Human perception inherently operates in a multimodal manner. Similarly, as machines interpret the empirical world, their learning processes ought to be multimodal. The recent, remarkable successes in empirical multimodal learning underscore the significance of understanding this paradigm. Yet, a solid theoretical foundation for multimodal learning has eluded the field for some time. While a recent study by Lu (2023) has shown the superior sample complexity of multimodal learning compared to its unimodal counterpart, another basic question remains: does multimodal learning also offer computational advantages over unimodal learning? This work initiates a study on the computational benefit of multimodal learning. We demonstrate that, under certain conditions, multimodal learning can outpace unimodal learning exponentially in terms of computation. Specifically, we present a learning task that is NP-hard for unimodal learning but is solvable in polynomial time by a multimodal algorithm. Our construction is based on a novel modification to the intersection of two half-spaces problem.
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This paper discusses the different roles that explicit knowledge, in particular ontologies, can play in Explainable AI and in the development of human-centric explainable systems and intelligible explanations. We consider three main perspectives in which ontologies can contribute significantly, namely reference modelling, common-sense reasoning, and knowledge refinement and complexity management. We overview some of the existing approaches in the literature, and we position them according to these three proposed perspectives. The paper concludes by discussing what challenges still need to be addressed to enable ontology-based approaches to explanation and to evaluate their human-understandability and effectiveness.
The fundamental diagram serves as the foundation of traffic flow modeling for almost a century. With the increasing availability of road sensor data, deterministic parametric models have proved inadequate in describing the variability of real-world data, especially in congested area of the density-flow diagram. In this paper we estimate the stochastic density-flow relation introducing a nonparametric method called convex quantile regression. The proposed method does not depend on any prior functional form assumptions, but thanks to the concavity constraints, the estimated function satisfies the theoretical properties of the density-flow curve. The second contribution is to develop the new convex quantile regression with bags (CQRb) approach to facilitate practical implementation of CQR to the real-world data. We illustrate the CQRb estimation process using the road sensor data from Finland in years 2016-2018. Our third contribution is to demonstrate the excellent out-of-sample predictive power of the proposed CQRb method in comparison to the standard parametric deterministic approach.
Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.
We extend classical methods of computational complexity to the setting of distributed computing, where they are sometimes more effective than in their original context. Our focus is on distributed decision in the LOCAL model, where multiple networked computers communicate via synchronous message-passing to collectively answer a question about their network topology. Rather unusually, we impose two orthogonal constraints on the running time of this model: the number of communication rounds is bounded by a constant, and the number of computation steps of each computer is polynomially bounded by the size of its local input and the messages it receives. By letting two players take turns assigning certificates to all computers in the network, we obtain a generalization of the polynomial hierarchy (and hence of the complexity classes $\mathbf{P}$ and $\mathbf{NP}$). We then extend some key results of complexity theory to this setting, in particular the Cook-Levin theorem (which identifies Boolean satisfiability as a complete problem for $\mathbf{NP}$), and Fagin's theorem (which characterizes $\mathbf{NP}$ as the problems expressible in existential second-order logic). The original results can be recovered as the special case where the network consists of a single computer. But perhaps more surprisingly, the task of separating complexity classes becomes easier in the general case: we can show that our hierarchy is infinite, while it remains notoriously open whether the same is true in the case of a single computer. (By contrast, a collapse of our hierarchy would have implied a collapse of the polynomial hierarchy.) As an application, we propose quantifier alternation as a new approach to measuring the locality of problems in distributed computing.
Fish tracking is a key technology for obtaining movement trajectories and identifying abnormal behavior. However, it faces considerable challenges, including occlusion, multi-scale tracking, and fish deformation. Notably, extant reviews have focused more on behavioral analysis rather than providing a comprehensive overview of computer vision-based fish tracking approaches. This paper presents a comprehensive review of the advancements of fish tracking technologies over the past seven years (2017-2023). It explores diverse fish tracking techniques with an emphasis on fundamental localization and tracking methods. Auxiliary plugins commonly integrated into fish tracking systems, such as underwater image enhancement and re-identification, are also examined. Additionally, this paper summarizes open-source datasets, evaluation metrics, challenges, and applications in fish tracking research. Finally, a comprehensive discussion offers insights and future directions for vision-based fish tracking techniques. We hope that our work could provide a partial reference in the development of fish tracking algorithms.
In human interactions, emotion recognition is crucial. For this reason, the topic of computer-vision approaches for automatic emotion recognition is currently being extensively researched. Processing multi-channel electroencephalogram (EEG) information is one of the most researched methods for automatic emotion recognition. This paper presents a new model for an affective computing-driven Quality of Experience (QoE) prediction. In order to validate the proposed model, a publicly available dataset is used. The dataset contains EEG, ECG, and respiratory data and is focused on a multimedia QoE assessment context. The EEG data are retained on which the differential entropy and the power spectral density are calculated with an observation window of three seconds. These two features were extracted to train several deep-learning models to investigate the possibility of predicting QoE with five different factors. The performance of these models is compared, and the best model is optimized to improve the results. The best results were obtained with an LSTM-based model, presenting an F1-score from 68% to 78%. An analysis of the model and its features shows that the Delta frequency band is the least necessary, that two electrodes have a higher importance, and that two other electrodes have a very low impact on the model's performances.
One of the most famous conjectures in combinatorial optimization is the four-thirds conjecture, which states that the integrality gap of the subtour LP relaxation of the TSP is equal to $\frac43$. For 40 years, the best known upper bound was 1.5, due to Wolsey (1980). Recently, Karlin, Klein, and Oveis Gharan (2022) showed that the max entropy algorithm for the TSP gives an improved bound of $1.5 - 10^{-36}$. In this paper, we show that the approximation ratio of the max entropy algorithm is at least 1.375, even for graphic TSP. Thus the max entropy algorithm does not appear to be the algorithm that will ultimately resolve the four-thirds conjecture in the affirmative, should that be possible.
We proposed an extension of Akaike's relative power contribution that could be applied to data with correlations between noises. This method decomposes the power spectrum into a contribution of the terms caused by correlation between two noises, in addition to the contributions of the independent noises. Numerical examples confirm that some of the correlated noise has the effect of reducing the power spectrum.
Internet of Things (IoT) technologies are the foundation of a fully connected world. Currently, IoT devices (or nodes) primarily use dedicated sensors to sense and collect data at large scales, and then transmit the data to target nodes or gateways through wireless communication for further processing and analytics. In recent years, research efforts have been made to explore the feasibility of using wireless communication for sensing (while assiduously improving the transmission performance of wireless signals), in an attempt to achieve integrated sensing and communication (ISAC) for smart IoT of the future. In this paper, we leverage the capabilities of LoRa, a long-range IoT communication technology, to explore the possibility of using LoRa signals for both sensing and communication. Based on LoRa, we propose ISAC designs in two typical scenarios of smart IoT, and verify the feasibility and effectiveness of our designs in soil moisture monitoring and human presence detection.
Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.
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