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models.py
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models.py
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import logsumexp
import numpy as np
import pytorch_wavelets.dwt.lowlevel as lowlevel
import pywt
import torch as th
import conv
import shltutils.shearlet as sh
import util
class SimplexWeights(th.nn.Module):
def __init__(
self,
n_f: int = 32,
n_w: int = 63,
symmetric: bool = True,
vmin: float = -1,
vmax: float = 1,
w_init: str = 'student-t',
softmax: bool = False,
):
super().__init__()
self.w = th.nn.Parameter(
util.init_params(w_init, vmin, vmax, n_f, n_w, symmetric)
)
if softmax:
self.w.data = th.log(self.w.data)
self.symmetric = symmetric
self.softmax = softmax
if not softmax:
def proj():
weights = self.get().data
simplex_weights = util.proj_simplex_simul(weights
).clamp_min(1e-14)
if self.symmetric:
self.w.data.copy_(simplex_weights[:, self.w.shape[1] - 1:])
else:
self.w.data.copy_(simplex_weights)
self.w.proj = proj
self.w.reduction_dim = (1, )
self.w.proj()
def get(self):
if self.symmetric:
weights = th.cat((th.flip(self.w, (1, ))[:, :-1], self.w), dim=1)
else:
weights = self.w
if self.softmax:
return th.nn.functional.softmax(weights, dim=1)
else:
return weights
class GMMConv(th.nn.Module):
def __init__(
self,
in_channels: int = 1,
symmetric: bool = True,
vmin: float = -1,
vmax: float = 1,
n_w: int = 34,
w_init: str = 'abs',
sigmas=None,
n_scales=1,
dims=(128, 128),
lamda=None,
h=None,
P=None
):
super().__init__()
self.vmin = vmin
self.n_w = n_w
self.vmax = vmax
self.lamda = th.nn.Parameter(lamda)
self.dims = dims
self.h = th.nn.Parameter(h)
self.P = th.nn.Parameter(P)
def proj():
self.h.data.copy_(
self.h.data - (self.h.data.sum() - 1) / self.h.data.shape[0]
)
self.h.proj = proj
self.h.proj()
self.h.reduction_dim = (0, )
def proj_P():
sign = th.sign(self.P.data)
abs_simplex_proj = util.proj_simplex(self.P.data.abs().view(-1))
self.P.data.copy_(sign * abs_simplex_proj.view(self.P.shape))
self.P.proj = proj_P
self.P.proj()
self.P.reduction_dim = (0, 1)
def proj_lamda():
self.lamda.data.copy_(th.clamp(self.lamda.data, min=0, max=None))
self.lamda.data[-1] = 0
self.lamda.proj = proj_lamda
self.lamda.proj()
self.w = SimplexWeights(21, n_w, symmetric, vmin, vmax, w_init)
self._sigma_0 = (vmax - vmin) / (n_w - 1)
self.register_buffer('mus', th.linspace(vmin, vmax, n_w))
self.register_buffer('sigma_0', th.ones((21, )) * self._sigma_0)
def pot_act(self, x):
weights = self.w.get()
return logsumexp.pot_act(x, weights, self.mus, self.sigma)
def grad(self, x):
Kx = self.lamda[None, :, None, None] * self.K(x.squeeze())
pot, act = self.pot_act(Kx)
e1 = pot.sum((1, 2, 3), keepdim=True)
g1 = self.K.backward(self.lamda[None, :, None, None] * act)
return e1, g1
def set_eta(self, shape=(96, 96)):
# We have to construct the shearlet system each time since
# we learn the mother shearlets
self.K = sh.ShearletSystem2D(2, shape, self.h, self.P, 1)
# Apparently we didnt take lambda into account here when training the
# old model
self.eta = th.abs(self.K.shearlets).amax((1, 2))
# self.eta = self.lamda.data * th.abs(self.K.shearlets).amax((1, 2))
def set_sigma(
self,
sigma: float,
shape=(96, 96),
):
self.sigma = th.sqrt(self.sigma_0**2 + self.eta**2 * sigma**2)
class WaveletGMM(th.nn.Module):
def __init__(
self,
mus,
levels: int = 2,
vmin: float = -1,
vmax: float = 1,
n_w: int = 65,
im_sz: int = 32,
n_c: int = 32,
w_init: str = 'abs',
wave: str = 'db1',
):
super().__init__()
self.n_f = 3 * levels
self.levels = levels
self.lambdas = th.nn.Parameter(th.ones((self.n_f + 1, )).cuda())
self.lambdas.proj = lambda: self.lambdas.data.clamp_(min=1e-9)
self.h = th.nn.Parameter(
th.from_numpy(np.array(pywt.Wavelet(wave).dec_lo)).flip(0)
)
self.lamdas = th.rand((2 + len(self.h) - 1, ))
def proj_c():
h_tilde = self.h.data
x_ = th.cat((h_tilde, self.lamdas.to(self.h.device)))
for _ in range(10):
def nabla_l(args):
h = args[:h_tilde.shape[0]]
lamda = args[h_tilde.shape[0]:]
alternating = th.tensor([1, -1] * (len(h) // 2),
device=h.device,
dtype=h.dtype).flip(0)
nabla_h = h - h_tilde + lamda[0] + lamda[1] * alternating
nabla_lamda_ortho = []
for i in range(-len(h) // 2 + 1, len(h) // 2):
