rotary.py

# Copyright (c) 2023, Tri Dao.

import math
from typing import Optional, Tuple

import rotary_emb
import torch
from einops import rearrange, repeat


def rotate_half(x, interleaved=False):
    if not interleaved:
        x1, x2 = x.chunk(2, dim=-1)
        return torch.cat((-x2, x1), dim=-1)
    else:
        x1, x2 = x[..., ::2], x[..., 1::2]
        return rearrange(torch.stack((-x2, x1), dim=-1), "... d two -> ... (d two)", two=2)


def apply_rotary_emb_torch(x, cos, sin, interleaved=False):
    """
    x: (batch_size, seqlen, nheads, headdim)
    cos, sin: (seqlen, rotary_dim / 2)
    """
    ro_dim = cos.shape[-1] * 2
    assert ro_dim <= x.shape[-1]
    cos = repeat(cos, "s d -> s 1 (2 d)")
    sin = repeat(sin, "s d -> s 1 (2 d)")
    return torch.cat(
        [x[..., :ro_dim] * cos + rotate_half(x[..., :ro_dim], interleaved) * sin, x[..., ro_dim:]],
        dim=-1,
    )


class ApplyRotaryEmb(torch.autograd.Function):
    @staticmethod
    def forward(ctx, x, cos, sin, interleaved=False, inplace=False):
        """
            x: (batch_size, seqlen, nheads, headdim)
            cos, sin: (seqlen, rotary_dim / 2)
            interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead
                of 1st half and 2nd half (GPT-NeoX style).
        rotary_dim must be <= headdim
        Apply rotary embedding to the first rotary_dim of x.
        """
        batch, seqlen, nheads, headdim = x.shape
        rotary_seqlen, rotary_dim = cos.shape
        rotary_dim *= 2
        assert rotary_dim <= headdim
        assert seqlen <= rotary_seqlen
        assert sin.shape == (rotary_seqlen, rotary_dim // 2)
        x_ro = x[..., :rotary_dim]
        x1, x2 = x_ro.chunk(2, dim=-1) if not interleaved else (x_ro[..., ::2], x_ro[..., 1::2])
        out = torch.empty_like(x) if not inplace else x
        out_ro = out[..., :rotary_dim]
        if inplace:
            o1, o2 = x1, x2
        else:
            o1, o2 = (
                out_ro.chunk(2, dim=-1)
                if not interleaved
                else (out_ro[..., ::2], out_ro[..., 1::2])
            )
        rotary_emb.apply_rotary(
            x1,
            x2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            o1,
            o2,
            False,
        )
        if not inplace and rotary_dim < headdim:
            out[..., rotary_dim:].copy_(x[..., rotary_dim:])
        ctx.save_for_backward(cos, sin)
        ctx.interleaved = interleaved
        ctx.inplace = inplace
        return out if not inplace else x

    @staticmethod
    def backward(ctx, do):
        cos, sin = ctx.saved_tensors
        _, seqlen, _, headdim = do.shape
        rotary_dim = cos.shape[-1]
        rotary_dim *= 2
        inplace = ctx.inplace
        do_ro = do[..., :rotary_dim]
        do1, do2 = (
            do_ro.chunk(2, dim=-1) if not ctx.interleaved else (do_ro[..., ::2], do_ro[..., 1::2])
        )
        dx = torch.empty_like(do) if not inplace else do
        if inplace:
            dx1, dx2 = do1, do2
        else:
            dx_ro = dx[..., :rotary_dim]
            dx1, dx2 = (
                dx_ro.chunk(2, dim=-1)
                if not ctx.interleaved
                else (dx_ro[..., ::2], dx_ro[..., 1::2])
            )
        rotary_emb.apply_rotary(
            do1,
            do2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            dx1,
            dx2,
            True,
        )
        if not inplace and rotary_dim < headdim:
            dx[..., rotary_dim:].copy_(do[..., rotary_dim:])
        return dx, None, None, None, None


