def forward(self, x):
residual = x
y1 = residual
if self.downsample is not None:
y1 = self.downsample(residual)
y2 = F.conv2d(residual, self.weight1)
y2 = self.bn1(y2)
y2 = F.softshrink(y2, self.tau)
w = self.weight2.repeat(self.out_chnls, 1, 1, 1)
y2 = F.conv2d(y2,
w,
stride=self.stride,
padding=self.padding,
groups=self.out_chnls)
y2 = self.bn2(y2)
y2 = self.activation(y2)
y2 = self.conv3(y2)
y2 = self.bn3(y2)
y = y1 + y2
y = F.softshrink(y, self.tau)
return y
def encode(model, x):
n = x.shape[1]
N = x.shape[0]
x = x.t()
tol = 1e-10
D = model.D.detach()
lambd_eta = lambd = model.eta * model.lambd
Dtx = torch.matmul(D.t(), x).detach()
z_ = F.softshrink(model.eta * Dtx, lambd_eta)
for i in range(model.T):
res = torch.matmul(D, z_) - x
Dtres = torch.matmul(D.t(), res).detach()
z = F.softshrink(z_ - model.eta * Dtres, lambd=model.lambd * model.eta)
if torch.norm(z - z_) < tol:
break
else:
z_ = z
# computing closed form solution given sign pattern
alfa = z
SIGNS = torch.sign(z)
for i in range(N):
S = (z[:, i] != 0)
if np.sum(S.numpy()) == 0:
break
else:
Gs = torch.matmul(model.D[:, S].t(), model.D[:, S])
b = (torch.matmul(model.D[:, S].t(), x[:, i]) -
model.lambd * SIGNS[S, i])
alfa[S, i] = torch.matmul(torch.inverse(Gs), b)
return alfa
def coord_descent(x, W, z0=None, alpha=1.0, maxiter=1000, tol=1e-6, verbose=False):
input_dim, code_dim = W.shape # [D,K]
batch_size, input_dim1 = x.shape # [N,D]
assert input_dim1 == input_dim
tol = tol * code_dim
if z0 is None:
z = x.new_zeros(batch_size, code_dim) # [N,K]
else:
assert z0.shape == (batch_size, code_dim)
z = z0
# initialize b
# TODO: how should we initialize b when 'z0' is provided?
b = torch.mm(x, W) # [N,K]
# precompute S = I - W^T @ W
S = - torch.mm(W.T, W) # [K,K]
S.diagonal().add_(1.)
# loss function
def fn(z):
x_hat = torch.matmul(z, W.T)
loss = 0.5 * (x_hat - x).pow(2).sum() + alpha * z.abs().sum()
return loss
# update function
def cd_update(z, b):
z_next = F.softshrink(b, alpha) # [N,K]
z_diff = z_next - z # [N,K]
k = z_diff.abs().argmax(1) # [N]
kk = k.unsqueeze(1) # [N,1]
b = b + S[:,k].T * z_diff.gather(1, kk) # [N,K] += [N,K] * [N,1]
z = z.scatter(1, kk, z_next.gather(1, kk))
return z, b
active = torch.arange(batch_size, device=W.device)
for i in range(maxiter):
if len(active) == 0:
break
z_old = z[active]
z_new, b[active] = cd_update(z_old, b[active])
update = (z_new - z_old).abs().sum(1)
z[active] = z_new
active = active[update > tol]
if verbose:
print('iter %i - loss: %0.4f' % (i, fn(F.softshrink(b, alpha))))
z = F.softshrink(b, alpha)
return z
def fista_forward(self, data, return_loss=False):
"""
Implements FISTA.
"""
if return_loss:
loss = []
# Initializations.
yk = self.We(data)
xprev = torch.zeros(yk.size()).to(self.device)
t = 1
# Iterations.
for it in range(self.n_iter):
# Update logistics.
residual = F.linear(yk, self.We.weight.t()) - data
# ISTA step
tmp = yk - self.We(residual) / self.L
xk = F.softshrink(tmp, lambd=self.thresh)
# FISTA stepsize update:
tnext = (1 + (1 + 4 * (t**2))**.5) / 2
fact = (t - 1) / tnext
# Use momentum to update code estimate.
yk = xk + (xk - xprev) * fact
# Update "prev" stuff.
xprev = xk
t = tnext
if return_loss:
loss += [self.lossFcn(yk, data)]
