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import typing as tp |
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from einops import rearrange, repeat |
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import flashy |
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import torch |
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from torch import nn, einsum |
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import torch.nn.functional as F |
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def exists(val: tp.Optional[tp.Any]) -> bool: |
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return val is not None |
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def default(val: tp.Any, d: tp.Any) -> tp.Any: |
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return val if exists(val) else d |
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def l2norm(t): |
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return F.normalize(t, p=2, dim=-1) |
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def ema_inplace(moving_avg, new, decay: float): |
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moving_avg.data.mul_(decay).add_(new, alpha=(1 - decay)) |
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def laplace_smoothing(x, n_categories: int, epsilon: float = 1e-5): |
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return (x + epsilon) / (x.sum() + n_categories * epsilon) |
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def uniform_init(*shape: int): |
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t = torch.empty(shape) |
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nn.init.kaiming_uniform_(t) |
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return t |
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def sample_vectors(samples, num: int): |
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num_samples, device = samples.shape[0], samples.device |
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if num_samples >= num: |
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indices = torch.randperm(num_samples, device=device)[:num] |
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else: |
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indices = torch.randint(0, num_samples, (num,), device=device) |
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return samples[indices] |
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def kmeans(samples, num_clusters: int, num_iters: int = 10): |
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dim, dtype = samples.shape[-1], samples.dtype |
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means = sample_vectors(samples, num_clusters) |
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for _ in range(num_iters): |
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diffs = rearrange(samples, "n d -> n () d") - rearrange( |
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means, "c d -> () c d" |
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) |
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dists = -(diffs ** 2).sum(dim=-1) |
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buckets = dists.max(dim=-1).indices |
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bins = torch.bincount(buckets, minlength=num_clusters) |
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zero_mask = bins == 0 |
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bins_min_clamped = bins.masked_fill(zero_mask, 1) |
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new_means = buckets.new_zeros(num_clusters, dim, dtype=dtype) |
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new_means.scatter_add_(0, repeat(buckets, "n -> n d", d=dim), samples) |
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new_means = new_means / bins_min_clamped[..., None] |
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means = torch.where(zero_mask[..., None], means, new_means) |
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return means, bins |
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def orthgonal_loss_fn(t): |
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n = t.shape[0] |
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normed_codes = l2norm(t) |
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identity = torch.eye(n, device=t.device) |
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cosine_sim = einsum("i d, j d -> i j", normed_codes, normed_codes) |
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return ((cosine_sim - identity) ** 2).sum() / (n ** 2) |
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class EuclideanCodebook(nn.Module): |
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"""Codebook with Euclidean distance. |
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Args: |
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dim (int): Dimension. |
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codebook_size (int): Codebook size. |
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kmeans_init (bool): Whether to use k-means to initialize the codebooks. |
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If set to true, run the k-means algorithm on the first training batch and use |
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the learned centroids as initialization. |
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kmeans_iters (int): Number of iterations used for k-means algorithm at initialization. |
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decay (float): Decay for exponential moving average over the codebooks. |
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epsilon (float): Epsilon value for numerical stability. |
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threshold_ema_dead_code (int): Threshold for dead code expiration. Replace any codes |
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that have an exponential moving average cluster size less than the specified threshold with |
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randomly selected vector from the current batch. |
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""" |
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def __init__( |
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self, |
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dim: int, |
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codebook_size: int, |
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kmeans_init: int = False, |
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kmeans_iters: int = 10, |
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decay: float = 0.8, |
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epsilon: float = 1e-5, |
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threshold_ema_dead_code: int = 2, |
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): |
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super().__init__() |
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self.decay = decay |
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init_fn: tp.Union[tp.Callable[..., torch.Tensor], tp.Any] = uniform_init if not kmeans_init else torch.zeros |
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embed = init_fn(codebook_size, dim) |
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self.codebook_size = codebook_size |
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self.kmeans_iters = kmeans_iters |
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self.epsilon = epsilon |
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self.threshold_ema_dead_code = threshold_ema_dead_code |
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self.register_buffer("inited", torch.Tensor([not kmeans_init])) |
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self.register_buffer("cluster_size", torch.zeros(codebook_size)) |
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self.register_buffer("embed", embed) |
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self.register_buffer("embed_avg", embed.clone()) |
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@torch.jit.ignore |
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def init_embed_(self, data): |
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if self.inited: |
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return |
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embed, cluster_size = kmeans(data, self.codebook_size, self.kmeans_iters) |
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self.embed.data.copy_(embed) |
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self.embed_avg.data.copy_(embed.clone()) |
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self.cluster_size.data.copy_(cluster_size) |
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self.inited.data.copy_(torch.Tensor([True])) |
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flashy.distrib.broadcast_tensors(self.buffers()) |
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def replace_(self, samples, mask): |
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modified_codebook = torch.where( |
