Representing the temporal evolution of legal norms is a critical challenge for automated processing. While foundational frameworks exist, they lack a formal pattern for granular, component-level versioning, hindering the deterministic point-in-time reconstruction of legal texts required by reliable AI applications. This paper proposes a structured, temporal modeling pattern grounded in the LRMoo ontology. Our approach models a norm's evolution as a diachronic chain of versioned F1 Works, distinguishing between language-agnostic Temporal Versions (TV)-each being a distinct Work-and their monolingual Language Versions (LV), modeled as F2 Expressions. The legislative amendment process is formalized through event-centric modeling, allowing changes to be traced precisely. Using the Brazilian Constitution as a case study, we demonstrate that our architecture enables the exact reconstruction of any part of a legal text as it existed on a specific date. This provides a verifiable semantic backbone for legal knowledge graphs, offering a deterministic foundation for trustworthy legal AI.

The world may be going to hell, but the writer and director James Gunn has graced it with a sunshine "Superman." The most recent installments in the franchise--Zack Snyder's diptych "Man of Steel" (2013) and "Batman v Superman: Dawn of Justice" (2016)--had a hectic, howling, near-apocalyptic sense of tragedy, but Gunn's vision is bright, chipper, and sentimental. A title card announces that Superman has endured his first defeat, and the hero (played by David Corenswet) is shown tumbling from the sky and slamming with a sickening thud onto the surface of a frozen wasteland, where he lies prostrate, spitting red blood on the snow. Fear not: no sooner does the wounded combatant put his lips together and whistle for Krypto than his faithful and frisky canine companion arrives and drags his master back to the Fortress of Solitude. There, loyal robots examine the patient and, by exposing him to sunlight, begin to heal him.

We show that head functions on syntactic objects extend the magma structure to a hypermagma, with the c-command relation compatible with the magma operation and the m-command relation with the hypermagma. We then show that the structure of head and complement and specifier, additional modifier positions, and the structure of phases in the Extended Projection can be formulated as a bud generating system of a colored operad, in a form similar to the structure of theta roles. We also show that, due to the special form of the colored operad generators, the filtering of freely generated syntactic objects by these coloring rules can be equivalently formulated as a filtering in the course of structure formation via a colored Merge, which can in turn be related to the hypermagma structure. The rules on movement by Internal Merge with respect to phases, the Extended Projection Principle, Empty Category Principle, and Phase Impenetrability Condition are all subsumed into the form of the colored operad generators. Movement compatibilities between the phase structure and the theta roles assignments can then be formulated in terms of the respective colored operads and a transduction of colored operads.

This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an online Frank-Wolfe algorithm along with its conceptually simple potential-based proof, and (ii) shows how to leverage semidefinite programming to jointly design and analyze online Frank-Wolfe-type algorithms numerically in a variety of settings-that include the design of the variant (i). Based on the semidefinite technique, we conclude with strong numerical evidence suggesting that no pure online Frank-Wolfe algorithm within our model class can have a regret guarantee better than O(T^3/4) (T is the time horizon) without additional assumptions, that the current algorithms do not have optimal constants, that the algorithm benefits from similar anytime properties O(t^3/4) not requiring to know T in advance, and that multiple linear optimization rounds do not generally help to obtain better regret bounds.

Leveraging the in-context learning (ICL) capability of Large Language Models (LLMs) for tabular classification has gained significant attention for its training-free adaptability across diverse datasets. Recent advancements, like TabPFN, excel in small-scale tabular datasets but struggle to scale for large and complex datasets. Our work enhances the efficiency and scalability of TabPFN for larger datasets by incorporating linear attention mechanisms as a scalable alternative to complexity-quadratic self-attention. Our model, TabFlex, efficiently handles tabular datasets with thousands of features and hundreds of classes, scaling seamlessly to millions of samples. For instance, TabFlex processes the poker-hand dataset with over a million samples in just 5 seconds. Our extensive evaluations demonstrate that TabFlex can achieve over a 2x speedup compared to TabPFN and a 1.5x speedup over XGBoost, outperforming 25 tested baselines in terms of efficiency across a diverse range of datasets. Furthermore, TabFlex remains highly effective on large-scale datasets, delivering strong performance with significantly reduced computational costs, especially when combined with data-efficient techniques such as dimensionality reduction and data sampling.

