Optic deconvolution in light microscopy (LM) refers to recovering the object details from images, revealing the ground truth of samples. Traditional explicit methods in LM rely on the point spread function (PSF) during image acquisition. Yet, these approaches often fall short due to inaccurate PSF models and noise artifacts, hampering the overall restoration quality. In this paper, we approached the optic deconvolution as an inverse problem. Motivated by the nonstandard-form compression scheme introduced by Beylkin, Coifman, and Rokhlin (BCR), we proposed an innovative physics-informed neural network Multi-Stage Residual-BCR Net (m-rBCR) to approximate the optic deconvolution. We validated the m-rBCR model on four microscopy datasets - two simulated microscopy datasets from ImageNet and BioSR, real dSTORM microscopy images, and real widefield microscopy images. In contrast to the explicit deconvolution methods (e.g. Richardson-Lucy) and other state-of-the-art NN models (U-Net, DDPM, CARE, DnCNN, ESRGAN, RCAN, Noise2Noise, MPRNet, and MIMO-U-Net), the m-rBCR model demonstrates superior performance to other candidates by PSNR and SSIM in two real microscopy datasets and the simulated BioSR dataset. In the simulated ImageNet dataset, m-rBCR ranks the second-best place (right after MIMO-U-Net). With the backbone from the optical physics, m-rBCR exploits the trainable parameters with better performances (from ~30 times fewer than the benchmark MIMO-U-Net to ~210 times than ESRGAN). This enables m-rBCR to achieve a shorter runtime (from ~3 times faster than MIMO-U-Net to ~300 times faster than DDPM). To summarize, by leveraging physics constraints our model reduced potentially redundant parameters significantly in expertise-oriented NN candidates and achieved high efficiency with superior performance.

Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the (weighted) network and the interaction kernel, which determine, respectively, which agents are interacting and the rules of such interactions. Our estimator is based on a non-convex optimization problem, and we investigate two approaches to solve it: one based on an alternating least squares (ALS) algorithm, and another based on a new algorithm named operator regression with alternating least squares (ORALS). Both algorithms are scalable to large ensembles of data trajectories. We establish coercivity conditions guaranteeing identifiability and well-posedness. The ALS algorithm appears statistically efficient and robust even in the small data regime, but lacks performance and convergence guarantees. The ORALS estimator is consistent and asymptotically normal under a coercivity condition. We conduct several numerical experiments ranging from Kuramoto particle systems on networks to opinion dynamics in leader-follower models.

MALA is a popular gradient-based Markov chain Monte Carlo method to access the Gibbs-posterior distribution. Stochastic MALA (sMALA) scales to large data sets, but changes the target distribution from the Gibbs-posterior to a surrogate posterior which only exploits a reduced sample size. We introduce a corrected stochastic MALA (csMALA) with a simple correction term for which distance between the resulting surrogate posterior and the original Gibbs-posterior decreases in the full sample size while retaining scalability. In a nonparametric regression model, we prove a PAC-Bayes oracle inequality for the surrogate posterior. Uncertainties can be quantified by sampling from the surrogate posterior. Focusing on Bayesian neural networks, we analyze the diameter and coverage of credible balls for shallow neural networks and we show optimal contraction rates for deep neural networks. Our credibility result is independent of the correction and can also be applied to the standard Gibbs-posterior. A simulation study in a high-dimensional parameter space demonstrates that an estimator drawn from csMALA based on its surrogate Gibbs-posterior indeed exhibits these advantages in practice.

