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Identifying gene splicing is a core and significant task confronted in modern collaboration between artificial intelligence and bioinformatics. Past decades have witnessed great efforts on this concern, such as the bio-plausible splicing pattern AT-CG and the famous SpliceAI. In this paper, we propose a novel framework for the task of gene splicing identification, named Horizon-wise Gene Splicing Identification (H-GSI). The proposed H-GSI follows the horizon-wise identification paradigm and comprises four components: the pre-processing procedure transforming string data into tensors, the sliding window technique handling long sequences, the SeqLab model, and the predictor. In contrast to existing studies that process gene information with a truncated fixed-length sequence, H-GSI employs a horizon-wise identification paradigm in which all positions in a sequence are predicted with only one forward computation, improving accuracy and efficiency. The experiments conducted on the real-world Human dataset show that our proposed H-GSI outperforms SpliceAI and achieves the best accuracy of 97.20\%. The source code is available from this link.

Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian processes. Two predominant approaches have emerged: the Neural Network Gaussian Process (NNGP) and the Neural Tangent Kernel (NTK). The former, rooted in Bayesian inference, represents a zero-order kernel, while the latter, grounded in the tangent space of gradient descents, is a first-order kernel. In this paper, we present the Unified Neural Kernel (UNK), which characterizes the learning dynamics of neural networks with gradient descents and parameter initialization. The proposed UNK kernel maintains the limiting properties of both NNGP and NTK, exhibiting behaviors akin to NTK with a finite learning step and converging to NNGP as the learning step approaches infinity. Besides, we also theoretically characterize the uniform tightness and learning convergence of the UNK kernel, providing comprehensive insights into this unified kernel. Experimental results underscore the effectiveness of our proposed method.

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and complexity, i.e., showing which architecture and size are sufficient to handle the concerned tasks. This work takes one step on this direction by theoretically studying the approximation and complexity of deep neural networks to invariant functions. We first prove that the invariant functions can be universally approximated by deep neural networks. Then we show that a broad range of invariant functions can be asymptotically approximated by various types of neural network models that includes the complex-valued neural networks, convolutional neural networks, and Bayesian neural networks using a polynomial number of parameters or optimization iterations. We also provide a feasible application that connects the parameter estimation and forecasting of high-resolution signals with our theoretical conclusions. The empirical results obtained on simulation experiments demonstrate the effectiveness of our method.

Recent years have emerged a surge of interest in SNNs owing to their remarkable potential to handle time-dependent and event-driven data. The performance of SNNs hinges not only on selecting an apposite architecture and fine-tuning connection weights, similar to conventional ANNs, but also on the meticulous configuration of intrinsic structures within spiking computations. However, there has been a dearth of comprehensive studies examining the impact of intrinsic structures. Consequently, developers often find it challenging to apply a standardized configuration of SNNs across diverse datasets or tasks. This work delves deep into the intrinsic structures of SNNs. Initially, we unveil two pivotal components of intrinsic structures: the integration operation and firing-reset mechanism, by elucidating their influence on the expressivity of SNNs. Furthermore, we draw two key conclusions: the membrane time hyper-parameter is intimately linked to the eigenvalues of the integration operation, dictating the functional topology of spiking dynamics, and various hyper-parameters of the firing-reset mechanism govern the overall firing capacity of an SNN, mitigating the injection ratio or sampling density of input data. These findings elucidate why the efficacy of SNNs hinges heavily on the configuration of intrinsic structures and lead to a recommendation that enhancing the adaptability of these structures contributes to improving the overall performance and applicability of SNNs. Inspired by this recognition, we propose two feasible approaches to enhance SNN learning. These involve leveraging self-connection architectures and employing stochastic spiking neurons to augment the adaptability of the integration operation and firing-reset mechanism, respectively. We verify the effectiveness of the proposed methods from perspectives of theory and practice.

This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN) combining with the residual-based adaptive refinement (RAR-PINN) algorithm. Different from the traditional PINN algorithm which takes points randomly, the RAR-PINN algorithm uses an adaptive point-fetching approach to improve the training efficiency for the solutions with steep gradients. A series of experiment comparisons between the RAR-PINN and traditional PINN algorithms are implemented to a coupled generalized nonlinear Schr\"{o}dinger (CGNLS) equation as an example. The results indicate that the RAR-PINN algorithm has faster convergence rate and better approximation ability, especially in modeling the shape-changing vector-soliton interactions in the coupled systems. Finally, the RAR-PINN method is applied to perform the data-driven discovery of the CGNLS equation, which shows the dispersion and nonlinear coefficients can be well approximated.

