模块出处

[SPL 25] [link] [code] KAN See In the Dark

模块名称

Kolmogorov-Arnold Network Block (KAN-Block)

模块作用

用于vision的KAN结构

模块结构

模块代码

import torch
import torch.nn as nn
import torch.nn.functional as F
import math


class Swish(nn.Module):
    def forward(self, x):
        return x * torch.sigmoid(x)


class KANLinear(torch.nn.Module):
    def __init__(
        self,
        in_features,
        out_features,
        grid_size=5,
        spline_order=3,
        scale_noise=0.1,
        scale_base=1.0,
        scale_spline=1.0,
        enable_standalone_scale_spline=True,
        base_activation=torch.nn.SiLU,
        grid_eps=0.02,
        grid_range=[-1, 1],
    ):
        super(KANLinear, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.grid_size = grid_size
        self.spline_order = spline_order
        self.weight = nn.Parameter(torch.Tensor(out_features, in_features))
        self.bias = nn.Parameter(torch.Tensor(out_features))
        h = (grid_range[1] - grid_range[0]) / grid_size
        grid = (
            (
                torch.arange(-spline_order, grid_size + spline_order + 1) * h
                + grid_range[0]
            )
            .expand(in_features, -1)
            .contiguous()
        )
        self.register_buffer("grid", grid)
        self.base_weight = torch.nn.Parameter(torch.Tensor(out_features, in_features))
        self.spline_weight = torch.nn.Parameter(
            torch.Tensor(out_features, in_features, grid_size + spline_order)
        )
        if enable_standalone_scale_spline:
            self.spline_scaler = torch.nn.Parameter(
                torch.Tensor(out_features, in_features)
            )
        self.scale_noise = scale_noise
        self.scale_base = scale_base
        self.scale_spline = scale_spline
        self.enable_standalone_scale_spline = enable_standalone_scale_spline
        self.base_activation = base_activation()
        self.grid_eps = grid_eps
        self.reset_parameters()

    def reset_parameters(self):
        torch.nn.init.kaiming_uniform_(self.base_weight, a=math.sqrt(5) * self.scale_base)
        with torch.no_grad():
            noise = (
                (
                    torch.rand(self.grid_size + 1, self.in_features, self.out_features)
                    - 1 / 2
                )
                * self.scale_noise
                / self.grid_size
            )
            self.spline_weight.data.copy_(
                (self.scale_spline if not self.enable_standalone_scale_spline else 1.0)
                * self.curve2coeff(
                    self.grid.T[self.spline_order : -self.spline_order],
                    noise,
                )
            )
            if self.enable_standalone_scale_spline:
                # torch.nn.init.constant_(self.spline_scaler, self.scale_spline)
                torch.nn.init.kaiming_uniform_(self.spline_scaler, a=math.sqrt(5) * self.scale_spline)

    def b_splines(self, x: torch.Tensor):
        """
        Compute the B-spline bases for the given input tensor.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_features).

        Returns:
            torch.Tensor: B-spline bases tensor of shape (batch_size, in_features, grid_size + spline_order).
        """
        assert x.dim() == 2 and x.size(1) == self.in_features

        grid: torch.Tensor = (
            self.grid
        )  # (in_features, grid_size + 2 * spline_order + 1)
        x = x.unsqueeze(-1)
        bases = ((x >= grid[:, :-1]) & (x < grid[:, 1:])).to(x.dtype)
        for k in range(1, self.spline_order + 1):
            bases = (
                (x - grid[:, : -(k + 1)])
                / (grid[:, k:-1] - grid[:, : -(k + 1)])
                * bases[:, :, :-1]
            ) + (
                (grid[:, k + 1 :] - x)
                / (grid[:, k + 1 :] - grid[:, 1:(-k)])
                * bases[:, :, 1:]
            )

        assert bases.size() == (
            x.size(0),
            self.in_features,
            self.grid_size + self.spline_order,
        )
        return bases.contiguous()

    def curve2coeff(self, x: torch.Tensor, y: torch.Tensor):
        """
        Compute the coefficients of the curve that interpolates the given points.