In the past decades, automated high-content microscopy demonstrated its ability to deliver large quantities of image-based data powering the versatility of phenotypic drug screening and systems biology applications. However, as the sizes of image-based datasets grew, it became infeasible for humans to control, avoid and overcome the presence of imaging and sample preparation artefacts in the images. While novel techniques like machine learning and deep learning may address these shortcomings through generative image inpainting, when applied to sensitive research data this may come at the cost of undesired image manipulation. Undesired manipulation may be caused by phenomena such as neural hallucinations, to which some artificial neural networks are prone. To address this, here we evaluate the state-of-the-art inpainting methods for image restoration in a high-content fluorescence microscopy dataset of cultured cells with labelled nuclei. We show that architectures like DeepFill V2 and Edge Connect can faithfully restore microscopy images upon fine-tuning with relatively little data. Our results demonstrate that the area of the region to be restored is of higher importance than shape. Furthermore, to control for the quality of restoration, we propose a novel phenotype-preserving metric design strategy. In this strategy, the size and count of the restored biological phenotypes like cell nuclei are quantified to penalise undesirable manipulation. We argue that the design principles of our approach may also generalise to other applications.

Recent advancements in Graph Neural Networks (GNN) have facilitated their widespread adoption in various applications, including recommendation systems. GNNs have proven to be effective in addressing the challenges posed by recommendation systems by efficiently modeling graphs in which nodes represent users or items and edges denote preference relationships. However, current GNN techniques represent nodes by means of a single static vector, which may inadequately capture the intricate complexities of users and items. To overcome these limitations, we propose a solution integrating a cutting-edge model inspired by category theory: Sheaf4Rec. Unlike single vector representations, Sheaf Neural Networks and their corresponding Laplacians represent each node (and edge) using a vector space. Our approach takes advantage from this theory and results in a more comprehensive representation that can be effectively exploited during inference, providing a versatile method applicable to a wide range of graph-related tasks and demonstrating unparalleled performance. Our proposed model exhibits a noteworthy relative improvement of up to 8.53% on F1-Score@10 and an impressive increase of up to 11.29% on NDCG@10, outperforming existing state-of-the-art models such as Neural Graph Collaborative Filtering (NGCF), KGTORe and other recently developed GNN-based models. In addition to its superior predictive capabilities, Sheaf4Rec shows remarkable improvements in terms of efficiency: we observe substantial runtime improvements ranging from 2.5% up to 37% when compared to other GNN-based competitor models, indicating a more efficient way of handling information while achieving better performance. Code is available at https://github.com/antoniopurificato/Sheaf4Rec.

Feature importance inference is critical for the interpretability and reliability of machine learning models. There has been increasing interest in developing model-agnostic approaches to interpret any predictive model, often in the form of feature occlusion or leave-one-covariate-out (LOCO) inference. Existing methods typically make limiting distributional assumptions, modeling assumptions, and require data splitting. In this work, we develop a novel, mostly model-agnostic, and distribution-free inference framework for feature importance in regression or classification tasks that does not require data splitting. Our approach leverages a form of random observation and feature subsampling called minipatch ensembles; it utilizes the trained ensembles for inference and requires no model-refitting or held-out test data after training. We show that our approach enjoys both computational and statistical efficiency as well as circumvents interpretational challenges with data splitting. Further, despite using the same data for training and inference, we show the asymptotic validity of our confidence intervals under mild assumptions. Additionally, we propose theory-supported solutions to critical practical issues including vanishing variance for null features and inference after data-driven tuning for hyperparameters. We demonstrate the advantages of our approach over existing methods on a series of synthetic and real data examples.

We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $σ^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $κ$, we prove that $T$ iterations of SGD with exponentially decreasing step-sizes and knowledge of the smoothness can achieve an $\tilde{O} \left(\exp \left( \frac{-T}κ \right) + \frac{σ^2}{T} \right)$ rate, without knowing $σ^2$. In order to be adaptive to the smoothness, we use a stochastic line-search (SLS) and show (via upper and lower-bounds) that SGD with SLS converges at the desired rate, but only to a neighbourhood of the solution. On the other hand, we prove that SGD with an offline estimate of the smoothness converges to the minimizer. However, its rate is slowed down proportional to the estimation error. Next, we prove that SGD with Nesterov acceleration and exponential step-sizes (referred to as ASGD) can achieve the near-optimal $\tilde{O} \left(\exp \left( \frac{-T}{\sqrtκ} \right) + \frac{σ^2}{T} \right)$ rate, without knowledge of $σ^2$. When used with offline estimates of the smoothness and strong-convexity, ASGD still converges to the solution, albeit at a slower rate. We empirically demonstrate the effectiveness of exponential step-sizes coupled with a novel variant of SLS.

