def get_coefficients(self):
ar, cr, a, b, c, d = self.term.get_coefficients()
# Real componenets
crd = cr * self.delta
coeffs = [2 * ar * (torch.cosh(crd) - 1) / crd**2, cr]
# Imaginary coefficients
cd = c * self.delta
dd = d * self.delta
c2 = c**2
d2 = d**2
factor = 2.0 / (self.delta * (c2 + d2))**2
cos_term = torch.cosh(cd) * torch.cos(dd) - 1
sin_term = torch.sinh(cd) * torch.sin(dd)
C1 = a * (c2 - d2) + 2 * b * c * d
C2 = b * (c2 - d2) - 2 * a * c * d
coeffs += [
factor * (C1 * cos_term - C2 * sin_term),
factor * (C2 * cos_term + C1 * sin_term),
c,
d,
]
return coeffs
def double_soliton(x: torch.tensor, t: torch.tensor, c: float,
x0: float) -> torch.tensor:
"""Single soliton solution of the KdV equation (u_t + u_{xxx} - 6 u u_x = 0)
source: http://lie.math.brocku.ca/~sanco/solitons/kdv_solitons.php
Args:
x ([Tensor]): Input vector of spatial coordinates.
t ([Tensor]): Input vector of temporal coordinates.
c ([Array]): Array containing the velocities of the two solitons, note that c[0] > c[1].
x0 ([Array]): Array containing the offsets of the two solitons.
Returns:
[Tensor]: Solution.
"""
assert c[0] > c[1], "c1 has to be bigger than c[2]"
xi0 = (np.sqrt(c[0]) / 2 * (x - c[0] * t - x0[0])
) # switch to moving coordinate frame
xi1 = np.sqrt(c[1]) / 2 * (x - c[1] * t - x0[1])
part_1 = 2 * (c[0] - c[1])
numerator = c[0] * torch.cosh(xi1)**2 + c[1] * torch.sinh(xi0)**2
denominator_1 = (np.sqrt(c[0]) - np.sqrt(c[1])) * torch.cosh(xi0 + xi1)
denominator_2 = (np.sqrt(c[0]) + np.sqrt(c[1])) * torch.cosh(xi0 - xi1)
u = part_1 * numerator / (denominator_1 + denominator_2)**2
coords = torch.cat((t.reshape(-1, 1), x.reshape(-1, 1)), dim=1)
return coords, u.view(-1, 1)
def forward(self):
M = torch.eye(6)
if self.K1 < 0:
K1 = -self.K1
flip = True
else:
K1 = self.K1
flip = False
k = torch.sqrt(K1)
kl = self.L * k
M[0,0] = torch.cos(kl)
M[0,1] = torch.sin(kl) / k
M[1,0] = -k * torch.sin(kl)
M[1,1] = torch.cos(kl)
M[2,2] = torch.cosh(kl)
M[2,3] = torch.sinh(kl) / k
M[3,2] = k * torch.sinh(kl)
M[3,3] = torch.cosh(kl)
if flip:
M = rot(- np.pi / 2) @ M @ rot(np.pi / 2)
return M
def generate_data_labels(ka_period_list, x0, y0, z0, b, dt, kd, kdmin):
a = torch.from_numpy(ka_period_list[:, 0]).double().cpu()
k = torch.from_numpy(ka_period_list[:, 1]).double().cpu()
xp = torch.from_numpy(np.ones(360000) * x0).double().cpu()
yp = torch.from_numpy(np.ones(360000) * y0).double().cpu()
zp = torch.from_numpy(np.ones(360000) * z0).double().cpu()
yokr = torch.from_numpy(np.zeros((360000, 1000))).double().cpu()
l_bif = torch.from_numpy(np.zeros(360000)).long().cpu()
l_okr = torch.from_numpy(np.zeros(360000)).long().cpu()
# xml[0] = x0
for i in range(1, kd + 1):
xx = xp
yy = yp
zz = zp
kx1 = a * torch.log(b * torch.cosh(yy)) - a * torch.log(xx + b)
ky1 = k * yy - zz - (xx + b) * torch.tanh(yy)
kz1 = (2 * k + 1) * yy - 2 * zz
x1 = xx + (dt * kx1) / 2
y1 = yy + (dt * ky1) / 2
z1 = zz + (dt * kz1) / 2
kx2 = a * torch.log(b * torch.cosh(y1)) - a * torch.log(x1 + b)
ky2 = k * y1 - z1 - (x1 + b) * torch.tanh(y1)
kz2 = (2 * k + 1) * y1 - 2 * z1
x2 = xx + (dt * kx2) / 2
y2 = yy + (dt * ky2) / 2
z2 = zz + (dt * kz2) / 2
kx3 = a * torch.log(b * torch.cosh(y2)) - a * torch.log(x2 + b)
ky3 = k * y2 - z2 - (x2 + b) * torch.tanh(y2)
kz3 = (2 * k + 1) * y2 - 2 * z2
x3 = xx + (dt * kx3)
y3 = yy + (dt * ky3)
z3 = zz + (dt * kz3)
kx4 = a * torch.log(b * torch.cosh(y3)) - a * torch.log(x3 + b)
ky4 = k * y3 - z3 - (x3 + b) * torch.tanh(y3)