Retrieval-Augmented Generation (RAG) has emerged as an effective paradigm for generating contextually accurate answers by integrating Large Language Models (LLMs) with retrieval mechanisms. However, in legal contexts, users frequently reference norms by their labels or nicknames (e.g., Article 5 of the Constitution or Consumer Defense Code (CDC)), rather than by their content, posing challenges for traditional RAG approaches that rely solely on semantic embeddings of text. Furthermore, legal texts themselves heavily rely on explicit cross-references (e.g., "pursuant to Article 34") that function as pointers. Both scenarios pose challenges for traditional RAG approaches that rely solely on semantic embeddings of text, often failing to retrieve the necessary referenced content. This paper introduces Poly-Vector Retrieval, a method assigning multiple distinct embeddings to each legal provision: one embedding captures the content (the full text), another captures the label (the identifier or proper name), and optionally additional embeddings capture alternative denominations. Inspired by Frege's distinction between Sense and Reference, this poly-vector retrieval approach treats labels, identifiers and reference markers as rigid designators and content embeddings as carriers of semantic substance. Experiments on the Brazilian Federal Constitution demonstrate that Poly-Vector Retrieval significantly improves retrieval accuracy for label-centric queries and potential to resolve internal and external cross-references, without compromising performance on purely semantic queries. The study discusses philosophical and practical implications of explicitly separating reference from content in vector embeddings and proposes future research directions for applying this approach to broader legal datasets and other domains characterized by explicit reference identifiers.

Assembly Calculus (AC), proposed by Papadimitriou et al., aims to reproduce advanced cognitive functions through simulating neural activities, with several applications based on AC having been developed, including a natural language parser proposed by Mitropolsky et al. However, this parser lacks the ability to handle Kleene closures, preventing it from parsing all regular languages and rendering it weaker than Finite Automata (FA). In this paper, we propose a new bionic natural language parser (BNLP) based on AC and integrates two new biologically rational structures, Recurrent Circuit and Stack Circuit which are inspired by RNN and short-term memory mechanism. In contrast to the original parser, the BNLP can fully handle all regular languages and Dyck languages. Therefore, leveraging the Chomsky-Sch \H{u}tzenberger theorem, the BNLP which can parse all Context-Free Languages can be constructed. We also formally prove that for any PDA, a Parser Automaton corresponding to BNLP can always be formed, ensuring that BNLP has a description ability equal to that of PDA and addressing the deficiencies of the original parser.

A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We propose a general deep probabilistic model designed to produce interpretable predictions. The model parameters can be learned via maximum likelihood, and the method can be adapted to any predictor network architecture and any type of prediction problem. Our method is a case of amortized interpretability models, where a neural network is used as a selector to allow for fast interpretation at inference time. Several popular interpretability methods are shown to be particular cases of regularised maximum likelihood for our general model. We propose new datasets with ground truth selection which allow for the evaluation of the features importance map. Using these datasets, we show experimentally that using multiple imputation provides more reasonable interpretations.

Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a theory-guided machine learning approach that employs a generalized Bayesian algorithm to make ensemble forecasts. We employ Lipschitz predictors and determine fixed-time and any-time PAC Bayesian bounds in the batch learning setting. Performing causal forecast is a highlight of our methodology as its potential application to data with spatial and temporal short and long-range dependence. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a spatio-temporal Ornstein-Uhlenbeck process.

In this preference elicitation setting, our focus is on determining the parameters of a decision model that accurately captures the pairwise preferences of a Decision Maker (DM) over subsets, by comparing subsets of elements. The preferences are depicted using a highly adaptable model whose versatility stems from its ability to incorporate positive or negative synergies between elements [24]. Moreover, we provide an ordinally robust approach, in the sense that the preferences we infer do not rely on arbitrarily specified parameter values, but on the set of all parameter values that are compatible with the observed preferences. Importantly, another distinctive feature of our approach is its ability to learn the parameter set itself (not only the values of parameters). The preference model we consider can be used in different contexts, depending on the nature of the subsets we are comparing. The subsets are represented by binary vectors, showing the presence or absence of an element in the subset. The elements of a subset can be for example: individuals (in the comparison of coalitions, teams, etc.), binary attributes (in the comparison of multiattribute alternatives), objects (in the comparison of subsets in a subset choice problem), etc. For illustration, a toy example of such an elicitation context could be a coffee shop trying to determine its customers' favorite frozen yogurt flavor combination by offering them to test a small number of flavor combinations rather than having them taste each combination.