In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be learned sufficiently well. We introduce a general procedure based on persistent homology to investigate topological invariants of the manifold on which we suspect the data set. We specify the required dimensions precisely, assuming that there is a smooth manifold on or near which the data are located. Furthermore, we require that this space is connected and has a commutative group structure in the mathematical sense. These assumptions allow us to derive a decomposition of the underlying space whose topology is well known. We use the representatives of the $k$-dimensional homology groups from the persistence landscape to determine an integer dimension for this decomposition. This number is the dimension of the embedding that is capable of capturing the topology of the data manifold. We derive the theory and validate it experimentally on toy data sets.

In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact calculating the persistent homology on it after each iteration to capture the changing topology of the data. The boundary points are identified as critical. The Bottleneck and Wasserstein distance serve as a measure of quality between the original point set and the interpolation. If the norm of two distances exceeds a heuristically determined threshold, the algorithm terminates. We give the theoretical basis for this approach and justify its validity with numerical experiments.

Adversarial-example-based fingerprinting approaches, which leverage the decision boundary characteristics of deep neural networks (DNNs) to craft fingerprints, have proven effective for model ownership protection. However, a fundamental challenge remains unresolved: how far a fingerprint should be placed from the decision boundary to simultaneously satisfy two essential properties, i.e., robustness and uniqueness, for effective and reliable ownership protection. Despite the importance of the fingerprint-to-boundary distance, existing works lack a theoretical solution and instead rely on empirical heuristics, which may violate either robustness or uniqueness properties. We propose AnaFP, an analytical fingerprinting scheme that constructs fingerprints under theoretical guidance. Specifically, we formulate fingerprint generation as controlling the fingerprint-to-boundary distance through a tunable stretch factor. To ensure both robustness and uniqueness, we mathematically formalize these properties that determine the lower and upper bounds of the stretch factor. These bounds jointly define an admissible interval within which the stretch factor must lie, thereby establishing a theoretical connection between the two constraints and the fingerprint-to-boundary distance. To enable practical fingerprint generation, we approximate the original (infinite) sets of pirated and independently trained models using two finite surrogate model pools and employ a quantile-based relaxation strategy to relax the derived bounds. Due to the circular dependency between the lower bound and the stretch factor, we apply grid search over the admissible interval to determine the most feasible stretch factor. Extensive experimental results show that AnaFP consistently outperforms prior methods, achieving effective ownership verification across diverse model architectures and model modification attacks.

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead of the entire noising path, that allows efficient training of standard generative modeling architectures with clear probabilistic interpretation. Our experiments on large-vocabulary discrete generation tasks suggest that the proposed framework outperforms existing discrete diffusion methods in terms of training efficiency and generation quality, and beats autoregressive models for the first time at this scale. We provide the code along with a blog post on the project page : \href{https://oussamazekri.fr/gdds}{https://oussamazekri.fr/gdds}.

We present FinRL-X, a modular and deployment-consistent trading architecture that unifies data processing, strategy construction, backtesting, and broker execution under a weight-centric interface. While existing open-source platforms are often backtesting- or model-centric, they rarely provide system-level consistency between research evaluation and live deployment. FinRL-X addresses this gap through a composable strategy pipeline that integrates stock selection, portfolio allocation, timing, and portfolio-level risk overlays within a unified protocol. The framework supports both rule-based and AI-driven components, including reinforcement learning allocators and LLM-based sentiment signals, without altering downstream execution semantics. FinRL-X provides an extensible foundation for reproducible, end-to-end quantitative trading research and deployment. The official FinRL-X implementation is available at https://github.com/AI4Finance-Foundation/FinRL-Trading.

