Entailment cones compute the wrong angle?

[FremyCompany]

Hi,

I could be wrong, but I have the impression the entailment cones energy function is wrong, and optimizes the inverted order relationship between concepts.

If I understood correctly...:

• In our data files, id2 should be the generic concept, and id1 the more specific one.
• After training norm(embedding(id2)) should usually be lower than norm(embedding(id1)) as cones have more space on the edge, so generic concepts should be close to the origin and specific concepts should be far from it.

However, after training, I observe the reverse to be true:

• Generic concepts are as far as possible from the center.
• In their cones, one can find even-more-generic concepts, and no more specific concepts.

I'm either doing something very wrong, or have incorrect assumptions, or the energy function is reversed compared to what it should be according to the entailment cones article, no?

[FremyCompany]

I should specify that I am using the poincare manifold.

[ericaltendorf]

Same question. I haven't fully understood the source code yet, but training with the included mammals data, with

       -model entailment_cones \
       -manifold poincare \

produces embeddings where the norms of more specific mammal entries seem smaller than the norms of more general.

What did you end up doing with this?

[marlin-codes]

I also found a similar problem. And from the understanding of the Cone formula, the angel_at_u should be

    def angle_at_u(self, u, v):
        eps = 1e-6
        norm_u = u.norm(2, dim=-1)
        norm_v = v.norm(2, dim=-1)
        dot_prod = (u * v).sum(dim=-1)
        edist = (u - v).norm(2, dim=-1)  # euclidean distance
        num = (dot_prod * (1 + norm_u ** 2) - norm_u ** 2 * (1 + norm_v ** 2))
        denom = (norm_u * edist * ((1 + norm_v**2 * norm_u**2 - 2 * dot_prod).clamp(min=eps).sqrt())) + eps
        return (num / denom).clamp_(min=-1 + eps, max=1 - eps).acos()

In the author's code, angle_at_u is given by the following and it actually computes the angle_at_v. Please let me know if I am wrong, thanks.

    def angle_at_u(self, u, v):
        norm_u = u.norm(2, dim=-1)
        norm_v = v.norm(2, dim=-1)
        dot_prod = (u * v).sum(dim=-1)
        edist = (u - v).norm(2, dim=-1)  # euclidean distance
        num = (dot_prod * (1 + norm_v ** 2) - norm_v ** 2 * (1 + norm_u ** 2))
        denom = (norm_v * edist * (1 + norm_v**2 * norm_u**2 - 2 * dot_prod).sqrt())
        return (num / denom).clamp_(min=-1 + self.eps, max=1 - self.eps).acos()