hyvideo/modules/posemb_layers.py

import torch
from typing import Union, Tuple, List, Optional
import numpy as np


###### Thanks to the RifleX project (https://github.com/thu-ml/RIFLEx/) for this alternative pos embed for long videos
#  
def get_1d_rotary_pos_embed_riflex(
    dim: int,
    pos: Union[np.ndarray, int],
    theta: float = 10000.0,
    use_real=False,
    k: Optional[int] = None,
    L_test: Optional[int] = None,
):
    """
    RIFLEx: Precompute the frequency tensor for complex exponentials (cis) with given dimensions.

    This function calculates a frequency tensor with complex exponentials using the given dimension 'dim' and the end
    index 'end'. The 'theta' parameter scales the frequencies. The returned tensor contains complex values in complex64
    data type.

    Args:
        dim (`int`): Dimension of the frequency tensor.
        pos (`np.ndarray` or `int`): Position indices for the frequency tensor. [S] or scalar
        theta (`float`, *optional*, defaults to 10000.0):
            Scaling factor for frequency computation. Defaults to 10000.0.
        use_real (`bool`, *optional*):
            If True, return real part and imaginary part separately. Otherwise, return complex numbers.
        k (`int`, *optional*, defaults to None): the index for the intrinsic frequency in RoPE
        L_test (`int`, *optional*, defaults to None): the number of frames for inference
    Returns:
        `torch.Tensor`: Precomputed frequency tensor with complex exponentials. [S, D/2]
    """
    assert dim % 2 == 0

    if isinstance(pos, int):
        pos = torch.arange(pos)
    if isinstance(pos, np.ndarray):
        pos = torch.from_numpy(pos)  # type: ignore  # [S]

    freqs = 1.0 / (
            theta ** (torch.arange(0, dim, 2, device=pos.device)[: (dim // 2)].float() / dim)
    )  # [D/2]

    # === Riflex modification start ===
    # Reduce the intrinsic frequency to stay within a single period after extrapolation (see Eq. (8)).
    # Empirical observations show that a few videos may exhibit repetition in the tail frames.
    # To be conservative, we multiply by 0.9 to keep the extrapolated length below 90% of a single period.
    if k is not None:
        freqs[k-1] = 0.9 * 2 * torch.pi / L_test
    # === Riflex modification end ===

    freqs = torch.outer(pos, freqs)  # type: ignore   # [S, D/2]
    if use_real:
        freqs_cos = freqs.cos().repeat_interleave(2, dim=1).float()  # [S, D]
        freqs_sin = freqs.sin().repeat_interleave(2, dim=1).float()  # [S, D]
        return freqs_cos, freqs_sin
    else:
        # lumina
        freqs_cis = torch.polar(torch.ones_like(freqs), freqs)  # complex64     # [S, D/2]
        return freqs_cis

def identify_k( b: float, d: int, N: int):
    """
    This function identifies the index of the intrinsic frequency component in a RoPE-based pre-trained diffusion transformer.

    Args:
        b (`float`): The base frequency for RoPE.
        d (`int`): Dimension of the frequency tensor
        N (`int`): the first observed repetition frame in latent space
    Returns:
        k (`int`): the index of intrinsic frequency component
        N_k (`int`): the period of intrinsic frequency component in latent space
    Example:
        In HunyuanVideo, b=256 and d=16, the repetition occurs approximately 8s (N=48 in latent space).
        k, N_k = identify_k(b=256, d=16, N=48)
        In this case, the intrinsic frequency index k is 4, and the period N_k is 50.
    """

    # Compute the period of each frequency in RoPE according to Eq.(4)
    periods = []
    for j in range(1, d // 2 + 1):
        theta_j = 1.0 / (b ** (2 * (j - 1) / d))
        N_j = round(2 * torch.pi / theta_j)
        periods.append(N_j)

    # Identify the intrinsic frequency whose period is closed to N（see Eq.(7)）
    diffs = [abs(N_j - N) for N_j in periods]
    k = diffs.index(min(diffs)) + 1
    N_k = periods[k-1]
    return k, N_k

def _to_tuple(x, dim=2):
    if isinstance(x, int):
        return (x,) * dim
    elif len(x) == dim:
        return x
    else:
        raise ValueError(f"Expected length {dim} or int, but got {x}")


def get_meshgrid_nd(start, *args, dim=2):
    """
    Get n-D meshgrid with start, stop and num.

