Consequently, as γ → 0, P r[c ⊙ i; d, w] in Eq.
8 approaches a Kronecker delta function centered on the cluster containing the max-scoring mention, thus reducing to the best-link case of L 3 M. PL 3 M, when tuning the value of γ, is a strictly more general model than L 3 M. Learning with PL 3 M We use a likelihood-based approach to learning with PL 3 M, and first compute the probability P r[C; d, w] of generating a clustering C, given w. We then learn w by minimizing the regularized negative log-likelihood of the data, augmenting the partition function with a loss-based margin (Gimpel and Smith, 2010).