        Args:
            x (torch.Tensor): Input tensor of shape (batch_size, in_features).
            y (torch.Tensor): Output tensor of shape (batch_size, in_features, out_features).

        Returns:
            torch.Tensor: Coefficients tensor of shape (out_features, in_features, grid_size + spline_order).
        """
        assert x.dim() == 2 and x.size(1) == self.in_features
        assert y.size() == (x.size(0), self.in_features, self.out_features)

        A = self.b_splines(x).transpose(
            0, 1
        )  # (in_features, batch_size, grid_size + spline_order)
        B = y.transpose(0, 1)  # (in_features, batch_size, out_features)
        solution = torch.linalg.lstsq(
            A, B
        ).solution  # (in_features, grid_size + spline_order, out_features)
        result = solution.permute(
            2, 0, 1
        )  # (out_features, in_features, grid_size + spline_order)

        assert result.size() == (
            self.out_features,
            self.in_features,
            self.grid_size + self.spline_order,
        )
        return result.contiguous()

    @property
    def scaled_spline_weight(self):
        return self.spline_weight * (
            self.spline_scaler.unsqueeze(-1)
            if self.enable_standalone_scale_spline
            else 1.0
        )

    def forward(self, x: torch.Tensor):
        assert x.dim() == 2 and x.size(1) == self.in_features
        base_output = F.linear(self.base_activation(x), self.base_weight)
        spline_output = F.linear(
            self.b_splines(x).view(x.size(0), -1),
            self.scaled_spline_weight.view(self.out_features, -1),
        )
        return base_output + spline_output

    @torch.no_grad()
    def update_grid(self, x: torch.Tensor, margin=0.01):
        assert x.dim() == 2 and x.size(1) == self.in_features
        batch = x.size(0)

        splines = self.b_splines(x)  # (batch, in, coeff)
        splines = splines.permute(1, 0, 2)  # (in, batch, coeff)
        orig_coeff = self.scaled_spline_weight  # (out, in, coeff)
        orig_coeff = orig_coeff.permute(1, 2, 0)  # (in, coeff, out)
        unreduced_spline_output = torch.bmm(splines, orig_coeff)  # (in, batch, out)
        unreduced_spline_output = unreduced_spline_output.permute(
            1, 0, 2
        )  # (batch, in, out)

        # sort each channel individually to collect data distribution
        x_sorted = torch.sort(x, dim=0)[0]
        grid_adaptive = x_sorted[
            torch.linspace(
                0, batch - 1, self.grid_size + 1, dtype=torch.int64, device=x.device
            )
        ]

        uniform_step = (x_sorted[-1] - x_sorted[0] + 2 * margin) / self.grid_size
        grid_uniform = (
            torch.arange(
                self.grid_size + 1, dtype=torch.float32, device=x.device
            ).unsqueeze(1)
            * uniform_step
            + x_sorted[0]
            - margin
        )

        grid = self.grid_eps * grid_uniform + (1 - self.grid_eps) * grid_adaptive
        grid = torch.concatenate(
            [
                grid[:1]
                - uniform_step
                * torch.arange(self.spline_order, 0, -1, device=x.device).unsqueeze(1),
                grid,
                grid[-1:]
                + uniform_step
                * torch.arange(1, self.spline_order + 1, device=x.device).unsqueeze(1),
            ],
            dim=0,
        )

        self.grid.copy_(grid.T)
        self.spline_weight.data.copy_(self.curve2coeff(x, unreduced_spline_output))

    def regularization_loss(self, regularize_activation=1.0, regularize_entropy=1.0):
        """
        Compute the regularization loss.

        This is a dumb simulation of the original L1 regularization as stated in the
        paper, since the original one requires computing absolutes and entropy from the
        expanded (batch, in_features, out_features) intermediate tensor, which is hidden
        behind the F.linear function if we want an memory efficient implementation.

