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In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and demonstrating their properties. We establish the uniqueness of derivations, drawing upon Rosens 1975 research, and verify the Church-Rosser theorem using Ehrigs and Kreowskis 1976 proof, thereby demonstrating the effectiveness of our formalisation approach. The paper details our methodology in employing Isabelle/HOL, including key design decisions that shaped the current iteration. We explore the technical complexities involved in applying higher-order logic, aiming to give readers an insightful perspective into the engaging aspects of working with an Interactive Theorem Prover. This work emphasizes the increasing importance of formal verification tools in clarifying complex mathematical concepts.

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This paper presents the design and implementation of a self-reconfigurable V-shape formation controller for multiple unmanned aerial vehicles (UAVs) navigating through narrow spaces in a dense obstacle environment. The selection of the V-shape formation is motivated by its maneuverability and visibility advantages. The main objective is to develop an effective formation control strategy that allows UAVs to autonomously adjust their positions to form the desired formation while navigating through obstacles. To achieve this, we propose a distributed behavior-based control algorithm that combines the behaviors designed for individual UAVs so that they together navigate the UAVs to their desired positions. The reconfiguration process is automatic, utilizing individual UAV sensing within the formation, allowing for dynamic adaptations such as opening/closing wings or merging into a straight line. Simulation results show that the self-reconfigurable V-shape formation offers adaptability and effectiveness for UAV formations in complex operational scenarios.

There are many evaluation strategies for term rewrite systems, but proving termination automatically is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination. We adapt these criteria to the probabilistic setting, e.g., we show when it suffices to analyze almost-sure termination (AST) w.r.t. innermost rewriting to prove full AST of probabilistic term rewrite systems (PTRSs). These criteria also apply to other notions of termination like positive AST. We implemented and evaluated our new contributions in the tool AProVE.

Arora & Ge introduced a noise-free polynomial system to compute the secret of a Learning With Errors (LWE) instance via linearization. Albrecht et al. later utilized the Arora-Ge polynomial model to study the complexity of Gr\"obner basis computations on LWE polynomial systems under the assumption of semi-regularity. In this paper we revisit the Arora-Ge polynomial and prove that it satisfies a genericity condition recently introduced by Caminata & Gorla, called being in generic coordinates. For polynomial systems in generic coordinates one can always estimate the complexity of DRL Gr\"obner basis computations in terms of the Castelnuovo-Mumford regularity and henceforth also via the Macaulay bound. Moreover, we generalize the Gr\"obner basis algorithm of Semaev & Tenti to arbitrary polynomial systems with a finite degree of regularity. In particular, existence of this algorithm yields another approach to estimate the complexity of DRL Gr\"obner basis computations in terms of the degree of regularity. In practice, the degree of regularity of LWE polynomial systems is not known, though one can always estimate the lowest achievable degree of regularity. Consequently, from a designer's worst case perspective this approach yields sub-exponential complexity estimates for general, binary secret, and binary error LWE. In recent works by Dachman-Soled et al. the hardness of LWE in the presence of side information was analyzed. Utilizing their framework we discuss how hints can be incorporated into LWE polynomial systems and how they affect the complexity of Gr\"obner basis computations.

In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any graph. We then provide sequent calculi operating on these formulas, we prove cut-elimination and that formula encoding the same graph are logically equivalent. We show that these systems provide conservative extensions of multiplicative linear logic (with and without mix) and classical propositional logic. We conclude by showing that one of these systems is equivalent to the graphical logic GS defined via a system of context-free graph rewiring rules, therefore providing an alternative proof of analyticity for this logic over graphs.

In this paper, we demonstrate that an inherent waveform pattern in the attention allocation of large language models (LLMs) significantly affects their performance in tasks demanding a high degree of context awareness, such as utilizing LLMs for tool-use. Specifically, the crucial information in the context will be potentially overlooked by model when it is positioned in the trough zone of the attention waveform, leading to decreased performance. To address this issue, we propose a novel inference method named Attention Buckets. It allows LLMs to process their input through multiple parallel processes. Each process utilizes a distinct base angle for the rotary position embedding, thereby creating a unique attention waveform. By compensating an attention trough of a particular process with an attention peak of another process, our approach enhances LLM's awareness to various contextual positions, thus mitigating the risk of overlooking crucial information. In the largest tool-use benchmark, our method elevates a 7B model to achieve state-of-the-art performance, comparable to that of GPT-4. On other benchmarks and some RAG tasks, which also demand a thorough understanding of contextual content, Attention Buckets also exhibited notable enhancements in performance.

Standard context-aware neural machine translation (NMT) typically relies on parallel document-level data, exploiting both source and target contexts. Concatenation-based approaches in particular, still a strong baseline for document-level NMT, prepend source and/or target context sentences to the sentences to be translated, with model variants that exploit equal amounts of source and target data on each side achieving state-of-the-art results. In this work, we investigate whether target data should be further promoted within standard concatenation-based approaches, as most document-level phenomena rely on information that is present on the target language side. We evaluate novel concatenation-based variants where the target context is prepended to the source language, either in isolation or in combination with the source context. Experimental results in English-Russian and Basque-Spanish show that including target context in the source leads to large improvements on target language phenomena. On source-dependent phenomena, using only target language context in the source achieves parity with state-of-the-art concatenation approaches, or slightly underperforms, whereas combining source and target context on the source side leads to significant gains across the board.

The paper aims to address load imbalance caused by high in-degree distribution in graphs by applying the idea of rhizome to vertex-centric message-driven graph processing. Rhizome construction of the graph creates multiple named vertex address for any number of single large in-degree vertices. It then allows other vertices to point to any of the named addresses thus sharing the in-degree load. The rhizomes internally communicate and remain consistent to provide a unified and correct view of the vertex. Simulated experimental results show performance speed ups for BFS graph traversal on large chip sizes for the tested input graph datasets containing highly skewed in-degree distribution. The improvements come from sharing the in-degree compute workload among memory-processing elements and also lowering contention on the network-on-chip.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.

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