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Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t) given by a number of function values. The approximation can effectively be learned by simply solving a linear equation system; no backpropagation or similar methods are needed. Furthermore, and this is probably the main contribution of this article, the size of an LRNN can be reduced significantly in one step after inspecting the spectrum of the network transition matrix, i.e., its eigenvalues, by taking only the most relevant components. Therefore, in contrast to other approaches, we do not only learn network weights but also the network architecture. LRNNs have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions. We demonstrate this by several experiments, among them multiple superimposed oscillators (MSO), robotic soccer, and predicting stock prices. LRNNs outperform the previous state-of-the-art for the MSO task with a minimal number of units.

Networks of spiking neurons underpin the extraordinary information-processing capabilities of the brain and have emerged as pillar models in neuromorphic intelligence. Despite extensive research on spiking neural networks (SNNs), most are established on deterministic models. Integrating noise into SNNs leads to biophysically more realistic neural dynamics and may benefit model performance. This work presents the noisy spiking neural network (NSNN) and the noise-driven learning rule (NDL) by introducing a spiking neuron model incorporating noisy neuronal dynamics. Our approach shows how noise may act as a resource for computation and learning and theoretically provides a framework for general SNNs. Moreover, NDL provides an insightful rationale for surrogate gradients. By incorporating various SNN architectures and algorithms, we show that our approach exhibits competitive performance and improved robustness against challenging perturbations than deterministic SNNs. Additionally, we demonstrate the utility of the NSNN model for neural coding studies. Overall, NSNN offers a powerful, flexible, and easy-to-use tool for machine learning practitioners and computational neuroscience researchers.

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

To alleviate the practical constraints for deploying deep neural networks (DNNs) on edge devices, quantization is widely regarded as one promising technique. It reduces the resource requirements for computational power and storage space by quantizing the weights and/or activation tensors of a DNN into lower bit-width fixed-point numbers, resulting in quantized neural networks (QNNs). While it has been empirically shown to introduce minor accuracy loss, critical verified properties of a DNN might become invalid once quantized. Existing verification methods focus on either individual neural networks (DNNs or QNNs) or quantization error bound for partial quantization. In this work, we propose a quantization error bound verification method, named QEBVerif, where both weights and activation tensors are quantized. QEBVerif consists of two parts, i.e., a differential reachability analysis (DRA) and a mixed-integer linear programming (MILP) based verification method. DRA performs difference analysis between the DNN and its quantized counterpart layer-by-layer to compute a tight quantization error interval efficiently. If DRA fails to prove the error bound, then we encode the verification problem into an equivalent MILP problem which can be solved by off-the-shelf solvers. Thus, QEBVerif is sound, complete, and reasonably efficient. We implement QEBVerif and conduct extensive experiments, showing its effectiveness and efficiency.

Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-Chervonenkis theory. Yet those guarantees are based on intractable algorithms, which has led to the theory of surrogate methods in classification. Guarantees offered by surrogate methods are based on calibration inequalities, which have been shown to be highly sub-optimal under some margin conditions, failing short to capture exponential convergence phenomena. Those "super" fast rates are becoming to be well understood for smooth surrogates, but the picture remains blurry for non-smooth losses such as the hinge loss, associated with the renowned support vector machines. In this paper, we present a simple mechanism to obtain fast convergence rates and we investigate its usage for SVM. In particular, we show that SVM can exhibit exponential convergence rates even without assuming the hard Tsybakov margin condition.

Object detection is a fundamental task in computer vision and image processing. Current deep learning based object detectors have been highly successful with abundant labeled data. But in real life, it is not guaranteed that each object category has enough labeled samples for training. These large object detectors are easy to overfit when the training data is limited. Therefore, it is necessary to introduce few-shot learning and zero-shot learning into object detection, which can be named low-shot object detection together. Low-Shot Object Detection (LSOD) aims to detect objects from a few or even zero labeled data, which can be categorized into few-shot object detection (FSOD) and zero-shot object detection (ZSD), respectively. This paper conducts a comprehensive survey for deep learning based FSOD and ZSD. First, this survey classifies methods for FSOD and ZSD into different categories and discusses the pros and cons of them. Second, this survey reviews dataset settings and evaluation metrics for FSOD and ZSD, then analyzes the performance of different methods on these benchmarks. Finally, this survey discusses future challenges and promising directions for FSOD and ZSD.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to different inputs, leading to notable advantages in terms of accuracy, computational efficiency, adaptiveness, etc. In this survey, we comprehensively review this rapidly developing area by dividing dynamic networks into three main categories: 1) instance-wise dynamic models that process each instance with data-dependent architectures or parameters; 2) spatial-wise dynamic networks that conduct adaptive computation with respect to different spatial locations of image data and 3) temporal-wise dynamic models that perform adaptive inference along the temporal dimension for sequential data such as videos and texts. The important research problems of dynamic networks, e.g., architecture design, decision making scheme, optimization technique and applications, are reviewed systematically. Finally, we discuss the open problems in this field together with interesting future research directions.

Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.

Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.