    Args:
        start (int or tuple): If len(args) == 0, start is num; If len(args) == 1, start is start, args[0] is stop,
            step is 1; If len(args) == 2, start is start, args[0] is stop, args[1] is num. For n-dim, start/stop/num
            should be int or n-tuple. If n-tuple is provided, the meshgrid will be stacked following the dim order in
            n-tuples.
        *args: See above.
        dim (int): Dimension of the meshgrid. Defaults to 2.

    Returns:
        grid (np.ndarray): [dim, ...]
    """
    if len(args) == 0:
        # start is grid_size
        num = _to_tuple(start, dim=dim)
        start = (0,) * dim
        stop = num
    elif len(args) == 1:
        # start is start, args[0] is stop, step is 1
        start = _to_tuple(start, dim=dim)
        stop = _to_tuple(args[0], dim=dim)
        num = [stop[i] - start[i] for i in range(dim)]
    elif len(args) == 2:
        # start is start, args[0] is stop, args[1] is num
        start = _to_tuple(start, dim=dim)  # Left-Top       eg: 12,0
        stop = _to_tuple(args[0], dim=dim)  # Right-Bottom   eg: 20,32
        num = _to_tuple(args[1], dim=dim)  # Target Size    eg: 32,124
    else:
        raise ValueError(f"len(args) should be 0, 1 or 2, but got {len(args)}")

    # PyTorch implement of np.linspace(start[i], stop[i], num[i], endpoint=False)
    axis_grid = []
    for i in range(dim):
        a, b, n = start[i], stop[i], num[i]
        g = torch.linspace(a, b, n + 1, dtype=torch.float32)[:n]
        axis_grid.append(g)
    grid = torch.meshgrid(*axis_grid, indexing="ij")  # dim x [W, H, D]
    grid = torch.stack(grid, dim=0)  # [dim, W, H, D]

    return grid


#################################################################################
#                   Rotary Positional Embedding Functions                       #
#################################################################################
# https://github.com/meta-llama/llama/blob/be327c427cc5e89cc1d3ab3d3fec4484df771245/llama/model.py#L80


def reshape_for_broadcast(
    freqs_cis: Union[torch.Tensor, Tuple[torch.Tensor]],
    x: torch.Tensor,
    head_first=False,
):
    """
    Reshape frequency tensor for broadcasting it with another tensor.

    This function reshapes the frequency tensor to have the same shape as the target tensor 'x'
    for the purpose of broadcasting the frequency tensor during element-wise operations.

    Notes:
        When using FlashMHAModified, head_first should be False.
        When using Attention, head_first should be True.

    Args:
        freqs_cis (Union[torch.Tensor, Tuple[torch.Tensor]]): Frequency tensor to be reshaped.
        x (torch.Tensor): Target tensor for broadcasting compatibility.
        head_first (bool): head dimension first (except batch dim) or not.

    Returns:
        torch.Tensor: Reshaped frequency tensor.

    Raises:
        AssertionError: If the frequency tensor doesn't match the expected shape.
        AssertionError: If the target tensor 'x' doesn't have the expected number of dimensions.
    """
    ndim = x.ndim
    assert 0 <= 1 < ndim

    if isinstance(freqs_cis, tuple):
        # freqs_cis: (cos, sin) in real space
        if head_first:
            assert freqs_cis[0].shape == (
                x.shape[-2],
                x.shape[-1],
            ), f"freqs_cis shape {freqs_cis[0].shape} does not match x shape {x.shape}"
            shape = [
                d if i == ndim - 2 or i == ndim - 1 else 1
                for i, d in enumerate(x.shape)
            ]
        else:
            assert freqs_cis[0].shape == (
                x.shape[1],
                x.shape[-1],
            ), f"freqs_cis shape {freqs_cis[0].shape} does not match x shape {x.shape}"
            shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)]
        return freqs_cis[0].view(*shape), freqs_cis[1].view(*shape)
    else:
        # freqs_cis: values in complex space
        if head_first:
            assert freqs_cis.shape == (
                x.shape[-2],
                x.shape[-1],
            ), f"freqs_cis shape {freqs_cis.shape} does not match x shape {x.shape}"
            shape = [
                d if i == ndim - 2 or i == ndim - 1 else 1
                for i, d in enumerate(x.shape)
            ]
        else:
            assert freqs_cis.shape == (
                x.shape[1],
                x.shape[-1],
            ), f"freqs_cis shape {freqs_cis.shape} does not match x shape {x.shape}"
            shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)]
        return freqs_cis.view(*shape)