# pretty sure padded and rolled are equivalent!
# Here we essentially have the same constraint twice
# rolled
# Actually not true, but rolling is probably good
# enough since we're close to a solution..
nabla_h += 2 * lamda[2 + i - (-len(h) // 2 +
1)] * h.roll(2 * i)
nabla_lamda_ortho.append((h *
h.roll(2 * i)).sum()[None] -
1 * (i == 0))
# padded
# pad = th.zeros((2 * abs(i), )).to(h.device)
# h_padded = th.cat(
# (h[2 * i:], pad)
# ) if i > 0 else th.cat((pad, h[:2 * abs(i)]))
# if i == 0:
# h_padded = h
# # print(h_padded)
# nabla_h += 2 * lamda[2 + i -
# (-len(h) // 2 + 1)] * h_padded
# nabla_lamda_ortho.append((h * h_padded).sum()[None] -
# 1 * (i == 0))
return th.cat((
nabla_h, h.sum()[None] - np.sqrt(2),
self.get_highpass(h).sum()[None], *nabla_lamda_ortho
))
jac = th.autograd.functional.jacobian(nabla_l, x_)
rhs = jac.T @ nabla_l(x_)
lhs = jac.mT @ jac + 1e-10 * th.eye(jac.shape[1]
).to(jac.device)
x_ -= th.linalg.solve(lhs, rhs)
self.h.data.copy_(x_[:h_tilde.shape[0]])
self.lamdas.copy_(x_[h_tilde.shape[0]:])
self.h.proj = proj_c
self.h.proj()
self.h.reduction_dim = (0, )
self.mode = 'reflect'
# Hacky way to get the shape of the lower features by just using the
# transform once
yl, yh = self.wave_forward(
th.ones((1, 1, im_sz, im_sz)).to(self.h.dtype)
)
feat_lowest = yl.shape[2]**2
self.pot_sizes = [yh[i].shape[3] for i in range(self.levels)]
self.w = SimplexWeights(
self.n_f, n_w, vmin=vmin, vmax=vmax, w_init=w_init, symmetric=True
)
self.register_buffer('mus', mus)
self._sigma_0 = (mus.amax(1) - mus.amin(1)) / (n_w - 1)
self.register_buffer('sigma_0', self._sigma_0)
def get_highpass(self, h):
# Not sure why this doesn't start with -1, but this complies with the
# library
alternating = th.tensor([1, -1] * (len(h) // 2),
device=h.device,
dtype=h.dtype)
return alternating * h.flip(0)
def _forward(self, x, h0_row, h1_row, h0_col, h1_col, mode):
# Taken from pytorch wavelets, but we need the gradient wrt h,
# so i just let autograd do it...
mode = lowlevel.int_to_mode(mode)
lohi = lowlevel.afb1d(x, h0_row, h1_row, mode=mode, dim=3)
y = lowlevel.afb1d(lohi, h0_col, h1_col, mode=mode, dim=2)
s = y.shape
y = y.reshape(s[0], -1, 4, s[-2], s[-1])
low = y[:, :, 0].contiguous()
highs = y[:, :, 1:].contiguous()
return low, highs
def wave_forward(self, x):
self.g = self.get_highpass(self.h)
yh = []
ll = x
mode = lowlevel.mode_to_int(self.mode)
for j in range(self.levels):
ll, high = self._forward(
ll, self.h[None, None, :, None], self.g[None, None, :, None],
self.h[None, None, None, :], self.g[None, None, None, :], mode
)
yh.append(high)
return ll, yh
def _backward(low, highs, g0_row, g1_row, g0_col, g1_col, mode):
