Search

The lightweight crowd counting models, in particular knowledge distillation (KD) based models, have attracted rising attention in recent years due to their superiority on computational efficiency and hardware requirement. However, existing KD based models usually suffer from the capacity gap issue, resulting in the performance of the student network being limited by the teacher network. In this paper, we address this issue by introducing a novel review mechanism following KD models, motivated by the review mechanism of human-beings during the study. Thus, the proposed model is dubbed ReviewKD. The proposed model consists of an instruction phase and a review phase, where we firstly exploit a well-trained heavy teacher network to transfer its latent feature to a lightweight student network in the instruction phase, then in the review phase yield a refined estimate of the density map based on the learned feature through a review mechanism. The effectiveness of ReviewKD is demonstrated by a set of experiments over six benchmark datasets via comparing to the state-of-the-art models. Numerical results show that ReviewKD outperforms existing lightweight models for crowd counting, and can effectively alleviate the capacity gap issue, and particularly has the performance beyond the teacher network. Besides the lightweight models, we also show that the suggested review mechanism can be used as a plug-and-play module to further boost the performance of a kind of heavy crowd counting models without modifying the neural network architecture and introducing any additional model parameter.

Zero-shot Chinese character recognition has attracted rising attention in recent years. Existing methods for this problem are mainly based on either certain low-level stroke-based decomposition or medium-level radical-based decomposition. Considering that the stroke- and radical-level decompositions can provide different levels of information, we propose an effective zero-shot Chinese character recognition method by combining them. The proposed method consists of a training stage and an inference stage. In the training stage, we adopt two similar encoder-decoder models to yield the estimates of stroke and radical encodings, which together with the true encodings are then used to formalize the associated stroke and radical losses for training. A similarity loss is introduced to regularize stroke and radical encoders to yield features of the same characters with high correlation. In the inference stage, two key modules, i.e., the stroke screening module (SSM) and feature matching module (FMM) are introduced to tackle the deterministic and confusing cases respectively. In particular, we introduce an effective stroke rectification scheme in FMM to enlarge the candidate set of characters for final inference. Numerous experiments over three benchmark datasets covering the handwritten, printed artistic and street view scenarios are conducted to demonstrate the effectiveness of the proposed method. Numerical results show that the proposed method outperforms the state-of-the-art methods in both character and radical zero-shot settings, and maintains competitive performance in the traditional seen character setting., Comment: 24 pages

The automatic generation of Chinese fonts is an important problem involved in many applications. The predominated methods for the Chinese font generation are based on the deep generative models, especially the generative adversarial networks (GANs). However, existing GAN-based methods (say, CycleGAN) for the Chinese font generation usually suffer from the mode collapse issue, mainly due to the lack of effective guidance information. This paper proposes a novel information guidance module called the skeleton guided channel expansion (SGCE) module for the Chinese font generation through integrating the skeleton information into the generator with the channel expansion way, motivated by the observation that the skeleton embodies both local and global structure information of Chinese characters. We conduct extensive experiments to show the effectiveness of the proposed module. Numerical results show that the mode collapse issue suffered by the known CycleGAN can be effectively alleviated by equipping with the proposed SGCE module, and the CycleGAN equipped with SGCE outperforms the state-of-the-art models in terms of four important evaluation metrics and visualization quality. Besides CycleGAN, we also show that the suggested SGCE module can be adapted to other models for Chinese font generation as a plug-and-play module to further improve their performance., Comment: 12 pages, 9 figures