kz4 = (2 * k + 1) * y3 - 2 * z3
xp = xx + ((kx1 + 2 * kx2 + 2 * kx3 + kx4) / 6) * dt
yp = yy + ((ky1 + 2 * ky2 + 2 * ky3 + ky4) / 6) * dt
zp = zz + ((kz1 + 2 * kz2 + 2 * kz3 + kz4) / 6) * dt
# xml[k] = xp
if i >= kdmin:
r00 = (yy - 1.0) * (yp - 1.0)
y00 = (xx - 1.0) - (yy - 1.0) * (xp - xx) / (yp - yy)
condition = (r00 <= 0) & (y00 > 0)
yokr[condition, l_bif[condition]] = y00[condition]
l_bif[condition] += 1
max_l_bif = max(l_bif).item()
for i in range(0, max_l_bif):
cond_i = l_bif == i + 1
if yokr[cond_i, 0:i + 1].nelement() != 0:
cond_i_idx = torch.where(cond_i)[0]
periods, indices = yokr[cond_i, 0:i + 1].sort(descending=True)
l_okr[cond_i] = 1
tmp = periods[:, 0]
for j in range(1, i + 1):
cond_abs = torch.abs(periods[:, j] - tmp) >= 0.01
cond_abs_idx = cond_i_idx[cond_abs]
tmp[cond_abs] = periods[cond_abs, j]
l_okr[cond_abs_idx] += 1
return a, k, l_okr
def train_epoch(self, t, x, y, thres_cosh=50, thres_emb=6):
self.model.train()
r = np.arange(x.size(0))
np.random.shuffle(r)
r = torch.LongTensor(r).cuda()
# Loop batches
for i in range(0, len(r), self.sbatch):
if i + self.sbatch <= len(r): b = r[i:i + self.sbatch]
else: b = r[i:]
# images=torch.autograd.Variable(x[b],volatile=False)
# targets=torch.autograd.Variable(y[b],volatile=False)
# task=torch.autograd.Variable(torch.LongTensor([t]).cuda(),volatile=False)
images = torch.autograd.Variable(x[b])
targets = torch.autograd.Variable(y[b])
task = torch.autograd.Variable(torch.LongTensor([t]).cuda())
s = (self.smax - 1 / self.smax) * i / len(r) + 1 / self.smax
# Forward
output, masks = self.model.forward(task, images, s=s)
if self.split:
output = output[t]
loss, _ = self.criterion(output, targets, masks)
# Backward
self.optimizer.zero_grad()
loss.backward()
# Restrict layer gradients in backprop
if t > 0:
for n, p in self.model.named_parameters():
if n in self.mask_back:
p.grad.data *= self.mask_back[n]
# Compensate embedding gradients
for n, p in self.model.named_parameters():
if n.startswith('e'):
num = torch.cosh(
torch.clamp(s * p.data, -thres_cosh, thres_cosh)) + 1
den = torch.cosh(p.data) + 1
p.grad.data *= self.smax / s * num / den
# Apply step
if args.optimizer == 'SGD' or args.optimizer == 'SGD_momentum_decay':
torch.nn.utils.clip_grad_norm(self.model.parameters(),
self.clipgrad)
self.optimizer.step()
# Constrain embeddings
for n, p in self.model.named_parameters():
if n.startswith('e'):
p.data = torch.clamp(p.data, -thres_emb, thres_emb)
#print(masks[-1].data.view(1,-1))
#if i>=5*self.sbatch: sys.exit()
#if i==0: print(masks[-2].data.view(1,-1),masks[-2].data.max(),masks[-2].data.min())
#print(masks[-2].data.view(1,-1))
return
def effective_energy(self, sample, frozen_nodes, tree_order, tree_hierarchy):
h = sample.matmul(self.J[frozen_nodes, :]) + self.h
tree_energy = torch.zeros(sample.shape[0], device=self.device, dtype=sample.dtype)
tree = torch.from_numpy(np.array(tree_order)).to(self.device)
for layer in tree_hierarchy:
index_matrix = torch.zeros(len(layer), 2, dtype=torch.int64,
device=self.device)
index_matrix[:, 0] = torch.arange(len(layer))
if len(self.J[layer][:, tree].nonzero()) != 0:
index_matrix.index_copy_(0,
self.J[layer][:, tree].nonzero()[:, 0],
self.J[layer][:, tree].nonzero())
index = index_matrix[:, 1]
root = tree[index]
hpj = self.J[layer, root] + h[:, layer]
hmj = -self.J[layer, root] + h[:, layer]
tree_energy += -torch.log(2 * (torch.cosh(self.beta * hpj) *
torch.cosh(self.beta * hmj)).sqrt()).sum(dim=1) / self.beta
