365 lines
15 KiB
Python
365 lines
15 KiB
Python
import torch
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import torch.nn as nn
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import numpy as np
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from .spline import *
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class KANLayer(nn.Module):
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"""
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KANLayer class
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Attributes:
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-----------
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in_dim: int
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input dimension
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out_dim: int
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output dimension
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size: int
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the number of splines = input dimension * output dimension
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k: int
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the piecewise polynomial order of splines
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grid: 2D torch.float
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grid points
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noises: 2D torch.float
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injected noises to splines at initialization (to break degeneracy)
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coef: 2D torch.tensor
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coefficients of B-spline bases
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scale_base: 1D torch.float
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magnitude of the residual function b(x)
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scale_sp: 1D torch.float
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mangitude of the spline function spline(x)
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base_fun: fun
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residual function b(x)
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mask: 1D torch.float
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mask of spline functions. setting some element of the mask to zero means setting the corresponding activation to zero function.
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grid_eps: float in [0,1]
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a hyperparameter used in update_grid_from_samples. When grid_eps = 0, the grid is uniform; when grid_eps = 1, the grid is partitioned using percentiles of samples. 0 < grid_eps < 1 interpolates between the two extremes.
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weight_sharing: 1D tensor int
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allow spline activations to share parameters
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lock_counter: int
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counter how many activation functions are locked (weight sharing)
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lock_id: 1D torch.int
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the id of activation functions that are locked
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device: str
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device
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Methods:
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--------
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__init__():
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initialize a KANLayer
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forward():
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forward
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update_grid_from_samples():
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update grids based on samples' incoming activations
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initialize_grid_from_parent():
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initialize grids from another model
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get_subset():
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get subset of the KANLayer (used for pruning)
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lock():
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lock several activation functions to share parameters
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unlock():
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unlock already locked activation functions
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"""
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def __init__(self, in_dim=3, out_dim=2, num=5, k=3, noise_scale=0.1, scale_base=1.0, scale_sp=1.0, base_fun=torch.nn.SiLU(), grid_eps=0.02, grid_range=[-1, 1], sp_trainable=True, sb_trainable=True, device='cpu'):
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''''
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initialize a KANLayer
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Args:
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-----
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in_dim : int
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input dimension. Default: 2.
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out_dim : int
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output dimension. Default: 3.
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num : int
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the number of grid intervals = G. Default: 5.
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k : int
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the order of piecewise polynomial. Default: 3.
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noise_scale : float
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the scale of noise injected at initialization. Default: 0.1.
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scale_base : float
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the scale of the residual function b(x). Default: 1.0.
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scale_sp : float
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the scale of the base function spline(x). Default: 1.0.
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base_fun : function
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residual function b(x). Default: torch.nn.SiLU()
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grid_eps : float
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When grid_eps = 0, the grid is uniform; when grid_eps = 1, the grid is partitioned using percentiles of samples. 0 < grid_eps < 1 interpolates between the two extremes. Default: 0.02.
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grid_range : list/np.array of shape (2,)
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setting the range of grids. Default: [-1,1].
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sp_trainable : bool
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If true, scale_sp is trainable. Default: True.
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sb_trainable : bool
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If true, scale_base is trainable. Default: True.
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device : str
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device
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Returns:
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--------
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self
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Example
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-------
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>>> model = KANLayer(in_dim=3, out_dim=5)
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>>> (model.in_dim, model.out_dim)
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(3, 5)
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'''
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super(KANLayer, self).__init__()
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# size
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self.size = size = out_dim * in_dim
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self.out_dim = out_dim
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self.in_dim = in_dim
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self.num = num
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self.k = k
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# shape: (size, num)
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self.grid = torch.einsum('i,j->ij', torch.ones(size, ), torch.linspace(grid_range[0], grid_range[1], steps=num + 1))
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self.grid = torch.nn.Parameter(self.grid).requires_grad_(False)
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noises = (torch.rand(size, self.grid.shape[1]) - 1 / 2) * noise_scale / num
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noises = noises.to(device)
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# shape: (size, coef)
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self.coef = torch.nn.Parameter(curve2coef(self.grid, noises, self.grid, k))
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if isinstance(scale_base, float):
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self.scale_base = torch.nn.Parameter(torch.ones(size, ) * scale_base).requires_grad_(sb_trainable) # make scale trainable