apply_rotary_emb_func = ApplyRotaryEmb.apply


class ApplyRotaryEmbQKV_(torch.autograd.Function):
    @staticmethod
    def forward(ctx, qkv, cos, sin, cos_k=None, sin_k=None, interleaved=False):
        """
            qkv: (batch_size, seqlen, 3, nheads, headdim)
            cos, sin: (seqlen, rotary_dim / 2)
            cos_k, sin_k: (seqlen, rotary_dim / 2), optional
            interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead of
                1st half and 2nd half (GPT-NeoX style).
        rotary_dim must be <= headdim
        Apply rotary embedding *inplace* to the first rotary_dim of q and k.
        """
        batch, seqlen, three, nheads, headdim = qkv.shape
        assert three == 3
        rotary_seqlen, rotary_dim = cos.shape
        rotary_dim *= 2
        assert rotary_dim <= headdim
        assert seqlen <= rotary_seqlen
        cos_k = cos if cos_k is None else cos_k
        sin_k = sin if sin_k is None else sin_k
        assert sin.shape == cos_k.shape == sin_k.shape == (rotary_seqlen, rotary_dim // 2)
        q_ro = qkv[:, :, 0, :, :rotary_dim]
        q1, q2 = q_ro.chunk(2, dim=-1) if not interleaved else (q_ro[..., ::2], q_ro[..., 1::2])
        rotary_emb.apply_rotary(
            q1,
            q2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            q1,
            q2,
            False,
        )
        k_ro = qkv[:, :, 1, :, :rotary_dim]
        k1, k2 = k_ro.chunk(2, dim=-1) if not interleaved else (k_ro[..., ::2], k_ro[..., 1::2])
        rotary_emb.apply_rotary(
            k1,
            k2,
            rearrange(cos_k[:seqlen], "s d -> s 1 d"),
            rearrange(sin_k[:seqlen], "s d -> s 1 d"),
            k1,
            k2,
            False,
        )
        ctx.save_for_backward(cos, sin, cos_k, sin_k)
        ctx.interleaved = interleaved
        return qkv

    @staticmethod
    def backward(ctx, dqkv):
        cos, sin, cos_k, sin_k = ctx.saved_tensors
        _, seqlen, _, _, headdim = dqkv.shape
        rotary_dim = cos.shape[-1]
        rotary_dim *= 2
        dq_ro = dqkv[:, :, 0, :, :rotary_dim]
        dq1, dq2 = (
            dq_ro.chunk(2, dim=-1) if not ctx.interleaved else (dq_ro[..., ::2], dq_ro[..., 1::2])
        )
        rotary_emb.apply_rotary(
            dq1,
            dq2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            dq1,
            dq2,
            True,
        )
        dk_ro = dqkv[:, :, 1, :, :rotary_dim]
        dk1, dk2 = (
            dk_ro.chunk(2, dim=-1) if not ctx.interleaved else (dk_ro[..., ::2], dk_ro[..., 1::2])
        )
        rotary_emb.apply_rotary(
            dk1,
            dk2,
            rearrange(cos_k[:seqlen], "s d -> s 1 d"),
            rearrange(sin_k[:seqlen], "s d -> s 1 d"),
            dk1,
            dk2,
            True,
        )
        return dqkv, None, None, None, None, None


apply_rotary_emb_qkv_ = ApplyRotaryEmbQKV_.apply


class ApplyRotaryEmbKV_(torch.autograd.Function):
    @staticmethod
    def forward(ctx, kv, cos, sin, interleaved=False):
        """
            kv: (batch_size, seqlen, 2, nheads, headdim)
            cos, sin: (seqlen, rotary_dim / 2)
            interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead of
                1st half and 2nd half (GPT-NeoX style).
        rotary_dim must be <= headdim
        Apply rotary embedding *inplace* to the first rotary_dim of k.
        """
        batch, seqlen, two, nheads, headdim = kv.shape
        assert two == 2
        rotary_seqlen, rotary_dim = cos.shape
        rotary_dim *= 2
        assert rotary_dim <= headdim
        assert seqlen <= rotary_seqlen
        k_ro = kv[:, :, 0, :, :rotary_dim]
        k1, k2 = k_ro.chunk(2, dim=-1) if not interleaved else (k_ro[..., ::2], k_ro[..., 1::2])
        rotary_emb.apply_rotary(
            k1,
            k2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            k1,
            k2,
            False,
        )  # conj=False since this is the forward pass
        ctx.save_for_backward(cos, sin)
        ctx.interleaved = interleaved
        return kv