for k in range(len(root)):
h[:, root[k]] += torch.log(torch.cosh(self.beta * hpj) /
torch.cosh(self.beta * hmj))[:, k] / (2 * self.beta)
tree = tree[len(layer):]
batch = sample.shape[0]
assert sample.shape[1] == len(frozen_nodes)
J = self.J[frozen_nodes][:, frozen_nodes].to_sparse()
fvs_energy = -torch.bmm(sample.view(batch, 1, len(frozen_nodes)),
torch.sparse.mm(J, sample.t()).t().view(batch, len(frozen_nodes), 1)).reshape(batch) / 2
fvs_energy -= sample @ self.h[frozen_nodes]
energy = fvs_energy + tree_energy
return self.beta * energy
def calc_loss(y_hat,
y_cuda,
mag_hat,
batch_size=20,
scale_by_freq=None,
l1_lambda=2e-5,
reg_logcosh=False):
# Reconstruction term plus regularization -> Slightly less wiggly waveform
#loss = logcosh(y_hat, y_cuda) + 1e-5*torch.abs(mag_hat).mean()
# loss = logcosh(y_hat, y_cuda) + 2e-5*torch.abs(mag_hat).mean()
#print("y_hat.dtype, y_cuda.dtype, mag_hat.dtype, scale_by_freq.dtype =",y_hat.dtype, y_cuda.dtype, mag_hat.dtype, scale_by_freq.dtype)
if not reg_logcosh:
if scale_by_freq is None:
loss = logcosh(y_hat, y_cuda) + l1_lambda * torch.abs(mag_hat).mean(
) # second term is an L1 regularization to help 'damp' high-freq noise
else:
loss = logcosh(
y_hat, y_cuda
) + l1_lambda / 10 * torch.abs(mag_hat * scale_by_freq).mean(
) # second term is an L1 regularization to help 'damp' high-freq noise
else:
if scale_by_freq is None:
loss = logcosh(y_hat, y_cuda) + l1_lambda * torch.mean(
torch.log(torch.cosh(mag_hat))
) # second term is an L1 regularization to help 'damp' high-freq noise
else:
loss = logcosh(y_hat, y_cuda) + l1_lambda / 10 * torch.mean(
scale_by_freq * torch.log(torch.cosh(mag_hat))
) # second term is an L1 regularization to help 'damp' high-freq noise
return loss
def expm(self, p, d_p, lr=None, out=None, normalize=False):
"""Exponential map for hyperboloid"""
if out is None:
out = p
if d_p.is_sparse:
ix, d_val = d_p._indices().squeeze(), d_p._values()
p_val = self.normalize(p.index_select(0, ix))
ldv = self.ldot(d_val, d_val, keepdim=True)
if self.debug:
assert all(ldv > 0), "Tangent norm must be greater 0"
assert all(ldv == ldv), "Tangent norm includes NaNs"
nd_p = ldv.clamp_(min=0).sqrt_()
t = th.clamp(nd_p, max=self.norm_clip)
nd_p.clamp_(min=self.eps)
newp = (th.cosh(t) * p_val).addcdiv_(th.sinh(t) * d_val, nd_p)
if normalize:
newp = self.normalize(newp)
p.index_copy_(0, ix, newp)
else:
if lr is not None:
d_p.narrow(-1, 0, 1).mul_(-1)
d_p.addcmul_((self.ldot(p, d_p, keepdim=True)).expand_as(p), p)
d_p.mul_(-lr)
ldv = self.ldot(d_p, d_p, keepdim=True)
if self.debug:
assert all(ldv > 0), "Tangent norm must be greater 0"
assert all(ldv == ldv), "Tangent norm includes NaNs"
nd_p = ldv.clamp_(min=0).sqrt_()
t = th.clamp(nd_p, max=self.norm_clip)
nd_p.clamp_(min=self.eps)
newp = (th.cosh(t) * p).addcdiv_(th.sinh(t) * d_p, nd_p)
if normalize:
newp = self.normalize(newp)
p.copy_(newp)
def log_cosh(pred, truth, sample_weight=None):
ey_t = truth - pred
if sample_weight is not None:
return torch.mean(torch.log(torch.cosh(ey_t + 1e-12)) * sample_weight)
else:
return torch.mean(torch.log(torch.cosh(ey_t + 1e-12)))
def compute_hmds(data=None, distance_matrix=None, model='poincare', dimensions=2):
"""
Compute h-MDS following the paper "Representation Tradeoffs for Hyperbolic Embeddings" (Algorithm 2)
It is the closest to PCA in the hyperbolic space
input model: hyperbolic model where data sits in, in order to compute distances
If distance matrix is computed, we do not use data.
