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"""rotary_embedding.py - Rotary Embedding based on https://github.com/lucidrains/rotary-embedding-torch"""
from typing import Literal, Union, Optional
from math import pi, log
from einops import rearrange, repeat
import torch
from torch.nn import Module, ModuleList
from torch.cuda.amp import autocast
from torch import nn, einsum, broadcast_tensors, Tensor
# helper functions
def exists(val):
return val is not None
def default(val, d):
return val if exists(val) else d
# broadcat, as tortoise-tts was using it
def broadcat(tensors, dim=-1):
broadcasted_tensors = broadcast_tensors(*tensors)
return torch.cat(broadcasted_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)')
@autocast(enabled=False)
def apply_rotary_emb(freqs, t, start_index=0, scale=1., seq_dim=-2):
"""Applies rotary embedding for pixels."""
if t.ndim == 3:
seq_len = t.shape[seq_dim]
freqs = freqs[-seq_len:].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() * scale) + (rotate_half(t) * freqs.sin() * scale)
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(Module):
def __init__(self,
dim,
custom_freqs: Optional[Tensor] = None,
freqs_for: Union[Literal['lang'], Literal['pixel'], Literal['constant']] = 'lang',
theta=10000,
max_freq=10,
num_freqs=1,
learned_freq=False,
use_xpos=False,
xpos_scale_base=512,
interpolate_factor=1.,
theta_rescale_factor=1.,
seq_before_head_dim=False,
cache_if_possible=True):
super().__init__()
# proposed by reddit user bloc97, to rescale rotary embeddings to longer sequence length without fine-tuning
# has some connection to NTK literature
# https://www.reddit.com/r/LocalLLaMA/comments/14lz7j5/ntkaware_scaled_rope_allows_llama_models_to_have/
theta *= theta_rescale_factor**(dim / (dim - 2))
self.freqs_for = freqs_for
if exists(custom_freqs):
freqs = custom_freqs
elif freqs_for == 'lang':
freqs = 1. / (theta**(torch.arange(0, dim, 2)[:(dim // 2)].float() / dim))
elif freqs_for == 'pixel':
freqs = torch.linspace(1., max_freq / 2, dim // 2) * pi
elif freqs_for == 'constant':
freqs = torch.ones(num_freqs).float()
self.cache_if_possible = cache_if_possible
self.tmp_store('cached_freqs', None)
self.tmp_store('cached_scales', None)
self.freqs = nn.Parameter(freqs, requires_grad=learned_freq)
self.learned_freq = learned_freq
# dummy for device
self.tmp_store('dummy', torch.tensor(0))
# default sequence dimension
self.seq_before_head_dim = seq_before_head_dim
self.default_seq_dim = -3 if seq_before_head_dim else -2
# interpolation factors
assert interpolate_factor >= 1.
self.interpolate_factor = interpolate_factor
# xpos
self.use_xpos = use_xpos
if not use_xpos:
self.tmp_store('scale', None)
return
scale = (torch.arange(0, dim, 2) + 0.4 * dim) / (1.4 * dim)
self.scale_base = xpos_scale_base
self.tmp_store('scale', scale)
@property
def device(self):
return self.dummy.device
def tmp_store(self, key, value):
self.register_buffer(key, value, persistent=False)
def get_seq_pos(self, seq_len, device, dtype, offset=0):
return (torch.arange(seq_len, device=device, dtype=dtype) + offset) / self.interpolate_factor
def rotate_queries_or_keys(self, t, seq_dim=None, offset=0, freq_seq_len=None):
seq_dim = default(seq_dim, self.default_seq_dim)
assert not self.use_xpos, 'you must use `.rotate_queries_and_keys` method instead and pass in both queries and keys, for length extrapolatable rotary embeddings'
device, dtype, seq_len = t.device, t.dtype, t.shape[seq_dim]
if exists(freq_seq_len):
assert freq_seq_len >= seq_len
seq_len = freq_seq_len
freqs = self.forward(self.get_seq_pos(seq_len, device=device, dtype=dtype, offset=offset),
seq_len=seq_len,
offset=offset)
if seq_dim == -3:
freqs = rearrange(freqs, 'n d -> n 1 d')
return apply_rotary_emb(freqs, t, seq_dim=seq_dim)
def rotate_queries_with_cached_keys(self, q, k, seq_dim=None, offset=0):
seq_dim = default(seq_dim, self.default_seq_dim)
q_len, k_len = q.shape[seq_dim], k.shape[seq_dim]
assert q_len <= k_len
