Let $A \in \mathbb{R}^{m \times n}$ be an arbitrary, known matrix and $e$ a $q$-sparse adversarial vector. Given $y = A x^\star + e$ and $q$, we seek the smallest set containing $x^\star$ -- hence the one conveying maximal information about $x^\star$ -- that is uniformly recoverable from $y$ without knowing $e$. While exact recovery of $x^\star$ via strong (and often impractical) structural assumptions on $A$ or $x^\star$ (e.g., restricted isometry, sparsity) is well studied, recoverability for arbitrary $A$ and $x^\star$ remains open. Our main result shows that the best that one can hope to recover is $x^\star + \ker(U)$, where $U$ is the unique projection matrix onto the intersection of rowspaces of all possible submatrices of $A$ obtained by deleting $2q$ rows. Moreover, we prove that every $x$ that minimizes the $\ell_0$-norm of $y - A x$ lies in $x^\star + \ker(U)$, which then gives a constructive approach to recover this set.

This paper introduces SpikeFit, a novel training method for Spiking Neural Networks (SNNs) that enables efficient inference on neuromorphic hardware, considering all its stringent requirements: the number of neurons and synapses that can fit on a single device, and lower bit-width representations (e.g., 4-bit, 8-bit). Unlike conventional compressing approaches that address only a subset of these requirements (limited numerical precision and limited number of neurons in the network), SpikeFit treats the allowed weights' discrete values themselves as learnable parameters co-optimized with the model, allowing for optimal Clusterization-Aware Training (CAT) of the model's weights at low precision (2-, 4-, or 8-bit) which results in higher network compression efficiency, as well as limiting the number of unique synaptic connections to a value required by neuromorphic processor. This joint optimization allows SpikeFit to find a discrete weight set aligned with hardware constraints, enabling the most complete deployment across a broader range of neuromorphic processors than existing methods of SNN compression support. Moreover, SpikeFit introduces a new hardware-friendly Fisher Spike Contribution (FSC) pruning method showing the state-of-the-art performance. We demonstrate that for spiking neural networks constrained to only four unique synaptic weight values (M = 4), our SpikeFit method not only outperforms state-of-the-art SNNs compression methods and conventional baselines combining extreme quantization schemes and clustering algorithms, but also meets a wider range of neuromorphic hardware requirements and provides the lowest energy use in experiments.

We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep Operator Network (DeepONet) architecture that incorporates Chunkwise Rational Kolmogorov-Arnold Network (CKAN) sub-networks for enhanced function approximation. The principles of Physics-Informed Neural Networks (PINNs) are integrated into the operator learning framework to enforce physical consistency. This design enables the efficient learning of physically consistent spatio-temporal solution operators and allows for rapid prediction for parametric time-dependent PDEs with varying inputs (e.g., parameters, initial/boundary conditions) after training. Validated on challenging benchmark problems, PO-CKAN demonstrates accurate operator learning with results closely matching high-fidelity solutions. PO-CKAN adopts a DeepONet-style branch--trunk architecture with its sub-networks instantiated as rational KAN modules, and enforces physical consistency via a PDE residual (PINN-style) loss. On Burgers' equation with $ν=0.01$, PO-CKAN reduces the mean relative $L^2$ error by approximately 48\% compared to PI-DeepONet, and achieves competitive accuracy on the Eikonal and diffusion--reaction benchmarks.

Large Language Models (LLMs) are transforming education by enabling personalization, feedback, and knowledge access, while also raising concerns about risks to students and learning systems. Yet empirical evidence on these risks remains fragmented. This paper presents a systematic review of 70 empirical studies across computer science, education, and psychology. Guided by four research questions, we examine: (i) which applications of LLMs in education have been most frequently explored; (ii) how researchers have measured their impact; (iii) which risks stem from such applications; and (iv) what mitigation strategies have been proposed. We find that research on LLMs clusters around three domains: operational effectiveness, personalized applications, and interactive learning tools. Across these, model-level risks include superficial understanding, bias, limited robustness, anthropomorphism, hallucinations, privacy concerns, and knowledge constraints. When learners interact with LLMs, these risks extend to cognitive and behavioural outcomes, including reduced neural activity, over-reliance, diminished independent learning skills, and a loss of student agency. To capture this progression, we propose an LLM-Risk Adapted Learning Model that illustrates how technical risks cascade through interaction and interpretation to shape educational outcomes. As the first synthesis of empirically assessed risks, this review provides a foundation for responsible, human-centred integration of LLMs in education.

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited, partly due to the complexity of incorporating partial differential equations (PDEs) for ageing physics and the scarcity of robust uncertainty quantification methods. This work introduces a Bayesian Physics-Informed Neural Network (B-PINN) framework for probabilistic prognostics estimation. By embedding Bayesian Neural Networks into the PINN architecture, the proposed approach produces principled, uncertainty-aware predictions. The method is applied to a transformer ageing case study, where insulation degradation is primarily driven by thermal stress. The heat diffusion PDE is used as the physical residual, and different prior distributions are investigated to examine their impact on predictive posterior distributions and their ability to encode a priori physical knowledge. The framework is validated against a finite element model developed and tested with real measurements from a solar power plant. Results, benchmarked against a dropout-PINN baseline, show that the proposed B-PINN delivers more reliable prognostic predictions by accurately quantifying predictive uncertainty. This capability is crucial for supporting robust and informed maintenance decision-making in critical power assets.

Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on massive computational and energy resources, neuromorphic systems exploit brain-inspired principles of computation to achieve orders of magnitude greater energy efficiency. By drawing on insights from a wide range of disciplines -- including artificial intelligence, physics, chemistry, biology, neuroscience, cognitive science and materials science -- neuromorphic computing promises to deliver intelligent systems that are sustainable, transparent, and widely accessible. A central challenge, however, is to identify a unifying theoretical framework capable of bridging these diverse disciplines. We argue that dynamical systems theory provides such a foundation. Rooted in differential calculus, it offers a principled language for modeling inference, learning, and control in both natural and artificial substrates. Within this framework, noise can be harnessed as a resource for learning, while differential genetic programming enables the discovery of dynamical systems that implement adaptive behaviors. Embracing this perspective paves the way toward emergent neuromorphic intelligence, where intelligent behavior arises from the dynamics of physical substrates, advancing both the science and sustainability of AI.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

GPUs running deep learning (DL) workloads are frequently underutilized. Collocating multiple DL training tasks on the same GPU can improve utilization but introduces two key risks: (1) out-of-memory (OOM) crashes for newly scheduled tasks, and (2) severe performance interference among co-running tasks, which can negate any throughput gains. These issues reduce system robustness, quality of service, and energy efficiency. We present CARMA, a task-level, collocation-aware resource management system for the server-scale. CARMA addresses collocation challenges via (1) fine-grained monitoring and bookkeeping of GPUs and a collocation risk analysis that filters out the high-risk GPUs; (2) task placement policies that cap GPU utilization to avoid OOMs and limit interference; (3) integration of GPU memory need estimators for DL tasks to minimize OOMs during collocation; and (4) a lightweight recovery method that relaunches jobs crashed due to OOMs. Our evaluation on a DL training workload derived from real-world traces shows that CARMA uses GPUs more efficiently by making more informed collocation decisions: for the best-performing collocation policy, CARMA increases GPU streaming multiprocessor (SM) utilization by 54%, the parallelism achieved per SM by 61%, and memory use by 62%. This results in a $\sim$35% and $\sim$15% reduction in the end-to-end execution time (makespan) and GPU energy consumption, respectively, for this workload.

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation trajectory as a function of the iterations, the proposed approach devises a surrogate version of the entire optimisation pipeline. First, the method predicts a quasi-optimal topology for a given problem configuration as a surrogate model of high-fidelity topologies optimised with the homogenisation method. This is achieved by means of a feed-forward net learning the mapping between the input parameters characterising the system setup and a latent space determined by encoder/decoder blocks reducing the dimensionality of the parametric topology optimisation problem and reconstructing a high-dimensional representation of the topology. Then, the predicted topology is used as an educated initial guess for a computationally efficient algorithm penalising the intermediate values of the design variable, while enforcing the governing equations of the system. This step allows the method to correct potential errors introduced by the surrogate model, eliminate artifacts, and refine the design in order to produce topologies consistent with the underlying physics. Different architectures are proposed and the approximation and generalisation capabilities of the resulting models are numerically evaluated. The quasi-optimal topologies allow to outperform the high-fidelity optimiser by reducing the average number of optimisation iterations by $53\%$ while achieving discrepancies below $4\%$ in the optimal value of the objective functional, even in the challenging scenario of testing the model to extrapolate beyond the training and validation domain.

The CHiME-7 and 8 distant speech recognition (DASR) challenges focus on multi-channel, generalizable, joint automatic speech recognition (ASR) and diarization of conversational speech. With participation from 9 teams submitting 32 diverse systems, these challenges have contributed to state-of-the-art research in the field. This paper outlines the challenges' design, evaluation metrics, datasets, and baseline systems while analyzing key trends from participant submissions. From this analysis it emerges that: 1) Most participants use end-to-end (e2e) ASR systems, whereas hybrid systems were prevalent in previous CHiME challenges. This transition is mainly due to the availability of robust large-scale pre-trained models, which lowers the data burden for e2e-ASR. 2) Despite recent advances in neural speech separation and enhancement (SSE), all teams still heavily rely on guided source separation, suggesting that current neural SSE techniques are still unable to reliably deal with complex scenarios and different recording setups. 3) All best systems employ diarization refinement via target-speaker diarization techniques. Accurate speaker counting in the first diarization pass is thus crucial to avoid compounding errors and CHiME-8 DASR participants especially focused on this part. 4) Downstream evaluation via meeting summarization can correlate weakly with transcription quality due to the remarkable effectiveness of large-language models in handling errors. On the NOTSOFAR-1 scenario, even systems with over 50% time-constrained minimum permutation WER can perform roughly on par with the most effective ones (around 11%). 5) Despite recent progress, accurately transcribing spontaneous speech in challenging acoustic environments remains difficult, even when using computationally intensive system ensembles.