import torch from typing import Tuple, Callable def do_nothing(x: torch.Tensor, mode:str=None): return x def mps_gather_workaround(input, dim, index): if input.shape[-1] == 1: return torch.gather( input.unsqueeze(-1), dim - 1 if dim < 0 else dim, index.unsqueeze(-1) ).squeeze(-1) else: return torch.gather(input, dim, index) def bipartite_soft_matching_random2d(metric: torch.Tensor, w: int, h: int, sx: int, sy: int, r: int, no_rand: bool = False, generator: torch.Generator = None) -> Tuple[Callable, Callable]: """ Partitions the tokens into src and dst and merges r tokens from src to dst. Dst tokens are partitioned by choosing one randomy in each (sx, sy) region. Args: - metric [B, N, C]: metric to use for similarity - w: image width in tokens - h: image height in tokens - sx: stride in the x dimension for dst, must divide w - sy: stride in the y dimension for dst, must divide h - r: number of tokens to remove (by merging) - no_rand: if true, disable randomness (use top left corner only) - rand_seed: if no_rand is false, and if not None, sets random seed. """ B, N, _ = metric.shape if r <= 0: return do_nothing, do_nothing gather = mps_gather_workaround if metric.device.type == "mps" else torch.gather with torch.no_grad(): hsy, wsx = h // sy, w // sx # For each sy by sx kernel, randomly assign one token to be dst and the rest src if no_rand: rand_idx = torch.zeros(hsy, wsx, 1, device=metric.device, dtype=torch.int64) else: rand_idx = torch.randint(sy*sx, size=(hsy, wsx, 1), device=generator.device, generator=generator).to(metric.device) # The image might not divide sx and sy, so we need to work on a view of the top left if the idx buffer instead idx_buffer_view = torch.zeros(hsy, wsx, sy*sx, device=metric.device, dtype=torch.int64) idx_buffer_view.scatter_(dim=2, index=rand_idx, src=-torch.ones_like(rand_idx, dtype=rand_idx.dtype)) idx_buffer_view = idx_buffer_view.view(hsy, wsx, sy, sx).transpose(1, 2).reshape(hsy * sy, wsx * sx) # Image is not divisible by sx or sy so we need to move it into a new buffer if (hsy * sy) < h or (wsx * sx) < w: idx_buffer = torch.zeros(h, w, device=metric.device, dtype=torch.int64) idx_buffer[:(hsy * sy), :(wsx * sx)] = idx_buffer_view else: idx_buffer = idx_buffer_view # We set dst tokens to be -1 and src to be 0, so an argsort gives us dst|src indices rand_idx = idx_buffer.reshape(1, -1, 1).argsort(dim=1) # We're finished with these del idx_buffer, idx_buffer_view # rand_idx is currently dst|src, so split them num_dst = hsy * wsx a_idx = rand_idx[:, num_dst:, :] # src b_idx = rand_idx[:, :num_dst, :] # dst def split(x): C = x.shape[-1] src = gather(x, dim=1, index=a_idx.expand(B, N - num_dst, C)) dst = gather(x, dim=1, index=b_idx.expand(B, num_dst, C)) return src, dst # Cosine similarity between A and B metric = metric / metric.norm(dim=-1, keepdim=True) a, b = split(metric) scores = a @ b.transpose(-1, -2) # Can't reduce more than the # tokens in src r = min(a.shape[1], r) # Find the most similar greedily node_max, node_idx = scores.max(dim=-1) edge_idx = node_max.argsort(dim=-1, descending=True)[..., None] unm_idx = edge_idx[..., r:, :] # Unmerged Tokens src_idx = edge_idx[..., :r, :] # Merged Tokens dst_idx = gather(node_idx[..., None], dim=-2, index=src_idx) def merge(x: torch.Tensor, mode="mean") -> torch.Tensor: src, dst = split(x) n, t1, c = src.shape unm = gather(src, dim=-2, index=unm_idx.expand(n, t1 - r, c)) src = gather(src, dim=-2, index=src_idx.expand(n, r, c)) dst = dst.scatter_reduce(-2, dst_idx.expand(n, r, c), src, reduce=mode) return torch.cat([unm, dst], dim=1) def unmerge(x: torch.Tensor) -> torch.Tensor: unm_len = unm_idx.shape[1] unm, dst = x[..., :unm_len, :], x[..., unm_len:, :] _, _, c = unm.shape src = gather(dst, dim=-2, index=dst_idx.expand(B, r, c)) # Combine back to the original shape out = torch.zeros(B, N, c, device=x.device, dtype=x.dtype) out.scatter_(dim=-2, index=b_idx.expand(B, num_dst, c), src=dst) out.scatter_(dim=-2, index=gather(a_idx.expand(B, a_idx.shape[1], 1), dim=1, index=unm_idx).expand(B, unm_len, c), src=unm) out.scatter_(dim=-2, index=gather(a_idx.expand(B, a_idx.shape[1], 1), dim=1, index=src_idx).expand(B, r, c), src=src) return out return merge, unmerge