def rotate_half(x):
    x_real, x_imag = (
        x.float().reshape(*x.shape[:-1], -1, 2).unbind(-1)
    )  # [B, S, H, D//2]
    return torch.stack([-x_imag, x_real], dim=-1).flatten(3)


def apply_rotary_emb( qklist,
    freqs_cis: Union[torch.Tensor, Tuple[torch.Tensor, torch.Tensor]],
    head_first: bool = False,
) -> Tuple[torch.Tensor, torch.Tensor]:
    """
    Apply rotary embeddings to input tensors using the given frequency tensor.

    This function applies rotary embeddings to the given query 'xq' and key 'xk' tensors using the provided
    frequency tensor 'freqs_cis'. The input tensors are reshaped as complex numbers, and the frequency tensor
    is reshaped for broadcasting compatibility. The resulting tensors contain rotary embeddings and are
    returned as real tensors.

    Args:
        xq (torch.Tensor): Query tensor to apply rotary embeddings. [B, S, H, D]
        xk (torch.Tensor): Key tensor to apply rotary embeddings.   [B, S, H, D]
        freqs_cis (torch.Tensor or tuple): Precomputed frequency tensor for complex exponential.
        head_first (bool): head dimension first (except batch dim) or not.

    Returns:
        Tuple[torch.Tensor, torch.Tensor]: Tuple of modified query tensor and key tensor with rotary embeddings.

    """
    xq, xk = qklist
    qklist.clear()
    xk_out = None
    if isinstance(freqs_cis, tuple):
        cos, sin = reshape_for_broadcast(freqs_cis, xq, head_first)  # [S, D]
        cos, sin = cos.to(xq.device), sin.to(xq.device)
        # real * cos - imag * sin
        # imag * cos + real * sin
        xq_dtype = xq.dtype
        xq_out = xq.to(torch.float)
        xq = None        
        xq_rot = rotate_half(xq_out)
        xq_out *= cos
        xq_rot *= sin
        xq_out += xq_rot
        del xq_rot
        xq_out = xq_out.to(xq_dtype)

        xk_out = xk.to(torch.float)
        xk = None
        xk_rot = rotate_half(xk_out)
        xk_out *= cos
        xk_rot *= sin
        xk_out += xk_rot
        del xk_rot
        xk_out = xk_out.to(xq_dtype)
    else:
        # view_as_complex will pack [..., D/2, 2](real) to [..., D/2](complex)
        xq_ = torch.view_as_complex(
            xq.float().reshape(*xq.shape[:-1], -1, 2)
        )  # [B, S, H, D//2]
        freqs_cis = reshape_for_broadcast(freqs_cis, xq_, head_first).to(
            xq.device
        )  # [S, D//2] --> [1, S, 1, D//2]
        # (real, imag) * (cos, sin) = (real * cos - imag * sin, imag * cos + real * sin)
        # view_as_real will expand [..., D/2](complex) to [..., D/2, 2](real)
        xq_out = torch.view_as_real(xq_ * freqs_cis).flatten(3).type_as(xq)
        xk_ = torch.view_as_complex(
            xk.float().reshape(*xk.shape[:-1], -1, 2)
        )  # [B, S, H, D//2]
        xk_out = torch.view_as_real(xk_ * freqs_cis).flatten(3).type_as(xk)

    return xq_out, xk_out

def get_nd_rotary_pos_embed_new(rope_dim_list, start, *args, theta=10000., use_real=False, 
                            theta_rescale_factor: Union[float, List[float]]=1.0,
                            interpolation_factor: Union[float, List[float]]=1.0,
                            concat_dict={},
                            k = 4,
                            L_test = 66,
                            enable_riflex = True
                            ):

    grid = get_meshgrid_nd(start, *args, dim=len(rope_dim_list))   # [3, W, H, D] / [2, W, H]
    if len(concat_dict)<1:
        pass
    else:
        if concat_dict['mode']=='timecat':
            bias = grid[:,:1].clone()
            bias[0] = concat_dict['bias']*torch.ones_like(bias[0])
            grid = torch.cat([bias, grid], dim=1)
            
