Created
January 9, 2020 19:46
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def ihvp(f, w, v, n, alpha): | |
# calculate the inverse hessian vector product | |
# cast to list (this is important if w is a generator) | |
w = list(w) | |
p = tuple(list(v).copy()) | |
for j in range(n): | |
grads = torch.autograd.grad(f, w, grad_outputs=v, retain_graph=True) | |
# the alpha makes the hessian contractive which is required | |
# for the Neumann series to converge | |
v = [vi - alpha * gi for vi, gi in zip(v, grads)] | |
p = [pi + vi for pi, vi in zip(p, v)] | |
# undo the scaling by alpha which is done above implicitly to make sure | |
# that the Hessian is contractive | |
if n > 0: | |
p = [alpha * i for i in p] | |
del v | |
p = [i.detach() for i in p] | |
return p | |
def hg(w, l, loss_v, loss_t, n, alpha): | |
# w: parameters | |
# l: hyperparameters | |
w = list(w) | |
l = list(l) | |
del_lv_del_l = torch.autograd.grad(loss_v, l, allow_unused=True, | |
retain_graph=True) | |
del_lv_del_w = torch.autograd.grad(loss_v, w, retain_graph=True) | |
del_lt_del_w = torch.autograd.grad(loss_t, w, retain_graph=True, | |
create_graph=True) | |
if n == 0: | |
ihvp_del_lv_del_w = [i for i in del_lv_del_w] | |
else: | |
ihvp_del_lv_del_w = ihvp(del_lt_del_w, w, del_lv_del_w, n, alpha) | |
del_w_del_l = torch.autograd.grad(del_lt_del_w, l, | |
grad_outputs=ihvp_del_lv_del_w, | |
retain_graph=True, allow_unused=True) | |
if sum([i is None for i in del_w_del_l]): | |
warnings.warn('del_w_del_l is null; this happens only if loss_t does ' | |
'not depend on parameters l. Please check if this is ' | |
'intended or a mistake.') | |
del_w_del_l = [i.detach() if i is not None else None for i in del_w_del_l] | |
del_lv_del_l = [i.detach() if i is not None else None for i in del_lv_del_l] | |
def sub_(a, b): | |
if a is None and b is None: | |
return None | |
if a is None and b is not None: | |
return -b | |
if a is not None and b is None: | |
return a | |
return a-b | |
gradients = [sub_(gi, vi) for gi, vi in zip(del_lv_del_l, del_w_del_l)] | |
del ihvp_del_lv_del_w | |
del del_lt_del_w | |
del del_lv_del_w | |
del del_lv_del_l | |
return gradients |
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