SQL query rewriting aims to reformulate a query into a more efficient form while preserving equivalence. Most existing methods rely on predefined rewrite rules. However, such rule-based approaches face fundamental limitations: (1) fixed rule sets generalize poorly to novel query patterns and struggle with complex queries; (2) a wide range of effective rewriting strategies cannot be fully captured by declarative rules. To overcome these issues, we propose using large language models (LLMs) to generate rewrites. LLMs can capture complex strategies, such as evaluation reordering and CTE rewriting. Despite this potential, directly applying LLMs often results in performance regressions or non-equivalent rewrites due to a lack of execution awareness and semantic grounding. To address these challenges, We present E3-Rewrite, an LLM-based SQL rewriting framework that produces executable, equivalent, and efficient queries. It integrates two core components: a context construction module and a reinforcement learning framework. First, the context module leverages execution plans and retrieved demonstrations to build bottleneck-aware prompts that guide inference-time rewriting. Second, we design a reward function targeting executability, equivalence, and efficiency, evaluated via syntax checks, equivalence verification, and cost estimation. Third, to ensure stable multi-objective learning, we adopt a staged curriculum that first emphasizes executability and equivalence, then gradually incorporates efficiency. Across multiple SQL benchmarks, our experiments demonstrate that E3-Rewrite can shorten query execution time by as much as 25.6% relative to leading baselines, while also producing up to 24.4% more rewrites that meet strict equivalence criteria. These gains extend to challenging query patterns that prior approaches could not effectively optimize.

However, their performance usually suffers from the overfitting problem seriously.

A recursive strategy is able to efficiently calculate the contributions of particular substring, pre-calculating contributions of the smaller sub-strings contained within the target string. Context-free grammars (CFG) are 4-tuples G = ( V, Σ,R,S), consisting of: a set of non-terminal symbols V, a set of terminal symbols Σ (also known as an alphabet), a set of production rules R, a non-terminal starting symbol S from which all strings are generated. The CFG for the symbolic regression task of Section 5.3 is given by the following rules: S S '+' T S S ' ' T S S '/' T S T T '(' S ')' T ' sin (' S ')' T'exp (' S ')' T'x' T '1' T '2' T '3', We now provide implementation details for our GA acquisition function optimizers. The GA begins with a randomly sampled population and ends once the best string in the population stops improving between iterations (Algorithm 1). Although seemingly simple tasks, our synthetic string optimization tasks of Section 5.1 are deceptively We now provide comprehensive experimental results across the synthetic string optimization tasks.

Over the past decade, machine learning (ML) models are being increasingly deployed to make a variety of consequential decisions ranging from hiring decisions to loan approvals.

Lifted inference rules exploit symmetries for fast reasoning in statistical rela-tional models. Computational complexity of these rules is highly dependent onthe choice of the constraint language they operate on and therefore coming upwith the right kind of representation is critical to the success of lifted inference.In this paper, we propose a new constraint language, called setineq, which allowssubset, equality and inequality constraints, to represent substitutions over the vari-ables in the theory. Our constraint formulation is strictly more expressive thanexisting representations, yet easy to operate on. We reformulate the three mainlifting rules: decomposer, generalized binomial and the recently proposed singleoccurrence for MAP inference, to work with our constraint representation. Exper-iments on benchmark MLNs for exact and sampling based inference demonstratethe effectiveness of our approach over several other existing techniques.

While quantitative evaluations of compositional and non-compositional approaches in SA exist in NLP, similar quantitative evaluations are very rare in FA in Linguistics that deal with linguistic expressions representing focus or emphasis such as "it was John who left". We fill this gap in research by arguing that compositional rules in SA also apply to FA because FA and SA are closely related meaning that SA is part of FA. Our compositional approach in SA exploits basic syntactic rules such as rules of modification, coordination, and negation represented in the formalism of Universal Dependencies (UDs) in English and applied to words representing sentiments from sentiment dictionaries. Some of the advantages of our compositional analysis method for SA in contrast to non-compositional analysis methods are interpretability and explainability. We test the accuracy of our compositional approach and compare it with a non-compositional approach VADER that uses simple heuristic rules to deal with negation, coordination and modification. In contrast to previous related work that evaluates compositionality in SA on long reviews, this study uses more appropriate datasets to evaluate compositionality. In addition, we generalize the results of compositional approaches in SA to compositional approaches in FA.

