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Deep neural networks excel in supervised learning tasks but are constrained by the need for extensive labeled data. Self-supervised learning emerges as a promising alternative, allowing models to learn without explicit labels. Information theory has shaped deep neural networks, particularly the information bottleneck principle. This principle optimizes the trade-off between compression and preserving relevant information, providing a foundation for efficient network design in supervised contexts. However, its precise role and adaptation in self-supervised learning remain unclear. In this work, we scrutinize various self-supervised learning approaches from an information-theoretic perspective, introducing a unified framework that encapsulates the self-supervised information-theoretic learning problem. This framework includes multiple encoders and decoders, suggesting that all existing work on self-supervised learning can be seen as specific instances. We aim to unify these approaches to understand their underlying principles better and address the main challenge: many works present different frameworks with differing theories that may seem contradictory. By weaving existing research into a cohesive narrative, we delve into contemporary self-supervised methodologies, spotlight potential research areas, and highlight inherent challenges. Moreover, we discuss how to estimate information-theoretic quantities and their associated empirical problems. Overall, this paper provides a comprehensive review of the intersection of information theory, self-supervised learning, and deep neural networks, aiming for a better understanding through our proposed unified approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose to quantitatively compare loss functions based on parameterized Tsallis–Havrda–Charvat entropy and classical Shannon entropy for the training of a deep network in the case of small datasets which are usually encountered in medical applications. Shannon cross-entropy is widely used as a loss function for most neural networks applied to the segmentation, classification and detection of images. Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy. In this work, we compare these two entropies through a medical application for predicting recurrence in patients with head–neck and lung cancers after treatment. Based on both CT images and patient information, a multitask deep neural network is proposed to perform a recurrence prediction task using cross-entropy as a loss function and an image reconstruction task. Tsallis–Havrda–Charvat cross-entropy is a parameterized cross-entropy with the parameter α. Shannon entropy is a particular case of Tsallis–Havrda–Charvat entropy for α = 1 . The influence of this parameter on the final prediction results is studied. In this paper, the experiments are conducted on two datasets including in total 580 patients, of whom 434 suffered from head–neck cancers and 146 from lung cancers. The results show that Tsallis–Havrda–Charvat entropy can achieve better performance in terms of prediction accuracy with some values of α. [ABSTRACT FROM AUTHOR]

With the remarkable development of deep learning in the field of science, deep neural networks provide a new way to solve the Stefan problem. In this paper, deep neural networks combined with small sample learning and a general deep learning framework are proposed to solve the two-dimensional Stefan problem. In the case of adding less sample data, the model can be modified and the prediction accuracy can be improved. In addition, by solving the forward and inverse problems of the two-dimensional single-phase Stefan problem, it is verified that the improved method can accurately predict the solutions of the partial differential equations of the moving boundary and the dynamic interface. [ABSTRACT FROM AUTHOR]

As a promising information theory, reinforcement learning has gained much attention. This paper researches a wind-storage cooperative decision-making strategy based on dueling double deep Q-network (D3QN). Firstly, a new wind-storage cooperative model is proposed. Besides wind farms, energy storage systems, and external power grids, demand response loads are also considered, including residential price response loads and thermostatically controlled loads (TCLs). Then, a novel wind-storage cooperative decision-making mechanism is proposed, which combines the direct control of TCLs with the indirect control of residential price response loads. In addition, a kind of deep reinforcement learning algorithm called D3QN is utilized to solve the wind-storage cooperative decision-making problem. Finally, the numerical results verify the effectiveness of D3QN for optimizing the decision-making strategy of a wind-storage cooperation system. [ABSTRACT FROM AUTHOR]

This paper demonstrates a novel approach to training deep neural networks using a Mutual Information (MI)-driven, decaying Learning Rate (LR), Stochastic Gradient Descent (SGD) algorithm. MI between the output of the neural network and true outcomes is used to adaptively set the LR for the network, in every epoch of the training cycle. This idea is extended to layer-wise setting of LR, as MI naturally provides a layer-wise performance metric. A LR range test determining the operating LR range is also proposed. Experiments compared this approach with popular alternatives such as gradient-based adaptive LR algorithms like Adam, RMSprop, and LARS. Competitive to better accuracy outcomes obtained in competitive to better time, demonstrate the feasibility of the metric and approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach to train a deep neural network with multiple intermediate auxiliary classifiers, branching from it. These 'multi-exits' models can be used to reduce the inference time by performing early exit on the intermediate branches, if the confidence of the prediction is higher than a threshold. They rely on the assumption that not all the samples require the same amount of processing to yield a good prediction. In this paper, we propose a way to train jointly all the branches of a multi-exit model without hyper-parameters, by weighting the predictions from each branch with a trained confidence score. Each confidence score is an approximation of the real one produced by the branch, and it is calculated and regularized while training the rest of the model. We evaluate our proposal on a set of image classification benchmarks, using different neural models and early-exit stopping criteria. [ABSTRACT FROM AUTHOR]

