from typing import Callable, Optional, Tuple, cast
from ..config import registry
from ..model import Model
from ..types import Floats1d, Floats2d
from ..util import get_width
InT = Tuple[Floats2d, Floats2d]
OutT = Floats1d
@registry.layers("CauchySimilarity.v1")
def CauchySimilarity(nI: Optional[int] = None) -> Model[InT, OutT]:
"""Compare input vectors according to the Cauchy similarity function proposed by
Chen (2013). Primarily used within Siamese neural networks.
"""
return Model(
"cauchy_similarity",
forward,
init=init,
dims={"nI": nI, "nO": 1},
params={"W": None},
)
def forward(
model: Model[InT, OutT], X1_X2: InT, is_train: bool
) -> Tuple[OutT, Callable]:
X1, X2 = X1_X2
W = cast(Floats2d, model.get_param("W"))
diff = X1 - X2
square_diff = diff**2
total = (W * square_diff).sum(axis=1)
sim, bp_sim = inverse(total)
def backprop(d_sim: OutT) -> InT:
d_total = bp_sim(d_sim)
d_total = model.ops.reshape2f(d_total, -1, 1)
model.inc_grad("W", (d_total * square_diff).sum(axis=0))
d_square_diff = W * d_total
d_diff = 2 * d_square_diff * diff
return (d_diff, -d_diff)
return sim, backprop
def init(
model: Model[InT, OutT], X: Optional[InT] = None, Y: Optional[OutT] = None
) -> None:
if X is not None:
model.set_dim("nI", get_width(X[0]))
# Initialize weights to 1
W = model.ops.alloc1f(model.get_dim("nI"))
W += 1
model.set_param("W", W)
def inverse(total: OutT) -> Tuple[OutT, Callable]:
inv = 1.0 / (1 + total)
def backward(d_inverse: OutT) -> OutT:
return d_inverse * (-1 / (total + 1) ** 2)
return inv, backward
