resnet.py

from abc import abstractmethod
from functools import partial

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F


def avg_pool_nd(dims, *args, **kwargs):
    """
    Create a 1D, 2D, or 3D average pooling module.
    """
    if dims == 1:
        return nn.AvgPool1d(*args, **kwargs)
    elif dims == 2:
        return nn.AvgPool2d(*args, **kwargs)
    elif dims == 3:
        return nn.AvgPool3d(*args, **kwargs)
    raise ValueError(f"unsupported dimensions: {dims}")


def conv_nd(dims, *args, **kwargs):
    """
    Create a 1D, 2D, or 3D convolution module.
    """
    if dims == 1:
        return nn.Conv1d(*args, **kwargs)
    elif dims == 2:
        return nn.Conv2d(*args, **kwargs)
    elif dims == 3:
        return nn.Conv3d(*args, **kwargs)
    raise ValueError(f"unsupported dimensions: {dims}")


def conv_transpose_nd(dims, *args, **kwargs):
    """
    Create a 1D, 2D, or 3D convolution module.
    """
    if dims == 1:
        return nn.ConvTranspose1d(*args, **kwargs)
    elif dims == 2:
        return nn.ConvTranspose2d(*args, **kwargs)
    elif dims == 3:
        return nn.ConvTranspose3d(*args, **kwargs)
    raise ValueError(f"unsupported dimensions: {dims}")


def Normalize(in_channels, num_groups=32, eps=1e-6):
    return torch.nn.GroupNorm(num_groups=num_groups, num_channels=in_channels, eps=eps, affine=True)


def nonlinearity(x, swish=1.0):
    # swish
    if swish == 1.0:
        return F.silu(x)
    else:
        return x * F.sigmoid(x * float(swish))


class TimestepBlock(nn.Module):
    """
    Any module where forward() takes timestep embeddings as a second argument.
    """

    @abstractmethod
    def forward(self, x, emb):
        """
        Apply the module to `x` given `emb` timestep embeddings.
        """


class Upsample(nn.Module):
    """
    An upsampling layer with an optional convolution.

    :param channels: channels in the inputs and outputs. :param use_conv: a bool determining if a convolution is
    applied. :param dims: determines if the signal is 1D, 2D, or 3D. If 3D, then
                 upsampling occurs in the inner-two dimensions.
    """

    def __init__(self, channels, use_conv=False, use_conv_transpose=False, dims=2, out_channels=None, name="conv"):
        super().__init__()
        self.channels = channels
        self.out_channels = out_channels or channels
        self.use_conv = use_conv
        self.dims = dims
        self.use_conv_transpose = use_conv_transpose
        self.name = name

        conv = None
        if use_conv_transpose:
            conv = conv_transpose_nd(dims, channels, self.out_channels, 4, 2, 1)
        elif use_conv:
            conv = conv_nd(dims, self.channels, self.out_channels, 3, padding=1)

        if name == "conv":
            self.conv = conv
        else:
            self.Conv2d_0 = conv

    def forward(self, x):
        assert x.shape[1] == self.channels
        if self.use_conv_transpose:
            return self.conv(x)

        if self.dims == 3:
            x = F.interpolate(x, (x.shape[2], x.shape[3] * 2, x.shape[4] * 2), mode="nearest")
        else:
            x = F.interpolate(x, scale_factor=2.0, mode="nearest")

        if self.use_conv:
            if self.name == "conv":
                x = self.conv(x)
            else:
                x = self.Conv2d_0(x)

        return x


class Downsample(nn.Module):
    """
    A downsampling layer with an optional convolution.

    :param channels: channels in the inputs and outputs. :param use_conv: a bool determining if a convolution is
    applied. :param dims: determines if the signal is 1D, 2D, or 3D. If 3D, then
                 downsampling occurs in the inner-two dimensions.
    """

    def __init__(self, channels, use_conv=False, dims=2, out_channels=None, padding=1, name="conv"):
        super().__init__()
        self.channels = channels
        self.out_channels = out_channels or channels
        self.use_conv = use_conv
        self.dims = dims
        self.padding = padding
        stride = 2 if dims != 3 else (1, 2, 2)
        self.name = name

        if use_conv:
            conv = conv_nd(dims, self.channels, self.out_channels, 3, stride=stride, padding=padding)
        else:
            assert self.channels == self.out_channels
            conv = avg_pool_nd(dims, kernel_size=stride, stride=stride)

        if name == "conv":
            self.conv = conv
        elif name == "Conv2d_0":
            self.Conv2d_0 = conv
        else:
            self.op = conv

    def forward(self, x):
        assert x.shape[1] == self.channels
        if self.use_conv and self.padding == 0 and self.dims == 2:
            pad = (0, 1, 0, 1)
            x = F.pad(x, pad, mode="constant", value=0)

        if self.name == "conv":
            return self.conv(x)
        elif self.name == "Conv2d_0":
            return self.Conv2d_0(x)
        else:
            return self.op(x)


