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We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits. To this end, we present affine Lagrangian relations by a particular class of undirected coloured graphs. In order to reason about composite systems, we introduce a powerful scalable notation where the vertices of these graphs are themselves coloured by graphs. In the setting of stabiliser quantum mechanics, this scalable notation gives an extremely concise description of graph states, which can be composed via ``phased spider fusion.'' Likewise, in the classical mechanical setting of electrical circuits, we show that impedance matrices for reciprocal networks are presented in essentially the same way.

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Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive 'adversary' tracks its target of interest via a stochastic framework such as a Kalman filter (KF). The target or 'defender' then employs another inverse stochastic filter to infer the forward filter estimates of the defender computed by the adversary. For linear systems, the inverse Kalman filter (I-KF) has been recently shown to be effective in these counter-adversarial applications. In the paper, contrary to prior works, we focus on non-linear system dynamics and formulate the inverse unscented KF (I-UKF) to estimate the defender's state based on the unscented transform, or equivalently, statistical linearization technique. We then generalize this framework to unknown systems by proposing reproducing kernel Hilbert space-based UKF (RKHS-UKF) to learn the system dynamics and estimate the state based on its observations. Our theoretical analyses to guarantee the stochastic stability of I-UKF and RKHS-UKF in the mean-squared sense show that, provided the forward filters are stable, the inverse filters are also stable under mild system-level conditions. We show that, despite being a suboptimal filter, our proposed I-UKF is a conservative estimator, i.e., I-UKF's estimated error covariance upper-bounds its true value. Our numerical experiments for several different applications demonstrate the estimation performance of the proposed filters using recursive Cram\'{e}r-Rao lower bound and non-credibility index (NCI).

Ontological representations of qualities, dispositions, and roles have been refined over the past decade, clarifying subtle distinctions in life science research. After articulating a widely-used characterization of these entities within the context of Basic Formal Ontology (BFO), we identify gaps in this treatment and motivate the need for supplementing the BFO characterization. By way of supplement, we propose definitions for grounding relations holding between qualities and dispositions, and dispositions and roles, illustrating our proposal by representing subtle aspects of host-pathogen interactions.

We introduce a new type of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalization of the determinacy method of Marks. The motivation for the construction comes from the adaptation of this method to the LOCAL model of distributed computing. Our approach unifies the previous results in the area, as well as produces new ones. In particular, we show that for $\Delta>2$ it is impossible to give a simple characterization of acyclic $\Delta$-regular Borel graphs with Borel chromatic number at most $\Delta$: such graphs form a $\mathbf{\Sigma}^1_2$-complete set. This implies a strong failure of Brooks'-like theorems in the Borel context.

The framework of approximate differential privacy is considered, and augmented by leveraging the notion of ``the total variation of a (privacy-preserving) mechanism'' (denoted by $\eta$-TV). With this refinement, an exact composition result is derived, and shown to be significantly tighter than the optimal bounds for differential privacy (which do not consider the total variation). Furthermore, it is shown that $(\varepsilon,\delta)$-DP with $\eta$-TV is closed under subsampling. The induced total variation of commonly used mechanisms are computed. Moreover, the notion of total variation of a mechanism is studied in the local privacy setting and privacy-utility tradeoffs are investigated. In particular, total variation distance and KL divergence are considered as utility functions and studied through the lens of contraction coefficients. Finally, the results are compared and connected to the locally differentially private setting.

Mobile Edge Computing (MEC) has emerged as a solution to the high latency and suboptimal Quality of Experience (QoE) associated with Mobile Cloud Computing (MCC). By processing data near the source, MEC reduces the need to send information to distant data centers, resulting in faster response times and lower latency. This paper explores the differences between MEC and traditional cloud computing, emphasizing architecture, data flow, and resource allocation. Key technologies like Network Function Virtualization (NFV) and Software-Defined Networking (SDN) are discussed for their role in achieving scalability and flexibility. Additionally, security and privacy challenges are addressed, underscoring the need for robust frameworks. We conclude with an examination of various edge computing applications and suggest future research directions to enhance the effectiveness and adoption of MEC in the evolving technological landscape.

Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers?

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.

Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.

Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.

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