        elif concat_dict['mode']=='timecat-w': 
            bias = grid[:,:1].clone()
            bias[0] = concat_dict['bias']*torch.ones_like(bias[0])
            bias[2] += start[-1]    ## ref https://github.com/Yuanshi9815/OminiControl/blob/main/src/generate.py#L178
            grid = torch.cat([bias, grid], dim=1)
    if isinstance(theta_rescale_factor, int) or isinstance(theta_rescale_factor, float):
        theta_rescale_factor = [theta_rescale_factor] * len(rope_dim_list)
    elif isinstance(theta_rescale_factor, list) and len(theta_rescale_factor) == 1:
        theta_rescale_factor = [theta_rescale_factor[0]] * len(rope_dim_list)
    assert len(theta_rescale_factor) == len(rope_dim_list), "len(theta_rescale_factor) should equal to len(rope_dim_list)"

    if isinstance(interpolation_factor, int) or isinstance(interpolation_factor, float):
        interpolation_factor = [interpolation_factor] * len(rope_dim_list)
    elif isinstance(interpolation_factor, list) and len(interpolation_factor) == 1:
        interpolation_factor = [interpolation_factor[0]] * len(rope_dim_list)
    assert len(interpolation_factor) == len(rope_dim_list), "len(interpolation_factor) should equal to len(rope_dim_list)"

    # use 1/ndim of dimensions to encode grid_axis
    embs = []
    for i in range(len(rope_dim_list)):
        # === RIFLEx modification start ===
        # apply RIFLEx for time dimension
        if i == 0 and enable_riflex:
            emb = get_1d_rotary_pos_embed_riflex(rope_dim_list[i], grid[i].reshape(-1), theta, use_real=True, k=k, L_test=L_test)
        # === RIFLEx modification end ===
        else:
            emb = get_1d_rotary_pos_embed(rope_dim_list[i], grid[i].reshape(-1), theta, use_real=True, theta_rescale_factor=theta_rescale_factor[i],interpolation_factor=interpolation_factor[i],)

        # emb = get_1d_rotary_pos_embed(rope_dim_list[i], grid[i].reshape(-1), theta, use_real=use_real,
        #                               theta_rescale_factor=theta_rescale_factor[i],
        #                        w       interpolation_factor=interpolation_factor[i])    # 2 x [WHD, rope_dim_list[i]]
        
        embs.append(emb)

    if use_real:
        cos = torch.cat([emb[0] for emb in embs], dim=1)    # (WHD, D/2)
        sin = torch.cat([emb[1] for emb in embs], dim=1)    # (WHD, D/2)
        return cos, sin
    else:
        emb = torch.cat(embs, dim=1)    # (WHD, D/2)
        return emb
    
def get_nd_rotary_pos_embed(
    rope_dim_list,
    start,
    *args,
    theta=10000.0,
    use_real=False,
    theta_rescale_factor: Union[float, List[float]] = 1.0,
    interpolation_factor: Union[float, List[float]] = 1.0,
    k = 4,
    L_test = 66,
    enable_riflex = True
):
    """
    This is a n-d version of precompute_freqs_cis, which is a RoPE for tokens with n-d structure.

    Args:
        rope_dim_list (list of int): Dimension of each rope. len(rope_dim_list) should equal to n.
            sum(rope_dim_list) should equal to head_dim of attention layer.
        start (int | tuple of int | list of int): If len(args) == 0, start is num; If len(args) == 1, start is start,
            args[0] is stop, step is 1; If len(args) == 2, start is start, args[0] is stop, args[1] is num.
        *args: See above.
        theta (float): Scaling factor for frequency computation. Defaults to 10000.0.
        use_real (bool): If True, return real part and imaginary part separately. Otherwise, return complex numbers.
            Some libraries such as TensorRT does not support complex64 data type. So it is useful to provide a real
            part and an imaginary part separately.
        theta_rescale_factor (float): Rescale factor for theta. Defaults to 1.0.

