The incorporation of LLMs in multi-agent systems (MASs) has the potential to significantly improve our ability to autonomously solve complex problems. However, such systems introduce unique challenges in monitoring, interpreting, and detecting system failures. Most existing MAS observability frameworks focus on analyzing each individual agent separately, overlooking failures associated with the entire MAS. To bridge this gap, we propose LumiMAS, a novel MAS observability framework that incorporates advanced analytics and monitoring techniques. The proposed framework consists of three key components: a monitoring and logging layer, anomaly detection layer, and anomaly explanation layer. LumiMAS's first layer monitors MAS executions, creating detailed logs of the agents' activity. These logs serve as input to the anomaly detection layer, which detects anomalies across the MAS workflow in real time. Then, the anomaly explanation layer performs classification and root cause analysis (RCA) of the detected anomalies. LumiMAS was evaluated on seven different MAS applications, implemented using two popular MAS platforms, and a diverse set of possible failures. The applications include two novel failure-tailored applications that illustrate the effects of a hallucination or bias on the MAS. The evaluation results demonstrate LumiMAS's effectiveness in failure detection, classification, and RCA.

Pollinating insects can obtain information from electric fields arising from flowers. The density and usefulness of electric information remain unknown. Here, we show that electric information can be used to reconstruct geometrical features of the field source. We develop an algorithm that infers the shapes of polarisable flowers from the electric field generated in response to a nearby charged arthropod. We computed the electric fields arising from arthropod flower interactions for varying petal geometries, and used these data to train a deep learning U Net model to recreate the floral shapes. The model accurately reconstructed diverse shapes, including more complex flower morphologies not included in training. Reconstruction performance peaked at an optimal arthropod flower distance, indicating distance dependent encoding of shape information. These findings indicate that electroreception can impart rich spatial detail, offering insights into the electric ecology of arthropods. Together, this work introduces a deep learning framework for solving the inverse electrostatic imaging problem, enabling object shape reconstruction directly from measured electric fields.

Independent Component Analysis (ICA) uses a measure of non-Gaussianity to identify latent sources from data and estimate their mixing coefficients (Shimizu et al., 2006). Meanwhile, higher-order Orthogonal Machine Learning (OML) exploits non-Gaussian treatment noise to provide more accurate estimates of treatment effects in the presence of confounding nuisance effects (Mackey et al., 2018). Remarkably, we find that the two approaches rely on the same moment conditions for consistent estimation. We then seize upon this connection to show how ICA can be effectively used for treatment effect estimation. Specifically, we prove that linear ICA can consistently estimate multiple treatment effects, even in the presence of Gaussian confounders, and identify regimes in which ICA is provably more sample-efficient than OML for treatment effect estimation. Our synthetic demand estimation experiments confirm this theory and demonstrate that linear ICA can accurately estimate treatment effects even in the presence of nonlinear nuisance.

As the data volume of astronomical imaging surveys rapidly increases, traditional methods for image anomaly detection, such as visual inspection by human experts, are becoming impractical. We introduce a machine-learning-based approach to detect poor-quality exposures in large imaging surveys, with a focus on the DECam Legacy Survey (DECaLS) in regions of low extinction (i.e., $E(B-V)<0.04$). Our semi-supervised pipeline integrates a vision transformer (ViT), trained via self-supervised learning (SSL), with a k-Nearest Neighbor (kNN) classifier. We train and validate our pipeline using a small set of labeled exposures observed by surveys with the Dark Energy Camera (DECam). A clustering-space analysis of where our pipeline places images labeled in ``good'' and ``bad'' categories suggests that our approach can efficiently and accurately determine the quality of exposures. Applied to new imaging being reduced for DECaLS Data Release 11, our pipeline identifies 780 problematic exposures, which we subsequently verify through visual inspection. Being highly efficient and adaptable, our method offers a scalable solution for quality control in other large imaging surveys.