# Fin.
if return_loss:
return yk, loss
return yk
def forward(self, input, k, d):
hks = k.shape[-1] // 2
hds = d.shape[-1] // 2
x_padding = (hks, hks, hks, hks)
r_padding = (hds, hds, hds, hds)
output = []
for c in range(input.size(1)):
y = input[:, c].unsqueeze(1)
x = y.clone()
for i in range(self.n_iter):
# z update
z = F.conv2d(F.pad(x, (2, 2, 2, 2), 'replicate'), self.weight)
z = F.softshrink(z,
self.lambd / max(1e-4, self.beta[i].item()))
# x update
for j in range(self.n_in):
r0 = y - F.conv2d(F.pad(x, x_padding, 'replicate'), k)
r1 = z - F.conv2d(F.pad(x, (2, 2, 2, 2), 'replicate'),
self.weight)
r = torch.cat([r0, r1], dim=1)
r_pad = F.pad(r, r_padding, 'replicate')
for l in range(3):
x = x + F.conv2d(r_pad[:, l].unsqueeze(0),
d[i, l].unsqueeze(0).unsqueeze(0))
x = x.clamp(0, 1)
output.append(x.clone())
output = torch.cat(output, 1)
return output
def resample(image: torch.Tensor, displacement, image_is_displacement=False):
shape = displacement[0].shape
grid = torch.meshgrid(
torch.linspace(-1, 2 * shape[0] / image.shape[0] - 1,
shape[0]).float().cuda(),
torch.linspace(-1, 2 * shape[1] / image.shape[1] - 1,
shape[1]).float().cuda())
df = torch.stack([
torch.add(grid[1 - i], 2 / image.shape[1 - i], displacement[i])
for i in range(2)
], 2)[None, ]
image = image[None, None, ]
if not image_is_displacement:
out = F.grid_sample(image, df, padding_mode='zeros')
else:
out = F.grid_sample(image, df, padding_mode='border')
dx = torch.mean((image[:, :, :, -1] - image[:, :, :, 0]), 2) / 2
dy = torch.mean((image[:, :, -1, :] - image[:, :, 0, :]), 2) / 2
pad_offset = F.softshrink(df, 1) * torch.stack(
(dx, dy), 2)[:, :, None, None, :]
pad_offset = torch.sum(pad_offset, 4)
out += pad_offset
return out[0][0]
def cd_update(z, b):
z_next = F.softshrink(b, alpha) # [N,K]
z_diff = z_next - z # [N,K]
k = z_diff.abs().argmax(1) # [N]
kk = k.unsqueeze(1) # [N,1]
b = b + S[:,k].T * z_diff.gather(1, kk) # [N,K] += [N,K] * [N,1]
z = z.scatter(1, kk, z_next.gather(1, kk))
return z, b
def evaluate(args, epoch, model, data_loader, writer):
model.eval()
losses = []
start = time.perf_counter()
with torch.no_grad():
if epoch != 0:
for iter, data in enumerate(data_loader):
input, target, mean, std, norm = data
input = input.to(args.device)
target = target.to(args.device)
output = model(input)
# output = transforms.complex_abs(output) # complex to real
# output = transforms.root_sum_of_squares(output, dim=1)
output = output.squeeze()
loss = F.l1_loss(output, target)
losses.append(loss.item())
x = model.module.get_trajectory()
v, a = get_vel_acc(x)
acc_loss = torch.sqrt(torch.sum(torch.pow(F.softshrink(a, args.a_max), 2)))
vel_loss = torch.sqrt(torch.sum(torch.pow(F.softshrink(v, args.v_max), 2)))
rec_loss = np.mean(losses)
writer.add_scalar('Rec_Loss', rec_loss, epoch)
writer.add_scalar('Acc_Loss', acc_loss.detach().cpu().numpy(), epoch)
writer.add_scalar('Vel_Loss', vel_loss.detach().cpu().numpy(), epoch)
writer.add_scalar('Total_Loss',
rec_loss + acc_loss.detach().cpu().numpy() + vel_loss.detach().cpu().numpy(), epoch)
x = model.module.get_trajectory()
v, a = get_vel_acc(x)
if args.TSP and epoch < args.TSP_epoch:
writer.add_figure('Scatter', plot_scatter(x.detach().cpu().numpy()), epoch)
else:
writer.add_figure('Trajectory', plot_trajectory(x.detach().cpu().numpy()), epoch)
writer.add_figure('Scatter', plot_scatter(x.detach().cpu().numpy()), epoch)
writer.add_figure('Accelerations_plot', plot_acc(a.cpu().numpy(), args.a_max), epoch)
writer.add_figure('Velocity_plot', plot_acc(v.cpu().numpy(), args.v_max), epoch)
writer.add_text('Coordinates', str(x.detach().cpu().numpy()).replace(' ', ','), epoch)
if epoch == 0:
return None, time.perf_counter() - start
else:
return np.mean(losses), time.perf_counter() - start
def __init__(self, num_basis, kernel_size, lam,
solver_type='fista_custom', solver_params=None,
size_average_recon=False,
size_average_l1=False, im_size=None, legacy_bias=False):
assert not size_average_recon
assert not size_average_l1
super().__init__()
# TODO: consistently change the semantic of size_average
# or I always use size_average_* = False and handle this later on.
self.lam = lam
self.linear_module = ConvTranspose2d(num_basis, 1, kernel_size, bias=legacy_bias)
# the official implement has bias.
if legacy_bias:
self.linear_module.bias.data.zero_()
# TODO handle weighted version.
self.cost = MSELoss(reduction='sum')
self.size_average_l1 = size_average_l1
self.solver_type = solver_type
self.solver_params = deepcopy(solver_params)
# save a template for later use.
assert im_size is not None
self.register_buffer('_template_weight', generate_weight_template(im_size,
im_size,
kernel_size))
# self.register_buffer('_template_weight', Variable(Tensor(np.ones((25, 25)))))
# define the function for fista_custom.
def f_fista(target: Tensor, code: Tensor, calc_grad):
with torch.no_grad():
recon = self.linear_module(code)
cost_recon = 0.5 * self.cost(recon, self._template_weight * target).item()
if not calc_grad:
return cost_recon
else:
# compute grad.
grad_this = conv2d(recon - self._template_weight * target,
self.linear_module.weight, None)
return cost_recon, grad_this
def g_fista(x: Tensor):
cost = torch.abs(x) * self.lam
if self.size_average_l1:
cost = cost.mean()
else:
cost = cost.sum()
return cost
self.f_fista = f_fista
self.g_fista = g_fista
self.pl = lambda x, L: softshrink(x, lambd=self.lam / L).data
if self.solver_type == 'fista_custom':
self.L = 0.1 # init L
def evaluate(args, epoch, model, data_loader, writer):
model.eval()
losses = []
psnrs= []
start = time.perf_counter()
with torch.no_grad():
if epoch != 0:
for iter, data in enumerate(data_loader):
input, target, mean, std, norm = data
input = input.unsqueeze(1).to(args.device)
target = target.to(args.device)
output = model(input).squeeze(1)
outputnorm,_,_=transforms.normalize_instance(output, eps=1e-11)
psnrs.append( psnr(target.cpu().numpy(), outputnorm.cpu().numpy()))
loss = args.rec_weight * F.l1_loss(output, target)
losses.append(loss.item())
x = model.get_trajectory()
v, a = get_vel_acc(x)
acc_loss = args.acc_weight * torch.sqrt(torch.sum(torch.pow(F.softshrink(a, args.a_max), 2)))
vel_loss = args.vel_weight * torch.sqrt(torch.sum(torch.pow(F.softshrink(v, args.v_max), 2)))
rec_loss = np.mean(losses)
psnr_avg = np.mean(psnrs)
writer.add_scalar('Rec_Loss', rec_loss, epoch)
writer.add_scalar('Acc_Loss', acc_loss.detach().cpu().numpy()/args.acc_weight, epoch)
writer.add_scalar('Vel_Loss', vel_loss.detach().cpu().numpy()/args.vel_weight, epoch)
writer.add_scalar('Acc_Weight',args.acc_weight,epoch)
writer.add_scalar('Total_Loss',
rec_loss + acc_loss.detach().cpu().numpy() + vel_loss.detach().cpu().numpy(), epoch)
writer.add_scalar('PSNR', psnr_avg, epoch)
x = model.get_trajectory()
v, a = get_vel_acc(x)
writer.add_figure('Trajectory_Proj_XY', plot_trajectory(x.detach().cpu().numpy(),0,1), epoch)
writer.add_figure('Trajectory_Proj_YZ', plot_trajectory(x.detach().cpu().numpy(),1,2), epoch)
writer.add_figure('Trajectory_Proj_XZ', plot_trajectory(x.detach().cpu().numpy(),0,2), epoch)
writer.add_figure('Trajectory_3D', plot_trajectory(x.detach().cpu().numpy(),d3=True), epoch)
writer.add_figure('Accelerations_plot', plot_acc(a.cpu().numpy(), args.a_max), epoch)
writer.add_figure('Velocity_plot', plot_acc(v.cpu().numpy(), args.v_max), epoch)
writer.add_text('Coordinates', str(x.cpu().numpy()).replace(' ', ','), epoch)
return np.mean(losses), time.perf_counter() - start
def step(self, normalizer=None, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
weight_decay = group['weight_decay']
momentum = group['momentum']
dampening = group['dampening']
nesterov = group['nesterov']
lamda = group['lamda']
normalize = group['normalize']
for p in group['params']:
if p.grad is None:
continue
if normalizer is None:
d_p = p.grad.data
else:
d_p = p.grad.data.div(normalizer)
if weight_decay != 0:
d_p.add_(weight_decay, p.data)
if momentum != 0:
param_state = self.state[p]
if 'momentum_buffer' not in param_state:
buf = param_state[
'momentum_buffer'] = torch.zeros_like(p.data)
buf.mul_(momentum).add_(d_p)
else:
buf = param_state['momentum_buffer']
buf.mul_(momentum).add_(1 - dampening, d_p)
if nesterov:
d_p = d_p.add(momentum, buf)
else:
d_p = buf
p.data.add_(-group['lr'], d_p)
if lamda != 0:
p.data = softshrink(p.data, group['lr'] * lamda)
if normalize:
p.data.div_(norm(p.data))
return loss
def step(self, closure=None):
"""Performs a single optimization step (parameter update).
Arguments:
closure (callable): A closure that reevaluates the model and
returns the loss. Optional for most optimizers.
"""
loss = None
if closure is not None:
loss = closure()
for pg in self.param_groups:
lr = pg['lr']
g = pg['gravity']
K = pg['truncate_freq']
weight_decay = pg['weight_decay']
truncate_state = self.state['truncate_state']
if 'index' not in truncate_state:
truncate_state['index'] = 1
truncate_index = truncate_state['index']
for p in pg['params']:
if p.grad is None:
continue
# # =============== debug code start ===============
# if 'global_step' not in self.state:
# self.state['global_step'] = 0
# else:
# self.state['global_step'] += 1
# if self.state['global_step'] % 20 == 0:
# print('-'*5 + 'Enter TruncateSGD step')
# print('index:{}, param.size:{}, lr:{}, g:{}, K:{}, weight_decay:{}'.format(
# truncate_index, p.size(), lr, g, K, weight_decay))
# num_nz_mask = len(p.data.nonzero())
# print('non-zero coefficient mask {}'.format(num_nz_mask))
# # =============== debug code end ===============
# gradient step
p_grad = p.grad.data
if weight_decay != 0:
p_grad.add_(weight_decay, p.data)
p.data.add_(-lr, p_grad)
# truncate step
if truncate_index > 0 and truncate_index % K == 0:
shrink_param = lr * K * g
p.data.copy_(F.softshrink(p.data, lambd=shrink_param).data)
truncate_state['index'] = 1
else:
truncate_state['index'] += 1
return loss
def train_epoch(args, epoch, model, data_loader, optimizer, writer):
model.train()
avg_loss = 0.
if epoch>=args.weight_increase_epoch:
args.vel_weight *= 1.5
args.acc_weight *= 1.5
start_epoch = start_iter = time.perf_counter()
for iter, data in enumerate(data_loader):
input, target, mean, std, norm = data
input = input.unsqueeze(1).to(args.device)
target = target.to(args.device)
output = model(input).squeeze(1)
x = model.get_trajectory()
v, a = get_vel_acc(x)
#During training, adjust the acc,vel for the coarse trajectory.
