rope_embeddings.py

from __future__ import annotations
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