The brain can only be fully understood through the lens of the behavior it generates -- a guiding principle in modern neuroscience research that nevertheless presents significant technical challenges. Many studies capture behavior with cameras, but video analysis approaches typically rely on specialized models requiring extensive labeled data. We address this limitation with BEAST(BEhavioral Analysis via Self-supervised pretraining of Transformers), a novel and scalable framework that pretrains experiment-specific vision transformers for diverse neuro-behavior analyses. BEAST combines masked autoencoding with temporal contrastive learning to effectively leverage unlabeled video data. Through comprehensive evaluation across multiple species, we demonstrate improved performance in three critical neuro-behavioral tasks: extracting behavioral features that correlate with neural activity, and pose estimation and action segmentation in both the single- and multi-animal settings. Our method establishes a powerful and versatile backbone model that accelerates behavioral analysis in scenarios where labeled data remains scarce.

Cross-Domain Sequential Recommendation (CDSR) predicts user behavior by leveraging historical interactions across multiple domains, focusing on modeling cross-domain preferences and capturing both intra- and inter-sequence item relationships. We propose LLM-Enhanced Multimodal Fusion for Cross-Domain Sequential Recommendation (LLM-EMF), a novel and advanced approach that enhances textual information with Large Language Models (LLM) knowledge and significantly improves recommendation performance through the fusion of visual and textual data. Using the frozen CLIP model, we generate image and text embeddings, thereby enriching item representations with multimodal data. A multiple attention mechanism jointly learns both single-domain and cross-domain preferences, effectively capturing and understanding complex user interests across diverse domains. Evaluations conducted on four e-commerce datasets demonstrate that LLM-EMF consistently outperforms existing methods in modeling cross-domain user preferences, thereby highlighting the effectiveness of multimodal data integration and its advantages in enhancing sequential recommendation systems. Our source code will be released.

Price signals from distribution networks (DNs) guide energy communities (ECs) in adjusting their energy usage, enabling effective coordination for reliable power system operation. However, this coordinated operation faces significant challenges due to the limited availability of ECs' internal information (i.e., only the aggregated energy usage of ECs is available to DNs), and the high computational burden of accounting for uncertainties and the associated risks through numerous scenarios. To address these challenges, we propose a quantum learning and estimation approach to enhance coordinated operation between DNs and ECs. Specifically, by leveraging advanced quantum properties such as quantum superposition and entanglement, we develop a hybrid quantum temporal convolutional network-long short-term memory (Q-TCN-LSTM) model to establish an end-to-end mapping between ECs' responses and the price incentives from DNs. Moreover, we develop a quantum estimation method based on quantum amplitude estimation (QAE) and two phase-rotation circuits to significantly accelerate the optimization process under numerous uncertainty scenarios. Numerical experiments demonstrate that, compared to classical neural networks, the proposed Q-TCN-LSTM model improves the mapping accuracy by 69.2\% while reducing the model size by 99.75\%. Compared to classical Monte Carlo simulation, QAE achieves comparable accuracy with a substantial reduction in computational resources. In addition, the estimated computation time for quantum learning and estimation on ideal quantum devices is over 90\% shorter than that of traditional methods.

Multi-modal medical image synthesis is pivotal for alleviating clinical data scarcity, yet existing methods fail to reconcile global anatomical consistency with high-fidelity local detail. We propose FermatSyn, which addresses three persistent limitations: (1)~a SAM2-based Prior Encoder that injects domain-aware anatomical knowledge via Lo-RA$^{+}$ efficient fine-tuning of a frozen SAM2 Vision Transformer; (2)~a Hierarchical Residual Downsampling Module (HRDM) coupled with a Cross-scale Integration Network (CIN) that preserves high-frequency lesion details and adaptively fuses global--local representations; and (3)~a continuity constrained Fermat Spiral Scanning strategy within a Bidirectional Fermat Scan Mamba (BFS-Mamba), constructing an approximately isotropic receptive field that substantially reduces the directional bias of raster or spiral serialization. Experiments on SynthRAD2023, BraTS2019, BraTS-MEN, and BraTS-MET show FermatSyn surpasses state-of-the-art methods in PSNR, SSIM, FID, and 3D structural consistency. Downstream segmentation on synthesized images yields no significant difference from real-image training ($p{>}0.05$), confirming clinical utility. Code will be released upon publication. \keywords{Medical image synthesis \and SAM2 \and Mamba \and Fermat spiral scanning \and Anatomical prior \and Cross-modal}