acc_loss = args.acc_weight * torch.sqrt(torch.sum(
torch.pow(F.softshrink(a, args.a_max * (args.realworld_points_per_shot / args.points_per_shot) ** 2 / 3),
2)))
vel_loss = args.vel_weight * torch.sqrt(torch.sum(
torch.pow(F.softshrink(v, args.v_max * args.realworld_points_per_shot / args.points_per_shot / 2), 2)))
rec_loss = args.rec_weight * F.l1_loss(output, target)
loss = rec_loss + vel_loss + acc_loss
optimizer.zero_grad()
loss.backward()
if args.initialization == '2dstackofstars':
x.grad[:,:,2]=0
optimizer.step()
avg_loss = 0.99 * avg_loss + 0.01 * loss.item() if iter > 0 else loss.item()
if iter % args.report_interval == 0:
logging.info(
f'Epoch = [{epoch:3d}/{args.num_epochs:3d}] '
f'Iter = [{iter:4d}/{len(data_loader):4d}] '
f'Loss = {loss.item():.4g} Avg Loss = {avg_loss:.4g} '
f'rec_loss: {rec_loss:.4g}, vel_loss: {vel_loss:.4g}, acc_loss: {acc_loss:.4g}, '
)
start_iter = time.perf_counter()
return avg_loss, time.perf_counter() - start_epoch
def __init__(self, **kwargs):
super().__init__(**kwargs)
self.init_zero_knot_indexes()
self.init_derivative_filters()
# Initializing the spline activation functions
# tensor with locations of spline coefficients
grid_tensor = self.grid_tensor # size: (num_activations, size)
coefficients = torch.zeros_like(grid_tensor) # spline coefficients
# The coefficients are initialized with the value of the activation
# at each knot (c[k] = f[k], since B1 splines are interpolators).
if self.init == 'even_odd':
# initalize half of the activations with an even function (abs) and
# and the other half with an odd function (soft threshold).
half = self.num_activations // 2
coefficients[0:half, :] = (grid_tensor[0:half, :]).abs()
coefficients[half::, :] = F.softshrink(grid_tensor[half::, :],
lambd=0.5)
elif self.init == 'relu':
coefficients = F.relu(grid_tensor)
elif self.init == 'leaky_relu':
coefficients = F.leaky_relu(grid_tensor, negative_slope=0.01)
elif self.init == 'softplus':
coefficients = F.softplus(grid_tensor, beta=3, threshold=10)
elif self.init == 'random':
coefficients.normal_()
elif self.init == 'identity':
coefficients = grid_tensor.clone()
elif self.init != 'zero':
raise ValueError(
'init should be even_odd/relu/leaky_relu/softplus/'
'random/identity/zero]')
# Need to vectorize coefficients to perform specific operations
self.coefficients_vect = nn.Parameter(
coefficients.contiguous().view(-1)) # size: (num_activations*size)
# Create the finite-difference matrix
self.init_D()
# Flag to keep track of sparsification process
self.sparsification_flag = False
def backtracking(z, x, weight, alpha, lr0, eta=1.5, maxiter=1000, verbose=False):
if eta <= 1:
raise ValueError('eta must be > 1.')
# store initial values
resid_0 = torch.matmul(z, weight.T) - x
fval_0 = 0.5 * resid_0.pow(2).sum()
fgrad_0 = torch.matmul(resid_0, weight)
def calc_F(z_1):
resid_1 = torch.matmul(z_1, weight.T) - x
return 0.5 * resid_1.pow(2).sum() + alpha * z_1.abs().sum()
def calc_Q(z_1, t):
dz = z_1 - z
return (fval_0
+ (dz * fgrad_0).sum()
+ (0.5 / t) * dz.pow(2).sum()
+ alpha * z_1.abs().sum())
lr = lr0
z_next = None
for i in range(maxiter):
z_next = F.softshrink(z - lr * fgrad_0, alpha * lr)
F_next = calc_F(z_next)
Q_next = calc_Q(z_next, lr)
if verbose:
print('iter: %4d, t: %0.5f, F-Q: %0.5f' % (i, lr, F_next-Q_next))
if F_next <= Q_next:
break
lr = lr / eta
else:
warnings.warn('backtracking line search failed. Reverting to initial '
'step size')
lr = lr0
z_next = F.softshrink(z - lr * fgrad_0, alpha * lr)
return z_next, lr
def ista(x, z0, weight, alpha=1.0, fast=True, lr='auto', maxiter=10,
tol=1e-5, backtrack=False, eta_backtrack=1.5, verbose=False):
if lr == 'auto':
# set lr based on the maximum eigenvalue of W^T @ W; i.e. the
# Lipschitz constant of \grad f(z), where f(z) = ||Wz - x||^2
L = _lipschitz_constant(weight)
lr = 1 / L
tol = z0.numel() * tol
def loss_fn(z_k):
resid = torch.matmul(z_k, weight.T) - x
loss = 0.5 * resid.pow(2).sum() + alpha * z_k.abs().sum()
return loss / x.size(0)
def rss_grad(z_k):
resid = torch.matmul(z_k, weight.T) - x
return torch.matmul(resid, weight)
# optimize
z = z0
if fast:
y, t = z0, 1
for _ in range(maxiter):
if verbose:
print('loss: %0.4f' % loss_fn(z))
# ista update
z_prev = y if fast else z
if backtrack:
# perform backtracking line search
z_next, _ = backtracking(z_prev, x, weight, alpha, lr, eta_backtrack)
else:
# constant step size
z_next = F.softshrink(z_prev - lr * rss_grad(z_prev), alpha * lr)
# check convergence
if (z - z_next).abs().sum() <= tol:
z = z_next
break
# update variables
if fast:
t_next = (1 + math.sqrt(1 + 4 * t**2)) / 2
y = z_next + ((t-1)/t_next) * (z_next - z)
t = t_next
z = z_next
return z
def step(self, closure=None):
"""Performs a single optimization step (parameter update).
