Dataset distillation aims to compress training data into fewer examples via a teacher, from which a student can learn effectively. While its success is often attributed to structure in the data, modern neural networks also memorize specific facts, but if and how such memorized information is can transferred in distillation settings remains less understood. In this work, we show that students trained on soft labels from teachers can achieve non-trivial accuracy on held-out memorized data they never directly observed. This effect persists on structured data when the teacher has not generalized.To analyze it in isolation, we consider finite random i.i.d. datasets where generalization is a priori impossible and a successful teacher fit implies pure memorization. Still, students can learn non-trivial information about the held-out data, in some cases up to perfect accuracy. In those settings, enough soft labels are available to recover the teacher functionally - the student matches the teacher's predictions on all possible inputs, including the held-out memorized data. We show that these phenomena strongly depend on the temperature with which the logits are smoothed, but persist across varying network capacities, architectures and dataset compositions.

Differential Evolution (DE) is a widely used evolutionary algorithm for black-box optimization problems. However, in modern DE implementations, a major challenge lies in the limited population diversity caused by the fixed population size enforced by the generational replacement. Population size is a critical control parameter that significantly affects DE performance. Larger populations inherently contain a more diverse set of individuals, thereby facilitating broader exploration of the search space. Conversely, when the maximum evaluation budgets is constrained, smaller populations focusing on a limited number of promising candidates may be more suitable. Many state-of-the-art DE variants incorporate an archive mechanism, in which a subset of discarded individuals is preserved in an archive during generation replacement and reused in mutation operations. However, maintaining what is essentially a secondary population via an archive introduces additional design considerations, such as policies for insertion, deletion, and appropriate sizing. To address these limitations, we propose a novel DE framework called Unbounded Differential Evolution (UDE), which adds all generated candidates to the population without discarding any individual based on fitness. Unlike conventional DE, which removes inferior individuals during generational replacement, UDE eliminates replacement altogether, along with the associated complexities of archive management and dynamic population sizing. UDE represents a fundamentally new approach to DE, relying solely on selection mechanisms and enabling a more straightforward yet powerful search algorithm.

With the technological advancements of the last couple of decades, machine learning (ML) and artificial intelligence (AI) play an important part in automated decision-making pipelines [1-3]. Even though these tools are generally created by optimising with respect to their accuracy and performance, there are other important aspects that should be considered, such as their fairness, robustness, and privacy [4]. One of these aspects, fairness, becomes even more crucial when AI-based tools are used for decision-making tasks such as checking whether accepting a credit application is profitable and risk-free, if an applicant is worthy of a job position, or if a defendant has a higher risk of committing a crime again.

Learning to optimize (L2O) is an emerging technique to solve mathematical optimization problems with learning-based methods. Although with great success in many real-world scenarios such as wireless communications, computer networks, and electronic design, existing L2O works lack theoretical demonstration of their performance and robustness in out-of-distribution (OOD) scenarios. W e address this gap by providing comprehensive proofs. First, we prove a sufficient condition for a robust L2O model with homogeneous convergence rates over all In-Distribution (InD) instances. W e assume an L2O model achieves robustness for an InD scenario. Based on our proposed methodology of aligning OOD problems to InD problems, we also demonstrate that the L2O model's convergence rate in OOD scenarios will deteriorate by an equation of the L2O model's input features. Moreover, we propose an L2O model with a concise gradient-only feature construction and a novel gradient-based history modeling method. Numerical simulation demonstrates that our proposed model outperforms the state-of-the-art baseline in both InD and OOD scenarios and achieves up to 10 convergence speedup. The code of our method can be found from https://github.

Temporal Betweenness Centrality (TBC) measures how often a node appears on optimal temporal paths, reflecting its importance in temporal networks. However, exact computation is highly expensive, and real-world TBC distributions are extremely imbalanced. The severe imbalance leads learning-based models to overfit to zero-centrality nodes, resulting in inaccurate TBC predictions and failure to identify truly central nodes. Existing graph neural network (GNN) methods either fail to handle such imbalance or ignore temporal dependencies altogether. To address these issues, we propose a scalable and inductive contrastive learning-based GNN (CLGNN) for accurate and efficient TBC prediction. CLGNN builds an instance graph to preserve path validity and temporal order, then encodes structural and temporal features using dual aggregation, i.e., mean and edge-to-node multi-head attention mechanisms, enhanced by temporal path count and time encodings. A stability-based clustering-guided contrastive module (KContrastNet) is introduced to separate high-, median-, and low-centrality nodes in representation space, mitigating class imbalance, while a regression module (ValueNet) estimates TBC values. CLGNN also supports multiple optimal path definitions to accommodate diverse temporal semantics. Extensive experiments demonstrate the effectiveness and efficiency of CLGNN across diverse benchmarks. CLGNN achieves up to a 663.7~$\times$ speedup compared to state-of-the-art exact TBC computation methods. It outperforms leading static GNN baselines with up to 31.4~$\times$ lower MAE and 16.7~$\times$ higher Spearman correlation, and surpasses state-of-the-art temporal GNNs with up to 5.7~$\times$ lower MAE and 3.9~$\times$ higher Spearman correlation.