Despite recent advances in applying large language models (LLMs) and machine learning (ML) techniques to open radio access network (O-RAN), critical challenges remain, such as insufficient cooperation between radio access network (RAN) intelligent controllers (RICs), high computational demands hindering real-time decisions, and the lack of domain-specific finetuning. Therefore, this article introduces the LLM-empowered hierarchical RIC (LLM-hRIC) framework to improve the collaboration between RICs in O-RAN. The LLM-empowered non-real-time RIC (non-RT RIC) acts as a guider, offering a strategic guidance to the near-real-time RIC (near-RT RIC) using global network information. The RL-empowered near-RT RIC acts as an implementer, combining this guidance with local real-time data to make near-RT decisions. We evaluate the feasibility and performance of the LLM-hRIC framework in an integrated access and backhaul (IAB) network setting, and finally, discuss the open challenges of the LLM-hRIC framework for O-RAN.

Large language models (LLMs) excel at generating human-like responses but often struggle with interactive tasks that require access to real-time information. This limitation poses challenges in finance, where models must access up-to-date information, such as recent news or price movements, to support decision-making. To address this, we introduce Financial Agent, a knowledge-grounding approach for LLMs to handle financial queries using real-time text and tabular data. Our contributions are threefold: First, we develop a Financial Context Dataset of over 50,000 financial queries paired with the required context. Second, we develop FinBloom 7B, a custom 7 billion parameter LLM, by fine-tuning Bloom 7B on 14 million financial news articles from Reuters and Deutsche Presse-Agentur (DPA), alongside a random sample of 25% from 12 million Securities and Exchange Commission (SEC) filings. Third, we fine-tune FinBloom 7B using the Financial Context Dataset to serve as a Financial Agent. This agent generates relevant financial context, enabling efficient real-time data retrieval to answer user queries. By reducing latency and eliminating the need for users to manually provide accurate data, our approach significantly enhances the capability of LLMs to handle dynamic financial tasks. Our proposed approach makes real-time financial decisions, algorithmic trading and other related tasks streamlined, and is valuable in contexts with high-velocity data flows.

Diffusion Transformers (DiTs) have shown remarkable performance in generating high-quality videos. However, the quadratic complexity of 3D full attention remains a bottleneck in scaling DiT training, especially with high-definition, lengthy videos, where it can consume up to 95% of processing time and demand specialized context parallelism. This paper introduces DSV to accelerate video DiT training by leveraging the dynamic attention sparsity we empirically observe. DSV uses a two-stage algorithm to capture the dynamic sparsity patterns via low-rank based approximation of the original query and key. It employs custom kernels to efficiently identify critical key-value pairs and compute the sparse attention. To accommodate the new sparsity dimension, DSV adopts a hybrid sparsity-aware context parallelism that re-balances the skewed workload across attention heads and blocks due to sparsity heterogeneity. DSV achieves up to 3.02x higher training throughput, scaling to 128 GPUs and 520k token lengths, without quality loss.

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they do not address \emph{complexity}: for broad operator classes described only through regularity (e.g.\ uniform continuity or $C^r$-regularity), information-theoretic lower bounds imply that minimax-optimal NO approximation rates scale \emph{exponentially} in the reciprocal accuracy $1/\varepsilon$. This has shifted the focus of NO theory toward identifying additional problem-specific structure, beyond regularity, under which suitably tailored NO architectures can leverage to unlock polynomial scaling in $1/\varepsilon$. We exhibit the first polynomial-scaling regime for NO approximations of solution operators in stochastic analysis; by identifying structured families of \emph{non-Markovian} BSDEs with randomized terminal condition parameterized by the Sobolev-regular terminal condition and by Sobolev-regular additive nonlinear perturbations of the generator. We prove that their solution operator can be approximated (uniformly over the family) by a tailored NO whose number of trainable parameters grows \emph{polynomially} in $1/\varepsilon$. We unlock this polynomial scaling regime by \emph{informing the NO's inductive bias} by factoring out the singular part of the associated semilinear elliptic PDE Green's function and by incorporating the Doléans--Dade exponential of the BSDE's common non-Markovian factor into the NO's decoding layers. As a byproduct, we extend polynomial-scaling guarantees from families of linear elliptic PDEs on regular domains to the semilinear setting.