Determining the cyclic-alternating-pattern (CAP) phases in sleep using electroencephalography (EEG) signals is crucial for assessing sleep quality. However, most current methods for CAP classification primarily rely on classical machine learning techniques, with limited implementation of deep-learning-based tools. Furthermore, these methods often require manual feature extraction. Herein, we propose a fully automatic deep-learning-based algorithm that leverages convolutional neural network architectures to classify the EEG signals via their time-frequency representations. Through our investigation, we explored using time-frequency analysis techniques and found that Wigner-based representations outperform the commonly used short-time Fourier transform for CAP classification. Additionally, our algorithm incorporates contextual information of the EEG signals and employs data augmentation techniques specifically designed to preserve the time-frequency structure. The model is developed using EEG signals of healthy subjects from the publicly available CAP sleep database (CAPSLPDB) on Physionet. An experimental study demonstrates that our algorithm surpasses existing machine-learning-based methods, achieving an accuracy of 77.5% on a balanced test set and 81.8% when evaluated on an unbalanced test set. Notably, the proposed algorithm exhibits efficiency and scalability, making it suitable for on-device implementation to enhance CAP identification procedures. [ABSTRACT FROM AUTHOR]

Sentiment analysis (SA) is an important task in natural language processing in which convolutional neural networks (CNNs) have been successfully applied. However, most existing CNNs can only extract predefined, fixed-scale sentiment features and cannot synthesize flexible, multi-scale sentiment features. Moreover, these models' convolutional and pooling layers gradually lose local detailed information. In this study, a new CNN model based on residual network technology and attention mechanisms is proposed. This model exploits more abundant multi-scale sentiment features and addresses the loss of locally detailed information to enhance the accuracy of sentiment classification. It is primarily composed of a position-wise gated Res2Net (PG-Res2Net) module and a selective fusing module. The PG-Res2Net module can adaptively learn multi-scale sentiment features over a large range using multi-way convolution, residual-like connections, and position-wise gates. The selective fusing module is developed to fully reuse and selectively fuse these features for prediction. The proposed model was evaluated using five baseline datasets. The experimental results demonstrate that the proposed model surpassed the other models in performance. In the best case, the model outperforms the other models by up to 1.2%. Ablation studies and visualizations further revealed the model's ability to extract and fuse multi-scale sentiment features. [ABSTRACT FROM AUTHOR]

Natural language processing (NLP) models based on deep neural networks (DNNs) are vulnerable to backdoor attacks. Existing backdoor defense methods have limited effectiveness and coverage scenarios. We propose a textual backdoor defense method based on deep feature classification. The method includes deep feature extraction and classifier construction. The method exploits the distinguishability of deep features of poisoned data and benign data. Backdoor defense is implemented in both offline and online scenarios. We conducted defense experiments on two datasets and two models for a variety of backdoor attacks. The experimental results demonstrate the effectiveness of this defense approach and outperform the baseline defense method. [ABSTRACT FROM AUTHOR]

As training Deep Neural Networks (DNNs) becomes more expensive, the interest in protecting the ownership of the models with watermarking techniques increases. Uchida et al. proposed a digital watermarking algorithm that embeds the secret message into the model coefficients. However, despite its appeal, in this paper, we show that its efficacy can be compromised by the optimization algorithm being used. In particular, we found through a theoretical analysis that, as opposed to Stochastic Gradient Descent (SGD), the update direction given by Adam optimization strongly depends on the sign of a combination of columns of the projection matrix used for watermarking. Consequently, as observed in the empirical results, this makes the coefficients move in unison giving rise to heavily spiked weight distributions that can be easily detected by adversaries. As a way to solve this problem, we propose a new method called Block-Orthonormal Projections (BOP) that allows one to combine watermarking with Adam optimization with a minor impact on the detectability of the watermark and an increased robustness. [ABSTRACT FROM AUTHOR]

