Recently, Gavazzo has developed a relational theory of symbolic manipulation, that allows to study syntax-based rewriting systems without relying on specific notions of syntax. This theory was obtained by extending the algebra of relations with syntax-inspired operators. Within the algebras thus obtained, it is possible to encode notions of parallel and full reduction for first-order rewriting systems, as well as to prove nontrivial properties about them in an algebraic and syntax-independent fashion. Sequential reduction, however, was not explored, but it was conjectured that it could be studied through a differential relational theory of rewriting. This manuscript proves the above conjecture by defining differential algebras of term relations, viz. algebras of term relations extended with novel operators inspired by the theory of functor derivatives. We give a set of axioms and rules for such operators and show that the resulting theory is expressive enough to define notions of parallel, full, and sequential reduction. We prove fundamental results relating all these notions in a purely algebraic and syntax-independent way, and showcase the effectiveness of our theory by proving the soundness of a proof technique for weak confluence akin to the so-called Critical Pair Lemma.
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Numerous current Quantum Machine Learning (QML) models exhibit an inadequacy in discerning the significance of quantum data, resulting in diminished efficacy when handling extensive quantum datasets. Hard Attention Mechanism (HAM), anticipated to efficiently tackle the above QML bottlenecks, encounters the substantial challenge of non-differentiability, consequently constraining its extensive applicability. In response to the dilemma of HAM and QML, a Grover-inspired Quantum Hard Attention Mechanism (GQHAM) consisting of a Flexible Oracle (FO) and an Adaptive Diffusion Operator (ADO) is proposed. Notably, the FO is designed to surmount the non-differentiable issue by executing the activation or masking of Discrete Primitives (DPs) with Flexible Control (FC) to weave various discrete destinies. Based on this, such discrete choice can be visualized with a specially defined Quantum Hard Attention Score (QHAS). Furthermore, a trainable ADO is devised to boost the generality and flexibility of GQHAM. At last, a Grover-inspired Quantum Hard Attention Network (GQHAN) based on QGHAM is constructed on PennyLane platform for Fashion MNIST binary classification. Experimental findings demonstrate that GQHAN adeptly surmounts the non-differentiability hurdle, surpassing the efficacy of extant quantum soft self-attention mechanisms in accuracies and learning ability. In noise experiments, GQHAN is robuster to bit-flip noise in accuracy and amplitude damping noise in learning performance. Predictably, the proposal of GQHAN enriches the Quantum Attention Mechanism (QAM), lays the foundation for future quantum computers to process large-scale data, and promotes the development of quantum computer vision.
Beyond attaining domain generalization (DG), visual recognition models should also be data-efficient during learning by leveraging limited labels. We study the problem of Semi-Supervised Domain Generalization (SSDG) which is crucial for real-world applications like automated healthcare. SSDG requires learning a cross-domain generalizable model when the given training data is only partially labelled. Empirical investigations reveal that the DG methods tend to underperform in SSDG settings, likely because they are unable to exploit the unlabelled data. Semi-supervised learning (SSL) shows improved but still inferior results compared to fully-supervised learning. A key challenge, faced by the best-performing SSL-based SSDG methods, is selecting accurate pseudo-labels under multiple domain shifts and reducing overfitting to source domains under limited labels. In this work, we propose new SSDG approach, which utilizes a novel uncertainty-guided pseudo-labelling with model averaging (UPLM). Our uncertainty-guided pseudo-labelling (UPL) uses model uncertainty to improve pseudo-labelling selection, addressing poor model calibration under multi-source unlabelled data. The UPL technique, enhanced by our novel model averaging (MA) strategy, mitigates overfitting to source domains with limited labels. Extensive experiments on key representative DG datasets suggest that our method demonstrates effectiveness against existing methods. Our code and chosen labelled data seeds are available on GitHub: //github.com/Adnan-Khan7/UPLM
Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a domain-agnostic model to address this issue termed the deep latent force model (DLFM), a deep Gaussian process with physics-informed kernels at each layer, derived from ordinary differential equations using the framework of process convolutions. Two distinct formulations of the DLFM are presented which utilise weight-space and variational inducing points-based Gaussian process approximations, both of which are amenable to doubly stochastic variational inference. We present empirical evidence of the capability of the DLFM to capture the dynamics present in highly nonlinear real-world multi-output time series data. Additionally, we find that the DLFM is capable of achieving comparable performance to a range of non-physics-informed probabilistic models on benchmark univariate regression tasks. We also empirically assess the negative impact of the inducing points framework on the extrapolation capabilities of LFM-based models.