The distances are the same independently of the hyperbolic model used.
"""
assert data is not None or distance_matrix is not None, 'We have to obtain the data somehow'
# Compute distance matrix, and then Y=cosh(d)
if distance_matrix is None:
x = data.unsqueeze(1).expand(data.shape[0], data.shape[0], data.shape[1]).contiguous().view(-1, data.shape[1])
y = data.unsqueeze(0).expand(data.shape[0], data.shape[0], data.shape[1]).contiguous().view(-1, data.shape[1])
if model == 'poincare':
distance_matrix = gmath.dist(x=x, y=y, k=torch.tensor(-1.0))
Y = torch.cosh(distance_matrix)
else: # model == 'hyperboloid'
Y = hyperboloid_distance(x, y)
else:
Y = torch.cosh(distance_matrix)
Y = Y.view(data.shape[0], data.shape[0]).detach()
pca = PCA(n_components=dimensions, svd_solver='full')
data_hyperboloid_reduced = pca.fit_transform(-Y.cpu().numpy())
x0 = np.sqrt((data_hyperboloid_reduced**2).sum(axis=-1, keepdims=True)+1)
data_hyperboloid_reduced = np.concatenate([data_hyperboloid_reduced, x0], axis=-1)
return data_hyperboloid_reduced
def backward(self, grad_output, grad_output_mean): #STE Part
input, = self.saved_tensors
grad_input = grad_output.clone()
grad_input = (2 / torch.cosh(input)) * (2 / torch.cosh(input)) * (
grad_input)
#grad_input[input.ge(1)] = 0 #great or equal
#grad_input[input.le(-1)] = 0 #less or equal
return grad_input
def get_value(self, tau0):
dt = self.delta
ar, cr, a, b, c, d = self.term.get_coefficients()
# Format the lags correctly
tau0 = torch.abs(as_tensor(tau0))
tau = tau0[..., None]
# Precompute some factors
dpt = dt + tau
dmt = dt - tau
# Real parts:
# tau > Delta
crd = cr * dt
cosh = torch.cosh(crd)
norm = 2 * ar / crd**2
K_large = torch.sum(norm * (cosh - 1) * torch.exp(-cr * tau), axis=-1)
# tau < Delta
crdmt = cr * dmt
K_small = K_large + torch.sum(norm * (crdmt - torch.sinh(crdmt)),
axis=-1)
# Complex part
cd = c * dt
dd = d * dt
c2 = c**2
d2 = d**2
c2pd2 = c2 + d2
C1 = a * (c2 - d2) + 2 * b * c * d
C2 = b * (c2 - d2) - 2 * a * c * d
norm = 1.0 / (dt * c2pd2)**2
k0 = torch.exp(-c * tau)
cdt = torch.cos(d * tau)
sdt = torch.sin(d * tau)
# For tau > Delta
cos_term = 2 * (torch.cosh(cd) * torch.cos(dd) - 1)
sin_term = 2 * (torch.sinh(cd) * torch.sin(dd))
factor = k0 * norm
K_large += torch.sum((C1 * cos_term - C2 * sin_term) * factor * cdt,
axis=-1)
K_large += torch.sum((C2 * cos_term + C1 * sin_term) * factor * sdt,
axis=-1)
# tau < Delta
edmt = torch.exp(-c * dmt)
edpt = torch.exp(-c * dpt)
cos_term = (edmt * torch.cos(d * dmt) + edpt * torch.cos(d * dpt) -
2 * k0 * cdt)
sin_term = (edmt * torch.sin(d * dmt) + edpt * torch.sin(d * dpt) -
2 * k0 * sdt)
K_small += torch.sum(2 * (a * c + b * d) * c2pd2 * dmt * norm, axis=-1)
K_small += torch.sum((C1 * cos_term + C2 * sin_term) * norm, axis=-1)
mask = tau0 >= dt
return K_large * mask + K_small * (~mask)
def forward(self, gaze_gt, hp_gt, gaze_pred, hp_pred):
# weight_hp = torch.sum(1 - torch.cos(hp_gt - hp_pred), dim=1)
# cos_distant = torch.sum(1 - torch.cos(gaze_gt - gaze_pred), dim=1)
hp_losls = torch.sum(torch.log(torch.cosh(hp_gt - hp_pred)), dim=1)
# L1_gaze = torch.sum(torch.abs(gaze_gt - gaze_pred) , dim=1)
gaze_loss = torch.sum(torch.log(torch.cosh(gaze_gt - gaze_pred)),
dim=1)
# return torch.mean(0.25* L2_hp_weight + (L2_gaze))
return torch.mean(0.2 * hp_losls + (gaze_loss))
def step(self, model, mask_back, t, s=None, thres_cosh=None, smax=None, clipgrad=None, finetune=False,
closure=None):
"""Performs a single optimization step.