Integrative analysis of multiple heterogeneous datasets has become standard practice in many research fields, especially in single-cell genomics and medical informatics. Existing approaches oftentimes suffer from limited power in capturing nonlinear structures, insufficient account of noisiness and effects of high-dimensionality, lack of adaptivity to signals and sample sizes imbalance, and their results are sometimes difficult to interpret. To address these limitations, we propose a novel kernel spectral method that achieves joint embeddings of two independently observed high-dimensional noisy datasets. The proposed method automatically captures and leverages possibly shared low-dimensional structures across datasets to enhance embedding quality. The obtained low-dimensional embeddings can be utilized for many downstream tasks such as simultaneous clustering, data visualization, and denoising. The proposed method is justified by rigorous theoretical analysis. Specifically, we show the consistency of our method in recovering the low-dimensional noiseless signals, and characterize the effects of the signal-to-noise ratios on the rates of convergence. Under a joint manifolds model framework, we establish the convergence of ultimate embeddings to the eigenfunctions of some newly introduced integral operators. These operators, referred to as duo-landmark integral operators, are defined by the convolutional kernel maps of some reproducing kernel Hilbert spaces (RKHSs). These RKHSs capture the either partially or entirely shared underlying low-dimensional nonlinear signal structures of the two datasets. Our numerical experiments and analyses of two single-cell omics datasets demonstrate the empirical advantages of the proposed method over existing methods in both embeddings and several downstream tasks.

Applying advanced digital technologies such as artificial intelligence (AI), blockchain (BLC), bigdata analytics (BDA) and digital twin (DT)/simulations to enhance supply chain resilience (SCRes) has been widely discussed in light of the global pandemic, regional conflicts, and the technology revolution such as Industry 4.0 and 5.0. Previous studies are limited at the conceptual level as the proactive SCRes measure with a standalone fashion. The intelligent recommendation system (IRS) obtains the capabilities for enhancing SCRes as a reactive digital measure. However, the utilization of the IRS as the SCRes enhancement tool is neglected, investigation on implementing the IRS for the SC disruption response is yet to come. To close these gaps, a data-driven supply chain disruption response IRS baseline framework was proposed by this research as an initial SCRes reactive solution. To guarantee the reliability of the proposed IRS as a stable, secure, and resilient decision support system, blockchain technology is integrated into the baseline architecture. The BLC-IRS framework is demonstrated with user prototype and industrial case to present its executable functions. A system dynamics (SD) simulation model is adopted to validate the BLC-IRS framework, the simulation results indicated that our proposed BLC-IRS can be implemented as an effective a SC disruption response measure. Our developed BLC-IRS contributes an executable SCRes digital solution with synthetic technologies as a reactive SCRes measure, enabled users to mitigate the firm and partial network level disruption in an agile and safe manner.

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no longer apply. These difficulties are particularly pronounced for spatio-temporal data, which exhibit dependencies across both space and time and are often characterized by nonlinear dynamics, time variance, and missing observations, hence calling for new accuracy assessment methodologies. This paper introduces a residual correlation analysis framework for assessing the optimality of spatio-temporal relational-enabled neural predictive models, notably in settings with incomplete and heterogeneous data. By leveraging the principle that residual correlation indicates information not captured by the model, enabling the identification and localization of regions in space and time where predictive performance can be improved. A strength of the proposed approach is that it operates under minimal assumptions, allowing also for robust evaluation of deep learning models applied to multivariate time series, even in the presence of missing and heterogeneous data. In detail, the methodology constructs tailored spatio-temporal graphs to encode sparse spatial and temporal dependencies and employs asymptotically distribution-free summary statistics to detect time intervals and spatial regions where the model underperforms. The effectiveness of what proposed is demonstrated through experiments on both synthetic and real-world datasets using state-of-the-art predictive models.