In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a `base' of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , K4, and S4, with $\square$ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between $\square$ and a natural presentation of $\lozenge$. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.
Mechanical metamaterial is a synthetic material that can possess extraordinary physical characteristics, such as abnormal elasticity, stiffness, and stability, by carefully designing its internal structure. To make metamaterials contain delicate local structures with unique mechanical properties, it is a potential method to represent them through high-resolution voxels. However, it brings a substantial computational burden. To this end, this paper proposes a fast inverse design method, whose core is an advanced deep generative AI algorithm, to generate voxel-based mechanical metamaterials. Specifically, we use the self-conditioned diffusion model, capable of generating a microstructure with a resolution of $128^3$ to approach the specified homogenized tensor matrix in just 3 seconds. Accordingly, this rapid reverse design tool facilitates the exploration of extreme metamaterials, the sequence interpolation in metamaterials, and the generation of diverse microstructures for multi-scale design. This flexible and adaptive generative tool is of great value in structural engineering or other mechanical systems and can stimulate more subsequent research.
Addressing the limitations of individual attribution scores via the Shapley value (SV), the field of explainable AI (XAI) has recently explored intricate interactions of features or data points. In particular, \mbox{extensions}~of~the SV, such as the Shapley Interaction Index (SII), have been proposed as a measure to still benefit from the axiomatic basis of the SV. However, similar to the SV, their exact computation remains computationally prohibitive. Hence, we propose with SVARM-IQ a sampling-based approach to efficiently approximate Shapley-based interaction indices of any order. SVARM-IQ can be applied to a broad class of interaction indices, including the SII, by leveraging a novel stratified representation. We provide non-asymptotic theoretical guarantees on its approximation quality and empirically demonstrate that SVARM-IQ achieves state-of-the-art estimation results in practical XAI scenarios on different model classes and application domains.
Forecasting complex system dynamics, particularly for long-term predictions, is persistently hindered by error accumulation and computational burdens. This study presents RefreshNet, a multiscale framework developed to overcome these challenges, delivering an unprecedented balance between computational efficiency and predictive accuracy. RefreshNet incorporates convolutional autoencoders to identify a reduced order latent space capturing essential features of the dynamics, and strategically employs multiple recurrent neural network (RNN) blocks operating at varying temporal resolutions within the latent space, thus allowing the capture of latent dynamics at multiple temporal scales. The unique "refreshing" mechanism in RefreshNet allows coarser blocks to reset inputs of finer blocks, effectively controlling and alleviating error accumulation. This design demonstrates superiority over existing techniques regarding computational efficiency and predictive accuracy, especially in long-term forecasting. The framework is validated using three benchmark applications: the FitzHugh-Nagumo system, the Reaction-Diffusion equation, and Kuramoto-Sivashinsky dynamics. RefreshNet significantly outperforms state-of-the-art methods in long-term forecasting accuracy and speed, marking a significant advancement in modeling complex systems and opening new avenues in understanding and predicting their behavior.
Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.
Multi-modal fusion is a fundamental task for the perception of an autonomous driving system, which has recently intrigued many researchers. However, achieving a rather good performance is not an easy task due to the noisy raw data, underutilized information, and the misalignment of multi-modal sensors. In this paper, we provide a literature review of the existing multi-modal-based methods for perception tasks in autonomous driving. Generally, we make a detailed analysis including over 50 papers leveraging perception sensors including LiDAR and camera trying to solve object detection and semantic segmentation tasks. Different from traditional fusion methodology for categorizing fusion models, we propose an innovative way that divides them into two major classes, four minor classes by a more reasonable taxonomy in the view of the fusion stage. Moreover, we dive deep into the current fusion methods, focusing on the remaining problems and open-up discussions on the potential research opportunities. In conclusion, what we expect to do in this paper is to present a new taxonomy of multi-modal fusion methods for the autonomous driving perception tasks and provoke thoughts of the fusion-based techniques in the future.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
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