Neural network models generally involve two important components, i.e., network architecture and neuron model. Although there are abundant studies about network architectures, only a few neuron models have been developed, such as the MP neuron model developed in 1943 and the spiking neuron model developed in the 1950s. Recently, a new bio-plausible neuron model, Flexible Transmitter (FT) model, has been proposed. It exhibits promising behaviors, particularly on temporal-spatial signals, even when simply embedded into the common feedforward network architecture. This paper attempts to understand the properties of the FT network (FTNet) theoretically. Under mild assumptions, we show that: i) FTNet is a universal approximator; ii) the approximation complexity of FTNet can be exponentially smaller than those of commonly-used real-valued neural networks with feedforward/recurrent architectures and is of the same order in the worst case; iii) any local minimum of FTNet is the global minimum, implying that it is possible to identify global minima by local search algorithms., Comment: 45 pages, to be published in IEEE Transactions on Neural Networks and Learning Systems (TNNLS)

Mimicking and learning the long-term memory of efficient markets is a fundamental problem in the interaction between machine learning and financial economics to sequential data. Despite the prominence of this issue, current treatments either remain largely limited to heuristic techniques or rely significantly on periodogram or Gaussianty assumptions. In this paper, we present the ApeRIodic SEmi-parametric (ARISE) process for investigating efficient markets. The ARISE process is formulated as an infinite-sum function of some known processes and employs the aperiodic spectrum estimation to determine the key hyper-parameters, thus possessing the power and potential of modeling the price data with long-term memory, non-stationarity, and aperiodic spectrum. We further theoretically show that the ARISE process has the mean-square convergence, consistency, and asymptotic normality without periodogram and Gaussianity assumptions. In practice, we apply the ARISE process to identify the efficiency of real-world markets. Besides, we also provide two alternative ARISE applications: studying the long-term memorability of various machine-learning models and developing a latent state-space model for inference and forecasting of time series. The numerical experiments confirm the superiority of our proposed approaches.

Multivariate time series (MTS) prediction is ubiquitous in real-world fields, but MTS data often contains missing values. In recent years, there has been an increasing interest in using end-to-end models to handle MTS with missing values. To generate features for prediction, existing methods either merge all input dimensions of MTS or tackle each input dimension independently. However, both approaches are hard to perform well because the former usually produce many unreliable features and the latter lacks correlated information. In this paper, we propose a Learning Individual Features (LIFE) framework, which provides a new paradigm for MTS prediction with missing values. LIFE generates reliable features for prediction by using the correlated dimensions as auxiliary information and suppressing the interference from uncorrelated dimensions with missing values. Experiments on three real-world data sets verify the superiority of LIFE to existing state-of-the-art models.

Recent years have witnessed an increasing interest in the correspondence between infinitely wide networks and Gaussian processes. Despite the effectiveness and elegance of the current neural network Gaussian process theory, to the best of our knowledge, all the neural network Gaussian processes are essentially induced by increasing width. However, in the era of deep learning, what concerns us more regarding a neural network is its depth as well as how depth impacts the behaviors of a network. Inspired by a width-depth symmetry consideration, we use a shortcut network to show that increasing the depth of a neural network can also give rise to a Gaussian process, which is a valuable addition to the existing theory and contributes to revealing the true picture of deep learning. Beyond the proposed Gaussian process by depth, we theoretically characterize its uniform tightness property and the smallest eigenvalue of the Gaussian process kernel. These characterizations can not only enhance our understanding of the proposed depth-induced Gaussian process but also pave the way for future applications. Lastly, we examine the performance of the proposed Gaussian process by regression experiments on two benchmark data sets.

Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this direction by introducing the \emph{complex-reaction network} with fully-connected feed-forward architecture. We prove the universal approximation property for complex-reaction networks, and show that a class of radial functions can be approximated by a complex-reaction network using the polynomial number of parameters, whereas real-valued networks need at least exponential parameters to reach the same approximation level. For empirical risk minimization, our theoretical result shows that the critical point set of complex-reaction networks is a proper subset of that of real-valued networks, which may show some insights on finding the optimal solutions more easily for complex-reaction networks.