Constraining joint objective based gradient and weight decay gradient.
Momentum is disregarded, as cancelled out neurons don't build up momentum anyway.
"""
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']
for p, (modp_name, modp) in zip(group['params'], model.named_parameters()):
assert modp is p
if p.grad is None:
continue
d_p = p.grad.data
if weight_decay != 0:
if 'embs' not in modp_name: # Don't decay embedding params, doesn't train
d_p.add_(weight_decay, p.data)
# Constrain grad
if t > 0: # Restrict layer gradients in backprop: a^{<t}
if modp_name in mask_back:
p.grad.data *= mask_back[modp_name] # See before: stored as (1 - x) with prev task masks
# Compensate embedding gradients
if not finetune:
if 'embs' in modp_name:
num = torch.cosh(torch.clamp(s * p.data, -thres_cosh, thres_cosh)) + 1
den = torch.cosh(p.data) + 1
p.grad.data *= smax / s * num / den
# Clip
torch.nn.utils.clip_grad_norm(p, clipgrad)
# Leave momentum as is
if momentum != 0:
param_state = self.state[p]
if 'momentum_buffer' not in param_state:
buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()
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)
return loss
def train_epoch(self, t, data, iter_bar, which_type):
self.model.train()
# Loop batches
for step, batch in enumerate(iter_bar):
batch = [
bat.to(self.device) if bat is not None else None
for bat in batch
]
input_ids, segment_ids, input_mask, targets, _ = batch
s = (self.smax - 1 / self.smax) * step / len(data) + 1 / self.smax
task = torch.autograd.Variable(torch.LongTensor([t]).cuda(),
volatile=True)
# Forward
outputs = self.model.forward(task, input_ids, segment_ids,
input_mask, which_type, s)
output = outputs[t]
loss = self.criterion(output, targets)
iter_bar.set_description('Train Iter (loss=%5.3f)' % loss.item())
# Backward
self.optimizer.zero_grad()
loss.backward()
if t > 0 and which_type == 'mcl':
task = torch.autograd.Variable(torch.LongTensor([t]).cuda(),
volatile=False)
mask = self.model.ac.mask(task, s=self.smax)
mask = torch.autograd.Variable(mask.data.clone(),
requires_grad=False)
for n, p in self.model.named_parameters():
if n in rnn_weights:
# print('n: ',n)
# print('p: ',p.grad.size())
p.grad.data *= self.model.get_view_for(n, mask)
# Compensate embedding gradients
for n, p in self.model.ac.named_parameters():
if 'ac.e' in n:
num = torch.cosh(
torch.clamp(s * p.data, -self.thres_cosh,
self.thres_cosh)) + 1
den = torch.cosh(p.data) + 1
p.grad.data *= self.smax / s * num / den
torch.nn.utils.clip_grad_norm(self.model.parameters(),
self.clipgrad)
self.optimizer.step()
# Constrain embeddings
for n, p in self.model.ac.named_parameters():
if 'ac.e' in n:
p.data = torch.clamp(p.data, -self.thres_emb,
self.thres_emb)
return
def backward(ctx, grad_output):
grad_input = None
shape = ctx.shape
lambd = ctx.fitter.lambd
max_slope = ctx.fitter.max_slope
monotonic = ctx.fitter.monotonic
eps = ctx.fitter.eps
power = ctx.fitter.power
order = ctx.fitter.order
dm = ctx.fitter.dm
m = ctx.fitter.m
a0 = ctx.fitter.a0.view(shape)
if ctx.needs_input_grad[0]:
dF = ctx.residual[torch.eye(
shape[0], dtype=bool).repeat_interleave(shape[1],
axis=0)].view(shape)
dF0 = ctx.residual.sum(axis=-1).view(shape) * -.5 * dm.view(-1, 1)
summation = dF + dF0
if order > 0:
a1 = ctx.fitter.a1.view(shape)
if max_slope is None:
dF1 = (ctx.residual * m).sum(
axis=-1).view(shape) * -1.5 * (dm * m).view(-1, 1)
summation += dF1
else:
a0 = max_slope * a0
dF1 = (ctx.residual*m).sum(axis=-1).view(shape) *\
(-1.5* (dm*m).view(-1,1) *(1/torch.cosh(a1/(a0+eps)))**2+\
-a1/(a0+eps)*(1/torch.cosh(a1/(a0+eps)))**2*-.5* dm.view(-1,1)*max_slope+\
torch.tanh(a1/(a0+eps))*-.5* dm.view(-1,1)*max_slope)
summation += dF1
if order > 1:
a2 = ctx.fitter.a2.view(shape)
if not monotonic:
dF2 = (ctx.residual*.5*(3*m**2-1)).sum(axis=-1).view(shape) *\
-2.5*(dm*0.5*(3*m**2-1)).view(-1,1) #dc_2/ds is this term
summation += dF2
else:
a1 = a1 / 3.