    Returns:
        pos_embed (torch.Tensor): [HW, D/2]
    """

    grid = get_meshgrid_nd(
        start, *args, dim=len(rope_dim_list)
    )  # [3, W, H, D] / [2, W, H]

    if isinstance(theta_rescale_factor, int) or isinstance(theta_rescale_factor, float):
        theta_rescale_factor = [theta_rescale_factor] * len(rope_dim_list)
    elif isinstance(theta_rescale_factor, list) and len(theta_rescale_factor) == 1:
        theta_rescale_factor = [theta_rescale_factor[0]] * len(rope_dim_list)
    assert len(theta_rescale_factor) == len(
        rope_dim_list
    ), "len(theta_rescale_factor) should equal to len(rope_dim_list)"

    if isinstance(interpolation_factor, int) or isinstance(interpolation_factor, float):
        interpolation_factor = [interpolation_factor] * len(rope_dim_list)
    elif isinstance(interpolation_factor, list) and len(interpolation_factor) == 1:
        interpolation_factor = [interpolation_factor[0]] * len(rope_dim_list)
    assert len(interpolation_factor) == len(
        rope_dim_list
    ), "len(interpolation_factor) should equal to len(rope_dim_list)"

    # use 1/ndim of dimensions to encode grid_axis
    embs = []
    for i in range(len(rope_dim_list)):
        # emb = get_1d_rotary_pos_embed(
        #     rope_dim_list[i],
        #     grid[i].reshape(-1),
        #     theta,
        #     use_real=use_real,
        #     theta_rescale_factor=theta_rescale_factor[i],
        #     interpolation_factor=interpolation_factor[i],
        # )  # 2 x [WHD, rope_dim_list[i]]


        # === RIFLEx modification start ===
        # apply RIFLEx for time dimension
        if i == 0 and enable_riflex:
            emb = get_1d_rotary_pos_embed_riflex(rope_dim_list[i], grid[i].reshape(-1), theta, use_real=True, k=k, L_test=L_test)
        # === RIFLEx modification end ===
        else:
            emb = get_1d_rotary_pos_embed(rope_dim_list[i], grid[i].reshape(-1), theta, use_real=True, theta_rescale_factor=theta_rescale_factor[i],interpolation_factor=interpolation_factor[i],)
        embs.append(emb)

    if use_real:
        cos = torch.cat([emb[0] for emb in embs], dim=1)  # (WHD, D/2)
        sin = torch.cat([emb[1] for emb in embs], dim=1)  # (WHD, D/2)
        return cos, sin
    else:
        emb = torch.cat(embs, dim=1)  # (WHD, D/2)
        return emb


def get_1d_rotary_pos_embed(
    dim: int,
    pos: Union[torch.FloatTensor, int],
    theta: float = 10000.0,
    use_real: bool = False,
    theta_rescale_factor: float = 1.0,
    interpolation_factor: float = 1.0,
) -> Union[torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]:
    """
    Precompute the frequency tensor for complex exponential (cis) with given dimensions.
    (Note: `cis` means `cos + i * sin`, where i is the imaginary unit.)

    This function calculates a frequency tensor with complex exponential using the given dimension 'dim'
    and the end index 'end'. The 'theta' parameter scales the frequencies.
    The returned tensor contains complex values in complex64 data type.

    Args:
        dim (int): Dimension of the frequency tensor.
        pos (int or torch.FloatTensor): Position indices for the frequency tensor. [S] or scalar
        theta (float, optional): Scaling factor for frequency computation. Defaults to 10000.0.
        use_real (bool, optional): If True, return real part and imaginary part separately.
                                   Otherwise, return complex numbers.
        theta_rescale_factor (float, optional): Rescale factor for theta. Defaults to 1.0.

    Returns:
        freqs_cis: Precomputed frequency tensor with complex exponential. [S, D/2]
        freqs_cos, freqs_sin: Precomputed frequency tensor with real and imaginary parts separately. [S, D]
    """
    if isinstance(pos, int):
        pos = torch.arange(pos).float()

    # proposed by reddit user bloc97, to rescale rotary embeddings to longer sequence length without fine-tuning
    # has some connection to NTK literature
    if theta_rescale_factor != 1.0:
        theta *= theta_rescale_factor ** (dim / (dim - 2))

    freqs = 1.0 / (
        theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim)
    )  # [D/2]
    # assert interpolation_factor == 1.0, f"interpolation_factor: {interpolation_factor}"
    freqs = torch.outer(pos * interpolation_factor, freqs)  # [S, D/2]
    if use_real:
        freqs_cos = freqs.cos().repeat_interleave(2, dim=1)  # [S, D]
        freqs_sin = freqs.sin().repeat_interleave(2, dim=1)  # [S, D]
        return freqs_cos, freqs_sin
    else:
        freqs_cis = torch.polar(
            torch.ones_like(freqs), freqs
        )  # complex64     # [S, D/2]
        return freqs_cis