Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a comprehensive account of IFNs, covering their theoretical foundations, construction methodologies, and diverse applications. Tracing their origins from early network-based models to advanced formulations such as the Triangulated Maximally Filtered Graph (TMFG) and the Maximally Filtered Clique Forest (MFCF), the paper highlights how IFNs address key challenges in high-dimensional data-driven modeling. IFNs and their construction methodologies are intrinsically higher-order networks that generate simplicial complexes-structures that are only now becoming popular in the broader literature. Applications span fields including finance, biology, psychology, and artificial intelligence, where IFNs improve interpretability, computational efficiency, and predictive performance. Special attention is given to their role in graphical modeling, where IFNs enable the estimation of sparse inverse covariance matrices with greater accuracy and scalability than traditional approaches like Graphical LASSO. Finally, the review discusses recent developments that integrate IFNs with machine learning and deep learning, underscoring their potential not only to bridge classical network theory with contemporary data-driven paradigms, but also to shape the architectures of deep learning models themselves.

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism, our framework ensures \emph{non-strict constraint feasibility}, \emph{better optimality gap}, and \emph{best convergence rate} with respect to the state-of-the-art learning-based methods. We provide a rigorous convergence analysis, showing that the algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the original problem even when the internal solver is a neural network, and the approximation error is bounded. We test our approach on a range of benchmark tasks including quadratic programming (QP), nonconvex programming, and large-scale AC optimal power flow problems. The results demonstrate that compared to existing solvers (e.g., \texttt{OSQP}, \texttt{IPOPT}) and the latest learning-based methods (e.g., DC3, PDL), our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.

Creative coding platforms like Scratch have democratized programming for children, yet translating imaginative ideas into functional code remains a significant hurdle for many young learners. While AI copilots assist adult programmers, few tools target children in block-based environments. Building on prior research \cite{druga_how_2021,druga2023ai, druga2023scratch}, we present Cognimates Scratch Copilot: an AI-powered assistant integrated into a Scratch-like environment, providing real-time support for ideation, code generation, debugging, and asset creation. This paper details the system architecture and findings from an exploratory qualitative evaluation with 18 international children (ages 7--12). Our analysis reveals how the AI Copilot supported key creative coding processes, particularly aiding ideation and debugging. Crucially, it also highlights how children actively negotiated the use of AI, demonstrating strong agency by adapting or rejecting suggestions to maintain creative control. Interactions surfaced design tensions between providing helpful scaffolding and fostering independent problem-solving, as well as learning opportunities arising from navigating AI limitations and errors. Findings indicate Cognimates Scratch Copilot's potential to enhance creative self-efficacy and engagement. Based on these insights, we propose initial design guidelines for AI coding assistants that prioritize youth agency and critical interaction alongside supportive scaffolding.

Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the Random Dot Product Graph (RDPG) model to accommodate weighted graphs, markedly broadening the model's scope to scenarios where edges exhibit heterogeneous weight distributions. We propose a nonparametric weighted (W)RDPG model that assigns a sequence of latent positions to each node. Inner products of these nodal vectors specify the moments of their incident edge weights' distribution via moment-generating functions. In this way, and unlike prior art, the WRDPG can discriminate between weight distributions that share the same mean but differ in other higher-order moments. We derive statistical guarantees for an estimator of the nodal's latent positions adapted from the workhorse adjacency spectral embedding, establishing its consistency and asymptotic normality. We also contribute a generative framework that enables sampling of graphs that adhere to a (prescribed or data-fitted) WRDPG, facilitating, e.g., the analysis and testing of observed graph metrics using judicious reference distributions. The paper is organized to formalize the model's definition, the estimation (or nodal embedding) process and its guarantees, as well as the methodologies for generating weighted graphs, all complemented by illustrative and reproducible examples showcasing the WRDPG's effectiveness in various network analytic applications.

To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive properties''. Therefore, hypotheses on the nature of clusters must be set: they can be either generative or discriminative. As the last decade witnessed the impressive growth of deep clustering methods that involve neural networks to handle high-dimensional data often in a discriminative manner; we concentrate mainly on the discriminative hypotheses. In this paper, our aim is to provide an accessible historical perspective on the evolution of discriminative clustering methods and notably how the nature of assumptions of the discriminative models changed over time: from decision boundaries to invariance critics. We notably highlight how mutual information has been a historical cornerstone of the progress of (deep) discriminative clustering methods. We also show some known limitations of mutual information and how discriminative clustering methods tried to circumvent those. We then discuss the challenges that discriminative clustering faces with respect to the selection of the number of clusters. Finally, we showcase these techniques using the dedicated Python package, GemClus, that we have developed for discriminative clustering.