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mask[..., None], sample_vectors(samples, self.codebook_size), self.embed |
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) |
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self.embed.data.copy_(modified_codebook) |
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def expire_codes_(self, batch_samples): |
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if self.threshold_ema_dead_code == 0: |
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return |
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expired_codes = self.cluster_size < self.threshold_ema_dead_code |
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if not torch.any(expired_codes): |
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return |
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batch_samples = rearrange(batch_samples, "... d -> (...) d") |
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self.replace_(batch_samples, mask=expired_codes) |
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flashy.distrib.broadcast_tensors(self.buffers()) |
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def preprocess(self, x): |
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x = rearrange(x, "... d -> (...) d") |
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return x |
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def quantize(self, x): |
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embed = self.embed.t() |
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dist = -( |
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x.pow(2).sum(1, keepdim=True) |
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- 2 * x @ embed |
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+ embed.pow(2).sum(0, keepdim=True) |
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) |
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embed_ind = dist.max(dim=-1).indices |
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return embed_ind |
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def postprocess_emb(self, embed_ind, shape): |
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return embed_ind.view(*shape[:-1]) |
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def dequantize(self, embed_ind): |
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quantize = F.embedding(embed_ind, self.embed) |
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return quantize |
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def encode(self, x): |
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shape = x.shape |
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x = self.preprocess(x) |
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embed_ind = self.quantize(x) |
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embed_ind = self.postprocess_emb(embed_ind, shape) |
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return embed_ind |
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def decode(self, embed_ind): |
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quantize = self.dequantize(embed_ind) |
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return quantize |
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def forward(self, x): |
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shape, dtype = x.shape, x.dtype |
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x = self.preprocess(x) |
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self.init_embed_(x) |
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embed_ind = self.quantize(x) |
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embed_onehot = F.one_hot(embed_ind, self.codebook_size).type(dtype) |
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embed_ind = self.postprocess_emb(embed_ind, shape) |
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quantize = self.dequantize(embed_ind) |
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if self.training: |
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self.expire_codes_(x) |
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ema_inplace(self.cluster_size, embed_onehot.sum(0), self.decay) |
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embed_sum = x.t() @ embed_onehot |
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ema_inplace(self.embed_avg, embed_sum.t(), self.decay) |
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cluster_size = ( |
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laplace_smoothing(self.cluster_size, self.codebook_size, self.epsilon) |
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* self.cluster_size.sum() |
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) |
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embed_normalized = self.embed_avg / cluster_size.unsqueeze(1) |
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self.embed.data.copy_(embed_normalized) |
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return quantize, embed_ind |
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class VectorQuantization(nn.Module): |
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"""Vector quantization implementation. |
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Currently supports only euclidean distance. |
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Args: |
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dim (int): Dimension |
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codebook_size (int): Codebook size |
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codebook_dim (int): Codebook dimension. If not defined, uses the specified dimension in dim. |
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decay (float): Decay for exponential moving average over the codebooks. |
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epsilon (float): Epsilon value for numerical stability. |
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kmeans_init (bool): Whether to use kmeans to initialize the codebooks. |
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kmeans_iters (int): Number of iterations used for kmeans initialization. |
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threshold_ema_dead_code (int): |
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channels_last (bool): Channels are the last dimension in the input tensors. |
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commitment_weight (float): Weight for commitment loss. |
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orthogonal_reg_weight (float): Orthogonal regularization weights. |
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orthogonal_reg_active_codes_only (bool): Apply orthogonal regularization only on active codes. |
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orthogonal_reg_max_codes (optional int): Maximum number of codes to consider |
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for orthogonal regulariation. |
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threshold_ema_dead_code (int): Threshold for dead code expiration. Replace any codes |
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that have an exponential moving average cluster size less than the specified threshold with |
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randomly selected vector from the current batch. |
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""" |
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def __init__( |
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self, |
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dim: int, |
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codebook_size: int, |
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codebook_dim: tp.Optional[int] = None, |
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decay: float = 0.8, |
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epsilon: float = 1e-5, |
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kmeans_init: bool = False, |
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kmeans_iters: int = 10, |
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threshold_ema_dead_code: int = 2, |
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channels_last: bool = False, |
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commitment_weight: float = 1., |
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orthogonal_reg_weight: float = 0.0, |
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orthogonal_reg_active_codes_only: bool = False, |
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orthogonal_reg_max_codes: tp.Optional[int] = None, |
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): |
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super().__init__() |
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_codebook_dim: int = default(codebook_dim, dim) |
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requires_projection = _codebook_dim != dim |
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self.project_in = (nn.Linear(dim, _codebook_dim) if requires_projection else nn.Identity()) |
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self.project_out = (nn.Linear(_codebook_dim, dim) if requires_projection else nn.Identity()) |
