Short note on two output-dependent hidden Markov models

The purpose of this note is to study the assumption of mutual information independence", which is used by Zhou (2005) for deriving an output-dependent hidden Markov model, the so-called discriminative HMM (D-HMM), in the context of determining a stochastic optimal sequence of hidden states. The assumption is extended to derive its generative counterpart, the G-HMM. In addition, state-dependent representations for two output-dependent HMMs, namely HMMSDO (Li, 2005) and D-HMM, are presented

On Tree-Based Neural Sentence Modeling

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of different tree structures, we replace the parsing trees with trivial trees (i.e., binary balanced tree, left-branching tree and right-branching tree) in the encoders. Though trivial trees contain no syntactic information, those encoders get competitive or even better results on all of the ten downstream tasks we investigated. This surprising result indicates that explicit syntax guidance may not be the main contributor to the superior performances of tree-based neural sentence modeling. Further analysis show that tree modeling gives better results when crucial words are closer to the final representation. Additional experiments give more clues on how to design an effective tree-based encoder. Our code is open-source and available at https://github.com/ExplorerFreda/TreeEnc.Comment: To Appear at EMNLP 201

Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity

We consider Einstein-Horndeski gravity with a negative bare constant as a holographic model to investigate whether a scale invariant quantum field theory can exist without the full conformal invariance. Einstein-Horndeski gravity can admit two different AdS vacua. One is conformal, and the holographic two-point functions of the boundary energy-momentum tensor are the same as the ones obtained in Einstein gravity. The other AdS vacuum, which arises at some critical point of the coupling constants, preserves the scale invariance but not the special conformal invariance due to the logarithmic radial dependence of the Horndeski scalar. In addition to the transverse and traceless graviton modes, the theory admits an additional trace/scalar mode in the scale invariant vacuum. We obtain the two-point functions of the corresponding boundary operators. We find that the trace/scalar mode gives rise to an non-vanishing two-point function, which distinguishes the scale invariant theory from the conformal theory. The two-point function vanishes in $d=2$, where the full conformal symmetry is restored. Our results indicate the strongly coupled scale invariant unitary quantum field theory may exist in $d\ge 3$ without the full conformal symmetry. The operator that is dual to the bulk trace/scalar mode however violates the dominant energy condition.Comment: Latex, 28 pages, comments and references adde