An optimizer is a function or an algorithm that modifies the attributes of the neural network, such as weights and learning rate, it also reduces the loss (loss can be calculated between the predicted value and actual value) and improves the accuracy. It takes an entire dataset for each iteration which consumes more time and there might be a chance of skipping the optimal value. SGD updates the weights after seeing each data point instead of the dataset. Momentum: it helps to move faster towards the loss function. Adding a fraction of the previous update to the current update will make the process a bit faster.

Logistic regression is a method to create a model by using binary data (0 and 1). The goal is to predict something independent variable based on a dependent variable. In a real application, logistic regression is applied to predict the number of customers who buy a product or who did not base on their previous transaction, to predict the number of fraud transactions in credit cards, and so on. In logistic regression, Y-axis lies from 0 – 1. Logistic regression cannot be solved by using a linear equation like linear regression. That is because if the Y-axis of the logistic function is transformed into a linear function, the boundary of the Y-axis lies from -infinity to infinity. Then, when we calculate the misfit error between actual data and predicted data, it will not get a good misfit error.

Support vector machines are supervised learning models that analyse data to find patterns useful in classification and regression. They are versatile: they can identify non-linear relationships, work with discrete and continuous data, and are used for two-class classification, multi-class classification as well as regression. They are remarkable for unifying geometric theory, elegant mathematics, and theoretical guarantees with practical solid use cases. They provide several specific benefits. With the use of Kernel functions, they are highly effective in higher dimensional spaces.

To address practical challenges in establishing and maintaining robust wireless connectivity such as multi-path effects, low latency, size reduction, and high data rate, the digital beamformer is performed by the hybrid antenna array at the frequency of operation of 10 GHz. The proposed digital beamformer, as a spatial filter, is capable of performing Direction of Arrival (DOA) estimation and beamforming. The most well-established machine learning technique of support vector machine (SVM) for the DoA estimation is limited to problems with linearly-separable datasets. To overcome the aforementioned constraint, in the proposed beamformer, the QS-SVM classifier with a small regularizer has been used for the DoA estimation in addition to the two beamforming techniques of LCMV and MVDR. The QS-SVM-based beamformer has been deployed in an FPGA board, as demonstrated in detail in this work. The implementation results have verified the strong performance of the QS-SVM-based beamformer in suppressing undesired signals, deep nulls with powers less than -10 dB in undesired signals, and transferring desired signals. Furthermore, we have demonstrated that the performance of the QS-SVM-based beamformer consists of other advantages of average latency time in the order of milliseconds, performance efficiency of more than 90%, and throughput of about 100%. Index Terms Digital beamforming, Support vector machine, Minimum variance distortionless response, Linearly constrained minimum variance, Direction of arrival estimation, and FPGA, Spatial filter, Massive wireless communications.

Time series datasets are often composed of a variety of sequences from the same domain, but from different entities, such as individuals, products, or organizations. We are interested in how time series models can be specialized to individual sequences (capturing the specific characteristics) while still retaining statistical power by sharing commonalities across the sequences. This paper describes the multi-task dynamical system (MTDS); a general methodology for extending multi-task learning (MTL) to time series models. Our approach endows dynamical systems with a set of hierarchical latent variables which can modulate all model parameters. To our knowledge, this is a novel development of MTL, and applies to time series both with and without control inputs. We apply the MTDS to motion-capture data of people walking in various styles using a multi-task recurrent neural network (RNN), and to patient drug-response data using a multi-task pharmacodynamic model.

While cross entropy (CE) is the most commonly used loss function to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is still a mystery, because there seem to be multiple factors affecting the answer, such as properties of the dataset, the choice of network architecture, and so on. This paper studies the choice of loss function by examining the last-layer features of deep networks, drawing inspiration from a recent line work showing that the global optimal solution of CE and mean-square-error (MSE) losses exhibits a Neural Collapse (N C) phenomenon. That is, for sufficiently large networks trained until convergence, (i) all features of the same class collapse to the corresponding class mean and (ii) the means associated with different classes are in a configuration where their pairwise distances are all equal and maximized. We extend such results and show through global solution and landscape analyses that a broad family of loss functions including commonly used label smoothing (LS) and focal loss (FL) exhibits N C. Hence, all relevant losses (i.e., CE, LS, FL, MSE) produce equivalent features on training data. In particular, based on the unconstrained feature model assumption, we provide either the global landscape analysis for LS loss or the local landscape analysis for FL loss and show that the (only!) global minimizers are N C solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions either in the global scope for LS loss or in the local scope for FL loss near the optimal solution. The experiments further show that N C features obtained from all relevant losses (i.e., CE, LS, FL, MSE) lead to largely identical performance on test data as well, provided that the network is sufficiently large and trained until convergence.

Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the low-level OT, which considers the weights of all the data samples in the base class. Experimental results on standard benchmarks demonstrate that our proposed plug-and-play model outperforms competing approaches and owns desired cross-domain generalization ability, indicating the effectiveness of the learned adaptive weights.

Current content filtering and blocking methods are susceptible to various circumvention techniques and are relatively slow in dealing with new threats. This is due to these methods using shallow pattern recognition that is based on regular expression rules found in crowdsourced block lists. We propose a novel system that aims to remedy the aforementioned issues by examining deep textual patterns of network-oriented content relating to the domain being interacted with. Moreover, we propose to use federated learning that allows users to take advantage of each other's localized knowledge/experience regarding what should or should not be blocked on a network without compromising privacy. Our experiments show the promise of our proposed approach in real world settings. We also provide data-driven recommendations on how to best implement the proposed system.

Quantifying the parameters and corresponding uncertainties of hundreds of strongly lensed quasar systems holds the key to resolving one of the most important scientific questions: the Hubble constant ($H_{0}$) tension. The commonly used Markov chain Monte Carlo (MCMC) method has been too time-consuming to achieve this goal, yet recent work has shown that convolution neural networks (CNNs) can be an alternative with seven orders of magnitude improvement in speed. With 31,200 simulated strongly lensed quasar images, we explore the usage of Vision Transformer (ViT) for simulated strong gravitational lensing for the first time. We show that ViT could reach competitive results compared with CNNs, and is specifically good at some lensing parameters, including the most important mass-related parameters such as the center of lens $\theta_{1}$ and $\theta_{2}$, the ellipticities $e_1$ and $e_2$, and the radial power-law slope $\gamma'$. With this promising preliminary result, we believe the ViT (or attention-based) network architecture can be an important tool for strong lensing science for the next generation of surveys. The open source of our code and data is in \url{https://github.com/kuanweih/strong_lensing_vit_resnet}.

The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision. However, when it comes to graph-structured data, transformers have not achieved competitive performance, especially on large graphs. In this paper, we identify the main deficiencies of current graph transformers:(1) Existing node sampling strategies in Graph Transformers are agnostic to the graph characteristics and the training process. (2) Most sampling strategies only focus on local neighbors and neglect the long-range dependencies in the graph. We conduct experimental investigations on synthetic datasets to show that existing sampling strategies are sub-optimal. To tackle the aforementioned problems, we formulate the optimization strategies of node sampling in Graph Transformer as an adversary bandit problem, where the rewards are related to the attention weights and can vary in the training procedure. Meanwhile, we propose a hierarchical attention scheme with graph coarsening to capture the long-range interactions while reducing computational complexity. Finally, we conduct extensive experiments on real-world datasets to demonstrate the superiority of our method over existing graph transformers and popular GNNs.