Arguments:
closure (callable): A closure that reevaluates the model and
returns the loss. Optional for most optimizers.
"""
loss = super(TruncateAdam, self).step(closure)
for pg in self.param_groups:
lr_truncate = pg['lr_truncate']
g = pg['gravity']
K = pg['truncate_freq']
truncate_state = self.state['truncate_state']
if 'index' not in truncate_state:
truncate_state['index'] = 1
truncate_index = truncate_state['index']
for p in pg['params']:
if p.grad is None:
continue
# truncate step
if truncate_index > 0 and truncate_index % K == 0:
shrink_param = lr_truncate * K * g
p.data.copy_(F.softshrink(p.data, lambd=shrink_param).data)
truncate_state['index'] = 1
else:
truncate_state['index'] += 1
# # =============== debug code start ===============
# if 'global_step' not in self.state:
# self.state['global_step'] = 0
# else:
# self.state['global_step'] += 1
# if self.state['global_step'] % 50 == 0:
# print('-'*5 + 'Enter TruncateAdam step')
# print('index:{}, param.size:{}, lr:{}, g:{}, K:{}'.format(
# truncate_index, p.size(), lr_truncate, g, K))
# num_nz_mask = len(p.data.nonzero())
# print('non-zero coefficient mask {}'.format(num_nz_mask))
# # =============== debug code end ===============
return loss
def loss_fn(input, target):
diff = target - input
if shrink and shrink > 0:
diff = F.softshrink(diff, shrink)
sqdf = diff**2
if cap and cap > 0:
abdf = diff.abs()
sqdf = torch.where(abdf < cap, sqdf, cap * (2 * abdf - cap))
if reduction is None or reduction.lower() == "none":
return sqdf
elif reduction.lower() == "mean":
return sqdf.mean()
elif reduction.lower() == "sum":
return sqdf.sum()
elif reduction.lower() in ("batch", "bmean"):
return sqdf.sum() / sqdf.shape[0]
else:
raise ValueError(f"{reduction} is not a valid reduction type")
def ista_forward(self, data, return_loss=False):
"""
Implements ISTA.
"""
if return_loss:
loss = []
# Initializations.
We_y = self.We(data)
x = We_y.clone()
# Iterations.
for n in range(self.n_iter):
x = F.softshrink(We_y + self.S(x), self.thresh)
if return_loss:
loss += [self.lossFcn(x, data)]
# Fin.
if return_loss:
return x, loss
return x
def __init__(self, input_size, num_basis, lam,
solver_type='spams', solver_params=None,
size_average_recon=False,
size_average_l1=False):
assert not size_average_recon
assert not size_average_l1
super().__init__()
# TODO: consistently change the semantic of size_average
# or I always use size_average_* = False and handle this later on.
self.lam = lam
self.linear_module = Linear(num_basis, input_size, bias=False)
self.cost = MSELoss(reduction='sum')
self.size_average_l1 = size_average_l1
self.solver_type = solver_type
self.solver_params = deepcopy(solver_params)
# define the function for fista_custom.
def f_fista(target: Tensor, code: Tensor, calc_grad):
recon = self.linear_module(code)
cost_recon = self.cost(recon, target).item()
if not calc_grad:
return cost_recon
else:
# compute grad.
grad_this = linear(recon - target,
self.linear_module.weight.t())
grad_this *= 2
return cost_recon, grad_this
def g_fista(x: Tensor):
cost = torch.abs(x) * self.lam
if self.size_average_l1:
cost = cost.mean()
else:
cost = cost.sum()
return cost
self.f_fista = f_fista
self.g_fista = g_fista
self.pl = lambda x, L: softshrink(x, lambd=self.lam / L).data
if self.solver_type == 'fista_custom':
self.L = 0.1 # init L
def salsa_forward(self, data, return_loss=False):
"""
Implements SALSA.
"""
if return_loss:
loss = []
We_y = self.We(data)
x = We_y
d = torch.zeros(We_y.size()).to(self.device)
for it in range(self.n_iter):
u = F.softshrink(x + d, lambd=self.thresh)
x = self.S(We_y + self.mu * (u - d))
d += x - u
if return_loss:
loss += [self.lossFcn(x, data)]
# Fin.
if return_loss:
return x, loss
return x
def test_softshrink(self):
inp = torch.randn(1, 3, 32, 32, device='cuda', dtype=self.dtype)
output = F.softshrink(inp, lambd=0.5)
def __init__(self, lambd, beta, N_l, N_c):
super(Line, self).__init__()
self.weightx = nn.Parameter(torch.arange(-500, 510, 10, dtype=torch.float) / 255, requires_grad=False)
l = lambd / max(beta, 1e-4)
self.weighty = nn.Parameter(F.softshrink(self.weightx.view(1,1,-1).repeat(N_l, N_c, 1), l).contiguous())
def basis_pursuit_admm(A, b, lambd, M_inv=None, tol=1e-4, max_iters=100,
return_stats=False):
r"""
Basis Pursuit solver for the :math:`Q_1^\epsilon` problem
.. math::
\min_x \frac{1}{2} \left|\left| \boldsymbol{A}\vec{x} - \vec{b}
\right|\right|_2^2 + \lambda \|x\|_1
via the alternating direction method of multipliers (ADMM).
