# Copyright (c) 2025 FoundationVision # SPDX-License-Identifier: MIT """ Binary Spherical Quantization Proposed in https://arxiv.org/abs/2406.07548 In the simplest setup, each dimension is quantized into {-1, 1}. An entropy penalty is used to encourage utilization. """ import random import copy from math import log2, ceil from functools import partial, cache from collections import namedtuple from contextlib import nullcontext import torch.distributed as dist from torch.distributed import nn as dist_nn import torch from torch import nn, einsum import torch.nn.functional as F from torch.nn import Module from torch.amp import autocast import numpy as np from einops import rearrange, reduce, pack, unpack # from einx import get_at # print(f"{dynamic_resolution_thw=}") # constants Return = namedtuple('Return', ['quantized', 'indices', 'bit_indices', 'entropy_aux_loss']) LossBreakdown = namedtuple('LossBreakdown', ['per_sample_entropy', 'batch_entropy', 'commitment']) # distributed helpers @cache def is_distributed(): return dist.is_initialized() and dist.get_world_size() > 1 def maybe_distributed_mean(t): if not is_distributed(): return t dist_nn.all_reduce(t) t = t / dist.get_world_size() return t # helper functions def exists(v): return v is not None def identity(t): return t def default(*args): for arg in args: if exists(arg): return arg() if callable(arg) else arg return None def round_up_multiple(num, mult): return ceil(num / mult) * mult def pack_one(t, pattern): return pack([t], pattern) def unpack_one(t, ps, pattern): return unpack(t, ps, pattern)[0] def l2norm(t): return F.normalize(t, dim = -1) # entropy def log(t, eps = 1e-5): return t.clamp(min = eps).log() def entropy(prob): return (-prob * log(prob)).sum(dim=-1) # cosine sim linear class CosineSimLinear(Module): def __init__( self, dim_in, dim_out, scale = 1. ): super().__init__() self.scale = scale self.weight = nn.Parameter(torch.randn(dim_in, dim_out)) def forward(self, x): x = F.normalize(x, dim = -1) w = F.normalize(self.weight, dim = 0) return (x @ w) * self.scale def repeat_schedule(scale_schedule, repeat_scales_num, times): new_scale_schedule = [] for i in range(repeat_scales_num): new_scale_schedule.extend([scale_schedule[i] for _ in range(times)]) new_scale_schedule.extend(scale_schedule[repeat_scales_num:]) return new_scale_schedule class BSQ(Module): def __init__( self, *, dim = None, entropy_loss_weight = 0.1, commitment_loss_weight = 0.25, num_codebooks = 1, keep_num_codebooks_dim = None, codebook_scale = 1., # for residual LFQ, codebook scaled down by 2x at each layer frac_per_sample_entropy = 1., # make less than 1. to only use a random fraction of the probs for per sample entropy soft_clamp_input_value = None, channel_first = None, experimental_softplus_entropy_loss = False, entropy_loss_offset = 5., # how much to shift the loss before softplus spherical = True, # from https://arxiv.org/abs/2406.07548 force_quantization_f32 = True, # will force the quantization step to be full precision inv_temperature = 100.0, gamma0=1.0, gamma=1.0, zeta=1.0, use_out_phi = False, # use output phi network use_out_phi_res = False, # residual out phi use_bernoulli = False, use_rot_trick = False, ): super().__init__() # some assert validations assert exists(dim) , 'dim must be specified for BSQ' codebook_dim = dim codebook_dims = codebook_dim * num_codebooks dim = default(dim, codebook_dims) self.codebook_dims = codebook_dims self.out_phi = nn.Linear(codebook_dims, codebook_dims) if use_out_phi else nn.Identity() self.use_out_phi_res = use_out_phi_res if self.use_out_phi_res: self.out_phi_scale = nn.Parameter(torch.zeros(codebook_dims), requires_grad=True) # init as zero self.dim = dim self.codebook_dim = codebook_dim self.num_codebooks = num_codebooks keep_num_codebooks_dim = default(keep_num_codebooks_dim, num_codebooks > 1) assert not (num_codebooks > 1 and not keep_num_codebooks_dim) self.keep_num_codebooks_dim = keep_num_codebooks_dim # channel first self.channel_first = channel_first # For BSQ (binary