In human conversation an input post is open to multiple potential responses, which is typically regarded as a one-to-many problem. Promising approaches mainly incorporate multiple latent mechanisms to build the one-to-many relationship. However, without accurate selection of the latent mechanism corresponding to the target response during training, these methods suffer from a rough optimization of latent mechanisms. In this paper, we propose a multi-mapping mechanism to better capture the one-to-many relationship, where multiple mapping modules are employed as latent mechanisms to model the semantic mappings from an input post to its diverse responses. For accurate optimization of latent mechanisms, a posterior mapping selection module is designed to select the corresponding mapping module according to the target response for further optimization. We also introduce an auxiliary matching loss to facilitate the optimization of posterior mapping selection. Empirical results demonstrate the superiority of our model in generating multiple diverse and informative responses over the state-of-the-art methods.
The problem @cite_10 in Seq2Seq models @cite_12 @cite_8 remains an open challenge. In order to generate multiple diverse responses, many approaches resort to enhanced beam search @cite_10 @cite_7 . But these methods are only applied to the decoding process and limited by the semantic similarity in the decoded responses. Another line of research turns to the different factors that determine the generation of diverse responses, such as sentence function @cite_5 , specificity @cite_11 , dialogue act @cite_3 and keywords @cite_20 . However, such methods require annotations and can capture only one aspect of one-to-many relationship. Work from @cite_0 @cite_26 combines Seq2Seq with Conditional Variational Auto-Encoder and employs a Gaussian distribution to capture discourse-level variations. But it is observed that these methods suffer from the problem @cite_23 . Moreover, the Gaussian distribution is not adaptive to the multi-modal nature of diverse responses.
@cite_26 @cite_7 @cite_8 @cite_3 @cite_0 @cite_23 @cite_5 @cite_20 @cite_10 @cite_12 @cite_11
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where (an)n ENo is some sequence of nonnegative numbers, (Sn),nENo is the sequence of partial sums, S0 = 0, Sn = XflXk, of another sequence (Xk)kEN of i.i.d. random variables, and A c R is a fixed Borel set such as [0,1] or [0, oo). Examples of such convolution series are subordinated distributions (f=0Oan = 1) which arise as distributions of random sums, and harmonic and ordinary renewal measures (a0 = 0, an = 1 n for all n C N in the first, an = 1 for all n C NO in the second case). These examples are in turn essential for the analysis of the large time behaviour of diverse applied models such as branching and queueing processes, they are also of interest in connection with representation theorems such as the Levy representation of infinitely divisible distributions. A traditional approach to such problems is via regular variation: If the underlying random variables are nonnegative we can use Laplace transforms and the related Abelian and Tauberian theorems [see, e.g., Stam (1973) in the context of subordination and Feller (1971, XIV.3) in connection with renewal theory; Embrechts, Maejima, and Omey (1984) is a recent treatment of generalized renewal measures along these lines]. The approach of the present paper is based on the Wiener-Levy-Gel'fand theorem and has occasionally been called the Banach algebra method. In Gruibel (1983) we gave a new variant of this method for the special case of lattice distributions, showing that by using the appropriate Banach algebras of sequences, arbitrarily fine expansions are possible under certain assumptions on the higher-order differences of (P(X1 = n))fnEN. Here we give a corresponding treatment of nonlattice distributions. We restrict ourselves to an analogue of first-order differences and obtain a number of theorems which perhaps are described best as next-term results. To explain this let us consider a special case in more detail. Given a large overcomplete dictionary of basis vectors, the goal is to simultaneously represent L>1 signal vectors using coefficient expansions marked by a common sparsity profile. This generalizes the standard sparse representation problem to the case where multiple responses exist that were putatively generated by the same small subset of features. Ideally, the associated sparse generating weights should be recovered, which can have physical significance in many applications (e.g., source localization). The generic solution to this problem is intractable and, therefore, approximate procedures are sought. Based on the concept of automatic relevance determination, this paper uses an empirical Bayesian prior to estimate a convenient posterior distribution over candidate basis vectors. This particular approximation enforces a common sparsity profile and consistently places its prominent posterior mass on the appropriate region of weight-space necessary for simultaneous sparse recovery. The resultant algorithm is then compared with multiple response extensions of matching pursuit, basis pursuit, FOCUSS, and Jeffreys prior-based Bayesian methods, finding that it often outperforms the others. Additional motivation for this particular choice of cost function is also provided, including the analysis of global and local minima and a variational derivation that highlights the similarities and differences between the proposed algorithm and previous approaches. In this paper, we propose a simple, fast decoding algorithm that fosters diversity in neural generation. The algorithm modifies the standard beam search algorithm by adding an inter-sibling ranking penalty, favoring choosing hypotheses from diverse parents. We evaluate the proposed model on the tasks of dialogue response generation, abstractive summarization and machine translation. We find that diverse decoding helps across all tasks, especially those for which reranking is needed. We further propose a variation that is capable of automatically adjusting its diversity decoding rates for different inputs using reinforcement learning (RL). We observe a further performance boost from this RL technique. This paper includes material from the unpublished script "Mutual Information and Diverse Decoding Improve Neural Machine Translation" (Li and Jurafsky, 2016). Topic models, such as Latent Dirichlet Allocation (LDA), posit that documents are drawn from admixtures of distributions over words, known as topics. The inference problem of recovering topics from admixtures, is NP-hard. Assuming separability, a strong assumption, [4] gave the first provable algorithm for inference. For LDA model, [6] gave a provable algorithm using tensor-methods. But [4,6] do not learn topic vectors with bounded @math error (a natural measure for probability vectors). Our aim is to develop a model which makes intuitive and empirically supported assumptions and to design an algorithm with natural, simple components such as SVD, which provably solves the inference problem for the model with bounded @math error. A topic in LDA and other models is essentially characterized by a group of co-occurring words. Motivated by this, we introduce topic specific Catchwords, group of words which occur with strictly greater frequency in a topic than any other topic individually and are required to have high frequency together rather than individually. A major contribution of the paper is to show that under this more realistic assumption, which is empirically verified on real corpora, a singular value decomposition (SVD) based algorithm with a crucial pre-processing step of thresholding, can provably recover the topics from a collection of documents drawn from Dominant admixtures. Dominant admixtures are convex combination of distributions in which one distribution has a significantly higher contribution than others. Apart from the simplicity of the algorithm, the sample complexity has near optimal dependence on @math , the lowest probability that a topic is dominant, and is better than [4]. Empirical evidence shows that on several real world corpora, both Catchwords and Dominant admixture assumptions hold and the proposed algorithm substantially outperforms the state of the art [5].