Solar energy is one of the most dependable renewable energy technologies, as it is feasible almost everywhere globally. However, improving the efficiency of a solar PV system remains a significant challenge. To enhance the robustness of the solar system, this paper proposes a trained convolutional neural network (CNN) based fault detection scheme to divide the images of photovoltaic modules. For binary classification, the algorithm classifies the input images of PV cells into two categories (i.e. faulty or normal). To further assess the network's capability, the defective PV cells are organized into shadowy, cracked, or dusty cells, and the model is utilized for multiple classifications. The success rate for the proposed CNN model is 91.1% for binary classification and 88.6% for multi-classification. Thus, the proposed trained CNN model remarkably outperforms the CNN model presented in a previous study which used the same datasets. The proposed CNN-based fault detection model is straightforward, simple and effective and could be applied in the fault detection of solar panel.

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many applications, particularly in physical sciences and engineering, but also in areas such as geostatistics and neuroscience, invariance to symmetries is one of the most fundamental forms of prior information one can consider. The invariance of a Gaussian process' covariance to such symmetries gives rise to the most natural generalization of the concept of stationarity to such spaces. In this work, we develop constructive and practical techniques for building stationary Gaussian processes on a very large class of non-Euclidean spaces arising in the context of symmetries. Our techniques make it possible to (i) calculate covariance kernels and (ii) sample from prior and posterior Gaussian processes defined on such spaces, both in a practical manner. This work is split into two parts, each involving different technical considerations: part I studies compact spaces, while part II studies non-compact spaces possessing certain structure. Our contributions make the non-Euclidean Gaussian process models we study compatible with well-understood computational techniques available in standard Gaussian process software packages, thereby making them accessible to practitioners.

Wavefunction-based quantum methods are some of the most accurate tools for predicting and analyzing the electronic structure of molecules, in particular for accounting for dynamical electron correlation. However, most methods of including dynamical correlation beyond the simple second-order Møller-Plesset perturbation theory (MP2) level are too computationally expensive to apply to large molecules. Approximations which reduce scaling with system size are a potential remedy, such as the tensor hyper-contraction (THC) technique of Hohenstein et al., but also result in additional sources of error. In this work, we correct errors in THC-approximated methods using machine learning. Specifically, we apply THC to third-order Møller-Plesset theory (MP3) as a simplified model for coupled cluster with single and double excitations (CCSD), and train several regression models on observed THC errors from the Main Group Chemistry Database (MGCDB84). We compare performance of multiple linear regression models and non-linear Kernel Ridge regression models. We also investigate correlation procedures using absolute and relative corrections and evaluate the corrections for both molecule and reaction energies. We discuss the potential for using regression techniques to correct THC-MP3 errors by comparing it to the "canonical" MP3 reference values and find the optimum technique based on accuracy. We find that non-linear regression models reduced root mean squared errors between THC- and canonical MP3 by a factor of 6-9$\times$ for total molecular energies and 2-3$\times$ for reaction energies.

Symbolic regression has recently gained traction in AI-driven scientific discovery, aiming to recover explicit closed-form expressions from data that reveal underlying physical laws. Despite recent advances, existing methods remain dominated by heuristic search algorithms or data-intensive approaches that assume low-noise regimes and lack principled uncertainty quantification. Fully probabilistic formulations are scarce, and existing Markov chain Monte Carlo-based Bayesian methods often struggle to efficiently explore the highly multimodal combinatorial space of symbolic expressions. We introduce VaSST, a scalable probabilistic framework for symbolic regression based on variational inference. VaSST employs a continuous relaxation of symbolic expression trees, termed soft symbolic trees, where discrete operator and feature assignments are replaced by soft distributions over allowable components. This relaxation transforms the combinatorial search over an astronomically large symbolic space into an efficient gradient-based optimization problem while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling principled uncertainty quantification. Across simulated experiments and Feynman Symbolic Regression Database within SRBench, VaSST achieves superior performance in both structural recovery and predictive accuracy compared to state-of-the-art symbolic regression methods.

