if self.separate_codebook_per_head:
            return codebook

        return rearrange(codebook, '1 ... -> ...')

    def forward(self, x):
        shape, device, heads, is_multiheaded, codebook_size = x.shape, x.device, self.heads, self.heads > 1, self.codebook_size

        need_transpose = not self.channel_last and not self.accept_image_fmap

        if self.accept_image_fmap:
            height, width = x.shape[-2:]
            x = rearrange(x, 'b c h w -> b (h w) c')

        if need_transpose:
            x = rearrange(x, 'b d n -> b n d')

        x = self.project_in(x)

        if is_multiheaded:
            ein_rhs_eq = 'h b n d' if self.separate_codebook_per_head else '1 (b h) n d'
            x = rearrange(x, f'b n (h d) -> {ein_rhs_eq}', h = heads)

        quantize, embed_ind = self._codebook(x)

        if self.training:
            quantize = x + (quantize - x).detach()

        loss = torch.tensor([0.], device = device, requires_grad = self.training)

        if self.training:
            if self.commitment_weight > 0:
                commit_loss = F.mse_loss(quantize.detach(), x)
                loss = loss + commit_loss * self.commitment_weight

            if self.orthogonal_reg_weight > 0:
                codebook = self._codebook.embed

                if self.orthogonal_reg_active_codes_only:
                    # only calculate orthogonal loss for the activated codes for this batch
                    unique_code_ids = torch.unique(embed_ind)
                    codebook = codebook[unique_code_ids]

                num_codes = codebook.shape[0]
                if exists(self.orthogonal_reg_max_codes) and num_codes > self.orthogonal_reg_max_codes:
                    rand_ids = torch.randperm(num_codes, device = device)[:self.orthogonal_reg_max_codes]
                    codebook = codebook[rand_ids]

                orthogonal_reg_loss = orthogonal_loss_fn(codebook)
                loss = loss + orthogonal_reg_loss * self.orthogonal_reg_weight

        if is_multiheaded:
            if self.separate_codebook_per_head:
                quantize = rearrange(quantize, 'h b n d -> b n (h d)', h = heads)
                embed_ind = rearrange(embed_ind, 'h b n -> b n h', h = heads)
            else:
                quantize = rearrange(quantize, '1 (b h) n d -> b n (h d)', h = heads)
                embed_ind = rearrange(embed_ind, '1 (b h) n -> b n h', h = heads)

        quantize = self.project_out(quantize)

        if need_transpose:
            quantize = rearrange(quantize, 'b n d -> b d n')

        if self.accept_image_fmap:
            quantize = rearrange(quantize, 'b (h w) c -> b c h w', h = height, w = width)
            embed_ind = rearrange(embed_ind, 'b (h w) ... -> b h w ...', h = height, w = width)

        return quantize, embed_ind, loss