dF2 = (ctx.residual*.5*(3*m**2-1)).sum(axis=-1).view(shape) *\
(1/torch.cosh(a2/(a1+eps))**2*(-2.5*dm*0.5*(3*m**2-1)).view(-1,1)+\
(1/torch.cosh(a2/(a1+eps))**2* -a2/(a1+eps)*-1.5*(dm*m).view(-1,1)/3. +\
-1.5*(dm*m).view(-1,1)/3.*(torch.tanh(a2/(a1+eps)))))
summation += dF2
summation *= (-power) / np.prod(shape)
if lambd is not None:
summation += -lambd*2/np.prod(shape) *\
3/2* ctx.fitter.a1.view(shape)*(m*dm).view(-1,1)
grad_input = grad_output * summation * ctx.weights
return grad_input, None, None, None, None
def expm(self, p, d_p, lr=None, out=None, normalize=False):
"""Exponential map for hyperboloid"""
if out is None:
out = p
# print("LORENTZIAN EXPONENTIAL MAP")
if d_p.is_sparse:
# t0 = time.time()
ix, d_val = d_p._indices().squeeze(), d_p._values()
# This pulls `ix` out of the original embedding table, which could
# be in a corrupted state. normalize it to fix it back to the
# surface of the hyperboloid...
# TODO: we should only do the normalize if we know that we are
# training with multiple threads, otherwise this is a bit wasteful
p_val = self.normalize(p.index_select(0, ix))
ldv = self.ldot(d_val, d_val, keepdim=True)
if self.debug:
assert all(ldv > 0), "Tangent norm must be greater 0"
assert all(ldv == ldv), "Tangent norm includes NaNs"
nd_p = ldv.clamp_(min=0).sqrt_()
t = th.clamp(nd_p, max=self.norm_clip)
nd_p.clamp_(min=self.eps)
newp = (th.cosh(t) * p_val).addcdiv_(th.sinh(t) * d_val, nd_p)
# print("is p_val sparse: {}".format(p_val.is_sparse))
# print("is nd_p sparse: {}".format(nd_p.is_sparse))
# print("is p sparse: {}".format(p.is_sparse))
# print("is newp sparse: {}".format(newp.is_sparse))
print(f"p = {p}")
print(f"d_p = {d_p}")
# print(newp)
if normalize:
newp = self.normalize(newp)
print(newp.shape)
p.index_copy_(0, ix, newp)
# t1 = time.time()
# print("iteration time = {}".format(t1-t0))
else:
if lr is not None:
d_p.narrow(-1, 0, 1).mul_(-1)
d_p.addcmul_((self.ldot(p, d_p, keepdim=True)).expand_as(p), p)
d_p.mul_(-lr)
ldv = self.ldot(d_p, d_p, keepdim=True)
if self.debug:
assert all(ldv > 0), "Tangent norm must be greater 0"
assert all(ldv == ldv), "Tangent norm includes NaNs"
nd_p = ldv.clamp_(min=0).sqrt_()
t = th.clamp(nd_p, max=self.norm_clip)
nd_p.clamp_(min=self.eps)
newp = (th.cosh(t) * p).addcdiv_(th.sinh(t) * d_p, nd_p)
if normalize:
newp = self.normalize(newp)
p.copy_(newp)
def train_epoch(self, t, x, y, thres_cosh=50, thres_emb=6):
self.model.train()
r = np.arange(x.size(0))
np.random.shuffle(r)
r = torch.LongTensor(r).cuda()
# Loop batches
for i in range(0, len(r), self.sbatch):
if i + self.sbatch <= len(r): b = r[i:i + self.sbatch]
else: b = r[i:]
images = torch.autograd.Variable(x[b])
targets = torch.autograd.Variable(y[b])
task = torch.autograd.Variable(torch.LongTensor([t]).cuda())
s = (self.smax - 1 / self.smax) * i / len(r) + 1 / self.smax
# Forward
output, masks = self.model.forward(task, images, s=s)
output = output[t]
loss, _ = self.criterion(output, targets, masks)
# Backward
self.optimizer.zero_grad()
loss.backward()
# Restrict layer gradients in backprop
if t > 0:
for n, p in self.model.named_parameters():
if n in self.mask_back:
p.grad.data *= self.mask_back[n]
# Compensate embedding gradients
for n, p in self.model.named_parameters():
if n.startswith('e'):
num = torch.cosh(