Automated placement of components on printed circuit boards (PCBs) is a critical stage in placement layout design. While reinforcement learning (RL) has been successfully applied to system-on-chip IP block placement and chiplet arrangement in complex packages, PCB component placement presents unique challenges due to several factors: variation in component sizes, single- and double-sided boards, wirelength constraints, board constraints, and non-overlapping placement requirements. In this work, we adopt a component-centric layout for automating PCB component placement using RL: first, the main component is fixed at the center, while passive components are placed in proximity to the pins of the main component. Free space around the main component is discretized, drastically reducing the search space while still covering all feasible placement; second, we leverage prior knowledge that each passive's position has to be near to its corresponding voltage source. This allows us to design the reward function which avoids wasted exploration of infeasible or irrelevant search space. Using the component centric layout, we implemented different methods including Deep Q-Network, Actor-Critic algorithm and Simulated Annealing. Evaluation on over nine real-world PCBs of varying complexity shows that our best proposed method approaches near human-like placements in terms of wirelength and feasibility.

Curation is a significant barrier to using 'big data' radiotherapy planning databases of 100,000+ patients. Anatomic site stratification is essential for downstream analyses, but current methods rely on inconsistent plan labels or target nomenclature, which is unreliable for multi-institutional data. We developed software to automate labeling by inferring anatomic regions directly from dose-volume overlap with deep-learning segmentations, eliminating metadata reliance. The software processes DICOM files in bulk, utilizing deep learning to segment 118 structures (organs, glands, and bones) categorized into six regions: Cranial, Head and Neck, Pelvis, Abdomen, Thorax, Extremity. The 85% and 50% isodose lines are converted to structures to compute organ-specific dose-overlap metrics. Plans are assigned ranked regional labels based on these intersections. The algorithm was refined using 109 expert-labeled cases and validated on 100 consecutive clinical plans. On the 100-plan test dataset, the algorithm achieved 91% Exact Accuracy (matching all expert labels and order), 94% Top-2 Accuracy (matching the top two expert regions regardless of order), and 95% Top-1 Accuracy (matching the primary expert label). The automated workflow demonstrated high accuracy and robustness. The 95% Top-1 Accuracy is particularly significant, as it enables reliable querying of plans based on the primary treatment site. Detailed analysis of the few mismatched cases showed most were treated areas at the border between anatomic regions and were ambiguous between these two regions in a common-sense interpretation. This algorithm provides a scalable, standardized solution for curating the large, multi-institutional datasets required for 'big data' in radiotherapy and provides an important complement to text-based approaches.

We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem, existing guarantees typically rely on structural assumptions about the domain or model geometry. We instead provide a general, information-theoretic characterization that depends only on the relationship between the proposal and target distributions. Our analysis introduces the integrated coverage profile, a functional that quantifies how much target mass lies in regions where the density ratio is large. We show that integrated coverage tightly characterizes the sample complexity of multiplicative partition function estimation and provide matching lower bounds. We further express these bounds in terms of $f$-divergences, yielding sharp phase transitions depending on the growth rate of f and recovering classical results as a special case while extending to heavy-tailed regimes. Matching lower bounds establish tightness in all regimes. As applications, we derive improved finite-sample guarantees for importance sampling and self-normalized importance sampling, and we show a strict separation between the complexity of approximate sampling and counting under the same divergence constraints. Our results unify and generalize prior analyses of importance sampling, rejection sampling, and heavy-tailed mean estimation, providing a minimal-assumption theory of partition function estimation. Along the way we introduce new technical tools including new connections between coverage and $f$-divergences as well as a generalization of the classical Paley-Zygmund inequality.