The generation of Chinese fonts has a wide range of applications. The currently predominated methods are mainly based on deep generative models, especially the generative adversarial networks (GANs). However, existing GAN-based models usually suffer from the well-known mode collapse problem. When mode collapse happens, the kind of GAN-based models will be failure to yield the correct fonts. To address this issue, we introduce a one-bit stroke encoding and a few-shot semi-supervised scheme (i.e., using a few paired data as semi-supervised information) to explore the local and global structure information of Chinese characters respectively, motivated by the intuition that strokes and characters directly embody certain local and global modes of Chinese characters. Based on these ideas, this paper proposes an effective model called \textit{StrokeGAN+}, which incorporates the stroke encoding and the few-shot semi-supervised scheme into the CycleGAN model. The effectiveness of the proposed model is demonstrated by amounts of experiments. Experimental results show that the mode collapse issue can be effectively alleviated by the introduced one-bit stroke encoding and few-shot semi-supervised training scheme, and that the proposed model outperforms the state-of-the-art models in fourteen font generation tasks in terms of four important evaluation metrics and the quality of generated characters. Besides CycleGAN, we also show that the proposed idea can be adapted to other existing models to improve their performance. The effectiveness of the proposed model for the zero-shot traditional Chinese font generation is also evaluated in this paper.

Automatic code generation is to generate the program code according to the given natural language description. The current mainstream approach uses neural networks to encode natural language descriptions, and output abstract syntax trees (AST) at the decoder, then convert the AST into program code. While the generated code largely conforms to specific syntax rules, two problems are still ignored. One is missing program testing, an essential step in the process of complete code implementation; the other is only focusing on the syntax compliance of the generated code, while ignoring the more important program functional requirements. The paper proposes a CodeGen-Test model, which adds program testing steps and incorporates program testing information to iteratively generate code that meets the functional requirements of the program, thereby improving the quality of code generation. At the same time, the paper proposes a new evaluation metric, test accuracy (Test-Acc), which represents the proportion of passing program test in generated code. Different from the previous evaluation metric, which only evaluates the quality of code generation from the perspective of character similarity, the Test-Acc can evaluate the quality of code generation from the Program functions. Moreover, the paper evaluates the CodeGen-test model on a python data set "hearthstone legend". The experimental results show the proposed method can effectively improve the quality of generated code. Compared with the existing optimal model, CodeGen-Test model improves the Bleu value by 0.2%, Rouge-L value by 0.3% and Test-Acc by 6%., Comment: 10 paper pages, 7 figures; 2 appendix pages, 5 appendix figures

The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but brings some new challenge to the analysis. The stochastic variance reduced gradient (SVRG) method has been regarded as one of the most effective methods. SVRG in general consists of two loops, where a reference full gradient is first evaluated in the outer loop and then used to yield a variance reduced estimate of the current gradient in the inner loop. Two options have been suggested to yield the output of the inner loop, where Option I sets the output as its last iterate, and Option II yields the output via random sampling from all the iterates in the inner loop. However, there is a significant gap between the theory and practice of SVRG when adapted to the stochastic semidefinite programming (SDP). SVRG practically works better with Option I, while most of existing theoretical results focus on Option II. In this paper, we fill this gap via exploiting a new semi-stochastic variant of the original SVRG with Option I adapted to the semidefinite optimization. Equipped with this, we establish the global linear submanifold convergence (i.e., converging exponentially fast to a submanifold of a global minimum under the orthogonal group action) of the proposed SVRG method, given a provable initialization scheme and under certain smoothness and restricted strongly convex assumptions. Our analysis includes the effects of the mini-batch size and update frequency in the inner loop as well as two practical step size strategies, the fixed and stabilized Barzilai-Borwein step sizes. Some numerical results in matrix sensing demonstrate the efficiency of proposed SVRG method outperforming Option II counterpart as well as others., Comment: 27 pages, 5 figures

