Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of the behavior of discrete trajectories of first-order methods within the geometrical landscape of these functions. This paper concerns convergence of first-order discrete methods to a local minimum of nonconvex optimization problems that comprise strict saddle points within the geometrical landscape. To this end, it focuses on analysis of discrete gradient trajectories around saddle neighborhoods, derives sufficient conditions under which these trajectories can escape strict-saddle neighborhoods in linear time, explores the contractive and expansive dynamics of these trajectories in neighborhoods of strict-saddle points that are characterized by gradients of moderate magnitude, characterizes the non-curving nature of these trajectories, and highlights the inability of these trajectories to re-enter the neighborhoods around strict-saddle points after exiting them. Based on these insights and analyses, the paper then proposes a simple variant of the vanilla gradient descent algorithm, termed Curvature Conditioned Regularized Gradient Descent (CCRGD) algorithm, which utilizes a check for an initial boundary condition to ensure its trajectories can escape strict-saddle neighborhoods in linear time. Convergence analysis of the CCRGD algorithm, which includes its rate of convergence to a local minimum within a geometrical landscape that has a maximum number of strict-saddle points, is also presented in the paper. Numerical experiments are then provided on a test function as well as a low-rank matrix factorization problem to evaluate the efficacy of the proposed algorithm.
Federated learning (FL) is a rapidly growing privacy-preserving collaborative machine learning paradigm. In practical FL applications, local data from each data silo reflect local usage patterns. Therefore, there exists heterogeneity of data distributions among data owners (a.k.a. FL clients). If not handled properly, this can lead to model performance degradation. This challenge has inspired the research field of heterogeneous federated learning, which currently remains open. In this paper, we propose a data heterogeneity-robust FL approach, FedGSP, to address this challenge by leveraging on a novel concept of dynamic Sequential-to-Parallel (STP) collaborative training. FedGSP assigns FL clients to homogeneous groups to minimize the overall distribution divergence among groups, and increases the degree of parallelism by reassigning more groups in each round. It is also incorporated with a novel Inter-Cluster Grouping (ICG) algorithm to assist in group assignment, which uses the centroid equivalence theorem to simplify the NP-hard grouping problem to make it solvable. Extensive experiments have been conducted on the non-i.i.d. FEMNIST dataset. The results show that FedGSP improves the accuracy by 3.7% on average compared with seven state-of-the-art approaches, and reduces the training time and communication overhead by more than 90%.
In this paper we present a foundational study on a constrained method that defines learning problems with Neural Networks in the context of the principle of least cognitive action, which very much resembles the principle of least action in mechanics. Starting from a general approach to enforce constraints into the dynamical laws of learning, this work focuses on an alternative way of defining Neural Networks, that is different from the majority of existing approaches. In particular, the structure of the neural architecture is defined by means of a special class of constraints that are extended also to the interaction with data, leading to "architectural" and "input-related" constraints, respectively. The proposed theory is cast into the time domain, in which data are presented to the network in an ordered manner, that makes this study an important step toward alternative ways of processing continuous streams of data with Neural Networks. The connection with the classic Backpropagation-based update rule of the weights of networks is discussed, showing that there are conditions under which our approach degenerates to Backpropagation. Moreover, the theory is experimentally evaluated on a simple problem that allows us to deeply study several aspects of the theory itself and to show the soundness of the model.
Multivariate dynamical processes can often be intuitively described by a weighted connectivity graph between components representing each individual time-series. Even a simple representation of this graph as a Pearson correlation matrix may be informative and predictive as demonstrated in the brain imaging literature. However, there is a consensus expectation that powerful graph neural networks (GNNs) should perform better in similar settings. In this work, we present a model that is considerably shallow than deep GNNs, yet outperforms them in predictive accuracy in a brain imaging application. Our model learns the autoregressive structure of individual time series and estimates directed connectivity graphs between the learned representations via a self-attention mechanism in an end-to-end fashion. The supervised training of the model as a classifier between patients and controls results in a model that generates directed connectivity graphs and highlights the components of the time-series that are predictive for each subject. We demonstrate our results on a functional neuroimaging dataset classifying schizophrenia patients and controls.
Deep Neural Networks are able to solve many complex tasks with less engineering effort and better performance. However, these networks often use data for training and evaluation without investigating its representation, i.e.~the form of the used data. In the present paper, we analyze the impact of data representations on the performance of Deep Neural Networks using energy time series forecasting. Based on an overview of exemplary data representations, we select four exemplary data representations and evaluate them using two different Deep Neural Network architectures and three forecasting horizons on real-world energy time series. The results show that, depending on the forecast horizon, the same data representations can have a positive or negative impact on the accuracy of Deep Neural Networks.