Foundation models pretrained on large-scale 3D medical imaging data face challenges when adapted to multiple downstream tasks under continual learning with limited labeled data. We address few-shot continual learning for 3D brain MRI by combining a frozen pretrained backbone with task-specific Low-Rank Adaptation (LoRA) modules. Tasks arrive sequentially -- tumor segmentation (BraTS) and brain age estimation (IXI) -- with no replay of previous task data. Each task receives a dedicated LoRA adapter; only the adapter and task-specific head are trained while the backbone remains frozen, thereby eliminating catastrophic forgetting by design (BWT=0). In continual learning, sequential full fine-tuning suffers severe forgetting (T1 Dice drops from 0.80 to 0.16 after T2), while sequential linear probing achieves strong T1 (Dice 0.79) but fails on T2 (MAE 1.45). Our LoRA approach achieves the best balanced performance across both tasks: T1 Dice 0.62$\pm$0.07, T2 MAE 0.16$\pm$0.05, with zero forgetting and $<$0.1\% trainable parameters per task, though with noted systematic age underestimation in T2 (Wilcoxon $p<0.001$). Frozen foundation models with task-specific LoRA adapters thus offer a practical solution when both tasks must be maintained under few-shot continual learning.

Deep generative models (DGMs) compress high-dimensional data but often entangle distinct physical factors in their latent spaces. We present an auxiliary-variable-guided framework for disentangling representations of thermal Sunyaev-Zel'dovich (tSZ) maps of dark matter halos. We introduce halo mass and concentration as auxiliary variables and apply a lightweight alignment penalty to encourage latent dimensions to reflect these physical quantities. To generate sharp and realistic samples, we extend latent conditional flow matching (LCFM), a state-of-the-art generative model, to enforce disentanglement in the latent space. Our Disentangled Latent-CFM (DL-CFM) model recovers the established mass-concentration scaling relation and identifies latent space outliers that may correspond to unusual halo formation histories. By linking latent coordinates to interpretable astrophysical properties, our method transforms the latent space into a diagnostic tool for cosmological structure. This work demonstrates that auxiliary guidance preserves generative flexibility while yielding physically meaningful, disentangled embeddings, providing a generalizable pathway for uncovering independent factors in complex astronomical datasets.

Medical image segmentation models are typically optimised with voxel-wise losses that constrain predictions only in the output space. This leaves latent feature representations largely unconstrained, potentially limiting generalisation. We propose {SegReg}, a latent-space regularisation framework that operates on feature maps of U-Net models to encourage structured embeddings while remaining fully compatible with standard segmentation losses. Integrated with the nnU-Net framework, we evaluate SegReg on prostate, cardiac, and hippocampus segmentation and demonstrate consistent improvements in domain generalisation. Furthermore, we show that explicit latent regularisation improves continual learning by reducing task drift and enhancing forward transfer across sequential tasks without adding memory or any extra parameters. These results highlight latent-space regularisation as a practical approach for building more generalisable and continual-learning-ready models.

We introduce spiky rank, a new matrix parameter that enhances blocky rank by combining the combinatorial structure of the latter with linear-algebraic flexibility. A spiky matrix is block-structured with diagonal blocks that are arbitrary rank-one matrices, and the spiky rank of a matrix is the minimum number of such matrices required to express it as a sum. This measure extends blocky rank to real matrices and is more robust for problems with both combinatorial and algebraic character. Our conceptual contribution is as follows: we propose spiky rank as a well-behaved candidate matrix complexity measure and demonstrate its potential through applications. We show that large spiky rank implies high matrix rigidity, and that spiky rank lower bounds yield lower bounds for depth-2 ReLU circuits, the basic building blocks of neural networks. On the technical side, we establish tight bounds for random matrices and develop a framework for explicit lower bounds, applying it to Hamming distance matrices and spectral expanders. Finally, we relate spiky rank to other matrix parameters, including blocky rank, sparsity, and the $γ_2$-norm.