Rule-based methods for knowledge graph completion provide explainable results but often require a significantly large number of rules to achieve competitive performance. This can hinder explainability due to overwhelmingly large rule sets. We discover rule contexts (meaningful subsets of rules that work together) from training data and use learned probability distribution (i.e. probabilistic circuits) over these rule contexts to more rapidly achieve performance of the full rule set. Our approach achieves a 70-96% reduction in number of rules used while outperforming baseline by up to 31$\times$ when using equivalent minimal number of rules and preserves 91% of peak baseline performance even when comparing our minimal rule sets against baseline's full rule sets. We show that our framework is grounded in well-known semantics of probabilistic logic, does not require independence assumptions, and that our tractable inference procedure provides both approximate lower bounds and exact probability of a given query. The efficacy of our method is validated by empirical studies on 8 standard benchmark datasets where we show competitive performance by using only a fraction of the rules required by AnyBURL's standard inference method, the current state-of-the-art for rule-based knowledge graph completion. This work may have further implications for general probabilistic reasoning over learned sets of rules.

This work focuses on validation of attack pattern mining in the context of Industrial Control System (ICS) security. A comprehensive security assessment of an ICS requires generating a large and variety of attack patterns. For this purpose we have proposed a data driven technique to generate attack patterns for an ICS. The proposed technique has been used to generate over 100,000 attack patterns from data gathered from an operational water treatment plant. In this work we present a detailed case study to validate the attack patterns.

We propose a novel machine learning architecture that departs from conventional neural network paradigms by leveraging quantum spectral methods, specifically Pade approximants and the Lanczos algorithm, for interpretable signal analysis and symbolic reasoning. The core innovation of our approach lies in its ability to transform raw time-domain signals into sparse, physically meaningful spectral representations without the use of backpropagation, high-dimensional embeddings, or data-intensive black-box models. Through rational spectral approximation, the system extracts resonant structures that are then mapped into symbolic predicates via a kernel projection function, enabling logical inference through a rule-based reasoning engine. This architecture bridges mathematical physics, sparse approximation theory, and symbolic artificial intelligence, offering a transparent and physically grounded alternative to deep learning models. We develop the full mathematical formalism underlying each stage of the pipeline, provide a modular algorithmic implementation, and demonstrate the system's effectiveness through comparative evaluations on time-series anomaly detection, symbolic classification, and hybrid reasoning tasks. Our results show that this spectral-symbolic architecture achieves competitive accuracy while maintaining interpretability and data efficiency, suggesting a promising new direction for physically-informed, reasoning-capable machine learning.

The emergence of Symbiotic AI (SAI) introduces new challenges to ethical decision-making as it deepens human-AI collaboration. As symbiosis grows, AI systems pose greater ethical risks, including harm to human rights and trust. Ethical Risk Assessment (ERA) thus becomes crucial for guiding decisions that minimize such risks. However, ERA is hindered by uncertainty, vagueness, and incomplete information, and morality itself is context-dependent and imprecise. This motivates the need for a flexible, transparent, yet robust framework for ERA. Our work supports ethical decision-making by quantitatively assessing and prioritizing multiple ethical risks so that artificial agents can select actions aligned with human values and acceptable risk levels. We introduce ff4ERA, a fuzzy framework that integrates Fuzzy Logic, the Fuzzy Analytic Hierarchy Process (FAHP), and Certainty Factors (CF) to quantify ethical risks via an Ethical Risk Score (ERS) for each risk type. The final ERS combines the FAHP-derived weight, propagated CF, and risk level. The framework offers a robust mathematical approach for collaborative ERA modeling and systematic, step-by-step analysis. A case study confirms that ff4ERA yields context-sensitive, ethically meaningful risk scores reflecting both expert input and sensor-based evidence. Risk scores vary consistently with relevant factors while remaining robust to unrelated inputs. Local sensitivity analysis shows predictable, mostly monotonic behavior across perturbations, and global Sobol analysis highlights the dominant influence of expert-defined weights and certainty factors, validating the model design. Overall, the results demonstrate ff4ERA ability to produce interpretable, traceable, and risk-aware ethical assessments, enabling what-if analyses and guiding designers in calibrating membership functions and expert judgments for reliable ethical decision support.