Netflix is giving its TV user interface a major overhaul. Alongside a fresh, cleaner look, you'll see recommendations that adapt to your activity as Netflix tries to better gauge what you might be in the mood to watch. The company plans to roll out the update over the coming weeks and months. It seems that the aim here, as has long been a goal for Netflix, is to help you find something you want to watch faster. That way, you won't spend an eternity scrolling through the various options while struggling to figure out what to start streaming.

We introduce STORY2GAME, a novel approach to using Large Language Models to generate text-based interactive fiction games that starts by generating a story, populates the world, and builds the code for actions in a game engine that enables the story to play out interactively. Whereas a given set of hard-coded actions can artificially constrain story generation, the ability to generate actions means the story generation process can be more open-ended but still allow for experiences that are grounded in a game state. The key to successful action generation is to use LLM-generated preconditions and effects of actions in the stories as guides for what aspects of the game state must be tracked and changed by the game engine when a player performs an action. We also introduce a technique for dynamically generating new actions to accommodate the player's desire to perform actions that they think of that are not part of the story. Dynamic action generation may require on-the-fly updates to the game engine's state representation and revision of previously generated actions. We evaluate the success rate of action code generation with respect to whether a player can interactively play through the entire generated story.

Recent advancements in artificial intelligence (AI) and machine learning have reignited interest in their impact on Computer-based Learning (CBL). AI-driven tools like ChatGPT and Intelligent Tutoring Systems (ITS) have enhanced learning experiences through personalisation and flexibility. ITSs can adapt to individual learning needs and provide customised feedback based on a student's performance, cognitive state, and learning path. Despite these advances, challenges remain in accommodating diverse learning styles and delivering real-time, context-aware feedback. Our research aims to address these gaps by integrating skill-aligned feedback via Retrieval Augmented Generation (RAG) into prompt engineering for Large Language Models (LLMs) and developing an application to enhance learning through personalised tutoring in a computer science programming context. The pilot study evaluated a proposed system using three quantitative metrics: readability score, response time, and feedback depth, across three programming tasks of varying complexity. The system successfully sorted simulated students into three skill-level categories and provided context-aware feedback. This targeted approach demonstrated better effectiveness and adaptability compared to general methods.

Inconsistent outputs and hallucinations from large language models (LLMs) are major obstacles to reliable AI systems. When different proprietary reasoning models (RMs), such as those by OpenAI, Google, Anthropic, DeepSeek, and xAI, are given the same complex request, they often produce divergent results due to variations in training and inference. This paper proposes a novel consensus mechanism, inspired by distributed ledger technology, to validate and converge these outputs, treating each RM as a black-box peer. Building on the Hashgraph consensus algorithm, our approach employs gossip-about-gossip communication and virtual voting to achieve agreement among an ensemble of RMs. We present an architectural design for a prototype system in which RMs iteratively exchange and update their answers, using information from each round to improve accuracy and confidence in subsequent rounds. This approach goes beyond simple majority voting by incorporating the knowledge and cross-verification content of every model. We justify the feasibility of this Hashgraph-inspired consensus for AI ensembles and outline its advantages over traditional ensembling techniques in reducing nonfactual outputs. Preliminary considerations for implementation, evaluation criteria for convergence and accuracy, and potential challenges are discussed. The proposed mechanism demonstrates a promising direction for multi-agent AI systems to self-validate and deliver high-fidelity responses in complex tasks.

We study the invertibility of nonlinear dynamical systems from the perspective of contraction and incremental stability analysis and propose a new invertible recurrent neural model: the BiLipREN. In particular, we consider a nonlinear state space model to be robustly invertible if an inverse exists with a state space realisation, and both the forward model and its inverse are contracting, i.e. incrementally exponentially stable, and Lipschitz, i.e. have bounded incremental gain. This property of bi-Lipschitzness implies both robustness in the sense of sensitivity to input perturbations, as well as robust distinguishability of different inputs from their corresponding outputs, i.e. the inverse model robustly reconstructs the input sequence despite small perturbations to the initial conditions and measured output. Building on this foundation, we propose a parameterization of neural dynamic models: bi-Lipschitz recurrent equilibrium networks (biLipREN), which are robustly invertible by construction. Moreover, biLipRENs can be composed with orthogonal linear systems to construct more general bi-Lipschitz dynamic models, e.g., a nonlinear analogue of minimum-phase/all-pass (inner/outer) factorization. We illustrate the utility of our proposed approach with numerical examples.