# TODO (patil-suraj): needs test
# class Upsample1d(nn.Module):
#    def __init__(self, dim):
#        super().__init__()
#        self.conv = nn.ConvTranspose1d(dim, dim, 4, 2, 1)
#
#    def forward(self, x):
#        return self.conv(x)


# unet.py, unet_grad_tts.py, unet_ldm.py, unet_glide.py, unet_score_vde.py
class ResnetBlock(nn.Module):
    def __init__(
        self,
        *,
        in_channels,
        out_channels=None,
        conv_shortcut=False,
        dropout=0.0,
        temb_channels=512,
        groups=32,
        groups_out=None,
        pre_norm=True,
        eps=1e-6,
        non_linearity="swish",
        time_embedding_norm="default",
        kernel=None,
        output_scale_factor=1.0,
        use_nin_shortcut=None,
        up=False,
        down=False,
        overwrite_for_grad_tts=False,
        overwrite_for_ldm=False,
        overwrite_for_glide=False,
        overwrite_for_score_vde=False,
    ):
        super().__init__()
        self.pre_norm = pre_norm
        self.in_channels = in_channels
        out_channels = in_channels if out_channels is None else out_channels
        self.out_channels = out_channels
        self.use_conv_shortcut = conv_shortcut
        self.time_embedding_norm = time_embedding_norm
        self.up = up
        self.down = down
        self.output_scale_factor = output_scale_factor

        if groups_out is None:
            groups_out = groups

        if self.pre_norm:
            self.norm1 = Normalize(in_channels, num_groups=groups, eps=eps)
        else:
            self.norm1 = Normalize(out_channels, num_groups=groups, eps=eps)

        self.conv1 = torch.nn.Conv2d(in_channels, out_channels, kernel_size=3, stride=1, padding=1)

        if time_embedding_norm == "default":
            self.temb_proj = torch.nn.Linear(temb_channels, out_channels)
        elif time_embedding_norm == "scale_shift":
            self.temb_proj = torch.nn.Linear(temb_channels, 2 * out_channels)

        self.norm2 = Normalize(out_channels, num_groups=groups_out, eps=eps)
        self.dropout = torch.nn.Dropout(dropout)
        self.conv2 = torch.nn.Conv2d(out_channels, out_channels, kernel_size=3, stride=1, padding=1)

        if non_linearity == "swish":
            self.nonlinearity = nonlinearity
        elif non_linearity == "mish":
            self.nonlinearity = Mish()
        elif non_linearity == "silu":
            self.nonlinearity = nn.SiLU()

        self.upsample = self.downsample = None
        if self.up:
            if kernel == "fir":
                fir_kernel = (1, 3, 3, 1)
                self.upsample = lambda x: upsample_2d(x, k=fir_kernel)
            elif kernel == "sde_vp":
                self.upsample = partial(F.interpolate, scale_factor=2.0, mode="nearest")
            else:
                self.upsample = Upsample(in_channels, use_conv=False, dims=2)
        elif self.down:
            if kernel == "fir":
                fir_kernel = (1, 3, 3, 1)
                self.downsample = lambda x: downsample_2d(x, k=fir_kernel)
            elif kernel == "sde_vp":
                self.downsample = partial(F.avg_pool2d, kernel_size=2, stride=2)
            else:
                self.downsample = Downsample(in_channels, use_conv=False, dims=2, padding=1, name="op")

        self.use_nin_shortcut = self.in_channels != self.out_channels if use_nin_shortcut is None else use_nin_shortcut

        self.nin_shortcut = None
        if self.use_nin_shortcut:
            self.nin_shortcut = torch.nn.Conv2d(in_channels, out_channels, kernel_size=1, stride=1, padding=0)

