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from math import pi, log
import torch
from torch.amp import autocast
from torch.nn import Module
from torch import nn, broadcast_tensors, is_tensor, tensor, Tensor
from typing import Literal
def exists(val):
return val is not None
def default(val, d):
return val if exists(val) else d
def broadcat(tensors, dim=-1):
broadcasted_tensors = broadcast_tensors(*tensors)
return torch.cat(broadcasted_tensors, dim=dim)
def slice_at_dim(t, dim_slice: slice, *, dim):
dim += (t.ndim if dim < 0 else 0)
colons = [slice(None)] * t.ndim
colons[dim] = dim_slice
return t[tuple(colons)]
def rotate_half(x):
orig_shape = x.shape
d_head = orig_shape[-1]
x = x.view(*orig_shape[:-1], d_head // 2, 2)
x1 = x[..., 0]
x2 = x[..., 1]
res = torch.stack((-x2, x1), dim=-1)
return res.view(*orig_shape)
@autocast('cuda', enabled=False)
def apply_rotary_emb(
freqs,
t,
start_index=0,
scale=1.,
seq_dim=-2,
freqs_seq_dim=None
):
dtype = t.dtype
if not exists(freqs_seq_dim):
if freqs.ndim == 2 or t.ndim == 3:
freqs_seq_dim = 0
if t.ndim == 3 or exists(freqs_seq_dim):
seq_len = t.shape[seq_dim]
freqs = slice_at_dim(freqs, slice(-seq_len, None), dim=freqs_seq_dim)
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[..., :start_index]
t_middle = t[..., start_index:end_index]
t_right = t[..., end_index:]
t_transformed = (t_middle * freqs.cos() * scale) + (rotate_half(t_middle) * freqs.sin() * scale)
out = torch.cat((t_left, t_transformed, t_right), dim=-1)
return out.type(dtype)
def apply_learned_rotations(rotations, t, start_index=0, freq_ranges=None):
if exists(freq_ranges):
rotations = torch.einsum('..., f -> ... f', rotations, freq_ranges)
rotations = rotations.reshape(*rotations.shape[:-2], -1)
rotations = rotations.repeat_interleave(2, dim=-1)
return apply_rotary_emb(rotations, t, start_index=start_index)
class RotaryEmbedding(Module):
def __init__(
self,
dim,
custom_freqs: Tensor | None = None,
freqs_for: Literal['lang', 'pixel', '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,
cache_max_seq_len = 8192
):
super().__init__()
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.cache_max_seq_len = cache_max_seq_len
self.register_buffer('cached_freqs', torch.zeros(cache_max_seq_len, dim), persistent=False)
self.cached_freqs_seq_len = 0
self.freqs = nn.Parameter(freqs, requires_grad=learned_freq)
self.learned_freq = learned_freq
self.register_buffer('dummy', torch.tensor(0), persistent=False)
self.seq_before_head_dim = seq_before_head_dim
self.default_seq_dim = -3 if seq_before_head_dim else -2
assert interpolate_factor >= 1.
self.interpolate_factor = interpolate_factor
self.use_xpos = use_xpos
if not use_xpos:
return
scale = (torch.arange(0, dim, 2) + 0.4 * dim) / (1.4 * dim)
self.scale_base = xpos_scale_base
self.register_buffer('scale', scale, persistent=False)
self.register_buffer('cached_scales', torch.zeros(cache_max_seq_len, dim), persistent=False)
self.cached_scales_seq_len = 0
self.apply_rotary_emb = staticmethod(apply_rotary_emb)
@property
def device(self):
return self.dummy.device
def get_seq_pos(self, seq_len, device=None, dtype=None, offset=0):
device = default(device, self.device)
dtype = default(dtype, self.cached_freqs.dtype)
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, scale=None):
seq_dim = default(seq_dim, self.default_seq_dim)
assert not self.use_xpos or exists(scale), 'you must use `.rotate_queries_and_keys` method instead'
device, dtype, seq_len = t.device, t.dtype, t.shape[seq_dim]
seq = self.get_seq_pos(seq_len, device=device, dtype=dtype, offset=offset)
freqs = self.forward(seq, seq_len=seq_len, offset=offset)
if seq_dim == -3:
freqs = freqs.unsqueeze(1)
return apply_rotary_emb(freqs, t, scale=default(scale, 1.), seq_dim=seq_dim)
def rotate_queries_with_cached_keys(self, q, k, seq_dim=None, offset=0):
dtype, device, seq_dim = q.dtype, q.device, default(seq_dim, self.default_seq_dim)
q_len, k_len = q.shape[seq_dim], k.shape[seq_dim]
assert q_len <= k_len
q_scale = k_scale = 1.
if self.use_xpos:
seq = self.get_seq_pos(k_len, dtype=dtype, device=device)
q_scale = self.get_scale(seq[-q_len:]).type(dtype)
k_scale = self.get_scale(seq).type(dtype)
rotated_q = self.rotate_queries_or_keys(q, seq_dim=seq_dim, scale=q_scale, offset=k_len - q_len + offset)
rotated_k = self.rotate_queries_or_keys(k, seq_dim=seq_dim, scale=k_scale ** -1)
return rotated_q.type(q.dtype), rotated_k.type(k.dtype)
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 = freqs.unsqueeze(1)
scale = scale.unsqueeze(1)
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)
return rotated_q.type(q.dtype), rotated_k.type(k.dtype)
def get_scale(self, t: Tensor, seq_len: int | None = None, offset=0):
assert self.use_xpos
should_cache = self.cache_if_possible and exists(seq_len) and (offset + seq_len) <= self.cache_max_seq_len
if should_cache and (seq_len + offset) <= self.cached_scales_seq_len:
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 ** power.unsqueeze(-1)
scale = scale.repeat_interleave(2, dim=-1)
if should_cache and offset == 0:
self.cached_scales[:seq_len] = scale.detach()
self.cached_scales_seq_len = seq_len
return scale
def get_axial_freqs(self, *dims, offsets: tuple[int | float, ...] | Tensor | None = None):
Colon = slice(None)
all_freqs = []
if exists(offsets):
if not is_tensor(offsets):
offsets = tensor(offsets)
assert len(offsets) == len(dims)
for ind, dim in enumerate(dims):
offset = 0
if exists(offsets):
offset = offsets[ind]
if self.freqs_for == 'pixel':
pos = torch.linspace(-1, 1, steps=dim, device=self.device)
else:
pos = torch.arange(dim, device=self.device)
pos = pos + offset
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('cuda', enabled=False)
def forward(self, t: Tensor, seq_len: int | None = None, offset=0):
should_cache = (
self.cache_if_possible and not self.learned_freq and
exists(seq_len) and self.freqs_for != 'pixel' and
(offset + seq_len) <= self.cache_max_seq_len
)
if should_cache and (offset + seq_len) <= self.cached_freqs_seq_len:
return self.cached_freqs[offset:(offset + seq_len)].detach()
freqs = self.freqs
freqs = torch.einsum('..., f -> ... f', t.type(freqs.dtype), freqs)
freqs = freqs.repeat_interleave(2, dim=-1)
if should_cache and offset == 0:
self.cached_freqs[:seq_len] = freqs.detach()
self.cached_freqs_seq_len = seq_len
return freqs |