Recently, deep learning have achieved promising results in Estimated Time of Arrival (ETA), which is considered as predicting the travel time from the origin to the destination along a given path. One of the key techniques is to use embedding vectors to represent the elements of road network, such as the links (road segments). However, the embedding suffers from the data sparsity problem that many links in the road network are traversed by too few floating cars even in large ride-hailing platforms like Uber and DiDi. Insufficient data makes the embedding vectors in an under-fitting status, which undermines the accuracy of ETA prediction. To address the data sparsity problem, we propose the Road Network Metric Learning framework for ETA (RNML-ETA). It consists of two components: (1) a main regression task to predict the travel time, and (2) an auxiliary metric learning task to improve the quality of link embedding vectors. We further propose the triangle loss, a novel loss function to improve the efficiency of metric learning. We validated the effectiveness of RNML-ETA on large scale real-world datasets, by showing that our method outperforms the state-of-the-art model and the promotion concentrates on the cold links with few data.
Machine-part interaction classification is a key capability required by Cyber-Physical Systems (CPS), a pivotal enabler of Smart Manufacturing (SM). While previous relevant studies on the subject have primarily focused on time series classification, change point detection is equally important because it provides temporal information on changes in behavior of the machine. In this work, we address point detection and time series classification for machine-part interactions with a deep Convolutional Neural Network (CNN) based framework. The CNN in this framework utilizes a two-stage encoder-classifier structure for efficient feature representation and convenient deployment customization for CPS. Though data-driven, the design and optimization of the framework are Subject Matter Expertise (SME) guided. An SME defined Finite State Machine (FSM) is incorporated into the framework to prohibit intermittent misclassifications. In the case study, we implement the framework to perform machine-part interaction classification on a milling machine, and the performance is evaluated using a testing dataset and deployment simulations. The implementation achieved an average F1-Score of 0.946 across classes on the testing dataset and an average delay of 0.24 seconds on the deployment simulations.
Just as user preferences change with time, item reviews also reflect those same preference changes. In a nutshell, if one is to sequentially incorporate review content knowledge into recommender systems, one is naturally led to dynamical models of text. In the present work we leverage the known power of reviews to enhance rating predictions in a way that (i) respects the causality of review generation and (ii) includes, in a bidirectional fashion, the ability of ratings to inform language review models and vice-versa, language representations that help predict ratings end-to-end. Moreover, our representations are time-interval aware and thus yield a continuous-time representation of the dynamics. We provide experiments on real-world datasets and show that our methodology is able to outperform several state-of-the-art models. Source code for all models can be found at [1].
Despite the many attempts and approaches for anomaly detection explored over the years, the automatic detection of rare events in data communication networks remains a complex problem. In this paper we introduce Net-GAN, a novel approach to network anomaly detection in time-series, using recurrent neural networks (RNNs) and generative adversarial networks (GAN). Different from the state of the art, which traditionally focuses on univariate measurements, Net-GAN detects anomalies in multivariate time-series, exploiting temporal dependencies through RNNs. Net-GAN discovers the underlying distribution of the baseline, multivariate data, without making any assumptions on its nature, offering a powerful approach to detect anomalies in complex, difficult to model network monitoring data. We further exploit the concepts behind generative models to conceive Net-VAE, a complementary approach to Net-GAN for network anomaly detection, based on variational auto-encoders (VAE). We evaluate Net-GAN and Net-VAE in different monitoring scenarios, including anomaly detection in IoT sensor data, and intrusion detection in network measurements. Generative models represent a promising approach for network anomaly detection, especially when considering the complexity and ever-growing number of time-series to monitor in operational networks.
Online 3-dimensional bin packing problem (O3D-BPP) is getting renewed prominence due to the industrial automation brought by Industry 4.0. However, due to limited attention in the past and its challenging nature, a good approximate algorithm is in scarcity as compared to 1D or 2D problems. This paper considers real-time O$3$D-BPP of cuboidal boxes with partial information (look-ahead) in an automated robotic sorting center. We present two rolling-horizon mixed-integer linear programming (MILP) cum-heuristic based algorithms: MPack (for bench-marking) and MPackLite (for real-time deployment). Additionally, we present a framework OPack that adapts and improves the performance of BP heuristics by utilizing information in an online setting with a look-ahead. We then perform a comparative analysis of BP heuristics (with and without OPack), MPack, and MPackLite on synthetic and industry provided data with increasing look-ahead. MPackLite and the baseline heuristics perform within bounds of robot operations and thus, can be used in real-time.