rotated_q = self.rotate_queries_or_keys(q, seq_dim=seq_dim, freq_seq_len=k_len)
rotated_k = self.rotate_queries_or_keys(k, seq_dim=seq_dim)
rotated_q = rotated_q.type(q.dtype)
rotated_k = rotated_k.type(k.dtype)
return rotated_q, rotated_k
def rotate_queries_and_keys(self, q, k, seq_dim=None):
seq_dim = default(seq_dim, self.default_seq_dim)
assert self.use_xpos
device, dtype, seq_len = q.device, q.dtype, q.shape[seq_dim]
seq = self.get_seq_pos(seq_len, dtype=dtype, device=device)
freqs = self.forward(seq, seq_len=seq_len)
scale = self.get_scale(seq, seq_len=seq_len).to(dtype)
if seq_dim == -3:
freqs = rearrange(freqs, 'n d -> n 1 d')
scale = rearrange(scale, 'n d -> n 1 d')
rotated_q = apply_rotary_emb(freqs, q, scale=scale, seq_dim=seq_dim)
rotated_k = apply_rotary_emb(freqs, k, scale=scale**-1, seq_dim=seq_dim)
rotated_q = rotated_q.type(q.dtype)
rotated_k = rotated_k.type(k.dtype)
return rotated_q, rotated_k
def get_scale(self, t: Tensor, seq_len: Optional[int] = None, offset=0):
assert self.use_xpos
should_cache = (self.cache_if_possible and exists(seq_len))
if (
should_cache and \
exists(self.cached_scales) and \
(seq_len + offset) <= self.cached_scales.shape[0]
):
return self.cached_scales[offset:(offset + seq_len)]
scale = 1.
if self.use_xpos:
power = (t - len(t) // 2) / self.scale_base
scale = self.scale**rearrange(power, 'n -> n 1')
scale = torch.cat((scale, scale), dim=-1)
if should_cache:
self.tmp_store('cached_scales', scale)
return scale
def get_axial_freqs(self, *dims):
Colon = slice(None)
all_freqs = []
for ind, dim in enumerate(dims):
if self.freqs_for == 'pixel':
pos = torch.linspace(-1, 1, steps=dim, device=self.device)
else:
pos = torch.arange(dim, device=self.device)
freqs = self.forward(pos, seq_len=dim)
all_axis = [None] * len(dims)
all_axis[ind] = Colon
new_axis_slice = (Ellipsis, *all_axis, Colon)
all_freqs.append(freqs[new_axis_slice])
all_freqs = broadcast_tensors(*all_freqs)
return torch.cat(all_freqs, dim=-1)
@autocast(enabled=False)
def forward(self, t: Tensor, seq_len=None, offset=0):
should_cache = (
self.cache_if_possible and \
not self.learned_freq and \
exists(seq_len) and \
self.freqs_for != 'pixel'
)
if (
should_cache and \
exists(self.cached_freqs) and \
(offset + seq_len) <= self.cached_freqs.shape[0]
):
return self.cached_freqs[offset:(offset + seq_len)].detach()
freqs = self.freqs
freqs = einsum('..., f -> ... f', t.type(freqs.dtype), freqs)
freqs = repeat(freqs, '... n -> ... (n r)', r=2)
if should_cache:
self.tmp_store('cached_freqs', freqs.detach())
return freqs
# custom method for applying rotary embeddings
@torch.compiler.disable
def apply_rotary_custom(self, t: torch.Tensor):
"""Apply rotary embeddings to queries and keys, if k is None, only q is rotated.
Depending on the freqs type, the rotation will be different."""
if self.freqs_for == 'lang':
return self.rotate_queries_or_keys(t, seq_dim=-2)
elif self.freqs_for == 'pixel':
return apply_rotary_emb(self.get_axial_freqs(t.shape[-2]), t)
else:
raise ValueError(f"freqs_for must be 'lang' or 'pixel', but got {self.freqs_for}")
def test_rotary_embedding_lang():
d = 32 # d by head
q = torch.ones(1, 4, 110, 32) # (B, H, T, D) for multi-head attention
rdim = d // 2 # will do a partial rotation on half, or d
rotary = RotaryEmbedding(dim=rdim, freqs_for="lang")
q = rotary.rotate_queries_or_keys(q, seq_dim=-2)
# visualize
import matplotlib.pyplot as plt
plt.imshow(q[0, 0, :, :].numpy().T, origin='lower')
def test_rotary_embedding_pixel():
d = 32 # d by head
q = torch.ones(1, 4, 128, 32) # (B*T, H, F, C/H) for multi-head attention
rdim = d // 2 # will do a partial rotation on half
rotary = RotaryEmbedding(dim=rdim, freqs_for="pixel", max_freq=10)
freqs = rotary.get_axial_freqs(128)
q = apply_rotary_emb(freqs, q) # also k, if needed
# visualize
import matplotlib.pyplot as plt
plt.imshow(q[0, 0, :, :].numpy().T, origin='lower')
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