Spatially variant dynamic convolution provides a principled approach of integrating spatial adaptivity into deep neural networks. However, mainstream designs in medical segmentation commonly generate dynamic kernels through average pooling, which implicitly collapses high-frequency spatial details into a coarse, spatially-compressed representation, leading to over-smoothed predictions that degrade the fidelity of fine-grained clinical structures. To address this limitation, we propose a novel Structure-Guided Dynamic Convolution (SGDC) mechanism, which leverages an explicitly supervised structure-extraction branch to guide the generation of dynamic kernels and gating signals for structure-aware feature modulation. Specifically, the high-fidelity boundary information from this auxiliary branch is fused with semantic features to enable spatially-precise feature modulation. By replacing context aggregation with pixel-wise structural guidance, the proposed design effectively prevents the information loss introduced by average pooling. Experimental results show that SGDC achieves state-of-the-art performance on ISIC 2016, PH2, ISIC 2018, and CoNIC datasets, delivering superior boundary fidelity by reducing the Hausdorff Distance (HD95) by 2.05, and providing consistent IoU gains of 0.99\%-1.49\% over pooling-based baselines. Moreover, the mechanism exhibits strong potential for extension to other fine-grained, structure-sensitive vision tasks, such as small-object detection, offering a principled solution for preserving structural integrity in medical image analysis. To facilitate reproducibility and encourage further research, the implementation code for both our SGE and SGDC modules has been is publicly released at https://github.com/solstice0621/SGDC.

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements in isolation, implicitly accounting for the complex relationships between them. Graph neural networks, in contrast, explicitly model these relationships through higher order interactions but are often unable to adequately capture their evolution over time, limiting their use for predicting the next interaction. To fill this gap, we present a new framework that combines transformers and graph neural networks and aligns different representations for solving next-item prediction task. Our solution simultaneously encodes structural dependencies in the interaction graph and tracks their dynamic change. Experimental results on a number of open datasets demonstrate that the proposed framework consistently outperforms both pure sequential and graph approaches in terms of recommendation quality, as well as recent methods that combine both types of signals.

Can Machine Learning (ML) autonomously recover interpretable mathematical structure from raw numerical data? We aim to answer this question using the classification of real-root configurations of polynomials up to degree five as a structured benchmark. We tested an extensive set of ML models, including decision trees, logistic regression, support vector machines, random forest, gradient boosting, XGBoost, symbolic regression, and neural networks. Neural networks achieved strong in-distribution performance on quintic classification using raw coefficients alone (84.3% + or - 0.9% balanced accuracy), whereas decision trees perform substantially worse (59.9% + or - 0.9\%). However, when provided with an explicit feature capturing sign changes at critical points, decision trees match neural performance (84.2% + or - 1.2%) and yield explicit classification rules. Knowledge distillation reveals that this single invariant accounts for 97.5% of the extracted decision structure. Out-of-distribution, data-efficiency, and noise robustness analyses indicate that neural networks learn continuous, data-dependent geometric approximations of the decision boundary rather than recovering scale-invariant symbolic rules. This distinction between geometric approximation and symbolic invariance explains the gap between predictive performance and interpretability observed across models. Although high predictive accuracy is attainable, we find no evidence that the evaluated ML models autonomously recover discrete, human-interpretable mathematical rules from raw coefficients. These results suggest that, in structured mathematical domains, interpretability may require explicit structural inductive bias rather than purely data-driven approximation.

Lightweight neural network accelerators are essential for edge devices with limited resources and power constraints. While quantization and binarization can efficiently reduce hardware cost, they still rely on the conventional Artificial Neural Network (ANN) computation pattern. The recently proposed Kolmogorov-Arnold Network (KAN) presents a novel network paradigm built on learnable nonlinear functions. However, it is computationally expensive for hardware deployment. Inspired by KAN, we propose BiKA, a multiply-free architecture that replaces nonlinear functions with binary, learnable thresholds, introducing an extremely lightweight computational pattern that requires only comparators and accumulators. Our FPGA prototype on Ultra96-V2 shows that BiKA reduces hardware resource usage by 27.73% and 51.54% compared with binarized and quantized neural network systolic array accelerators, while maintaining competitive accuracy. BiKA provides a promising direction for hardware-friendly neural network design on edge devices.