Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word formation, organized into a magma of morphological trees. However, unlike syntax, we do not have movement within morphology. A coproduct decomposition exists, but it requires extending the set of morphological trees beyond those which are generated solely by the magma, to a larger set of possible morphological inputs to syntactic trees. These participate in the formation of morphosyntactic trees as an algebra over an operad, and a correspondence between algebras over an operad . The process of structure formation for morphosyntactic trees can then be described in terms of this operadic correspondence that pairs syntactic and morphological data and the morphology coproduct. We reinterpret in this setting certain operations of Distributed Morphology as transformation that allow for flexibility in moving the boundary between syntax and morphology within the morphosyntactic objects.

Vertical Federated Learning (VFL) has emerged as a popular machine learning paradigm, enabling model training across the data and the task parties with different features about the same user set while preserving data privacy. In production environment, VFL usually involves one task party and one data party. Fair and economically efficient feature trading is crucial to the commercialization of VFL, where the task party is considered as the data consumer who buys the data party's features. However, current VFL feature trading practices often price the data party's data as a whole and assume transactions occur prior to the performing VFL. Neglecting the performance gains resulting from traded features may lead to underpayment and overpayment issues. In this study, we propose a bargaining-based feature trading approach in VFL to encourage economically efficient transactions. Our model incorporates performance gain-based pricing, taking into account the revenue-based optimization objectives of both parties. We analyze the proposed bargaining model under perfect and imperfect performance information settings, proving the existence of an equilibrium that optimizes the parties' objectives. Moreover, we develop performance gain estimation-based bargaining strategies for imperfect performance information scenarios and discuss potential security issues and solutions. Experiments on three real-world datasets demonstrate the effectiveness of the proposed bargaining model.

Morphological tasks use large multi-lingual datasets that organize words into inflection tables, which then serve as training and evaluation data for various tasks. However, a closer inspection of these data reveals profound cross-linguistic inconsistencies, that arise from the lack of a clear linguistic and operational definition of what is a word, and that severely impair the universality of the derived tasks. To overcome this deficiency, we propose to view morphology as a clause-level phenomenon, rather than word-level. It is anchored in a fixed yet inclusive set of features, that encapsulates all functions realized in a saturated clause. We deliver MightyMorph, a novel dataset for clause-level morphology covering 4 typologically-different languages: English, German, Turkish and Hebrew. We use this dataset to derive 3 clause-level morphological tasks: inflection, reinflection and analysis. Our experiments show that the clause-level tasks are substantially harder than the respective word-level tasks, while having comparable complexity across languages. Furthermore, redefining morphology to the clause-level provides a neat interface with contextualized language models (LMs) and allows assessing the morphological knowledge encoded in these models and their usability for morphological tasks. Taken together, this work opens up new horizons in the study of computational morphology, leaving ample space for studying neural morphology cross-linguistically.

One of the requirements of the population-based approach to Structural Health Monitoring (SHM) proposed in the earlier papers in this sequence, is that structures be represented by points in an abstract space. Furthermore, these spaces should be metric spaces in a loose sense; i.e. there should be some measure of distance applicable to pairs of points; similar structures should then be close in the metric. However, this geometrical construction is not enough for the framing of problems in data-based SHM, as it leaves undefined the notion of feature spaces. Interpreting the feature values on a structure-by-structure basis as a type of field over the space of structures, it seems sensible to borrow an idea from modern theoretical physics, and define feature assignments as sections in a vector bundle over the structure space. With this idea in place, one can interpret the effect of environmental and operational variations as gauge degrees of freedom, as in modern gauge field theories. This paper will discuss the various geometrical structures required for an abstract theory of feature spaces in SHM, and will draw analogies with how these structures have shown their power in modern physics. In the second part of the paper, the problem of determining the normal condition cross section of a feature bundle is addressed. The solution is provided by the application of Graph Neural Networks (GNN), a versatile non-Euclidean machine learning algorithm which is not restricted to inputs and outputs from vector spaces. In particular, the algorithm is well suited to operating directly on the sort of graph structures which are an important part of the proposed framework for PBSHM. The solution of the normal section problem is demonstrated for a heterogeneous population of truss structures for which the feature of interest is the first natural frequency.

Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming. To tackle this problem, we propose two novel techniques: \emph{Gradient-based One-Side Sampling} (GOSS) and \emph{Exclusive Feature Bundling} (EFB). With GOSS, we exclude a significant proportion of data instances with small gradients, and only use the rest to estimate the information gain. We prove that, since the data instances with larger gradients play a more important role in the computation of information gain, GOSS can obtain quite accurate estimation of the information gain with a much smaller data size. With EFB, we bundle mutually exclusive features (i.e., they rarely take nonzero values simultaneously), to reduce the number of features. We prove that finding the optimal bundling of exclusive features is NP-hard, but a greedy algorithm can achieve quite good approximation ratio (and thus can effectively reduce the number of features without hurting the accuracy of split point determination by much). We call our new GBDT implementation with GOSS and EFB \emph{LightGBM}. Our experiments on multiple public datasets show that, LightGBM speeds up the training process of conventional GBDT by up to over 20 times while achieving almost the same accuracy.