/
kernels.py
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/
kernels.py
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import torch
import torch.nn.functional as F
def gram_lap_1d(X: torch.tensor, Y: torch.tensor, sigma=1):
'''
X, Y tensors of shape P, 1, d
'''
n_x = X.size(0)
n_y = Y.size(0)
d = X.size(2)
assert Y.size(2) == d, 'data have different dimension!'
Xlift = X.reshape(1, n_x, d)
Ylift = Y.reshape(1, n_y, d)
kernel = torch.exp( -torch.cdist(Xlift, Ylift, p=2) / sigma)
return kernel.squeeze()
def gram_llap_1d(X: torch.tensor, Y: torch.tensor, filtersize, stride=1, sigma=1, pbc=False):
'''
X, Y tensors of shape P, 1, d
'''
n_x = X.size(0)
n_y = Y.size(0)
d = X.size(2)
assert Y.size(2) == d, 'data have different dimension!'
if pbc:
X = F.pad(X, (0, filtersize-1), mode='circular')
Y = F.pad(Y, (0, filtersize-1), mode='circular')
d += filtersize-1
Xpatch = F.unfold(X.reshape(n_x, 1, 1, d), kernel_size=(1,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
Ypatch = F.unfold(Y.reshape(n_y, 1, 1, d), kernel_size=(1,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
np = Xpatch.size(1)
gram = torch.zeros( n_x, n_y, dtype=X.dtype, device=X.device)
for i in range(np):
gram_tmp = torch.exp( -torch.cdist(Xpatch[:,i,:].reshape(1, n_x, -1), Ypatch[:,i,:].reshape(1, n_y, -1) , p=2) / sigma) / ( np)
gram.add_(gram_tmp.squeeze())
return gram
def gram_llap_2d(X: torch.tensor, Y: torch.tensor, filtersize, stride=1, sigma=1, pbc=False):
'''
X, Y tensors of shape P, 1, d, d
'''
n_x = X.size(0)
n_y = Y.size(0)
d = X.size(2)
assert Y.size(2) == d, 'data have different dimension!'
assert X.size(3) == d, 'input not a square!'
assert Y.size(3) == d, 'data have different dimension!'
if pbc:
X = F.pad(X, (0, filtersize-1, 0, filtersize-1), mode='circular')
Y = F.pad(Y, (0, filtersize-1, 0, filtersize-1), mode='circular')
d += filtersize-1
Xpatch = F.unfold(X.reshape(n_x, 1, d, d), kernel_size=(filtersize,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
Ypatch = F.unfold(Y.reshape(n_y, 1, d, d), kernel_size=(filtersize,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
np = Xpatch.size(1)
gram = torch.zeros( n_x, n_y, dtype=X.dtype, device=X.device)
for i in range(np):
gram_tmp = torch.exp( -torch.cdist(Xpatch[:,i,:].reshape(1, n_x, -1), Ypatch[:,i,:].reshape(1, n_y, -1) , p=2) / sigma) / ( np)
gram.add_(gram_tmp.squeeze())
return gram
def gram_clap_1d(X: torch.tensor, Y: torch.tensor, filtersize, stride=1, sigma=1, pbc=False):
'''
X,Y tensors of shape (P,1,d)
'''
n_x = X.size(0)
n_y = Y.size(0)
d = X.size(2)
assert Y.size(2) == d, 'data have different dimension!'
if pbc:
X = F.pad(X, (0, filtersize-1), mode='circular')
Y = F.pad(Y, (0, filtersize-1), mode='circular')
d += filtersize-1
Xpatch = F.unfold(X.reshape(n_x, 1, 1, d), kernel_size=(1,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
Ypatch = F.unfold(Y.reshape(n_y, 1, 1, d), kernel_size=(1,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
np = Xpatch.size(1)
gram = torch.zeros( n_x, n_y, dtype=X.dtype, device=X.device)
for i in range(np):
for j in range(np):
gram_tmp = torch.exp( -torch.cdist(Xpatch[:,i,:].reshape(1, n_x, -1), Ypatch[:,j,:].reshape(1, n_y, -1) , p=2) / sigma) / ( np * np)
gram.add_(gram_tmp.squeeze())
return gram
def gram_clap_2d(X: torch.tensor, Y: torch.tensor, filtersize, stride=1, sigma=1, pbc=False):
'''
X, Y tensors of shape P, 1, d, d
'''
n_x = X.size(0)
n_y = Y.size(0)
d = X.size(2)
assert Y.size(2) == d, 'data have different dimension!'
assert X.size(3) == d, 'input not a square!'
assert Y.size(3) == d, 'data have different dimension!'
if pbc:
X = F.pad(X, (0, filtersize-1, 0, filtersize-1), mode='circular')
Y = F.pad(Y, (0, filtersize-1, 0, filtersize-1), mode='circular')
d += filtersize-1
Xpatch = F.unfold(X.reshape(n_x, 1, d, d), kernel_size=(filtersize,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
Ypatch = F.unfold(Y.reshape(n_y, 1, d, d), kernel_size=(filtersize,filtersize), dilation=1, padding=0, stride=stride).transpose(1,2)
np = Xpatch.size(1)
gram = torch.zeros( n_x, n_y, dtype=X.dtype, device=X.device)
for i in range(np):
for j in range(np):
gram_tmp = torch.exp( -torch.cdist(Xpatch[:,i,:].reshape(1, n_x, -1), Ypatch[:,j,:].reshape(1, n_y, -1) , p=2) / sigma) / ( np)
gram.add_(gram_tmp.squeeze())
return gram
"""
Computes the Gram matrix for the NTK of a given model f
"""
def compute_kernels(f, xtr, xte, parameters=None):
from hessian import gradient
if parameters is None:
parameters = list(f.parameters())
ktrtr = xtr.new_zeros(len(xtr), len(xtr))
ktetr = xtr.new_zeros(len(xte), len(xtr))
ktete = xtr.new_zeros(len(xte), len(xte))
params = []
current = []
for p in sorted(parameters, key=lambda p: p.numel(), reverse=True):
current.append(p)
if sum(p.numel() for p in current) > 2e9 // (8 * (len(xtr) + len(xte))):
if len(current) > 1:
params.append(current[:-1])
current = current[-1:]
else:
params.append(current)
current = []
if len(current) > 0:
params.append(current)
for i, p in enumerate(params):
print("[{}/{}] [len={} numel={}]".format(i, len(params), len(p), sum(x.numel() for x in p)), flush=True)
jtr = xtr.new_empty(len(xtr), sum(u.numel() for u in p)) # (P, N~)
jte = xte.new_empty(len(xte), sum(u.numel() for u in p)) # (P, N~)
for j, x in enumerate(xtr):
jtr[j] = gradient(f(x[None]), p) # (N~)
for j, x in enumerate(xte):
jte[j] = gradient(f(x[None]), p) # (N~)
ktrtr.add_(jtr @ jtr.t())
ktetr.add_(jte @ jtr.t())
ktete.add_(jte @ jte.t())
del jtr, jte
return ktrtr, ktetr, ktete