spherical quantization) if not spherical: raise ValueError("For BSQ, spherical must be True.") self.persample_entropy_compute = 'analytical' self.inv_temperature = inv_temperature self.gamma0 = gamma0 # loss weight for entropy penalty self.gamma = gamma # loss weight for entropy penalty self.zeta = zeta # loss weight for entire entropy penalty self.use_bernoulli = use_bernoulli self.use_rot_trick = use_rot_trick # entropy aux loss related weights assert 0 < frac_per_sample_entropy <= 1. self.frac_per_sample_entropy = frac_per_sample_entropy self.entropy_loss_weight = entropy_loss_weight # codebook scale self.codebook_scale = codebook_scale # commitment loss self.commitment_loss_weight = commitment_loss_weight # whether to soft clamp the input value from -value to value self.soft_clamp_input_value = soft_clamp_input_value assert not exists(soft_clamp_input_value) or soft_clamp_input_value >= codebook_scale # whether to make the entropy loss positive through a softplus (experimental, please report if this worked or not in discussions) self.entropy_loss_offset = entropy_loss_offset self.experimental_softplus_entropy_loss = experimental_softplus_entropy_loss # for no auxiliary loss, during inference self.register_buffer('mask', 2 ** torch.arange(codebook_dim - 1, -1, -1)) self.register_buffer('zero', torch.tensor(0.), persistent = False) # whether to force quantization step to be f32 self.force_quantization_f32 = force_quantization_f32 def bits_to_codes(self, bits): return bits * self.codebook_scale * 2 - self.codebook_scale # @property # def dtype(self): # return self.codebook.dtype def indices_to_codes( self, indices, label_type = 'int_label', project_out = True ): assert label_type in ['int_label', 'bit_label'] is_img_or_video = indices.ndim >= (3 + int(self.keep_num_codebooks_dim)) should_transpose = default(self.channel_first, is_img_or_video) if not self.keep_num_codebooks_dim: if label_type == 'int_label': indices = rearrange(indices, '... -> ... 1') else: indices = indices.unsqueeze(-2) # indices to codes, which are bits of either -1 or 1 if label_type == 'int_label': assert indices[..., None].int().min() > 0 bits = ((indices[..., None].int() & self.mask) != 0).float() # .to(self.dtype) else: bits = indices codes = self.bits_to_codes(bits).float() codes = l2norm(codes) # must normalize when using BSQ codes = rearrange(codes, '... c d -> ... (c d)') # whether to project codes out to original dimensions # if the input feature dimensions were not log2(codebook size) # rearrange codes back to original shape if should_transpose: codes = rearrange(codes, 'b ... d -> b d ...') return codes def quantize(self, z): assert z.shape[-1] == self.codebook_dims, f"Expected {self.codebook_dims} dimensions, got {z.shape[-1]}" zhat = torch.where(z > 0, torch.tensor(1, dtype=z.dtype, device=z.device), torch.tensor(-1, dtype=z.dtype, device=z.device)) q_scale = 1. / (self.codebook_dims ** 0.5) zhat = q_scale * zhat # on unit sphere return z + (zhat - z).detach() def quantize_new_bernoulli(self, z, prob_z): assert z.shape[-1] == self.codebook_dims, f"Expected {self.codebook_dims} dimensions, got {z.shape[-1]}" zhat = (torch.bernoulli(prob_z) - 0.5) * 2.0 q_scale = 1. / (self.codebook_dims ** 0.5) zhat = q_scale * zhat # on unit sphere return z + (zhat - z).detach() def rot_quantize(self, z, inference=False): assert z.shape[-1] == self.codebook_dims, f"Expected {self.codebook_dims} dimensions, got {z.shape[-1]}" q_scale = 1. / (self.codebook_dims ** 0.5) zhat = torch.where(z > 0, torch.tensor(1, dtype=z.dtype, device=z.device), torch.tensor(-1, dtype=z.dtype, device=z.device)) * q_scale if inference: return zhat w = ((z + zhat) / torch.norm(z + zhat, dim=-1, keepdim=True)).detach() z = z.unsqueeze(1) - 2*torch.bmm(torch.bmm(z.unsqueeze(1), w.unsqueeze(-1)), w.unsqueeze(1)) + 2 * torch.bmm( torch.bmm(z.unsqueeze(1), z.unsqueeze(-1).detach()), zhat.unsqueeze(1).detach()) return z.squeeze() def soft_entropy_loss(self, z): if self.persample_entropy_compute == 'analytical': # if