Parameters
----------
A : (N, M) torch.Tensor
The input weight matrix :math:`\boldsymbol{A}`.
b : (B, N) torch.Tensor
The right side of the equation :math:`\boldsymbol{A}\vec{x} = \vec{b}`.
lambd : float
:math:`\lambda`, controls the sparsity of :math:`\vec{x}`.
tol : float
The accuracy tolerance of ADMM.
max_iters : int
Run for at most `max_iters` iterations.
Returns
-------
torch.Tensor
(B, M) The solution vector batch :math:`\vec{x}`.
"""
A_dot_b = b.matmul(A)
if M_inv is None:
M = A.t().matmul(A) + torch.eye(A.shape[1], device=A.device)
M_inv = M.inverse().t()
del M
batch_size = b.shape[0]
v = torch.zeros(batch_size, A.shape[1], device=A.device)
u = torch.zeros(batch_size, A.shape[1], device=A.device)
v_prev = v.clone()
v_solution = v.clone()
solved = torch.zeros(batch_size, dtype=torch.bool)
iter_id = 0
dv_norm = None
for iter_id in range(max_iters):
b_eff = A_dot_b + v - u
x = b_eff.matmul(M_inv) # M_inv is already transposed
# x is of shape (<=B, m_atoms)
v = F.softshrink(x + u, lambd)
u = u + x - v
v_norm = v.norm(dim=1)
if (v_norm == 0).any():
warnings.warn(f"Lambda ({lambd}) is set too large: "
f"the output vector is zero-valued.")
dv_norm = (v - v_prev).norm(dim=1) / (v_norm + 1e-9)
solved_batch = dv_norm < tol
v, u, A_dot_b = _reduce(solved, solved_batch, v_solution, v, u,
A_dot_b)
if v.shape[0] == 0:
# all solved
break
v_prev = v.clone()
if iter_id != max_iters - 1:
assert solved.all()
v_solution[~solved] = v # dump unsolved iterations
if return_stats:
return v_solution, dv_norm.mean(), iter_id
return v_solution
def step(self, normalizer=None, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
loss = closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
if normalizer is None:
grad = p.grad.data
else:
grad = p.grad.data.div(normalizer)
if grad.is_sparse:
raise RuntimeError(
'Adam does not support sparse gradients, please consider SparseAdam instead'
)
amsgrad = group['amsgrad']
lamda = group['lamda']
normalize = group['normalize']
state = self.state[p]
# State initialization
if len(state) == 0:
state['step'] = 0
# Exponential moving average of gradient values
state['exp_avg'] = torch.zeros_like(p.data)
# Exponential moving average of squared gradient values
state['exp_avg_sq'] = torch.zeros_like(p.data)
if amsgrad:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_exp_avg_sq'] = torch.zeros_like(p.data)
exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
if amsgrad:
max_exp_avg_sq = state['max_exp_avg_sq']
beta1, beta2 = group['betas']
state['step'] += 1
if group['weight_decay'] != 0:
grad.add_(group['weight_decay'], p.data)
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(1 - beta1, grad)
exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom = max_exp_avg_sq.sqrt().add_(group['eps'])
else:
denom = exp_avg_sq.sqrt().add_(group['eps'])
bias_correction1 = 1 - beta1**state['step']
bias_correction2 = 1 - beta2**state['step']
step_size = group['lr'] * math.sqrt(
bias_correction2) / bias_correction1
p.data.addcdiv_(-step_size, exp_avg, denom)
if lamda != 0:
p.data = softshrink(p.data, lamda)
if normalize:
p.data.div_(norm(p.data))
return loss
def train_epoch(args, epoch, model, data_loader, optimizer, writer):
model.train()
avg_loss = 0.
if epoch == args.TSP_epoch and args.TSP:
x = model.get_trajectory()
x = x.detach().cpu().numpy()
if not args.KMEANS:
x = tsp_solver(x)
else:
x = kmeans_tsp(x)
v, a = get_vel_acc(x)
writer.add_figure('TSP_Trajectory_Proj_XY', plot_trajectory(x, 0, 1),
epoch)
writer.add_figure('TSP_Trajectory_Proj_YZ', plot_trajectory(x, 1, 2),
epoch)
writer.add_figure('TSP_Trajectory_Proj_XZ', plot_trajectory(x, 0, 2),
epoch)
writer.add_figure('TSP_Trajectory_3D', plot_trajectory(x, d3=True),
epoch)
writer.add_figure('TSP_Acc', plot_acc(a, args.a_max), epoch)
writer.add_figure('TSP_Vel', plot_acc(v, args.v_max), epoch)
np.save('trajTSP', x)
with torch.no_grad():
model.subsampling.x.data = torch.tensor(x, device='cuda')
args.a_max *= 2
args.v_max *= 2
if args.TSP and epoch > args.TSP_epoch and epoch <= args.TSP_epoch * 2:
v0 = args.gamma * args.G_max * args.FOV * args.dt
a0 = args.gamma * args.S_max * args.FOV * args.dt**2 * 1e3
args.a_max -= a0 / args.TSP_epoch
args.v_max -= v0 / args.TSP_epoch
if args.TSP and epoch == args.TSP_epoch * 2:
args.vel_weight *= 10
args.acc_weight *= 10
if args.TSP and epoch == args.TSP_epoch * 2 + 10:
args.vel_weight *= 10
args.acc_weight *= 10
if args.TSP and epoch == args.TSP_epoch * 2 + 20:
args.vel_weight *= 10
args.acc_weight *= 10
start_epoch = start_iter = time.perf_counter()
for iter, data in enumerate(data_loader):
input, target, mean, std, norm = data
input = input.unsqueeze(1).to(args.device)
target = target.to(args.device)
output = model(input).squeeze(1)
x = model.get_trajectory()
v, a = get_vel_acc(x)
acc_loss = args.acc_weight * torch.sqrt(
torch.sum(torch.pow(F.softshrink(a, args.a_max), 2)))
vel_loss = args.vel_weight * torch.sqrt(
torch.sum(torch.pow(F.softshrink(v, args.v_max), 2)))
rec_loss = args.rec_weight * F.l1_loss(output, target)
if args.TSP and epoch < args.TSP_epoch:
loss = rec_loss
else:
loss = rec_loss + vel_loss + acc_loss
optimizer.zero_grad()
loss.backward()
optimizer.step()
avg_loss = 0.99 * avg_loss + 0.01 * loss.item(
) if iter > 0 else loss.item()
#writer.add_scalar('TrainLoss', loss.item(), iter)
if iter % args.report_interval == 0:
logging.info(
f'Epoch = [{epoch:3d}/{args.num_epochs:3d}] '
f'Iter = [{iter:4d}/{len(data_loader):4d}] '
f'Loss = {loss.item():.4g} Avg Loss = {avg_loss:.4g} '
f'rec_loss: {rec_loss:.4g}, vel_loss: {vel_loss:.4g}, acc_loss: {acc_loss:.4g}, '
)
start_iter = time.perf_counter()
return avg_loss, time.perf_counter() - start_epoch
def train_epoch(args, epoch, model, data_loader, optimizer, writer):
model.train()
avg_loss = 0.