        # TODO(SURAJ, PATRICK): ALL OF THE FOLLOWING OF THE INIT METHOD CAN BE DELETED ONCE WEIGHTS ARE CONVERTED
        self.is_overwritten = False
        self.overwrite_for_glide = overwrite_for_glide
        self.overwrite_for_grad_tts = overwrite_for_grad_tts
        self.overwrite_for_ldm = overwrite_for_ldm or overwrite_for_glide
        self.overwrite_for_score_vde = overwrite_for_score_vde
        if self.overwrite_for_grad_tts:
            dim = in_channels
            dim_out = out_channels
            time_emb_dim = temb_channels
            self.mlp = torch.nn.Sequential(Mish(), torch.nn.Linear(time_emb_dim, dim_out))
            self.pre_norm = pre_norm

            self.block1 = Block(dim, dim_out, groups=groups)
            self.block2 = Block(dim_out, dim_out, groups=groups)
            if dim != dim_out:
                self.res_conv = torch.nn.Conv2d(dim, dim_out, 1)
            else:
                self.res_conv = torch.nn.Identity()
        elif self.overwrite_for_ldm:
            dims = 2
            channels = in_channels
            emb_channels = temb_channels
            use_scale_shift_norm = False
            non_linearity = "silu"

            self.in_layers = nn.Sequential(
                normalization(channels, swish=1.0),
                nn.Identity(),
                conv_nd(dims, channels, self.out_channels, 3, padding=1),
            )
            self.emb_layers = nn.Sequential(
                nn.SiLU(),
                linear(
                    emb_channels,
                    2 * self.out_channels if self.time_embedding_norm == "scale_shift" else self.out_channels,
                ),
            )
            self.out_layers = nn.Sequential(
                normalization(self.out_channels, swish=0.0 if use_scale_shift_norm else 1.0),
                nn.SiLU() if use_scale_shift_norm else nn.Identity(),
                nn.Dropout(p=dropout),
                zero_module(conv_nd(dims, self.out_channels, self.out_channels, 3, padding=1)),
            )
            if self.out_channels == in_channels:
                self.skip_connection = nn.Identity()
            else:
                self.skip_connection = conv_nd(dims, channels, self.out_channels, 1)
        elif self.overwrite_for_score_vde:
            in_ch = in_channels
            out_ch = out_channels

            eps = 1e-6
            num_groups = min(in_ch // 4, 32)
            num_groups_out = min(out_ch // 4, 32)
            temb_dim = temb_channels
            #            output_scale_factor = np.sqrt(2.0)
            #            non_linearity = "silu"
            #            use_nin_shortcut = in_channels != out_channels or use_nin_shortcut = True

            self.GroupNorm_0 = nn.GroupNorm(num_groups=num_groups, num_channels=in_ch, eps=eps)
            self.up = up
            self.down = down
            self.Conv_0 = conv2d(in_ch, out_ch, kernel_size=3, padding=1)
            if temb_dim is not None:
                self.Dense_0 = nn.Linear(temb_dim, out_ch)
                self.Dense_0.weight.data = variance_scaling()(self.Dense_0.weight.shape)
                nn.init.zeros_(self.Dense_0.bias)

            self.GroupNorm_1 = nn.GroupNorm(num_groups=num_groups_out, num_channels=out_ch, eps=eps)
            self.Dropout_0 = nn.Dropout(dropout)
            self.Conv_1 = conv2d(out_ch, out_ch, init_scale=0.0, kernel_size=3, padding=1)
            if in_ch != out_ch or up or down:
                # 1x1 convolution with DDPM initialization.
                self.Conv_2 = conv2d(in_ch, out_ch, kernel_size=1, padding=0)

            #            self.skip_rescale = skip_rescale
            self.in_ch = in_ch
            self.out_ch = out_ch

            # TODO(Patrick) - move to main init
            self.is_overwritten = False

    def set_weights_grad_tts(self):
        self.conv1.weight.data = self.block1.block[0].weight.data
        self.conv1.bias.data = self.block1.block[0].bias.data
        self.norm1.weight.data = self.block1.block[1].weight.data
        self.norm1.bias.data = self.block1.block[1].bias.data

        self.conv2.weight.data = self.block2.block[0].weight.data
        self.conv2.bias.data = self.block2.block[0].bias.data
        self.norm2.weight.data = self.block2.block[1].weight.data
        self.norm2.bias.data = self.block2.block[1].bias.data

        self.temb_proj.weight.data = self.mlp[1].weight.data
        self.temb_proj.bias.data = self.mlp[1].bias.data

        if self.in_channels != self.out_channels:
            self.nin_shortcut.weight.data = self.res_conv.weight.data
            self.nin_shortcut.bias.data = self.res_conv.bias.data