# Taken from pytorch wavelets, but we need the gradient wrt h,
# so i just let autograd do it...
mode = lowlevel.int_to_mode(mode)
lh, hl, hh = th.unbind(highs, dim=2)
lo = lowlevel.sfb1d(low, lh, g0_col, g1_col, mode=mode, dim=2)
hi = lowlevel.sfb1d(hl, hh, g0_col, g1_col, mode=mode, dim=2)
y = lowlevel.sfb1d(lo, hi, g0_row, g1_row, mode=mode, dim=3)
return y
def wave_backward(self, coeffs):
self.g = self.get_highpass(self.h)
yl, yh = coeffs
ll = yl
mode = lowlevel.mode_to_int(self.mode)
for h in yh[::-1]:
if ll.shape[-2] > h.shape[-2]:
ll = ll[..., :-1, :]
if ll.shape[-1] > h.shape[-1]:
ll = ll[..., :-1]
ll = lowlevel.SFB2D.apply(
ll, h, self.h[None, None, :, None], self.g[None, None, :,
None],
self.h[None, None, None, :], self.g[None, None, None, :], mode
)
return ll
def grad(self, x):
Kx = self.wave_forward(x)
act_buf = [
x.new_zeros(
(*x.shape[:2], 3, self.pot_sizes[i], self.pot_sizes[i])
) for i in range(self.levels)
]
# pot_global, act_global = self.global_gmm.grad(self.lambdas[-1] * Kx[0])
act_global = th.zeros_like(Kx[0], requires_grad=True)
pot_sum = 0 # pot_global[:, None, None, None]
for level in range(self.levels):
for direction in range(3):
idx_flat = level * 3 + direction
pot, act = logsumexp.pot_act(
self.lambdas[idx_flat] * Kx[1][level][:, :, direction],
self.w.get()[idx_flat:idx_flat + 1],
self.mus[idx_flat],
self.sigma[idx_flat:idx_flat + 1],
)
pot_sum += pot.sum((1, 2, 3), keepdim=True)
act_buf[level][:, :,
direction] = act * self.lambdas[level * 3 +
direction]
g1 = self.wave_backward((0 * self.lambdas[-1] * act_global, act_buf))
return pot_sum, g1
def set_sigma(self, sigma):
self.sigma = th.sqrt(
(self.sigma_0**2 + self.lambdas[:-1]**2 * sigma**2)
)
class ProductGSM(th.nn.Module):
def __init__(
self,
in_channels: int = 1,
n_f: int = 5**2 - 1,
kernel_size: int = 5,
bound_norm: bool = False,
zero_mean: bool = True,
ortho: bool = True,
n_scales: int = 20,
K_init: str = 'random',
sigma_0: float = 0.01,
mult: float = 1.4,
):
super().__init__()
self.n_f = n_f
self.n_scales = n_scales
self.K = conv.Conv2d(
in_channels,
n_f,
kernel_size,
zero_mean=zero_mean,
bound_norm=bound_norm,
ortho=ortho,
init=K_init,
)
self.w = SimplexWeights(
n_f, n_scales, symmetric=False, w_init='random'
)
sigmas_0 = th.tensor([sigma_0 * mult**i for i in range(self.n_scales)]
)[None].repeat(self.n_f, 1).clone()
self.register_buffer('sigmas_0', sigmas_0)
self.set_sigma(0)
def pot_act(self, x):
'''
too lazy to implement in cuda, although would help
here we have to broadcast over the mixture dimension
'''
_w = self.w.get()[None, :, :, None, None]
_sigmas = self.sigmas[None, :, :, None, None]
_x = x[:, :, None]
max_exp = (-(_x / _sigmas)**2 / 2).amax(2, keepdim=True)
gsm = th.sum(
_w / _sigmas / np.sqrt(2 * np.pi) *
th.exp(-(_x / _sigmas)**2 / 2 - max_exp),
dim=(2, ),
)
pot = -(th.log(gsm) + max_exp[:, :, 0])
act = th.sum(
_w * _x / _sigmas**3 / np.sqrt(2 * np.pi) *
th.exp(-(_x / _sigmas)**2 / 2 - max_exp),
dim=(2, )
) / gsm
return pot, act
def grad(self, x):
Kx = self.K(x)
pot, act = self.pot_act(Kx)
e1 = pot.sum((1, 2, 3), keepdim=True)
g1 = self.K.backward(act)
return e1, g1
def set_sigma(
self,
sigma: float,
):
norm_k2 = (self.K.weight**2).sum((1, 2, 3))
self.sigmas = th.sqrt(self.sigmas_0**2 + norm_k2[:, None] * sigma**2)
class ProductGMM(th.nn.Module):
def __init__(
self,
in_channels: int = 1,
n_f: int = 32,
kernel_size: int = 7,
bound_norm: bool = False,
zero_mean: bool = True,
symmetric: bool = True,
ortho: bool = True,
vmin: float = -1,
vmax: float = 1,
n_w: int = 34,
w_init: str = 'abs',
K_init: str = 'dct',
sigmas=None,
):
super().__init__()
self.n_f = n_f
self.vmin = vmin
self.n_w = n_w
self.vmax = vmax
self.K = conv.Conv2d(
in_channels,
n_f,
kernel_size,
zero_mean=zero_mean,
bound_norm=bound_norm,
ortho=ortho,
init=K_init,
)
self.symmetric = symmetric
self._sigma_0 = (vmax - vmin) / (n_w - 1)
self.w = SimplexWeights(n_f, n_w, symmetric, vmin, vmax, w_init)
self.register_buffer('mus', th.linspace(vmin, vmax, n_w))
self.register_buffer('sigma_0', th.ones((n_f, )) * self._sigma_0)
def pot_act(self, x):
weights = self.w.get()
return logsumexp.pot_act(x, weights, self.mus, self.sigma)
def grad(self, x):
Kx = self.K(x)
pot, act = self.pot_act(Kx)
e1 = pot.sum((1, 2, 3), keepdim=True)
g1 = self.K.backward(act)
return e1, g1
def set_sigma(
self,
sigma: float,
):
norm_k2 = (self.K.weight**2).sum((1, 2, 3))
self.sigma = th.sqrt(self.sigma_0**2 + norm_k2 * sigma**2)