Deep Neural Networks (DNNs) usually work in an end-to-end manner. This makes the trained DNNs easy to use, but they remain an ambiguous decision process for every test case. Unfortunately, the interpretability of decisions is crucial in some scenarios, such as medical or financial data mining and decision-making. In this paper, we propose a Tree-Network-Tree (TNT) learning framework for explainable decision-making, where the knowledge is alternately transferred between the tree model and DNNs. Specifically, the proposed TNT learning framework exerts the advantages of different models at different stages: (1) a novel James–Stein Decision Tree (JSDT) is proposed to generate better knowledge representations for DNNs, especially when the input data are in low-frequency or low-quality; (2) the DNNs output high-performing prediction result from the knowledge embedding inputs and behave as a teacher model for the following tree model; and (3) a novel distillable Gradient Boosted Decision Tree (dGBDT) is proposed to learn interpretable trees from the soft labels and make a comparable prediction as DNNs do. Extensive experiments on various machine learning tasks demonstrated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

To generate more high-quality aerodynamic data using the information provided by different fidelity data, where low-fidelity aerodynamic data provides the trend information and high-fidelity aerodynamic data provides value information, we applied a deep neural network (DNN) algorithm to fuse the information of multi-fidelity aerodynamic data. We discuss the relationships between the low-fidelity and high-fidelity data, and then we describe the proposed architecture for an aerodynamic data fusion model. The architecture consists of three fully-connected neural networks that are employed to approximate low-fidelity data, and the linear part and nonlinear part of correlation for the low- and high-fidelity data, respectively. To test the proposed multi-fidelity aerodynamic data fusion method, we calculated Euler and Navier–Stokes simulations for a typical airfoil at various Mach numbers and angles of attack to obtain the aerodynamic coefficients as low- and high-fidelity data. A fusion model of the longitudinal coefficients of lift C L and drag C D was constructed with the proposed method. For comparisons, variable complexity modeling and cokriging models were also built. The accuracy spread between the predicted value and true value was discussed for both the training and test data of the three different methods. We calculated the root mean square error and average relative deviation to demonstrate the performance of the three different methods. The fusion result of the proposed method was satisfactory on the test case, and showed a better performance compared with the other two traditional methods presented. The results provide evidence that the method proposed in this paper can be useful in dealing with the multi-fidelity aerodynamic data fusion problem. [ABSTRACT FROM AUTHOR]

Convolutional neural networks have powerful performances in many visual tasks because of their hierarchical structures and powerful feature extraction capabilities. SPD (symmetric positive definition) matrix is paid attention to in visual classification, because it has excellent ability to learn proper statistical representation and distinguish samples with different information. In this paper, a deep neural network signal detection method based on spectral convolution features is proposed. In this method, local features extracted from convolutional neural network are used to construct the SPD matrix, and a deep learning algorithm for the SPD matrix is used to detect target signals. Feature maps extracted by two kinds of convolutional neural network models are applied in this study. Based on this method, signal detection has become a binary classification problem of signals in samples. In order to prove the availability and superiority of this method, simulated and semi-physical simulated data sets are used. The results show that, under low SCR (signal-to-clutter ratio), compared with the spectral signal detection method based on the deep neural network, this method can obtain a gain of 0.5–2 dB on simulated data sets and semi-physical simulated data sets. [ABSTRACT FROM AUTHOR]

Information theory concepts are leveraged with the goal of better understanding and improving Deep Neural Networks (DNNs). The information plane of neural networks describes the behavior during training of the mutual information at various depths between input/output and hidden-layer variables. Previous analysis revealed that most of the training epochs are spent on compressing the input, in some networks where finiteness of the mutual information can be established. However, the estimation of mutual information is nontrivial for high-dimensional continuous random variables. Therefore, the computation of the mutual information for DNNs and its visualization on the information plane mostly focused on low-complexity fully connected networks. In fact, even the existence of the compression phase in complex DNNs has been questioned and viewed as an open problem. In this paper, we present the convergence of mutual information on the information plane for a high-dimensional VGG-16 Convolutional Neural Network (CNN) by resorting to Mutual Information Neural Estimation (MINE), thus confirming and extending the results obtained with low-dimensional fully connected networks. Furthermore, we demonstrate the benefits of regularizing a network, especially for a large number of training epochs, by adopting mutual information estimates as additional terms in the loss function characteristic of the network. Experimental results show that the regularization stabilizes the test accuracy and significantly reduces its variance. [ABSTRACT FROM AUTHOR]

