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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.

Despite recent attention and exploration of depth for various tasks, it is still an unexplored modality for weakly-supervised object detection (WSOD). We propose an amplifier method for enhancing the performance of WSOD by integrating depth information. Our approach can be applied to any WSOD method based on multiple-instance learning, without necessitating additional annotations or inducing large computational expenses. Our proposed method employs a monocular depth estimation technique to obtain hallucinated depth information, which is then incorporated into a Siamese WSOD network using contrastive loss and fusion. By analyzing the relationship between language context and depth, we calculate depth priors to identify the bounding box proposals that may contain an object of interest. These depth priors are then utilized to update the list of pseudo ground-truth boxes, or adjust the confidence of per-box predictions. Our proposed method is evaluated on six datasets (COCO, PASCAL VOC, Conceptual Captions, Clipart1k, Watercolor2k, and Comic2k) by implementing it on top of two state-of-the-art WSOD methods, and we demonstrate a substantial enhancement in performance.

We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree three and those graphs of girth at least four that arise an undirected square of an oriented graph. In contrast to the recognition problem for graphs that admit a quasi-transitive orientation, we find it is NP-complete to decide if a graph admits a partial orientation as a quasi-transitive mixed graph. We prove the problem is Polynomial when restricted to inputs of maximum degree three, but remains NP-complete when restricted to inputs with maximum degree at least five. Our proof further implies that for fixed $k \geq 3$, it is NP-complete to decide if a graph arises as an undirected square of an orientation of a graph with $\Delta = k$.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of $d$-order ($d \geq 2$) interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of $d$-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.

The centralized PKI is not a suitable solution to provide identities in large-scale IoT systems. The main problem is the high cost of managing X.509 certificates throughout their lifecycle, from installation to regular updates and revocation. The Self-Sovereign Identity (SSI) is a decentralised option that reduces the need for human intervention, and therefore has the potential to significantly reduce the complexity and cost associated to identity management in large-scale IoT systems. However, to leverage the full potential of SSI, the authentication of IoT nodes needs to be moved from the application to the Transport Layer Security (TLS) level. This paper contributes to the adoption of SSI in large-scale IoT systems by addressing, for the first time, the extension of the original TLS 1.3 handshake to support two new SSI authentication modes while maintaining the interoperability with nodes implementing the original handshake protocol. The open source implementation of the new TLS 1.3 handshake protocol in OpenSSL is used to experimentally prove the feasibility of the approach.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured Deep Operator Network (DeepONet) framework that effectively combines low and high-fidelity datasets, leveraging the strengths of each. In our methodology, we began by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network's output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the Trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts.

Adversarial examples in machine learning has emerged as a focal point of research due to their remarkable ability to deceive models with seemingly inconspicuous input perturbations, potentially resulting in severe consequences. In this study, we embark on a comprehensive exploration of adversarial machine learning models, shedding light on their intrinsic complexity and interpretability. Our investigation reveals intriguing links between machine learning model complexity and Einstein's theory of special relativity, all through the lens of entanglement. While our work does not primarily center on quantum entanglement, we instead define the entanglement correlations we have discovered to be computational, and demonstrate that distant feature samples can be entangled, strongly resembling entanglement correlation in the quantum realm. This revelation bestows fresh insights for understanding the phenomenon of emergent adversarial examples in modern machine learning, potentially paving the way for more robust and interpretable models in this rapidly evolving field.

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.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.