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self.epsilon = epsilon |
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self.commitment_weight = commitment_weight |
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self.orthogonal_reg_weight = orthogonal_reg_weight |
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self.orthogonal_reg_active_codes_only = orthogonal_reg_active_codes_only |
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self.orthogonal_reg_max_codes = orthogonal_reg_max_codes |
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self._codebook = EuclideanCodebook(dim=_codebook_dim, codebook_size=codebook_size, |
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kmeans_init=kmeans_init, kmeans_iters=kmeans_iters, |
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decay=decay, epsilon=epsilon, |
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threshold_ema_dead_code=threshold_ema_dead_code) |
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self.codebook_size = codebook_size |
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self.channels_last = channels_last |
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@property |
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def codebook(self): |
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return self._codebook.embed |
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@property |
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def inited(self): |
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return self._codebook.inited |
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def _preprocess(self, x): |
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if not self.channels_last: |
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x = rearrange(x, "b d n -> b n d") |
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return x |
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def _postprocess(self, quantize): |
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if not self.channels_last: |
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quantize = rearrange(quantize, "b n d -> b d n") |
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return quantize |
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def encode(self, x): |
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x = self._preprocess(x) |
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x = self.project_in(x) |
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embed_in = self._codebook.encode(x) |
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return embed_in |
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def decode(self, embed_ind): |
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quantize = self._codebook.decode(embed_ind) |
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quantize = self.project_out(quantize) |
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quantize = self._postprocess(quantize) |
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return quantize |
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def forward(self, x): |
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device = x.device |
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x = self._preprocess(x) |
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x = self.project_in(x) |
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quantize, embed_ind = self._codebook(x) |
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if self.training: |
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quantize = x + (quantize - x).detach() |
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loss = torch.tensor([0.0], device=device, requires_grad=self.training) |
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if self.training: |
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if self.commitment_weight > 0: |
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commit_loss = F.mse_loss(quantize.detach(), x) |
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loss = loss + commit_loss * self.commitment_weight |
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if self.orthogonal_reg_weight > 0: |
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codebook = self.codebook |
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if self.orthogonal_reg_active_codes_only: |
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unique_code_ids = torch.unique(embed_ind) |
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codebook = codebook[unique_code_ids] |
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num_codes = codebook.shape[0] |
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if exists(self.orthogonal_reg_max_codes) and num_codes > self.orthogonal_reg_max_codes: |
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rand_ids = torch.randperm(num_codes, device=device)[:self.orthogonal_reg_max_codes] |
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codebook = codebook[rand_ids] |
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orthogonal_reg_loss = orthgonal_loss_fn(codebook) |
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loss = loss + orthogonal_reg_loss * self.orthogonal_reg_weight |
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quantize = self.project_out(quantize) |
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quantize = self._postprocess(quantize) |
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return quantize, embed_ind, loss |
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class ResidualVectorQuantization(nn.Module): |
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"""Residual vector quantization implementation. |
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Follows Algorithm 1. in https://arxiv.org/pdf/2107.03312.pdf |
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""" |
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def __init__(self, *, num_quantizers, **kwargs): |
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super().__init__() |
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self.layers = nn.ModuleList( |
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[VectorQuantization(**kwargs) for _ in range(num_quantizers)] |
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) |
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def forward(self, x, n_q: tp.Optional[int] = None): |
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quantized_out = 0.0 |
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residual = x |
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all_losses = [] |
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all_indices = [] |
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n_q = n_q or len(self.layers) |
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for i, layer in enumerate(self.layers[:n_q]): |
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quantized, indices, loss = layer(residual) |
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residual = residual - quantized |
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quantized_out = quantized_out + quantized |
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all_indices.append(indices) |
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all_losses.append(loss) |
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out_losses, out_indices = map(torch.stack, (all_losses, all_indices)) |
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return quantized_out, out_indices, out_losses |
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def encode(self, x: torch.Tensor, n_q: tp.Optional[int] = None) -> torch.Tensor: |
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residual = x |
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all_indices = [] |
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n_q = n_q or len(self.layers) |
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for layer in self.layers[:n_q]: |
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indices = layer.encode(residual) |
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quantized = layer.decode(indices) |
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residual = residual - quantized |
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all_indices.append(indices) |
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out_indices = torch.stack(all_indices) |
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return out_indices |
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def decode(self, q_indices: torch.Tensor) -> torch.Tensor: |
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quantized_out = torch.tensor(0.0, device=q_indices.device) |
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for i, indices in enumerate(q_indices): |
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layer = self.layers[i] |
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quantized = layer.decode(indices) |
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quantized_out = quantized_out + quantized |
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return quantized_out |
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