    def set_weights_ldm(self):
        self.norm1.weight.data = self.in_layers[0].weight.data
        self.norm1.bias.data = self.in_layers[0].bias.data

        self.conv1.weight.data = self.in_layers[-1].weight.data
        self.conv1.bias.data = self.in_layers[-1].bias.data

        self.temb_proj.weight.data = self.emb_layers[-1].weight.data
        self.temb_proj.bias.data = self.emb_layers[-1].bias.data

        self.norm2.weight.data = self.out_layers[0].weight.data
        self.norm2.bias.data = self.out_layers[0].bias.data

        self.conv2.weight.data = self.out_layers[-1].weight.data
        self.conv2.bias.data = self.out_layers[-1].bias.data

        if self.in_channels != self.out_channels:
            self.nin_shortcut.weight.data = self.skip_connection.weight.data
            self.nin_shortcut.bias.data = self.skip_connection.bias.data

    def set_weights_score_vde(self):
        self.conv1.weight.data = self.Conv_0.weight.data
        self.conv1.bias.data = self.Conv_0.bias.data
        self.norm1.weight.data = self.GroupNorm_0.weight.data
        self.norm1.bias.data = self.GroupNorm_0.bias.data

        self.conv2.weight.data = self.Conv_1.weight.data
        self.conv2.bias.data = self.Conv_1.bias.data
        self.norm2.weight.data = self.GroupNorm_1.weight.data
        self.norm2.bias.data = self.GroupNorm_1.bias.data

        self.temb_proj.weight.data = self.Dense_0.weight.data
        self.temb_proj.bias.data = self.Dense_0.bias.data

        if self.in_channels != self.out_channels or self.up or self.down:
            self.nin_shortcut.weight.data = self.Conv_2.weight.data
            self.nin_shortcut.bias.data = self.Conv_2.bias.data

    def forward(self, x, temb, mask=1.0):
        # TODO(Patrick) eventually this class should be split into multiple classes
        # too many if else statements
        if self.overwrite_for_grad_tts and not self.is_overwritten:
            self.set_weights_grad_tts()
            self.is_overwritten = True
        elif self.overwrite_for_ldm and not self.is_overwritten:
            self.set_weights_ldm()
            self.is_overwritten = True
        elif self.overwrite_for_score_vde and not self.is_overwritten:
            self.set_weights_score_vde()
            self.is_overwritten = True

        h = x
        h = h * mask
        if self.pre_norm:
            h = self.norm1(h)
            h = self.nonlinearity(h)

        if self.upsample is not None:
            x = self.upsample(x)
            h = self.upsample(h)
        elif self.downsample is not None:
            x = self.downsample(x)
            h = self.downsample(h)

        h = self.conv1(h)

        if not self.pre_norm:
            h = self.norm1(h)
            h = self.nonlinearity(h)
        h = h * mask

        temb = self.temb_proj(self.nonlinearity(temb))[:, :, None, None]

        if self.time_embedding_norm == "scale_shift":
            scale, shift = torch.chunk(temb, 2, dim=1)

            h = self.norm2(h)
            h = h + h * scale + shift
            h = self.nonlinearity(h)
        elif self.time_embedding_norm == "default":
            h = h + temb
            h = h * mask
            if self.pre_norm:
                h = self.norm2(h)
                h = self.nonlinearity(h)

        h = self.dropout(h)
        h = self.conv2(h)

        if not self.pre_norm:
            h = self.norm2(h)
            h = self.nonlinearity(h)
        h = h * mask

        x = x * mask
        if self.nin_shortcut is not None:
            x = self.nin_shortcut(x)

        return (x + h) / self.output_scale_factor


# TODO(Patrick) - just there to convert the weights; can delete afterward
class Block(torch.nn.Module):
    def __init__(self, dim, dim_out, groups=8):
        super(Block, self).__init__()
        self.block = torch.nn.Sequential(
            torch.nn.Conv2d(dim, dim_out, 3, padding=1), torch.nn.GroupNorm(groups, dim_out), Mish()
        )


# unet_rl.py
class ResidualTemporalBlock(nn.Module):
    def __init__(self, inp_channels, out_channels, embed_dim, horizon, kernel_size=5):
        super().__init__()

        self.blocks = nn.ModuleList(
            [
                Conv1dBlock(inp_channels, out_channels, kernel_size),
                Conv1dBlock(out_channels, out_channels, kernel_size),
            ]
        )

        self.time_mlp = nn.Sequential(
            nn.Mish(),
            nn.Linear(embed_dim, out_channels),
            RearrangeDim(),
            #            Rearrange("batch t -> batch t 1"),
        )

        self.residual_conv = (
            nn.Conv1d(inp_channels, out_channels, 1) if inp_channels != out_channels else nn.Identity()
        )

    def forward(self, x, t):
        """
        x : [ batch_size x inp_channels x horizon ] t : [ batch_size x embed_dim ] returns: out : [ batch_size x
        out_channels x horizon ]
        """
        out = self.blocks[0](x) + self.time_mlp(t)
        out = self.blocks[1](out)
        return out + self.residual_conv(x)


# HELPER Modules


def normalization(channels, swish=0.0):
    """
    Make a standard normalization layer, with an optional swish activation.

