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In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. Furthermore, the training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset. This structure is given in terms of signed volumes of triangles and parallelotopes generated by data vectors. The convex problem finds a small subset of samples via $\ell_1$ regularization to discover only relevant wedge product features. Our analysis provides a novel perspective on the inner workings of deep neural networks and sheds light on the role of the hidden layers.

In this paper, we introduce a novel training framework designed to comprehensively address the acoustic howling issue by examining its fundamental formation process. This framework integrates a neural network (NN) module into the closed-loop system during training with signals generated recursively on the fly to closely mimic the streaming process of acoustic howling suppression (AHS). The proposed recursive training strategy bridges the gap between training and real-world inference scenarios, marking a departure from previous NN-based methods that typically approach AHS as either noise suppression or acoustic echo cancellation. Within this framework, we explore two methodologies: one exclusively relying on NN and the other combining NN with the traditional Kalman filter. Additionally, we propose strategies, including howling detection and initialization using pre-trained offline models, to bolster trainability and expedite the training process. Experimental results validate that this framework offers a substantial improvement over previous methodologies for acoustic howling suppression.

Consensus algorithms are central to blockchain technology and an emerging research area. In this paper, we begin with an overview of the different types and architectures of blockchain networks. Then, with a focus on consortium blockchains, we survey, classify, and assess their principal consensus mechanisms. Furthermore, as consensus mechanisms determine network reliability, enhance performance efficiency, and ensure system security, we conduct a critical analysis of the strengths and weaknesses of consensus algorithms using a taxonomy of three different criteria: reliability, performance, and security. We conclude with insights into current and future research challenges and opportunities in this domain.

In this paper, we consider the problem where a drone has to collect semantic information to classify multiple moving targets. In particular, we address the challenge of computing control inputs that move the drone to informative viewpoints, position and orientation, when the information is extracted using a "black-box" classifier, e.g., a deep learning neural network. These algorithms typically lack of analytical relationships between the viewpoints and their associated outputs, preventing their use in information-gathering schemes. To fill this gap, we propose a novel attention-based architecture, trained via Reinforcement Learning (RL), that outputs the next viewpoint for the drone favoring the acquisition of evidence from as many unclassified targets as possible while reasoning about their movement, orientation, and occlusions. Then, we use a low-level MPC controller to move the drone to the desired viewpoint taking into account its actual dynamics. We show that our approach not only outperforms a variety of baselines but also generalizes to scenarios unseen during training. Additionally, we show that the network scales to large numbers of targets and generalizes well to different movement dynamics of the targets.

In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through one-sided core and dual-core inverses, we have shown the existence of a generalized weighted Moore-Penrose inverse of matrices. Further, by applying a new representation and using the properties of the weighted core inverse of a matrix, we discuss some new results related to the reverse order law for these inverses.

In this paper, we study the design and analysis of experiments conducted on a set of units over multiple time periods where the starting time of the treatment may vary by unit. The design problem involves selecting an initial treatment time for each unit in order to most precisely estimate both the instantaneous and cumulative effects of the treatment. We first consider non-adaptive experiments, where all treatment assignment decisions are made prior to the start of the experiment. For this case, we show that the optimization problem is generally NP-hard, and we propose a near-optimal solution. Under this solution, the fraction entering treatment each period is initially low, then high, and finally low again. Next, we study an adaptive experimental design problem, where both the decision to continue the experiment and treatment assignment decisions are updated after each period's data is collected. For the adaptive case, we propose a new algorithm, the Precision-Guided Adaptive Experiment (PGAE) algorithm, that addresses the challenges at both the design stage and at the stage of estimating treatment effects, ensuring valid post-experiment inference accounting for the adaptive nature of the design. Using realistic settings, we demonstrate that our proposed solutions can reduce the opportunity cost of the experiments by over 50%, compared to static design benchmarks.

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In particular, we consider several variants of SCP including the general case, the case where $f$ is additionally assumed to be monotone, and finally the case where $f$ is a regularized monotone submodular function. Our most significant contributions are that: (i) We propose a scalable algorithm for monotone SCP that achieves nearly the same approximation guarantees as the standard greedy algorithm in significantly faster time; (ii) We are the first to develop an algorithm for general SCP that achieves a solution arbitrarily close to being feasible; and finally (iii) we are the first to develop algorithms for regularized SCP. Our algorithms are then demonstrated to be effective in an extensive experimental section on data summarization and graph cut, two applications of SCP.

In this study, we propose to evaluate the use of deep learning methods for semantic classification at the sentence level to accelerate the process of corpus building in the field of humanities and linguistics, a traditional and time-consuming task. We introduce a novel corpus comprising around 2500 sentences spanning from 300 BCE to 900 CE including sexual semantics (medical, erotica, etc.). We evaluate various sentence classification approaches and different input embedding layers, and show that all consistently outperform simple token-based searches. We explore the integration of idiolectal and sociolectal metadata embeddings (centuries, author, type of writing), but find that it leads to overfitting. Our results demonstrate the effectiveness of this approach, achieving high precision and true positive rates (TPR) of respectively 70.60% and 86.33% using HAN. We evaluate the impact of the dataset size on the model performances (420 instead of 2013), and show that, while our models perform worse, they still offer a high enough precision and TPR, even without MLM, respectively 69% and 51%. Given the result, we provide an analysis of the attention mechanism as a supporting added value for humanists in order to produce more data.

In this paper, we propose a novel multi-task learning architecture, which incorporates recent advances in attention mechanisms. Our approach, the Multi-Task Attention Network (MTAN), consists of a single shared network containing a global feature pool, together with task-specific soft-attention modules, which are trainable in an end-to-end manner. These attention modules allow for learning of task-specific features from the global pool, whilst simultaneously allowing for features to be shared across different tasks. The architecture can be built upon any feed-forward neural network, is simple to implement, and is parameter efficient. Experiments on the CityScapes dataset show that our method outperforms several baselines in both single-task and multi-task learning, and is also more robust to the various weighting schemes in the multi-task loss function. We further explore the effectiveness of our method through experiments over a range of task complexities, and show how our method scales well with task complexity compared to baselines.

Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).