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"""Roatary embedding.
Stolen from lucidrains:
https://github.com/lucidrains/x-transformers/blob/main/x_transformers/x_transformers.py
Explanation of roatary:
https://blog.eleuther.ai/rotary-embeddings/
"""
from typing import Tuple
from einops import rearrange
import torch
from torch import nn
from torch import Tensor
class RotaryEmbedding(nn.Module):
def __init__(self, dim: int):
super().__init__()
inv_freq = 1.0 / (10000 ** (torch.arange(0, dim, 2).float() / dim))
self.register_buffer("inv_freq", inv_freq)
def forward(self, x: Tensor, seq_dim: int = 1) -> Tensor:
t = torch.arange(x.shape[seq_dim], device=x.device).type_as(self.inv_freq)
freqs = torch.einsum("i , j -> i j", t, self.inv_freq)
emb = torch.cat((freqs, freqs), dim=-1)
return emb[None, :, :]
def rotate_half(x: Tensor) -> Tensor:
x = rearrange(x, "... (j d) -> ... j d", j=2)
x1, x2 = x.unbind(dim=-2)
return torch.cat((-x2, x1), dim=-1)
def apply_rotary_pos_emb(q: Tensor, k: Tensor, freqs: Tensor) -> Tuple[Tensor, Tensor]:
q, k = map(lambda t: (t * freqs.cos()) + (rotate_half(t) * freqs.sin()), (q, k))
return q, k
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