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else:
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self.scale_base = torch.nn.Parameter(scale_base).requires_grad_(sb_trainable)
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self.scale_sp = torch.nn.Parameter(torch.ones(size, ) * scale_sp).requires_grad_(sp_trainable) # make scale trainable
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self.base_fun = base_fun
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self.mask = torch.nn.Parameter(torch.ones(size, )).requires_grad_(False)
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self.grid_eps = grid_eps
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self.weight_sharing = torch.arange(size)
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self.lock_counter = 0
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self.lock_id = torch.zeros(size)
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self.device = device
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def forward(self, x):
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'''
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KANLayer forward given input x
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Args:
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-----
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x : 2D torch.float
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inputs, shape (number of samples, input dimension)
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Returns:
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--------
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y : 2D torch.float
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outputs, shape (number of samples, output dimension)
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preacts : 3D torch.float
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fan out x into activations, shape (number of sampels, output dimension, input dimension)
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postacts : 3D torch.float
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the outputs of activation functions with preacts as inputs
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postspline : 3D torch.float
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the outputs of spline functions with preacts as inputs
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Example
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-------
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>>> model = KANLayer(in_dim=3, out_dim=5)
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>>> x = torch.normal(0,1,size=(100,3))
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>>> y, preacts, postacts, postspline = model(x)
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>>> y.shape, preacts.shape, postacts.shape, postspline.shape
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(torch.Size([100, 5]),
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torch.Size([100, 5, 3]),
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torch.Size([100, 5, 3]),
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torch.Size([100, 5, 3]))
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'''
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batch = x.shape[0]
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# x: shape (batch, in_dim) => shape (size, batch) (size = out_dim * in_dim)
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x = torch.einsum('ij,k->ikj', x, torch.ones(self.out_dim, ).to(self.device)).reshape(batch, self.size).permute(1, 0)
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preacts = x.permute(1, 0).clone().reshape(batch, self.out_dim, self.in_dim)
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base = self.base_fun(x).permute(1, 0) # shape (batch, size)
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y = coef2curve(x_eval=x, grid=self.grid[self.weight_sharing], coef=self.coef[self.weight_sharing], k=self.k, device=self.device) # shape (size, batch)
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y = y.permute(1, 0) # shape (batch, size)
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postspline = y.clone().reshape(batch, self.out_dim, self.in_dim)
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y = self.scale_base.unsqueeze(dim=0) * base + self.scale_sp.unsqueeze(dim=0) * y
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y = self.mask[None, :] * y
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postacts = y.clone().reshape(batch, self.out_dim, self.in_dim)
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y = torch.sum(y.reshape(batch, self.out_dim, self.in_dim), dim=2) # shape (batch, out_dim)
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# y shape: (batch, out_dim); preacts shape: (batch, in_dim, out_dim)
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# postspline shape: (batch, in_dim, out_dim); postacts: (batch, in_dim, out_dim)
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# postspline is for extension; postacts is for visualization
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return y, preacts, postacts, postspline
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def update_grid_from_samples(self, x):
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'''
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update grid from samples
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Args:
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-----
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x : 2D torch.float
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inputs, shape (number of samples, input dimension)
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Returns:
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--------
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None
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Example
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-------
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>>> model = KANLayer(in_dim=1, out_dim=1, num=5, k=3)
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>>> print(model.grid.data)
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>>> x = torch.linspace(-3,3,steps=100)[:,None]
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>>> model.update_grid_from_samples(x)
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>>> print(model.grid.data)
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tensor([[-1.0000, -0.6000, -0.2000, 0.2000, 0.6000, 1.0000]])
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tensor([[-3.0002, -1.7882, -0.5763, 0.6357, 1.8476, 3.0002]])
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'''
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batch = x.shape[0]
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x = torch.einsum('ij,k->ikj', x, torch.ones(self.out_dim, ).to(self.device)).reshape(batch, self.size).permute(1, 0)
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x_pos = torch.sort(x, dim=1)[0]
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y_eval = coef2curve(x_pos, self.grid, self.coef, self.k)
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num_interval = self.grid.shape[1] - 1
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ids = [int(batch / num_interval * i) for i in range(num_interval)] + [-1]
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grid_adaptive = x_pos[:, ids]
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margin = 0.01
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grid_uniform = torch.cat([grid_adaptive[:, [0]] - margin + (grid_adaptive[:, [-1]] - grid_adaptive[:, [0]] + 2 * margin) * a for a in np.linspace(0, 1, num=self.grid.shape[1])], dim=1)
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self.grid.data = self.grid_eps * grid_uniform + (1 - self.grid_eps) * grid_adaptive
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self.coef.data = curve2coef(x_pos, y_eval, self.grid, self.k)
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def initialize_grid_from_parent(self, parent, x):
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'''
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update grid from a parent KANLayer & samples
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Args:
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-----
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parent : KANLayer
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a parent KANLayer (whose grid is usually coarser than the current model)
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x : 2D torch.float
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inputs, shape (number of samples, input dimension)
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Returns:
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--------
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None
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Example
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-------
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>>> batch = 100
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>>> parent_model = KANLayer(in_dim=1, out_dim=1, num=5, k=3)
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>>> print(parent_model.grid.data)
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>>> model = KANLayer(in_dim=1, out_dim=1, num=10, k=3)
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>>> x = torch.normal(0,1,size=(batch, 1))