    :param channels: number of input channels. :return: an nn.Module for normalization.
    """
    return GroupNorm32(num_channels=channels, num_groups=32, swish=swish)


class GroupNorm32(nn.GroupNorm):
    def __init__(self, num_groups, num_channels, swish, eps=1e-5):
        super().__init__(num_groups=num_groups, num_channels=num_channels, eps=eps)
        self.swish = swish

    def forward(self, x):
        y = super().forward(x.float()).to(x.dtype)
        if self.swish == 1.0:
            y = F.silu(y)
        elif self.swish:
            y = y * F.sigmoid(y * float(self.swish))
        return y


def linear(*args, **kwargs):
    """
    Create a linear module.
    """
    return nn.Linear(*args, **kwargs)


def zero_module(module):
    """
    Zero out the parameters of a module and return it.
    """
    for p in module.parameters():
        p.detach().zero_()
    return module


class Mish(torch.nn.Module):
    def forward(self, x):
        return x * torch.tanh(torch.nn.functional.softplus(x))


class Conv1dBlock(nn.Module):
    """
    Conv1d --> GroupNorm --> Mish
    """

    def __init__(self, inp_channels, out_channels, kernel_size, n_groups=8):
        super().__init__()

        self.block = nn.Sequential(
            nn.Conv1d(inp_channels, out_channels, kernel_size, padding=kernel_size // 2),
            RearrangeDim(),
            #            Rearrange("batch channels horizon -> batch channels 1 horizon"),
            nn.GroupNorm(n_groups, out_channels),
            RearrangeDim(),
            #            Rearrange("batch channels 1 horizon -> batch channels horizon"),
            nn.Mish(),
        )

    def forward(self, x):
        return self.block(x)


class RearrangeDim(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, tensor):
        if len(tensor.shape) == 2:
            return tensor[:, :, None]
        if len(tensor.shape) == 3:
            return tensor[:, :, None, :]
        elif len(tensor.shape) == 4:
            return tensor[:, :, 0, :]
        else:
            raise ValueError(f"`len(tensor)`: {len(tensor)} has to be 2, 3 or 4.")


def conv2d(in_planes, out_planes, kernel_size=3, stride=1, bias=True, init_scale=1.0, padding=1):
    """nXn convolution with DDPM initialization."""
    conv = nn.Conv2d(in_planes, out_planes, kernel_size=kernel_size, stride=stride, padding=padding, bias=bias)
    conv.weight.data = variance_scaling(init_scale)(conv.weight.data.shape)
    nn.init.zeros_(conv.bias)
    return conv


def variance_scaling(scale=1.0, in_axis=1, out_axis=0, dtype=torch.float32, device="cpu"):
    """Ported from JAX."""
    scale = 1e-10 if scale == 0 else scale

    def _compute_fans(shape, in_axis=1, out_axis=0):
        receptive_field_size = np.prod(shape) / shape[in_axis] / shape[out_axis]
        fan_in = shape[in_axis] * receptive_field_size
        fan_out = shape[out_axis] * receptive_field_size
        return fan_in, fan_out

    def init(shape, dtype=dtype, device=device):
        fan_in, fan_out = _compute_fans(shape, in_axis, out_axis)
        denominator = (fan_in + fan_out) / 2
        variance = scale / denominator
        return (torch.rand(*shape, dtype=dtype, device=device) * 2.0 - 1.0) * np.sqrt(3 * variance)

    return init


def upfirdn2d(input, kernel, up=1, down=1, pad=(0, 0)):
    return upfirdn2d_native(input, kernel, up, up, down, down, pad[0], pad[1], pad[0], pad[1])


def upfirdn2d_native(input, kernel, up_x, up_y, down_x, down_y, pad_x0, pad_x1, pad_y0, pad_y1):
    _, channel, in_h, in_w = input.shape
    input = input.reshape(-1, in_h, in_w, 1)