Generative Adversarial Nets (GANs) are one of the most popular architectures for image generation, which has achieved significant progress in generating high-resolution, diverse image samples. The normal GANs are supposed to minimize the Kullback–Leibler divergence between distributions of natural and generated images. In this paper, we propose the Alpha-divergence Generative Adversarial Net (Alpha-GAN) which adopts the alpha divergence as the minimization objective function of generators. The alpha divergence can be regarded as a generalization of the Kullback–Leibler divergence, Pearson χ 2 divergence, Hellinger divergence, etc. Our Alpha-GAN employs the power function as the form of adversarial loss for the discriminator with two-order indexes. These hyper-parameters make our model more flexible to trade off between the generated and target distributions. We further give a theoretical analysis of how to select these hyper-parameters to balance the training stability and the quality of generated images. Extensive experiments of Alpha-GAN are performed on SVHN and CelebA datasets, and evaluation results show the stability of Alpha-GAN. The generated samples are also competitive compared with the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Previous works established that entropy is characterized uniquely as the first cohomology class in a topos and described some of its applications to the unsupervised classification of gene expression modules or cell types. These studies raised important questions regarding the statistical meaning of the resulting cohomology of information and its interpretation or consequences with respect to usual data analysis and statistical physics. This paper aims to present the computational methods of information cohomology and to propose its interpretations in terms of statistical physics and machine learning. In order to further underline the cohomological nature of information functions and chain rules, the computation of the cohomology in low degrees is detailed to show more directly that the k multivariate mutual information ( I k ) are (k − 1) -coboundaries. The (k − 1) -cocycles condition corresponds to I k = 0 , which generalizes statistical independence to arbitrary degree k. Hence, the cohomology can be interpreted as quantifying the statistical dependences and the obstruction to factorization. I develop the computationally tractable subcase of simplicial information cohomology represented by entropy H k and information I k landscapes and their respective paths, allowing investigation of Shannon's information in the multivariate case without the assumptions of independence or of identically distributed variables. I give an interpretation of this cohomology in terms of phase transitions in a model of k-body interactions, holding both for statistical physics without mean field approximations and for data points. The I 1 components define a self-internal energy functional U k and (− 1) k I k , k ≥ 2 components define the contribution to a free energy functional G k (the total correlation) of the k-body interactions. A basic mean field model is developed and computed on genetic data reproducing usual free energy landscapes with phase transition, sustaining the analogy of clustering with condensation. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, providing a trivial topological expression of the second law of thermodynamics. The local minima of free energy, related to conditional information negativity and conditional independence, characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. I give an interpretation of this complex in terms of unsupervised deep learning where the neural network architecture is given by the chain complex and conclude by discussing future supervised applications. [ABSTRACT FROM AUTHOR]

We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on 1 / ε can ε -approximate functions that are analytic on certain regions of C d . [ABSTRACT FROM AUTHOR]

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation ability of deep neural networks with a broad class of activation functions. This class of activation functions includes most of frequently used activation functions. We derive the required depth, width and sparsity of a deep neural network to approximate any Hölder smooth function upto a given approximation error for the large class of activation functions. Based on our approximation error analysis, we derive the minimax optimality of the deep neural network estimators with the general activation functions in both regression and classification problems. [ABSTRACT FROM AUTHOR]

The vulnerability of deep neural network (DNN)-based systems makes them susceptible to adversarial perturbation and may cause classification task failure. In this work, we propose an adversarial attack model using the Artificial Bee Colony (ABC) algorithm to generate adversarial samples without the need for a further gradient evaluation and training of the substitute model, which can further improve the chance of task failure caused by adversarial perturbation. In untargeted attacks, the proposed method obtained 100%, 98.6%, and 90.00% success rates on the MNIST, CIFAR-10 and ImageNet datasets, respectively. The experimental results show that the proposed ABCAttack can not only obtain a high attack success rate with fewer queries in the black-box setting, but also break some existing defenses to a large extent, and is not limited by model structure or size, which provides further research directions for deep learning evasion attacks and defenses. [ABSTRACT FROM AUTHOR]