        The L1 regularization is now computed as mean absolute value of the spline
        weights. The authors implementation also includes this term in addition to the
        sample-based regularization.
        """
        l1_fake = self.spline_weight.abs().mean(-1)
        regularization_loss_activation = l1_fake.sum()
        p = l1_fake / regularization_loss_activation
        regularization_loss_entropy = -torch.sum(p * p.log())
        return (
            regularize_activation * regularization_loss_activation
            + regularize_entropy * regularization_loss_entropy
        )


class DW_bn_relu(nn.Module):
    def __init__(self, dim=768):
        super(DW_bn_relu, self).__init__()
        self.dwconv = nn.Conv2d(dim, dim, 3, 1, 1, bias=True, groups=dim)
        self.bn = nn.BatchNorm2d(dim)
        self.relu = nn.ReLU()

    def forward(self, x, H, W):
        B, N, C = x.shape
        x = x.transpose(1, 2).view(B, C, H, W)
        x = self.dwconv(x)
        x = self.bn(x)
        x = self.relu(x)
        x = x.flatten(2).transpose(1, 2)
        return x


class KANBlock(nn.Module):
    def __init__(self, in_features, hidden_features=None, out_features=None, act_layer=nn.GELU, drop=0., shift_size=5, version=4):
        super().__init__()
        out_features = out_features or in_features
        hidden_features = hidden_features or in_features
        self.dim = in_features
        grid_size=5
        spline_order=3
        scale_noise=0.1
        scale_base=1.0
        scale_spline=1.0
        base_activation=torch.nn.SiLU
        grid_eps=0.02
        grid_range=[-1, 1]
        self.fc1 = KANLinear(
                    in_features,
                    hidden_features,
                    grid_size=grid_size,
                    spline_order=spline_order,
                    scale_noise=scale_noise,
                    scale_base=scale_base,
                    scale_spline=scale_spline,
                    base_activation=base_activation,
                    grid_eps=grid_eps,
                    grid_range=grid_range,
                )
        self.fc2 = KANLinear(
                    hidden_features,
                    out_features,
                    grid_size=grid_size,
                    spline_order=spline_order,
                    scale_noise=scale_noise,
                    scale_base=scale_base,
                    scale_spline=scale_spline,
                    base_activation=base_activation,
                    grid_eps=grid_eps,
                    grid_range=grid_range,
                )
        self.fc3 = KANLinear(
                    hidden_features,
                    out_features,
                    grid_size=grid_size,
                    spline_order=spline_order,
                    scale_noise=scale_noise,
                    scale_base=scale_base,
                    scale_spline=scale_spline,
                    base_activation=base_activation,
                    grid_eps=grid_eps,
                    grid_range=grid_range,
                )   
        self.dwconv_1 = DW_bn_relu(hidden_features)
        self.dwconv_2 = DW_bn_relu(hidden_features)
        self.dwconv_3 = DW_bn_relu(hidden_features)
        self.drop = nn.Dropout(drop)
        self.shift_size = shift_size
        self.pad = shift_size // 2

    def forward(self, x, H, W):
        B, N, C = x.shape
        x = self.fc1(x.reshape(B*N,C))
        x = x.reshape(B,N,C).contiguous()
        x = self.dwconv_1(x, H, W)
        x = self.fc2(x.reshape(B*N,C))
        x = x.reshape(B,N,C).contiguous()
        x = self.dwconv_2(x, H, W)
        x = self.fc3(x.reshape(B*N,C))
        x = x.reshape(B,N,C).contiguous()
        x = self.dwconv_3(x, H, W)
        return x
    

if __name__ == '__main__':
    x = torch.randn([1, 22*22, 128])
    kan = KANBlock(in_features=128)
    out = kan(x, H=22, W=22)
    print(out.shape)  # [1, 22*22, 128]