self.l2_norm: p = torch.sigmoid(-4 * z / (self.codebook_dims ** 0.5) * self.inv_temperature) # else: # p = torch.sigmoid(-4 * z * self.inv_temperature) prob = torch.stack([p, 1-p], dim=-1) # (b, h, w, 18, 2) per_sample_entropy = self.get_entropy(prob, dim=-1, normalize=False).sum(dim=-1).mean() # (b,h,w,18)->(b,h,w)->scalar else: per_sample_entropy = self.get_entropy(prob, dim=-1, normalize=False).sum(dim=-1).mean() # macro average of the probability of each subgroup avg_prob = reduce(prob, '... g d ->g d', 'mean') # (18, 2) codebook_entropy = self.get_entropy(avg_prob, dim=-1, normalize=False) # the approximation of the entropy is the sum of the entropy of each subgroup return per_sample_entropy, codebook_entropy.sum(), avg_prob def get_entropy(self, count, dim=-1, eps=1e-4, normalize=True): if normalize: # False probs = (count + eps) / (count + eps).sum(dim=dim, keepdim =True) else: # True probs = count H = -(probs * torch.log(probs + 1e-8)).sum(dim=dim) return H def forward( self, x, return_loss_breakdown = False, mask = None, entropy_weight=0.1 ): """ einstein notation b - batch n - sequence (or flattened spatial dimensions) d - feature dimension, which is also log2(codebook size) c - number of codebook dim """ is_img_or_video = x.ndim >= 4 should_transpose = default(self.channel_first, is_img_or_video) # standardize image or video into (batch, seq, dimension) if should_transpose: x = rearrange(x, 'b d ... -> b ... d') x, ps = pack_one(x, 'b * d') # x.shape [b, hwt, c] assert x.shape[-1] == self.dim, f'expected dimension of {self.dim} but received {x.shape[-1]}' # split out number of codebooks x = rearrange(x, 'b n (c d) -> b n c d', c = self.num_codebooks) if self.use_bernoulli: prob_x = torch.sigmoid(x) x = l2norm(x) # whether to force quantization step to be full precision or not force_f32 = self.force_quantization_f32 quantization_context = partial(autocast, 'cuda', enabled = False) if force_f32 else nullcontext with quantization_context(): if force_f32: orig_dtype = x.dtype x = x.float() # use straight-through gradients if self.use_rot_trick: x_f = x.flatten(end_dim=-2) # (b, hwt, 1, d) -> (bhwt, d) q_f = self.rot_quantize(x_f, inference= not self.training) quantized = q_f.reshape(x.shape) elif self.use_bernoulli: quantized = self.quantize_new_bernoulli(x, prob_x) else: quantized = self.quantize(x) # calculate indices indices = reduce((quantized > 0).int() * self.mask.int(), 'b n c d -> b n c', 'sum') bit_indices = (quantized > 0).int() # entropy aux loss if self.training: persample_entropy, cb_entropy, avg_prob = self.soft_entropy_loss(x) # compute entropy entropy_penalty = self.gamma0 * persample_entropy - self.gamma * cb_entropy else: # if not training, just return dummy 0 entropy_penalty = persample_entropy = cb_entropy = self.zero # commit loss if self.training and self.commitment_loss_weight > 0.: commit_loss = F.mse_loss(x, quantized.detach(), reduction = 'none') if exists(mask): commit_loss = commit_loss[mask] commit_loss = commit_loss.mean() else: commit_loss = self.zero # input back to original dtype if needed if force_f32: x = x.type(orig_dtype) # merge back codebook dim x = quantized # rename quantized to x for output if self.use_out_phi_res: x = x + self.out_phi_scale * self.out_phi(x) # apply out_phi on quant output as residual else: x = self.out_phi(x) # apply out_phi on quant output x = rearrange(x, 'b n c d -> b n (c d)') # reconstitute image or video dimensions if should_transpose: x = unpack_one(x, ps, 'b * d') x = rearrange(x, 'b ... d -> b d ...') bit_indices = unpack_one(bit_indices, ps, 'b * c d') # whether to remove single codebook dim if not self.keep_num_codebooks_dim: bit_indices = rearrange(bit_indices, '... 1 d -> ... d') # complete aux loss aux_loss = commit_loss * self.commitment_loss_weight + (self.zeta * entropy_penalty / self.inv_temperature)*entropy_weight # returns ret = Return(x, indices, bit_indices, aux_loss) if not return_loss_breakdown: return ret return ret, LossBreakdown(persample_entropy, cb_entropy, commit_loss)