We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.
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.
Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons in the number of input photons. We numerically verify this result using a tensor network algorithm with $U(1)$ symmetry, and overcome previous challenges due to the large local Hilbert space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.
The quality of generalized linear models (GLMs), frequently used by insurance companies, depends on the choice of interacting variables. The search for interactions is time-consuming, especially for data sets with a large number of variables, depends much on expert judgement of actuaries, and often relies on visual performance indicators. Therefore, we present an approach to automating the process of finding interactions that should be added to GLMs to improve their predictive power. Our approach relies on neural networks and a model-specific interaction detection method, which is computationally faster than the traditionally used methods like Friedman H-Statistic or SHAP values. In numerical studies, we provide the results of our approach on artificially generated data as well as open-source data.
Evidence Networks can enable Bayesian model comparison when state-of-the-art methods (e.g. nested sampling) fail and even when likelihoods or priors are intractable or unknown. Bayesian model comparison, i.e. the computation of Bayes factors or evidence ratios, can be cast as an optimization problem. Though the Bayesian interpretation of optimal classification is well-known, here we change perspective and present classes of loss functions that result in fast, amortized neural estimators that directly estimate convenient functions of the Bayes factor. This mitigates numerical inaccuracies associated with estimating individual model probabilities. We introduce the leaky parity-odd power (l-POP) transform, leading to the novel ``l-POP-Exponential'' loss function. We explore neural density estimation for data probability in different models, showing it to be less accurate and scalable than Evidence Networks. Multiple real-world and synthetic examples illustrate that Evidence Networks are explicitly independent of dimensionality of the parameter space and scale mildly with the complexity of the posterior probability density function. This simple yet powerful approach has broad implications for model inference tasks. As an application of Evidence Networks to real-world data we compute the Bayes factor for two models with gravitational lensing data of the Dark Energy Survey. We briefly discuss applications of our methods to other, related problems of model comparison and evaluation in implicit inference settings.
Transformer, first applied to the field of natural language processing, is a type of deep neural network mainly based on the self-attention mechanism. Thanks to its strong representation capabilities, researchers are looking at ways to apply transformer to computer vision tasks. In a variety of visual benchmarks, transformer-based models perform similar to or better than other types of networks such as convolutional and recurrent neural networks. Given its high performance and less need for vision-specific inductive bias, transformer is receiving more and more attention from the computer vision community. In this paper, we review these vision transformer models by categorizing them in different tasks and analyzing their advantages and disadvantages. The main categories we explore include the backbone network, high/mid-level vision, low-level vision, and video processing. We also include efficient transformer methods for pushing transformer into real device-based applications. Furthermore, we also take a brief look at the self-attention mechanism in computer vision, as it is the base component in transformer. Toward the end of this paper, we discuss the challenges and provide several further research directions for vision transformers.
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.
Current deep learning research is dominated by benchmark evaluation. A method is regarded as favorable if it empirically performs well on the dedicated test set. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving sets of benchmark data are investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten due to the iterative parameter updates. However, comparison of individual methods is nevertheless treated in isolation from real world application and typically judged by monitoring accumulated test set performance. The closed world assumption remains predominant. It is assumed that during deployment a model is guaranteed to encounter data that stems from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown instances and break down in the face of corrupted data. In this work we argue that notable lessons from open set recognition, the identification of statistically deviating data outside of the observed dataset, and the adjacent field of active learning, where data is incrementally queried such that the expected performance gain is maximized, are frequently overlooked in the deep learning era. Based on these forgotten lessons, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Our results show that this not only benefits each individual paradigm, but highlights the natural synergies in a common framework. We empirically demonstrate improvements when alleviating catastrophic forgetting, querying data in active learning, selecting task orders, while exhibiting robust open world application where previously proposed methods fail.
Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn node representations on the fixed and homogeneous graphs. The limitations especially become problematic when learning representations on a misspecified graph or a heterogeneous graph that consists of various types of nodes and edges. In this paper, we propose Graph Transformer Networks (GTNs) that are capable of generating new graph structures, which involve identifying useful connections between unconnected nodes on the original graph, while learning effective node representation on the new graphs in an end-to-end fashion. Graph Transformer layer, a core layer of GTNs, learns a soft selection of edge types and composite relations for generating useful multi-hop connections so-called meta-paths. Our experiments show that GTNs learn new graph structures, based on data and tasks without domain knowledge, and yield powerful node representation via convolution on the new graphs. Without domain-specific graph preprocessing, GTNs achieved the best performance in all three benchmark node classification tasks against the state-of-the-art methods that require pre-defined meta-paths from domain knowledge.
Graphs, which describe pairwise relations between objects, are essential representations of many real-world data such as social networks. In recent years, graph neural networks, which extend the neural network models to graph data, have attracted increasing attention. Graph neural networks have been applied to advance many different graph related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytical tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges, the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.
Salient object detection is a fundamental problem and has been received a great deal of attentions in computer vision. Recently deep learning model became a powerful tool for image feature extraction. In this paper, we propose a multi-scale deep neural network (MSDNN) for salient object detection. The proposed model first extracts global high-level features and context information over the whole source image with recurrent convolutional neural network (RCNN). Then several stacked deconvolutional layers are adopted to get the multi-scale feature representation and obtain a series of saliency maps. Finally, we investigate a fusion convolution module (FCM) to build a final pixel level saliency map. The proposed model is extensively evaluated on four salient object detection benchmark datasets. Results show that our deep model significantly outperforms other 12 state-of-the-art approaches.