To ensure that term pairs with the same lexical relation type have similar SphereRE vectors, the problem of optimizing J g can be reformulated by maximizing the probability of predicting the neighbors of (x i , y i ) given its SphereRE vector r i .
we define a new objective function J g to re- place J g based on the negative log likelihood: A remaining problem is to define the neighborhood N b(x i , y i ) properly, to preserve the hyperspherical similarity property of the distance func- In this work, we introduce a weight factor w i,j ∈ [0, 1] w.r.t.