def as_sat_solver():
p = {
'x': torch.nn.Parameter(torch.tensor([0.0])),
'y': torch.nn.Parameter(torch.tensor([0.0])),
'z': torch.nn.Parameter(torch.tensor([0.0]))
}
def generate_clauses():
return [
truthy(p['x']),
or_(neg_(truthy(p['x'])), truthy(p['y'])),
or_(neg_(truthy(p['y'])), truthy(p['z']))
]
sat_solver = SatSolver(parameters=p, generate_clauses=generate_clauses)
optimizer = torch.optim.Adam(sat_solver.parameters(), lr=1.0)
for i in range(10):
optimizer.zero_grad()
sat_val = sat_solver()
loss = neg_(sat_val)
print(f"Sat={sat_val.item()}, loss={loss.item()}")
loss.backward()
optimizer.step()
def get_clause():
return {
# truthy just adds a sigmoid, to avoid clamping but slows down training
'neg(x)_or_y': or_(neg_(truthy(x)), truthy(y)), # x -> y
'neg(y)_or_z': or_(neg_(truthy(y)), truthy(z)) # y -> z
}
def get_clause():
return {
'x': x,
'neg(x)_or_y': or_(neg_(x), y),
'neg(y)_or_z': or_(neg_(y), z)
}
def generate_clauses():
return [
truthy(p['x']),
or_(neg_(truthy(p['x'])), truthy(p['y'])),
or_(neg_(truthy(p['y'])), truthy(p['z']))
]
from loss import and_, or_, neg_, clause_loss, truthy
zero = torch.tensor([0])
one = torch.tensor([1])
assert and_(zero, zero).item() == 0
assert and_(zero, one).item() == 0
assert and_(one, zero).item() == 0
assert and_(one, one).item() == 1
assert or_(zero, zero).item() == 0
assert or_(zero, one).item() == 1
assert or_(one, zero).item() == 1
assert or_(one, one).item() == 1
assert neg_(zero).item() == 1
assert neg_(one).item() == 0
def simple_optim():
"""
Try to SAT:
x -- and
neg(x) or y -- and
neg(y) or z
should be all 1
neg(x) or y is equivalent to x -> y.
Thus the clauses are: x and x -> y and y -> z
"""