def test_ex_fig3_full():
""" Validate the implementation of DeepPoly domain (with ReLU) using concrete example of Fig. 3 in paper. """
dom = Dom()
input_bounds = torch.tensor([[[-1., 1.], [-1., 1.]]], device=device)
lb = input_bounds[:, :, 0]
ub = input_bounds[:, :, 1]
input = dom.Ele.by_intvl(lb, ub)
relu = dom.ReLU()
lin1 = dom.Linear(2, 2) # from [x1, x2] to [x3, x4]
lin2 = dom.Linear(2, 2) # from [x5, x6] to [x7, x8]
lin3 = dom.Linear(2, 2) # from [x9, x10] to [x11, x12]
with torch.no_grad():
lin1.weight.data = torch.tensor([[1., 1.], [1., -1.]])
lin1.bias.data.zero_()
lin2.weight.data = torch.tensor([[1., 1.], [1., -1.]])
lin2.bias.data.zero_()
lin3.weight.data = torch.tensor([[1., 1.], [0., 1.]])
lin3.bias.data = torch.tensor([1., 0.])
lin1 = lin1.to(device)
lin2 = lin2.to(device)
lin3 = lin3.to(device)
def _go(layer: torch.nn.Module, e: dom.Ele, ans_lb: Tensor,
ans_ub: Tensor) -> dom.Ele:
out = layer(e)
assert torch.equal(ans_lb, out.lb())
assert torch.equal(ans_ub, out.ub())
return out
out34 = _go(lin1,
input,
ans_lb=torch.tensor([[-2., -2.]], device=device),
ans_ub=torch.tensor([[2., 2.]], device=device))
out56 = _go(relu,
out34,
ans_lb=torch.tensor([[0., 0.]], device=device),
ans_ub=torch.tensor([[2., 2.]], device=device))
out78 = _go(lin2,
out56,
ans_lb=torch.tensor([[0., -2.]], device=device),
ans_ub=torch.tensor([[3., 2.]], device=device))
out910 = _go(relu,
out78,
ans_lb=torch.tensor([[0., 0.]], device=device),
ans_ub=torch.tensor([[3., 2.]], device=device))
# x11's UB is 5.5 on paper, but that should be wrong, 6.0 should be the correct answer
out1112 = _go(lin3,
out910,
ans_lb=torch.tensor([[1., 0.]], device=device),
ans_ub=torch.tensor([[6., 2.]], device=device))
return
def test_ex_fig3():
""" Validate the implementation of DeepPoly domain (without ReLU) using concrete example of Fig. 3 in paper. """
dom = Dom()
input_bounds = torch.tensor([[[-1., 1.], [-1., 1.]]], device=device)
lb = input_bounds[:, :, 0]
ub = input_bounds[:, :, 1]
e = dom.Ele.by_intvl(lb, ub)
lin = dom.Linear(2, 2)
with torch.no_grad():
lin.weight.data = torch.tensor([[1., 1.], [1., -1.]])
lin.bias.data.zero_()
lin = lin.to(device)
out = lin(e)
answer_lb = torch.tensor([[-2., -2.]], device=device)
answer_ub = torch.tensor([[2., 2.]], device=device)
out_lb, out_ub = out.gamma()
assert torch.equal(out_lb, answer_lb)
assert torch.equal(out_ub, answer_ub)
return