kan_linear.py

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

class KANLinear(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=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

        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 = nn.Parameter(torch.Tensor(out_features, in_features))
        self.spline_weight = nn.Parameter(torch.Tensor(out_features, in_features, grid_size + spline_order))
        if enable_standalone_scale_spline:
            self.spline_scaler = 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):
        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:
                nn.init.kaiming_uniform_(self.spline_scaler, a=math.sqrt(5) * self.scale_spline)

    def b_splines(self, x: torch.Tensor):
        assert x.dim() == 2 and x.size(1) == self.in_features
        grid = self.grid
        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):
        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)
        B = y.transpose(0, 1)
        solution = torch.linalg.lstsq(A, B).solution
        result = solution.permute(2, 0, 1)
        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).permute(1, 0, 2)
        orig_coeff = self.scaled_spline_weight.permute(1, 2, 0)
        unreduced_spline_output = torch.bmm(splines, orig_coeff).permute(1, 0, 2)
        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.cat([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):
        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