torch.clamp(s * p.data, -thres_cosh, thres_cosh)) + 1
den = torch.cosh(p.data) + 1
p.grad.data *= self.smax / s * num / den
# Apply step
self.optimizer.step()
# Constrain embeddings
for n, p in self.model.named_parameters():
if n.startswith('e'):
p.data = torch.clamp(p.data, -thres_emb, thres_emb)
return
def exp(self, X, G):
# check for multi dimenstions
G_lnorm = self.norm(X, G)
if self._k == 1:
ex = torch.cosh(G_lnorm) * X + torch.sinh(G_lnorm) * (G / G_lnorm)
if G_lnorm == 0:
ex = X
return ex
else:
G_lnorm = G_lnorm.view(-1, 1)
ex = torch.cosh(G_lnorm) * X + torch.sinh(G_lnorm) * (G / G_lnorm)
exclude = G_lnorm == 0
exclude = exclude.view(-1)
ex[exclude, :] = X[exclude, :]
return ex
def log_cosh_loss(y_pred, y_true):
loss = torch.cosh(y_pred - y_true)
loss = torch.log(loss)
loss = loss.mean(dim=0)
loss = torch.log(loss)
loss = torch.sum(loss)
return loss
def grad_log_prob(self, r):
c = __to_tensor__(self.c)
dim = self.dim
res = - r / self.sigma.pow(2) + (dim - 1) * c.sqrt() * \
torch.cosh(c.sqrt() * r) / torch.sinh(c.sqrt() * r)
res[r < 0] = 0.0
return res
def backward(ctx, grad_output):
input, weight, bias, output = ctx.saved_variables
grad_input = grad_weight = grad_bias = None
grad_stride = grad_padding = grad_dilation = grad_groups = grad_nonlinearity_g = None
# an easy way to get the gradient wrt the non-gaussianity is to calculate the
# nongaussianity, then just call backwards on this.
# From https://github.com/pytorch/pytorch/issues/1776
# (but perhaps isn't maximally efficient; one could calculate the derivative manually)
nongaussianity = torch.mean(torch.log(torch.cosh(output)))
if ctx.needs_input_grad[0]:
grad_input = torch.autograd.grad(nongaussianity, input,
grad_output)
if ctx.needs_input_grad[1]:
if ctx.super_or_sub == "super":
grad_weight = ctx.ica_strength * torch.autograd.grad(
nongaussianity, weight, grad_output)
elif ctx.super_or_sub == "sub":
grad_weight = -ctx.ica_strength * torch.autograd.grad(
nongaussianity, weight, grad_output)
# no change in bias gradient
return grad_input, grad_weight, grad_bias, grad_stride, grad_padding, grad_dilation, grad_groups, grad_nonlinearity_g
def pseudo_hyperbolic_gaussian(z, mu_h, cov, version, vt=None, u=None):
batch_size, n_h = mu_h.shape
n = n_h - 1
mu0 = to_cuda_var(torch.zeros(batch_size, n))
v0 = torch.cat((to_cuda_var(torch.ones(batch_size, 1)), mu0),
1) # origin of the hyperbolic space
# try not using inverse exp. mapping if vt is already known
if vt is None and u is None:
u = inv_exp_map(z, mu_h)
v = parallel_transport(u, mu_h, v0)
vt = v[:, 1:]
logp_vt = (MultivariateNormal(mu0, cov).log_prob(vt)).view(-1, 1)
else:
logp_vt = (MultivariateNormal(mu0, cov).log_prob(vt)).view(-1, 1)
r = lorentz_tangent_norm(u)
if version == 1:
alpha = -lorentz_product(v0, mu_h)
log_det_proj_mu = n * (torch.log(torch.sinh(r)) -
torch.log(r)) + torch.log(
torch.cosh(r)) + torch.log(alpha)
elif version == 2:
log_det_proj_mu = (n - 1) * (torch.log(torch.sinh(r)) - torch.log(r))
logp_z = logp_vt - log_det_proj_mu
return logp_vt, logp_z
def exp(self, lr):
""" Exponential map """
x = self.data.detach()
# print("norm", HyperboloidParameter.norm_h(x))
v = -lr * self.grad
retract = False
if retract:
# retraction
# print("retract")
self.data = x + v
else:
# print("tangent", HyperboloidParameter.dot_h(x, v))
assert torch.all(~torch.isnan(v))