    @staticmethod
    def backward(ctx, dkv):
        cos, sin = ctx.saved_tensors
        _, seqlen, _, _, headdim = dkv.shape
        rotary_dim = cos.shape[-1]
        rotary_dim *= 2
        dk_ro = dkv[:, :, 0, :, :rotary_dim]
        dk1, dk2 = (
            dk_ro.chunk(2, dim=-1) if not ctx.interleaved else (dk_ro[..., ::2], dk_ro[..., 1::2])
        )
        rotary_emb.apply_rotary(
            dk1,
            dk2,
            rearrange(cos[:seqlen], "s d -> s 1 d"),
            rearrange(sin[:seqlen], "s d -> s 1 d"),
            dk1,
            dk2,
            True,
        )  # conj=True since this is the backward pass
        return dkv, None, None, None


apply_rotary_emb_kv_ = ApplyRotaryEmbKV_.apply


class RotaryEmbedding(torch.nn.Module):
    """
    The rotary position embeddings from RoFormer_ (Su et. al).
    A crucial insight from the method is that the query and keys are
    transformed by rotation matrices which depend on the relative positions.

    Other implementations are available in the Rotary Transformer repo_ and in
    GPT-NeoX_, GPT-NeoX was an inspiration

    .. _RoFormer: https://arxiv.org/abs/2104.09864
    .. _repo: https://github.com/ZhuiyiTechnology/roformer
    .. _GPT-NeoX: https://github.com/EleutherAI/gpt-neox

    If scale_base is not None, this implements XPos (Sun et al., https://arxiv.org/abs/2212.10554).
    A recommended value for scale_base is 512: https://github.com/HazyResearch/flash-attention/issues/96
    Reference: https://github.com/sunyt32/torchscale/blob/main/torchscale/component/xpos_relative_position.py
    """

    def __init__(
        self,
        dim: int,
        base=10000.0,
        interleaved=False,
        scale_base=None,
        pos_idx_in_fp32=True,
        device=None,
    ):
        """
        interleaved: if True, rotate pairs of even and odd dimensions (GPT-J style) instead
            of 1st half and 2nd half (GPT-NeoX style).
        pos_idx_in_fp32: if True, the position indices [0.0, ..., seqlen - 1] are in fp32,
            otherwise they might be in lower precision.
            This option was added because previously (before 2023-07-02), when we construct
            the position indices, we use the dtype of self.inv_freq. In most cases this would
            be fp32, but if the model is trained in pure bf16 (not mixed precision), then
            self.inv_freq would be bf16, and the position indices are also in bf16.
            Because of the limited precision of bf16 (e.g. 1995.0 is rounded to 2000.0), the
            embeddings for some positions will coincide.
            To maintain compatibility with models previously trained in pure bf16,
            we add this option.
        """
        super().__init__()
        self.dim = dim
        self.base = float(base)
        self.pos_idx_in_fp32 = pos_idx_in_fp32
        # Generate and save the inverse frequency buffer (non trainable)
        inv_freq = self._compute_inv_freq(device)
        self.register_buffer("inv_freq", inv_freq, persistent=False)
        self.interleaved = interleaved
        self.scale_base = scale_base
        scale = (
            (torch.arange(0, dim, 2, device=device, dtype=torch.float32) + 0.4 * dim) / (1.4 * dim)
            if scale_base is not None
            else None
        )
        self.register_buffer("scale", scale, persistent=False)

        self._seq_len_cached = 0
        self._cos_cached = None
        self._sin_cached = None
        self._cos_k_cached = None
        self._sin_k_cached = None

    def _compute_inv_freq(self, device=None):
        return 1.0 / (
            self.base
            ** (torch.arange(0, self.dim, 2, device=device, dtype=torch.float32) / self.dim)
        )

