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| """ | |
| Copyright (c) Meta Platforms, Inc. and affiliates. | |
| All rights reserved. | |
| This source code is licensed under the license found in the | |
| LICENSE file in the root directory of this source tree. | |
| """ | |
| from inspect import isfunction | |
| from math import log, pi | |
| import torch | |
| from einops import rearrange, repeat | |
| from torch import einsum, nn | |
| # helper functions | |
| def exists(val): | |
| return val is not None | |
| def broadcat(tensors, dim=-1): | |
| num_tensors = len(tensors) | |
| shape_lens = set(list(map(lambda t: len(t.shape), tensors))) | |
| assert len(shape_lens) == 1, "tensors must all have the same number of dimensions" | |
| shape_len = list(shape_lens)[0] | |
| dim = (dim + shape_len) if dim < 0 else dim | |
| dims = list(zip(*map(lambda t: list(t.shape), tensors))) | |
| expandable_dims = [(i, val) for i, val in enumerate(dims) if i != dim] | |
| assert all( | |
| [*map(lambda t: len(set(t[1])) <= 2, expandable_dims)] | |
| ), "invalid dimensions for broadcastable concatentation" | |
| max_dims = list(map(lambda t: (t[0], max(t[1])), expandable_dims)) | |
| expanded_dims = list(map(lambda t: (t[0], (t[1],) * num_tensors), max_dims)) | |
| expanded_dims.insert(dim, (dim, dims[dim])) | |
| expandable_shapes = list(zip(*map(lambda t: t[1], expanded_dims))) | |
| tensors = list(map(lambda t: t[0].expand(*t[1]), zip(tensors, expandable_shapes))) | |
| return torch.cat(tensors, dim=dim) | |
| # rotary embedding helper functions | |
| def rotate_half(x): | |
| x = rearrange(x, "... (d r) -> ... d r", r=2) | |
| x1, x2 = x.unbind(dim=-1) | |
| x = torch.stack((-x2, x1), dim=-1) | |
| return rearrange(x, "... d r -> ... (d r)") | |
| def apply_rotary_emb(freqs, t, start_index=0): | |
| freqs = freqs.to(t) | |
| rot_dim = freqs.shape[-1] | |
| end_index = start_index + rot_dim | |
| assert ( | |
| rot_dim <= t.shape[-1] | |
| ), f"feature dimension {t.shape[-1]} is not of sufficient size to rotate in all the positions {rot_dim}" | |
| t_left, t, t_right = ( | |
| t[..., :start_index], | |
| t[..., start_index:end_index], | |
| t[..., end_index:], | |
| ) | |
| t = (t * freqs.cos()) + (rotate_half(t) * freqs.sin()) | |
| return torch.cat((t_left, t, t_right), dim=-1) | |
| # learned rotation helpers | |
| def apply_learned_rotations(rotations, t, start_index=0, freq_ranges=None): | |
| if exists(freq_ranges): | |
| rotations = einsum("..., f -> ... f", rotations, freq_ranges) | |
| rotations = rearrange(rotations, "... r f -> ... (r f)") | |
| rotations = repeat(rotations, "... n -> ... (n r)", r=2) | |
| return apply_rotary_emb(rotations, t, start_index=start_index) | |
| # classes | |
| class RotaryEmbedding(nn.Module): | |
| def __init__( | |
| self, | |
| dim, | |
| custom_freqs=None, | |
| freqs_for="lang", | |
| theta=10000, | |
| max_freq=10, | |
| num_freqs=1, | |
| learned_freq=False, | |
| ): | |
| super().__init__() | |
| if exists(custom_freqs): | |
| freqs = custom_freqs | |
| elif freqs_for == "lang": | |
| freqs = 1.0 / ( | |
| theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim) | |
| ) | |
| elif freqs_for == "pixel": | |
| freqs = torch.linspace(1.0, max_freq / 2, dim // 2) * pi | |
| elif freqs_for == "constant": | |
| freqs = torch.ones(num_freqs).float() | |
| else: | |
| raise ValueError(f"unknown modality {freqs_for}") | |
| self.cache = dict() | |
| if learned_freq: | |
| self.freqs = nn.Parameter(freqs) | |
| else: | |
| self.register_buffer("freqs", freqs) | |
| def rotate_queries_or_keys(self, t, seq_dim=-2): | |
| device = t.device | |
| seq_len = t.shape[seq_dim] | |
| freqs = self.forward( | |
| lambda: torch.arange(seq_len, device=device), cache_key=seq_len | |
| ) | |
| return apply_rotary_emb(freqs, t) | |
| def forward(self, t, cache_key=None): | |
| if exists(cache_key) and cache_key in self.cache: | |
| return self.cache[cache_key] | |
| if isfunction(t): | |
| t = t() | |
| freqs = self.freqs | |
| freqs = torch.einsum("..., f -> ... f", t.type(freqs.dtype), freqs) | |
| freqs = repeat(freqs, "... n -> ... (n r)", r=2) | |
| if exists(cache_key): | |
| self.cache[cache_key] = freqs | |
| return freqs |