    _, in_h, in_w, minor = input.shape
    kernel_h, kernel_w = kernel.shape

    out = input.view(-1, in_h, 1, in_w, 1, minor)
    out = F.pad(out, [0, 0, 0, up_x - 1, 0, 0, 0, up_y - 1])
    out = out.view(-1, in_h * up_y, in_w * up_x, minor)

    out = F.pad(out, [0, 0, max(pad_x0, 0), max(pad_x1, 0), max(pad_y0, 0), max(pad_y1, 0)])
    out = out[
        :,
        max(-pad_y0, 0) : out.shape[1] - max(-pad_y1, 0),
        max(-pad_x0, 0) : out.shape[2] - max(-pad_x1, 0),
        :,
    ]

    out = out.permute(0, 3, 1, 2)
    out = out.reshape([-1, 1, in_h * up_y + pad_y0 + pad_y1, in_w * up_x + pad_x0 + pad_x1])
    w = torch.flip(kernel, [0, 1]).view(1, 1, kernel_h, kernel_w)
    out = F.conv2d(out, w)
    out = out.reshape(
        -1,
        minor,
        in_h * up_y + pad_y0 + pad_y1 - kernel_h + 1,
        in_w * up_x + pad_x0 + pad_x1 - kernel_w + 1,
    )
    out = out.permute(0, 2, 3, 1)
    out = out[:, ::down_y, ::down_x, :]

    out_h = (in_h * up_y + pad_y0 + pad_y1 - kernel_h) // down_y + 1
    out_w = (in_w * up_x + pad_x0 + pad_x1 - kernel_w) // down_x + 1

    return out.view(-1, channel, out_h, out_w)


def upsample_2d(x, k=None, factor=2, gain=1):
    r"""Upsample a batch of 2D images with the given filter.

    Args:
    Accepts a batch of 2D images of the shape `[N, C, H, W]` or `[N, H, W, C]` and upsamples each image with the given
    filter. The filter is normalized so that if the input pixels are constant, they will be scaled by the specified
    `gain`. Pixels outside the image are assumed to be zero, and the filter is padded with zeros so that its shape is a:
    multiple of the upsampling factor.
        x: Input tensor of the shape `[N, C, H, W]` or `[N, H, W,
          C]`.
        k: FIR filter of the shape `[firH, firW]` or `[firN]`
          (separable). The default is `[1] * factor`, which corresponds to nearest-neighbor upsampling.
        factor: Integer upsampling factor (default: 2). gain: Scaling factor for signal magnitude (default: 1.0).

    Returns:
        Tensor of the shape `[N, C, H * factor, W * factor]`
    """
    assert isinstance(factor, int) and factor >= 1
    if k is None:
        k = [1] * factor
    k = _setup_kernel(k) * (gain * (factor**2))
    p = k.shape[0] - factor
    return upfirdn2d(x, torch.tensor(k, device=x.device), up=factor, pad=((p + 1) // 2 + factor - 1, p // 2))


def downsample_2d(x, k=None, factor=2, gain=1):
    r"""Downsample a batch of 2D images with the given filter.

    Args:
    Accepts a batch of 2D images of the shape `[N, C, H, W]` or `[N, H, W, C]` and downsamples each image with the
    given filter. The filter is normalized so that if the input pixels are constant, they will be scaled by the
    specified `gain`. Pixels outside the image are assumed to be zero, and the filter is padded with zeros so that its
    shape is a multiple of the downsampling factor.
        x: Input tensor of the shape `[N, C, H, W]` or `[N, H, W,
          C]`.
        k: FIR filter of the shape `[firH, firW]` or `[firN]`
          (separable). The default is `[1] * factor`, which corresponds to average pooling.
        factor: Integer downsampling factor (default: 2). gain: Scaling factor for signal magnitude (default: 1.0).

    Returns:
        Tensor of the shape `[N, C, H // factor, W // factor]`
    """

    assert isinstance(factor, int) and factor >= 1
    if k is None:
        k = [1] * factor
    k = _setup_kernel(k) * gain
    p = k.shape[0] - factor
    return upfirdn2d(x, torch.tensor(k, device=x.device), down=factor, pad=((p + 1) // 2, p // 2))


def _setup_kernel(k):
    k = np.asarray(k, dtype=np.float32)
    if k.ndim == 1:
        k = np.outer(k, k)
    k /= np.sum(k)
    assert k.ndim == 2
    assert k.shape[0] == k.shape[1]
    return k