    def _update_cos_sin_cache(self, seqlen, device=None, dtype=None):
        # Reset the tables if the sequence length has changed,
        # if we're on a new device (possibly due to tracing for instance),
        # or if we're switching from inference mode to training
        if (
            seqlen > self._seq_len_cached
            or self._cos_cached.device != device
            or self._cos_cached.dtype != dtype
            or (self.training and self._cos_cached.is_inference())
        ):
            self._seq_len_cached = seqlen
            # We want fp32 here, not self.inv_freq.dtype, since the model could be loaded in bf16
            # And the output of arange can be quite large, so bf16 would lose a lot of precision.
            # However, for compatibility reason, we add an option to use the dtype of self.inv_freq.
            if self.pos_idx_in_fp32:
                t = torch.arange(seqlen, device=device, dtype=torch.float32)
                # We want fp32 here as well since inv_freq will be multiplied with t, and the output
                # will be large. Having it in bf16 will lose a lot of precision and cause the
                # cos & sin output to change significantly.
                # We want to recompute self.inv_freq if it was not loaded in fp32
                if self.inv_freq.dtype != torch.float32:
                    inv_freq = self._compute_inv_freq(device=device)
                else:
                    inv_freq = self.inv_freq
            else:
                t = torch.arange(seqlen, device=device, dtype=self.inv_freq.dtype)
                inv_freq = self.inv_freq
            # Don't do einsum, it converts fp32 to fp16 under AMP
            # freqs = torch.einsum("i,j->ij", t, self.inv_freq)
            freqs = torch.outer(t, inv_freq)
            if self.scale is None:
                self._cos_cached = torch.cos(freqs).to(dtype)
                self._sin_cached = torch.sin(freqs).to(dtype)
            else:
                power = (
                    torch.arange(seqlen, dtype=self.scale.dtype, device=self.scale.device)
                    - seqlen // 2
                ) / self.scale_base
                scale = self.scale.to(device=power.device) ** rearrange(power, "s -> s 1")
                # We want the multiplication by scale to happen in fp32
                self._cos_cached = (torch.cos(freqs) * scale).to(dtype)
                self._sin_cached = (torch.sin(freqs) * scale).to(dtype)
                self._cos_k_cached = (torch.cos(freqs) / scale).to(dtype)
                self._sin_k_cached = (torch.sin(freqs) / scale).to(dtype)

    def forward(
        self, qkv: torch.Tensor, kv: Optional[torch.Tensor] = None, seqlen_offset: int = 0
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        qkv: (batch, seqlen, 3, nheads, headdim) if kv is none,
             else it's just q of shape (batch, seqlen, nheads, headdim)
        kv: (batch, seqlen, 2, nheads, headdim)
        seqlen_offset: can be used in generation where the qkv being passed in is only the last
        token in the batch.
        """
        seqlen = qkv.shape[1]
        self._update_cos_sin_cache(seqlen + seqlen_offset, device=qkv.device, dtype=qkv.dtype)
        if kv is None:
            if self.scale is None:
                return apply_rotary_emb_qkv_(
                    qkv,
                    self._cos_cached[seqlen_offset:],
                    self._sin_cached[seqlen_offset:],
                    None,
                    None,
                    self.interleaved,
                )
            else:
                return apply_rotary_emb_qkv_(
                    qkv,
                    self._cos_cached[seqlen_offset:],
                    self._sin_cached[seqlen_offset:],
                    self._cos_k_cached[seqlen_offset:],
                    self._sin_k_cached[seqlen_offset:],
                    self.interleaved,
                )
        else:
            q = qkv
            q = apply_rotary_emb_func(
                q,
                self._cos_cached[seqlen_offset:],
                self._sin_cached[seqlen_offset:],
                self.interleaved,
                True,
            )
            if self.scale is None:
                kv = apply_rotary_emb_kv_(
                    kv,
                    self._cos_cached[seqlen_offset:],
                    self._sin_cached[seqlen_offset:],
                    self.interleaved,
                )
            else:
                kv = apply_rotary_emb_kv_(
                    kv,
                    self._cos_k_cached[seqlen_offset:],
                    self._sin_k_cached[seqlen_offset:],
                    self.interleaved,
                )
            return q, kv