You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
65 lines
1.7 KiB
65 lines
1.7 KiB
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
|