if epoch == args.TSP_epoch and args.TSP:
x = model.module.get_trajectory()
x = x.detach().cpu().numpy()
for shot in range(x.shape[0]):
x[shot, :, :] = tsp_solver(x[shot, :, :])
v, a = get_vel_acc(x)
writer.add_figure('TSP_Trajectory', plot_trajectory(x), epoch)
writer.add_figure('TSP_Acc', plot_acc(a, args.a_max), epoch)
writer.add_figure('TSP_Vel', plot_acc(v, args.v_max), epoch)
np.save('trajTSP',x)
with torch.no_grad():
model.module.subsampling.x.data = torch.tensor(x, device='cuda')
args.a_max *= 2
args.v_max *= 2
args.vel_weight = 1e-3
args.acc_weight = 1e-3
# if epoch == 30:
# v0 = args.gamma * args.G_max * args.FOV * args.dt
# a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
# args.a_max = a0 *1.5
# args.v_max = v0 *1.5
# if args.TSP and epoch > args.TSP_epoch and epoch<=args.TSP_epoch*2:
# v0 = args.gamma * args.G_max * args.FOV * args.dt
# a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
# args.a_max -= a0/args.TSP_epoch
# args.v_max -= v0/args.TSP_epoch
#
# if args.TSP and epoch==args.TSP_epoch*2:
# v0 = args.gamma * args.G_max * args.FOV * args.dt
# a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
# args.a_max = a0
# args.v_max = v0
# args.vel_weight *= 10
# args.acc_weight *= 10
# if args.TSP and epoch==args.TSP_epoch*2+10:
# args.vel_weight *= 10
# args.acc_weight *= 10
# if args.TSP and epoch==args.TSP_epoch*2+20:
# args.vel_weight *= 10
# args.acc_weight *= 10
if args.TSP:
if epoch < args.TSP_epoch:
model.module.subsampling.interp_gap = 1
elif epoch < 10 + args.TSP_epoch:
model.module.subsampling.interp_gap = 10
v0 = args.gamma * args.G_max * args.FOV * args.dt
a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
args.a_max -= a0/args.TSP_epoch
args.v_max -= v0/args.TSP_epoch
elif epoch == 10 + args.TSP_epoch:
model.module.subsampling.interp_gap = 10
v0 = args.gamma * args.G_max * args.FOV * args.dt
a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
args.a_max -= a0 / args.TSP_epoch
args.v_max -= v0 / args.TSP_epoch
elif epoch == 15 + args.TSP_epoch:
model.module.subsampling.interp_gap = 10
v0 = args.gamma * args.G_max * args.FOV * args.dt
a0 = args.gamma * args.S_max * args.FOV * args.dt ** 2 * 1e3
args.a_max -= a0 / args.TSP_epoch
args.v_max -= v0 / args.TSP_epoch
elif epoch == 20 + args.TSP_epoch:
model.module.subsampling.interp_gap = 10
args.vel_weight *= 10
args.acc_weight *= 10
elif epoch == 23 + args.TSP_epoch:
model.module.subsampling.interp_gap = 5
args.vel_weight *= 10
args.acc_weight *= 10
elif epoch == 25 + args.TSP_epoch:
model.module.subsampling.interp_gap = 1
args.vel_weight *= 10
args.acc_weight *= 10
else:
if epoch < 10:
model.module.subsampling.interp_gap = 50
elif epoch == 10:
model.module.subsampling.interp_gap = 30
elif epoch == 15:
model.module.subsampling.interp_gap = 20
elif epoch == 20:
model.module.subsampling.interp_gap = 10
elif epoch == 23:
model.module.subsampling.interp_gap = 5
elif epoch == 25:
model.module.subsampling.interp_gap = 1
start_epoch = start_iter = time.perf_counter()
print(f'a_max={args.a_max}, v_max={args.v_max}')
for iter, data in enumerate(data_loader):
optimizer.zero_grad()
input, target, mean, std, norm = data
input = input.to(args.device)
target = target.to(args.device)
output = model(input)
# output = transforms.complex_abs(output) # complex to real
# output = transforms.root_sum_of_squares(output, dim=1)
output=output.squeeze()
x = model.module.get_trajectory()
v, a = get_vel_acc(x)
acc_loss = torch.sqrt(torch.sum(torch.pow(F.softshrink(a, args.a_max).abs()+1e-8, 2)))
vel_loss = torch.sqrt(torch.sum(torch.pow(F.softshrink(v, args.v_max).abs()+1e-8, 2)))
rec_loss = F.l1_loss(output, target)
if args.TSP and epoch < args.TSP_epoch:
loss = args.rec_weight * rec_loss
else:
loss = args.rec_weight * rec_loss + args.vel_weight * vel_loss + args.acc_weight * acc_loss