Boosting is a well-known method for improving the accuracy of weak learners in machine learning. However, its theoretical generalization guarantee is missing in literature. In this paper, we propose an efficient boosting method with theoretical generalization guarantees for binary classification. Three key ingredients of the proposed boosting method are: a) the \textit{fully-corrective greedy} (FCG) update in the boosting procedure, b) a differentiable \textit{squared hinge} (also called \textit{truncated quadratic}) function as the loss function, and c) an efficient alternating direction method of multipliers (ADMM) algorithm for the associated FCG optimization. The used squared hinge loss not only inherits the robustness of the well-known hinge loss for classification with outliers, but also brings some benefits for computational implementation and theoretical justification. Under some sparseness assumption, we derive a fast learning rate of the order ${\cal O}((m/\log m)^{-1/4})$ for the proposed boosting method, which can be further improved to ${\cal O}((m/\log m)^{-1/2})$ if certain additional noise assumption is imposed, where $m$ is the size of sample set. Both derived learning rates are the best ones among the existing generalization results of boosting-type methods for classification. Moreover, an efficient early stopping scheme is provided for the proposed method. A series of toy simulations and real data experiments are conducted to verify the developed theories and demonstrate the effectiveness of the proposed method., Comment: 14 pages

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world applications and direct training of small networks may be trapped in local optima. In this paper, instead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on differential inclusions of inverse scale spaces. Specifically, it generates a family of models from simple to complex ones that couples a pair of parameters to simultaneously train over-parameterized deep models and structural sparsity on weights of fully connected and convolutional layers. Such a differential inclusion scheme has a simple discretization, proposed as Deep structurally splitting Linearized Bregman Iteration (DessiLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that DessiLBI achieve comparable and even better performance than the competitive optimizers in exploring the structural sparsity of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, DessiLBI unveils "winning tickets" in early epochs: the effective sparse structure with comparable test accuracy to fully trained over-parameterized models., Comment: conference , 23 pages https://github.com/corwinliu9669/dS2LBI. arXiv admin note: text overlap with arXiv:1905.09449

In the era of big data, it is desired to develop efficient machine learning algorithms to tackle massive data challenges such as storage bottleneck, algorithmic scalability, and interpretability. In this paper, we develop a novel efficient classification algorithm, called fast polynomial kernel classification (FPC), to conquer the scalability and storage challenges. Our main tools are a suitable selected feature mapping based on polynomial kernels and an alternating direction method of multipliers (ADMM) algorithm for a related non-smooth convex optimization problem. Fast learning rates as well as feasibility verifications including the efficiency of an ADMM solver with convergence guarantees and the selection of center points are established to justify theoretical behaviors of FPC. Our theoretical assertions are verified by a series of simulations and real data applications. Numerical results demonstrate that FPC significantly reduces the computational burden and storage memory of existing learning schemes such as support vector machines, Nystr\"{o}m and random feature methods, without sacrificing their generalization abilities much., Comment: arXiv admin note: text overlap with arXiv:1402.4735 by other authors

In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called \textit{sigmoid-ADMM pair}), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of deep neural networks with sigmoid-type activations (called deep sigmoid nets) over their rectified linear unit (ReLU) counterparts (called deep ReLU nets) in terms of approximation. In particular, we prove that the approximation capability of deep sigmoid nets is not worse than that of deep ReLU nets by showing that ReLU activation function can be well approximated by deep sigmoid nets with two hidden layers and finitely many free parameters but not vice-verse. We also establish the global convergence of the proposed ADMM for the nonlinearly constrained formulation of the deep sigmoid nets training from arbitrary initial points to a Karush-Kuhn-Tucker (KKT) point at a rate of order ${\cal O}(1/k)$. Besides sigmoid activation, such a convergence theorem holds for a general class of smooth activations. Compared with the widely used stochastic gradient descent (SGD) algorithm for the deep ReLU nets training (called ReLU-SGD pair), the proposed sigmoid-ADMM pair is practically stable with respect to the algorithmic hyperparameters including the learning rate, initial schemes and the pro-processing of the input data. Moreover, we find that to approximate and learn simple but important functions the proposed sigmoid-ADMM pair numerically outperforms the ReLU-SGD pair., Comment: This is a revised version of our previous one entitled "A Convergence Analysis of Nonlinearly Constrained ADMM in Deep Learning, arXiv:1902.02060" with some significantly changes

Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training. However, theoretical studies on their convergence properties are limited due to the highly nonconvex nature of DNN training. In this paper, we aim at providing a general methodology for provable convergence guarantees for this type of methods. In particular, for most of the commonly used DNN training models involving both two- and three-splitting schemes, we establish the global convergence to a critical point at a rate of ${\cal O}(1/k)$, where $k$ is the number of iterations. The results extend to general loss functions which have Lipschitz continuous gradients and deep residual networks (ResNets). Our key development adds several new elements to the Kurdyka-{\L}ojasiewicz inequality framework that enables us to carry out the global convergence analysis of BCD in the general scenario of deep learning., Comment: 27 pages, 2 figures

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of parameters of DNNs and is used along with gradient descent-type algorithms for this optimization task. Recent work have shown the efficiency of block coordinate descent (BCD) type methods empirically for training DNNs. In view of this, we propose a novel algorithm based on the BCD method for training DNNs and provide its global convergence results built upon the powerful framework of the Kurdyka-Lojasiewicz (KL) property. Numerical experiments on standard datasets demonstrate its competitive efficiency against standard optimizers with backprop., Comment: The 6th International Conference on Learning Representations (ICLR 2018), Workshop Track

Orthogonal greedy learning (OGL) is a stepwise learning scheme that starts with selecting a new atom from a specified dictionary via the steepest gradient descent (SGD) and then builds the estimator through orthogonal projection. In this paper, we find that SGD is not the unique greedy criterion and introduce a new greedy criterion, called "$\delta$-greedy threshold" for learning. Based on the new greedy criterion, we derive an adaptive termination rule for OGL. Our theoretical study shows that the new learning scheme can achieve the existing (almost) optimal learning rate of OGL. Plenty of numerical experiments are provided to support that the new scheme can achieve almost optimal generalization performance, while requiring less computation than OGL., Comment: 12 pages, 6 figures. arXiv admin note: text overlap with arXiv:1411.3553

Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model selection. The first aim of this paper is to develop a strategy to select these parameters. On one hand, based on the worst-case learning rate analysis, we show that the regularization term in polynomial kernel regression is not necessary. In other words, the regularization parameter can decrease arbitrarily fast when the degree of the polynomial kernel is suitable tuned. On the other hand,taking account of the implementation of the algorithm, the regularization term is required. Summarily, the effect of the regularization term in polynomial kernel regression is only to circumvent the " ill-condition" of the kernel matrix. Based on this, the second purpose of this paper is to propose a new model selection strategy, and then design an efficient learning algorithm. Both theoretical and experimental analysis show that the new strategy outperforms the previous one. Theoretically, we prove that the new learning strategy is almost optimal if the regression function is smooth. Experimentally, it is shown that the new strategy can significantly reduce the computational burden without loss of generalization capability., There is critical wrong in the proof

Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a new atom from a dictionary via the steepest gradient descent and build the estimator via orthogonal projecting the target function to the space spanned by the selected atoms in each greedy step. Here, "greed" means choosing a new atom according to the steepest gradient descent principle. OGL then avoids the overfitting/underfitting by selecting an appropriate iteration number. In this paper, we point out that the overfitting/underfitting can also be avoided via redefining "greed" in OGL. To this end, we introduce a new greedy metric, called $\delta$-greedy thresholds, to refine "greed" and theoretically verifies its feasibility. Furthermore, we reveals that such a greedy metric can bring an adaptive termination rule on the premise of maintaining the prominent learning performance of OGL. Our results show that the steepest gradient descent is not the unique greedy metric of OGL and some other more suitable metric may lessen the hassle of model-selection of OGL., Comment: 33 pages, 8 figures

Regularization is a well recognized powerful strategy to improve the performance of a learning machine and $l^q$ regularization schemes with $0, Comment: 26 pages, 3 figures