n = self.__class__.norm_h(v).unsqueeze(-1)
assert torch.all(~torch.isnan(n))
n.clamp_(max=1.0)
# e = torch.cosh(n)*x + torch.sinh(n)*v/n
mask = torch.abs(n)<1e-7
cosh = torch.cosh(n)
cosh[mask] = 1.0
sinh = torch.sinh(n)
sinh[mask] = 0.0
n[mask] = 1.0
e = cosh*x + sinh/n*v
# assert torch.all(-HyperboloidParameter.dot_h(e,e) >= 0), torch.min(-HyperboloidParameter.dot_h(e,e))
self.data = e
self.proj()
def forward(self, y_t, y_prime_t):
ey_t = y_t - y_prime_t
value = torch.log(torch.cosh(ey_t + 1e-12))
if self.reduction == 'mean':
return torch.mean(value)
elif self.reduction == 'sum':
return torch.sum(value)
def train(args, epoch, net, trainLoader, optimizer):
net.train()
for batch_idx, (data, _) in enumerate(trainLoader):
if args.cuda:
data = data.cuda()
data = Variable(data)
data = torch.mean(data, 1).view(-1,32**2)
optimizer.zero_grad()
output = torch.squeeze(net(data))
# now reconstruct the input
data_r = output.mm(net.linear.weight)
# the loss
mse_loss = F.mse_loss(data,data_r)
nongaussianity = args.ica * torch.mean(torch.log(torch.cosh(output)))
loss = mse_loss + nongaussianity
loss.backward()
optimizer.step()
print('Train Epoch {}: Loss: {:.6f},\t Nongaussianity: {:.6f}\t'.format(epoch,
mse_loss.item(), nongaussianity.item()))
def forward(self, x, y, predict=False):
"""Computes logcosh-loss with weights
Arguments:
x {torch.Tensor} -- Predictions of shape (B, F), where F is number of targets
y {tuple} -- (targets, weights), where targets is of shape (B, F) and weights of shape (F)
Returns:
[torch.Tensor] -- Averaged, weighted loss over batch.
"""
# Unpack into targets and weights
targets, weights = y
# Calculate actual loss
logcosh = torch.log(torch.cosh(x - targets))
# weight to control contributions
# Now weigh it
loss_weighted = torch.sum(self._weights * logcosh, dim=-1)
# Mean over the batch
if not predict:
loss = torch.mean(loss_weighted)
else:
loss = loss_weighted
return loss
def get_celerite_matrices(self, x, diag):
dt = self.delta
ar, cr, a, b, c, d = self.term.get_coefficients()
# Real part
cd = cr * dt
delta_diag = 2 * torch.sum(ar * (cd - torch.sinh(cd)) / cd**2)
# Complex part
cd = c * dt
dd = d * dt
c2 = c**2
d2 = d**2
c2pd2 = c2 + d2
C1 = a * (c2 - d2) + 2 * b * c * d
C2 = b * (c2 - d2) - 2 * a * c * d
norm = (dt * c2pd2)**2
sinh = torch.sinh(cd)
cosh = torch.cosh(cd)
delta_diag += 2 * torch.sum(
(C2 * cosh * torch.sin(dd) - C1 * sinh * torch.cos(dd) +
(a * c + b * d) * dt * c2pd2) / norm)
new_diag = as_tensor(diag) + delta_diag
return super().get_celerite_matrices(x, new_diag)
def chart(self, inp):
"""
Map inp onto the hyperboloid using the global chart
"""
k = inp.shape[-1]
# inp_norm = torch.norm(inp, p=2, dim=-1, keepdim=True)
# d = F.normalize(inp, p=2, dim=-1)
cv = torch.cosh(inp.narrow(-1,1,1)).squeeze()
cu = torch.cosh(inp.narrow(-1,0,1)).squeeze()
sv = torch.sinh(inp.narrow(-1,1,1)).squeeze()
su = torch.sinh(inp.narrow(-1,0,1)).squeeze()
# h_ = inp
return torch.stack((cu*cv, cv*su, sv), dim=-1)
def __init__(self):
super().__init__()
self.activation_func_derivs = [
lambda ds, x: torch.tanh(x), lambda ds, x: 1 / torch.cosh(x)**2,
lambda ds, x: -2 * ds[0] * ds[1],
lambda ds, x: ds[2]**2 / ds[1] - 2 * ds[1]**2
] # ordered list of activation function and its derivatives