loss.backward()
optimizer.step()
avg_loss = 0.99 * avg_loss + 0.01 * loss.item() if iter > 0 else loss.item()
# writer.add_scalar('TrainLoss', loss.item(), global_step + iter)
if iter % args.report_interval == 0:
logging.info(
f'Epoch = [{epoch:3d}/{args.num_epochs:3d}] '
f'Iter = [{iter:4d}/{len(data_loader):4d}] '
f'Loss = {loss.item():.4g} Avg Loss = {avg_loss:.4g} '
f'rec_loss: {rec_loss:.4g}, vel_loss: {vel_loss:.4g}, acc_loss: {acc_loss:.4g}'
)
start_iter = time.perf_counter()
return avg_loss, time.perf_counter() - start_epoch
''' tanh/ hardtanh/ softsign ''' x = torch.arange(-5,5,0.1).view(-1,1) y = F.tanh(x) pic(x, y, (2,4,3), 'tanh') y = F.hardtanh(x) pic(x, y, (2,4,3), 'hardtanh') y = F.softsign(x) pic(x, y, (2,4,3), 'softsign') ''' hardshrink/ tanhshrink/ tanhshrink ''' x = torch.arange(-3,3,0.1).view(-1,1) y = F.hardshrink(x) pic(x, y, (2,4,4), 'hardshrink') y = F.tanhshrink(x) pic(x, y, (2,4,4), 'tanhshrink') y = F.softshrink(x) pic(x, y, (2,4,4), 'tanhshrink') ''' sigmoid ''' x = torch.arange(-5,5,0.1).view(-1,1) y = F.sigmoid(x) pic(x, y, (2,4,5), 'sigmoid') ''' relu6 ''' x = torch.arange(-5,10,0.1).view(-1,1) y = F.relu6(x) pic(x, y, (2,4,6), 'relu6') ''' logsigmoid ''' x = torch.arange(-3,3,0.1).view(-1,1) y = F.logsigmoid(x)
def coord_descent_mod(x, W, z0=None, alpha=1.0, max_iter=1000, tol=1e-4):
"""Modified variant of the CD algorithm
Based on `enet_coordinate_descent` from sklearn.linear_model._cd_fast
This version is much slower, but it produces more reliable results
as compared to the above.
x : Tensor of shape [n_samples, n_features]
W : Tensor of shape [n_features, n_components]
z : Tensor of shape [n_samples, n_components]
"""
n_features, n_components = W.shape
n_samples = x.shape[0]
assert x.shape[1] == n_features
if z0 is None:
z = x.new_zeros(n_features, n_components) # [N,K]
else:
assert z0.shape == (n_features, n_components)
z = z0
gap = z.new_full((n_samples,), tol + 1.)
converged = z.new_zeros(n_samples, dtype=torch.bool)
d_w_tol = tol
tol = tol * x.pow(2).sum(1) # [N,]
# compute squared norms of the columns of X
norm_cols_X = W.pow(2).sum(0) # [K,]
# function to check convergence state (per sample)
def _check_convergence(z_, x_, R_, tol_):
XtA = torch.mm(R_, W) # [N,K]
dual_norm_XtA = XtA.abs().max(1)[0] # [N,]
R_norm2 = R_.pow(2).sum(1) # [N,]
small_norm = dual_norm_XtA <= alpha
const = (alpha / dual_norm_XtA).masked_fill(small_norm, 1.)
gap = torch.where(small_norm, R_norm2, 0.5 * R_norm2 * (1 + const.pow(2)))
gap = gap + alpha * z_.abs().sum(1) - const * (R_ * x_).sum(1)
converged = gap < tol_
return converged, gap
# initialize residual
R = x - torch.matmul(z, W.T) # [N,D]
for n_iter in range(max_iter):
if converged.all():
break
active_ix, = torch.where(~converged)
z_max = z.new_zeros(len(active_ix))
d_z_max = z.new_zeros(len(active_ix))
for i in range(n_components): # Loop over components
if norm_cols_X[i] == 0:
continue
atom_i = W[:,i].contiguous()
z_i = z[active_ix, i].clone()
nonzero = z_i != 0
R[active_ix[nonzero]] += torch.outer(z_i[nonzero], atom_i)
z[active_ix, i] = F.softshrink(R[active_ix].matmul(atom_i), alpha)
z[active_ix, i] /= norm_cols_X[i]
z_new_i = z[active_ix, i]
nonzero = z_new_i != 0
R[active_ix[nonzero]] -= torch.outer(z_new_i[nonzero], atom_i)
# update the maximum absolute coefficient update
d_z_max = torch.maximum(d_z_max, (z_new_i - z_i).abs())
z_max = torch.maximum(z_max, z_new_i.abs())
### check convergence ###
check = (z_max == 0) | (d_z_max / z_max < d_w_tol) | (n_iter == max_iter-1)
if not check.any():
continue
check_ix = active_ix[check]
converged[check_ix], gap[check_ix] = \
_check_convergence(z[check_ix], x[check_ix], R[check_ix], tol[check_ix])
return z, gap
def softshrink(self, x, lambd=0.5):
return F.softshrink(x, lambd)