Conventionally, the maximum likelihood (ML) criterion is applied to train a deep belief network (DBN). We present a maximum entropy (ME) learning algorithm for DBNs, designed specifically to handle limited training data. Maximizing only the entropy of parameters in the DBN allows more effective generalization capability, less bias towards data distributions, and robustness to over-fitting compared to ML learning. Results of text classification and object recognition tasks demonstrate ME-trained DBN outperforms ML-trained DBN when training data is limited. [ABSTRACT FROM AUTHOR]

Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the Minimum Description Length (MDL) principle. Treating the neural network optimization process as a partially observable model selection problem, the regularity normalization constrains the implicit space by a normalization factor, the universal code length. We compute this universal code incrementally across neural network layers and demonstrate the flexibility to include data priors such as top-down attention and other oracle information. Empirically, our approach outperforms existing normalization methods in tackling limited, imbalanced and non-stationary input distribution in image classification, classic control, procedurally-generated reinforcement learning, generative modeling, handwriting generation and question answering tasks with various neural network architectures. Lastly, the unsupervised attention mechanisms is a useful probing tool for neural networks by tracking the dependency and critical learning stages across layers and recurrent time steps of deep networks. [ABSTRACT FROM AUTHOR]

Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem). [ABSTRACT FROM AUTHOR]

In many decision-making scenarios, ranging from recreational activities to healthcare and policing, the use of artificial intelligence coupled with the ability to learn from historical data is becoming ubiquitous. This widespread adoption of automated systems is accompanied by the increasing concerns regarding their ethical implications. Fundamental rights, such as the ones that require the preservation of privacy, do not discriminate based on sensible attributes (e.g., gender, ethnicity, political/sexual orientation), or require one to provide an explanation for a decision, are daily undermined by the use of increasingly complex and less understandable yet more accurate learning algorithms. For this purpose, in this work, we work toward the development of systems able to ensure trustworthiness by delivering privacy, fairness, and explainability by design. In particular, we show that it is possible to simultaneously learn from data while preserving the privacy of the individuals thanks to the use of Homomorphic Encryption, ensuring fairness by learning a fair representation from the data, and ensuring explainable decisions with local and global explanations without compromising the accuracy of the final models. We test our approach on a widespread but still controversial application, namely face recognition, using the recent FairFace dataset to prove the validity of our approach. [ABSTRACT FROM AUTHOR]

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here, we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution. [ABSTRACT FROM AUTHOR]

In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region's activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research. [ABSTRACT FROM AUTHOR]

Keywords: artificial intelligence; deep neural networks; interpretability; explainability; fairness; accountability; transparency; human-centric AI; human-like learning; intelligence augmentation EN artificial intelligence deep neural networks interpretability explainability fairness accountability transparency human-centric AI human-like learning intelligence augmentation 332 1 03/30/21 20210301 NES 210301 1. Artificial intelligence, deep neural networks, interpretability, fairness, accountability, transparency, human-centric AI, human-like learning, intelligence augmentation, explainability The presented study gives an uplifting example of the need for a mutualistic symbiosis of human intelligence (HI) and artificial intelligence (AI). We can explore this human-centered partnership of people and AI from two perspectives: (1) intelligence augmentation and the (2) Human Intelligence (HI) for Artificial Intelligence (AI) perspective (HI4AI). [Extracted from the article]

We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The modeling and forecasting of BBS (Bulletin Board System) posts time series is crucial for government agencies, corporations and website operators to monitor public opinion. Accurate prediction of the number of BBS posts will assist government agencies or corporations in making timely decisions and estimating the future number of BBS posts will help website operators to allocate resources to deal with the possible hot events pressure. By combining sample entropy (SampEn) and deep neural networks (DNN), an approach (SampEn-DNN) is proposed for BBS posts time series modeling and forecasting. The main idea of SampEn-DNN is to utilize SampEn to decide the input vectors of DNN with smallest complexity, and DNN to enhance the prediction performance of time series. Selecting Tianya Zatan new posts as the data source, the performances of SampEn-DNN were compared with auto-regressive integrated moving average (ARIMA), seasonal ARIMA, polynomial regression, neural networks, etc. approaches for prediction of the daily number of new posts. From the experimental results, it can be found that the proposed approach SampEn-DNN outperforms the state-of-the-art approaches for BBS posts time series modeling and forecasting. [ABSTRACT FROM AUTHOR]