Graph Neural Networks (GNNs) became useful for learning on non-Euclidean data. However, their best performance depends on choosing the right model architecture and the training objective, also called the loss function. Researchers have studied these parts separately, but a large-scale evaluation has not looked at how GNN models and many loss functions work together across different tasks. To fix this, we ran a thorough study - it included seven well-known GNN architectures. We also used a large group of 30 single plus mixed loss functions. The study looked at both inductive and transductive settings. Our evaluation spanned three distinct real-world datasets, assessing performance in both inductive and transductive settings using 21 comprehensive evaluation metrics. From these extensive results (detailed in supplementary information 1 \& 2), we meticulously analyzed the top ten model-loss combinations for each metric based on their average rank. Our findings reveal that, especially for the inductive case: 1) Hybrid loss functions generally yield superior and more robust performance compared to single loss functions, indicating the benefit of multi-objective optimization. 2) The GIN architecture always showed the highest-level average performance, especially with Cross-Entropy loss. 3) Although some combinations had overall lower average ranks, models such as GAT, particularly with certain hybrid losses, demonstrated incredible specialized strengths, maximizing the most top-1 results among the individual metrics, emphasizing subtle strengths for particular task demands. 4) On the other hand, the MPNN architecture typically lagged behind the scenarios it was tested against.

Developing agents capable of exploring, planning and learning in complex open-ended environments is a grand challenge in artificial intelligence (AI). Hierarchical reinforcement learning (HRL) offers a promising solution to this challenge by discovering and exploiting the temporal structure within a stream of experience. The strong appeal of the HRL framework has led to a rich and diverse body of literature attempting to discover a useful structure. However, it is still not clear how one might define what constitutes good structure in the first place, or the kind of problems in which identifying it may be helpful. This work aims to identify the benefits of HRL from the perspective of the fundamental challenges in decision-making, as well as highlight its impact on the performance trade-offs of AI agents. Through these benefits, we then cover the families of methods that discover temporal structure in HRL, ranging from learning directly from online experience to offline datasets, to leveraging large language models (LLMs). Finally, we highlight the challenges of temporal structure discovery and the domains that are particularly well-suited for such endeavours.

Alignment is no longer a luxury, it is a necessity. As large language models (LLMs) enter high-stakes domains like education, healthcare, governance, and law, their behavior must reliably reflect human-aligned values and safety constraints. Yet current evaluations rely heavily on behavioral proxies such as refusal rates, G-Eval scores, and toxicity classifiers, all of which have critical blind spots. Aligned models are often vulnerable to jailbreaking, stochasticity of generation, and alignment faking. To address this issue, we introduce the Alignment Quality Index (AQI). This novel geometric and prompt-invariant metric empirically assesses LLM alignment by analyzing the separation of safe and unsafe activations in latent space. By combining measures such as the Davies-Bouldin Score (DBS), Dunn Index (DI), Xie-Beni Index (XBI), and Calinski-Harabasz Index (CHI) across various formulations, AQI captures clustering quality to detect hidden misalignments and jailbreak risks, even when outputs appear compliant. AQI also serves as an early warning signal for alignment faking, offering a robust, decoding invariant tool for behavior agnostic safety auditing. Additionally, we propose the LITMUS dataset to facilitate robust evaluation under these challenging conditions. Empirical tests on LITMUS across different models trained under DPO, GRPO, and RLHF conditions demonstrate AQI's correlation with external judges and ability to reveal vulnerabilities missed by refusal metrics. We make our implementation publicly available to foster future research in this area.

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.

Clustering of Bandits (CB) methods enhance sequential decision-making by grouping bandits into clusters based on similarity and incorporating cluster-level contextual information, demonstrating effectiveness and adaptability in applications like personalized streaming recommendations. However, when extending CB algorithms to their neural version (commonly referred to as Clustering of Neural Bandits, or CNB), they suffer from loss of plasticity, where neural network parameters become rigid and less adaptable over time, limiting their ability to adapt to non-stationary environments (e.g., dynamic user preferences in recommendation). To address this challenge, we propose Selective Reinitialization (SeRe), a novel bandit learning framework that dynamically preserves the adaptability of CNB algorithms in evolving environments. SeRe leverages a contribution utility metric to identify and selectively reset underutilized units, mitigating loss of plasticity while maintaining stable knowledge retention. Furthermore, when combining SeRe with CNB algorithms, the adaptive change detection mechanism adjusts the reinitialization frequency according to the degree of non-stationarity, ensuring effective adaptation without unnecessary resets. Theoretically, we prove that SeRe enables sublinear cumulative regret in piecewise-stationary environments, outperforming traditional CNB approaches in long-term performances. Extensive experiments on six real-world recommendation datasets demonstrate that SeRe-enhanced CNB algorithms can effectively mitigate the loss of plasticity with lower regrets, improving adaptability and robustness in dynamic settings.