Lizhi Cheng

Hui Zhang, Wotao Yin, Lizhi Cheng

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leqσ$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining $I=\supp(x^*)$ and $s=\sign(x^*_I)$, $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.

Tao Sun, Hao Jiang, Lizhi Cheng et al.

In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under a special kind of summable assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed Kurdyka- Lojasiewicz property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to several classical nonconvex iterative algorithms and derive the corresponding convergence results

Peibing Du, Roberto Barrio, Hao Jiang et al.

The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm is obtained by applying error-free transformations to improve the traditional qd algorithm. We study in detail the error analysis of the qd and Compqd algorithms and we introduce new condition numbers so that the relative forward rounding error bounds can be derived directly. Our numerical experiments illustrate that the Compqd algorithm is much more accurate than the qd algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer. Three applications of the new algorithm in the obtention of continued fractions and in pole and zero detection are shown.

Lizhi Cheng, Wenmian Yang, Weijia Jia

Multi-Intent Spoken Language Understanding (SLU), a novel and more complex scenario of SLU, is attracting increasing attention. Unlike traditional SLU, each intent in this scenario has its specific scope. Semantic information outside the scope even hinders the prediction, which tremendously increases the difficulty of intent detection. More seriously, guiding slot filling with these inaccurate intent labels suffers error propagation problems, resulting in unsatisfied overall performance. To solve these challenges, in this paper, we propose a novel Scope-Sensitive Result Attention Network (SSRAN) based on Transformer, which contains a Scope Recognizer (SR) and a Result Attention Network (RAN). Scope Recognizer assignments scope information to each token, reducing the distraction of out-of-scope tokens. Result Attention Network effectively utilizes the bidirectional interaction between results of slot filling and intent detection, mitigating the error propagation problem. Experiments on two public datasets indicate that our model significantly improves SLU performance (5.4\% and 2.1\% on Overall accuracy) over the state-of-the-art baseline.

Lizhi Cheng, Weijia jia, Wenmian Yang

Spoken Language Understanding (SLU), a core component of the task-oriented dialogue system, expects a shorter inference facing the impatience of human users. Existing work increases inference speed by designing non-autoregressive models for single-turn SLU tasks but fails to apply to multi-turn SLU in confronting the dialogue history. The intuitive idea is to concatenate all historical utterances and utilize the non-autoregressive models directly. However, this approach seriously misses the salient historical information and suffers from the uncoordinated-slot problems. To overcome those shortcomings, we propose a novel model for multi-turn SLU named Salient History Attention with Layer-Refined Transformer (SHA-LRT), which composes of an SHA module, a Layer-Refined Mechanism (LRM), and a Slot Label Generation (SLG) task. SHA captures salient historical information for the current dialogue from both historical utterances and results via a well-designed history-attention mechanism. LRM predicts preliminary SLU results from Transformer's middle states and utilizes them to guide the final prediction, and SLG obtains the sequential dependency information for the non-autoregressive encoder. Experiments on public datasets indicate that our model significantly improves multi-turn SLU performance (17.5% on Overall) with accelerating (nearly 15 times) the inference process over the state-of-the-art baseline as well as effective on the single-turn SLU tasks.

Kang Zhao, Lizhi Cheng, Shengguo Li et al.

This paper concerns the model updating problems with no spillover of the quadratic palindromic system $P(λ)=λ^2 A^{\star}+λQ+A$

Tao Sun, Lizhi Cheng

In this paper, we propose a Bregman frame for several classical alternating minimization algorithms. In the frame, these algorithms have uniform mathematical formulation. We also present convergence analysis for the frame algorithm. Under the Kurdyka-Lojasiewicz property, stronger convergence is obtained.

Lizhi Cheng, Weijia Jia, Wenmian Yang

Spoken Language Understanding (SLU), a core component of the task-oriented dialogue system, expects a shorter inference latency due to the impatience of humans. Non-autoregressive SLU models clearly increase the inference speed but suffer uncoordinated-slot problems caused by the lack of sequential dependency information among each slot chunk. To gap this shortcoming, in this paper, we propose a novel non-autoregressive SLU model named Layered-Refine Transformer, which contains a Slot Label Generation (SLG) task and a Layered Refine Mechanism (LRM). SLG is defined as generating the next slot label with the token sequence and generated slot labels. With SLG, the non-autoregressive model can efficiently obtain dependency information during training and spend no extra time in inference. LRM predicts the preliminary SLU results from Transformer's middle states and utilizes them to guide the final prediction. Experiments on two public datasets indicate that our model significantly improves SLU performance (1.5\% on Overall accuracy) while substantially speed up (more than 10 times) the inference process over the state-of-the-art baseline.

Lizhi Cheng, Weijia Jia, Wenmian Yang

Spoken language understanding (SLU), which is a core component of the task-oriented dialogue system, has made substantial progress in the research of single-turn dialogue. However, the performance in multi-turn dialogue is still not satisfactory in the sense that the existing multi-turn SLU methods have low portability and compatibility for other single-turn SLU models. Further, existing multi-turn SLU methods do not exploit the historical predicted results when predicting the current utterance, which wastes helpful information. To gap those shortcomings, in this paper, we propose a novel Result-based Portable Framework for SLU (RPFSLU). RPFSLU allows most existing single-turn SLU models to obtain the contextual information from multi-turn dialogues and takes full advantage of predicted results in the dialogue history during the current prediction. Experimental results on the public dataset KVRET have shown that all SLU models in baselines acquire enhancement by RPFSLU on multi-turn SLU tasks.

Wei Peng, Yuhong Dai, Hui Zhang et al.

Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA) method to alleviate the cyclic behaviors. Under suitable conditions, gradient descent methods with either SCA or ACA are shown to be linearly convergent for bilinear games. Numerical experiments are conducted by applying ACA to existing gradient-based algorithms in a GAN setup scenario, which demonstrate the superiority of ACA.

Tao Sun, Hao Jiang, Lizhi Cheng et al.

In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under a special kind of summable assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed Kurdyka- Lojasiewicz property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to several classical nonconvex iterative algorithms and derive the corresponding convergence results

Tao Sun, Hao Jiang, Lizhi Cheng et al.

In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both mathematics and computations in solving the nonconvex and nonsmooth subproblem. In view of this, we propose a reweighted alternating direction method of multipliers. In this algorithm, all subproblems are convex and easy to solve. We also provide several guarantees for the convergence and prove that the algorithm globally converges to a critical point of an auxiliary function with the help of the Kurdyka-Łojasiewicz property. Several numerical results are presented to demonstrate the efficiency of the proposed algorithm.