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>>> model.initialize_grid_from_parent(parent_model, x)
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>>> print(model.grid.data)
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tensor([[-1.0000, -0.6000, -0.2000, 0.2000, 0.6000, 1.0000]])
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tensor([[-1.0000, -0.8000, -0.6000, -0.4000, -0.2000, 0.0000, 0.2000, 0.4000,
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0.6000, 0.8000, 1.0000]])
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'''
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batch = x.shape[0]
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# preacts: shape (batch, in_dim) => shape (size, batch) (size = out_dim * in_dim)
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x_eval = torch.einsum('ij,k->ikj', x, torch.ones(self.out_dim, ).to(self.device)).reshape(batch, self.size).permute(1, 0)
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x_pos = parent.grid
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sp2 = KANLayer(in_dim=1, out_dim=self.size, k=1, num=x_pos.shape[1] - 1, scale_base=0.).to(self.device)
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sp2.coef.data = curve2coef(sp2.grid, x_pos, sp2.grid, k=1)
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y_eval = coef2curve(x_eval, parent.grid, parent.coef, parent.k)
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percentile = torch.linspace(-1, 1, self.num + 1).to(self.device)
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self.grid.data = sp2(percentile.unsqueeze(dim=1))[0].permute(1, 0)
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self.coef.data = curve2coef(x_eval, y_eval, self.grid, self.k)
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def get_subset(self, in_id, out_id):
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'''
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get a smaller KANLayer from a larger KANLayer (used for pruning)
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Args:
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-----
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in_id : list
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id of selected input neurons
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out_id : list
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id of selected output neurons
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Returns:
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--------
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spb : KANLayer
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Example
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-------
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>>> kanlayer_large = KANLayer(in_dim=10, out_dim=10, num=5, k=3)
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>>> kanlayer_small = kanlayer_large.get_subset([0,9],[1,2,3])
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>>> kanlayer_small.in_dim, kanlayer_small.out_dim
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(2, 3)
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'''
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spb = KANLayer(len(in_id), len(out_id), self.num, self.k, base_fun=self.base_fun)
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spb.grid.data = self.grid.reshape(self.out_dim, self.in_dim, spb.num + 1)[out_id][:, in_id].reshape(-1, spb.num + 1)
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spb.coef.data = self.coef.reshape(self.out_dim, self.in_dim, spb.coef.shape[1])[out_id][:, in_id].reshape(-1, spb.coef.shape[1])
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spb.scale_base.data = self.scale_base.reshape(self.out_dim, self.in_dim)[out_id][:, in_id].reshape(-1, )
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spb.scale_sp.data = self.scale_sp.reshape(self.out_dim, self.in_dim)[out_id][:, in_id].reshape(-1, )
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spb.mask.data = self.mask.reshape(self.out_dim, self.in_dim)[out_id][:, in_id].reshape(-1, )
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spb.in_dim = len(in_id)
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spb.out_dim = len(out_id)
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spb.size = spb.in_dim * spb.out_dim
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return spb
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def lock(self, ids):
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'''
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lock activation functions to share parameters based on ids
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Args:
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-----
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ids : list
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list of ids of activation functions
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Returns:
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--------
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None
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Example
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-------
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>>> model = KANLayer(in_dim=3, out_dim=3, num=5, k=3)
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>>> print(model.weight_sharing.reshape(3,3))
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>>> model.lock([[0,0],[1,2],[2,1]]) # set (0,0),(1,2),(2,1) functions to be the same
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>>> print(model.weight_sharing.reshape(3,3))
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tensor([[0, 1, 2],
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[3, 4, 5],
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[6, 7, 8]])
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tensor([[0, 1, 2],
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[3, 4, 0],
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[6, 0, 8]])
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'''
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self.lock_counter += 1
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# ids: [[i1,j1],[i2,j2],[i3,j3],...]
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for i in range(len(ids)):
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if i != 0:
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self.weight_sharing[ids[i][1] * self.in_dim + ids[i][0]] = ids[0][1] * self.in_dim + ids[0][0]
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self.lock_id[ids[i][1] * self.in_dim + ids[i][0]] = self.lock_counter
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def unlock(self, ids):
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'''
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unlock activation functions
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Args:
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-----
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ids : list
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list of ids of activation functions
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Returns:
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--------
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None
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Example
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-------
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>>> model = KANLayer(in_dim=3, out_dim=3, num=5, k=3)
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>>> model.lock([[0,0],[1,2],[2,1]]) # set (0,0),(1,2),(2,1) functions to be the same
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>>> print(model.weight_sharing.reshape(3,3))
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>>> model.unlock([[0,0],[1,2],[2,1]]) # unlock the locked functions
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>>> print(model.weight_sharing.reshape(3,3))
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tensor([[0, 1, 2],
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[3, 4, 0],
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[6, 0, 8]])
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tensor([[0, 1, 2],
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[3, 4, 5],
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[6, 7, 8]])
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'''
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# check ids are locked
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num = len(ids)
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locked = True
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for i in range(num):
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locked *= (self.weight_sharing[ids[i][1] * self.in_dim + ids[i][0]] == self.weight_sharing[ids[0][1] * self.in_dim + ids[0][0]])
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if locked == False:
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print("they are not locked. unlock failed.")
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return 0
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for i in range(len(ids)):
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self.weight_sharing[ids[i][1] * self.in_dim + ids[i][0]] = ids[i][1] * self.in_dim + ids[i][0]
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self.lock_id[ids[i][1] * self.in_dim + ids[i][0]] = 0
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self.lock_counter -= 1
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