Understanding human intent is a high-level cognitive challenge for Large Language Models (LLMs), requiring sophisticated reasoning over noisy, conflicting, and non-linear discourse. While LLMs excel at following individual instructions, their ability to distill Collective Intent - the process of extracting consensus, resolving contradictions, and inferring latent trends from multi-source public discussions - remains largely unexplored. To bridge this gap, we introduce COIN-BENCH, a dynamic, real-world, live-updating benchmark specifically designed to evaluate LLMs on collective intent understanding within the consumer domain. Unlike traditional benchmarks that focus on transactional outcomes, COIN-BENCH operationalizes intent as a hierarchical cognitive structure, ranging from explicit scenarios to deep causal reasoning. We implement a robust evaluation pipeline that combines a rule-based method with an LLM-as-the-Judge approach. This framework incorporates COIN-TREE for hierarchical cognitive structuring and retrieval-augmented verification (COIN-RAG) to ensure expert-level precision in analyzing raw, collective human discussions. An extensive evaluation of 20 state-of-the-art LLMs across four dimensions - depth, breadth, informativeness, and correctness - reveals that while current models can handle surface-level aggregation, they still struggle with the analytical depth required for complex intent synthesis. COIN-BENCH establishes a new standard for advancing LLMs from passive instruction followers to expert-level analytical agents capable of deciphering the collective voice of the real world. See our project page on COIN-BENCH.

Jet flavor tagging plays an important role in precise Standard Model measurement enabling the extraction of mass dependence in jet-quark interaction and quark-gluon plasma (QGP) interactions. They also enable inferring the nature of particles produced in high-energy particle collisions that contain heavy quarks. The classification of bottom jets is vital for exploring new Physics scenarios in proton-proton collisions. In this research, we present a hybrid deep learning architecture that integrates edge convolutions with transformer self-attention mechanisms, into one single architecture called the Edge Convolution Transformer (ECT) model for bottom-quark jet tagging. ECT processes track-level features (impact parameters, momentum, and their significances) alongside jet-level observables (vertex information and kinematics) to achieve state-of-the-art performance. The study utilizes the ATLAS simulation dataset. We demonstrate that ECT achieves 0.9333 AUC for b-jet versus combined charm and light jet discrimination, surpassing ParticleNet (0.8904 AUC) and the pure transformer baseline (0.9216 AUC). The model maintains inference latency below 0.060 ms per jet on modern GPUs, meeting the stringent requirements for real-time event selection at the LHC. Our results demonstrate that hybrid architectures combining local and global features offer superior performance for challenging jet classification tasks. The proposed architecture achieves good results in b-jet tagging, particularly excelling in charm jet rejection (the most challenging task), while maintaining competitive light-jet discrimination comparable to pure transformer models.

Context: Static analysis captures software engineering knowledge and alerts on possibly problematic patterns. Previous work showed that they indeed have predictive power for various problems. However, the impact of removing the alerts is unclear. Aim: We would like to evaluate the impact of alert removals on code complexity and the tendency to bugs. Method: We evaluate the impact of removing alerts using three complementary methods. 1. We conducted a randomized controlled trial and built a dataset of 521 manual alert-removing interventions 2. We profiled intervention-like events using labeling functions. We applied these labeling functions to code commits, found intervention-like natural events, and used them to analyze the impact on the tendency to bugs. 3. We built a dataset of 8,245 alert removals, more than 15 times larger than our dataset of manual interventions. We applied supervised learning to the alert removals, aiming to predict their impact on the tendency to bugs. Results: We identified complexity-reducing interventions that reduce the probability of future bugs. Such interventions are relevant to 33\% of Python files and might reduce the tendency to bugs by 5.5 percentage points. Conclusions: We presented methods to evaluate the impact of interventions. The methods can identify a large number of natural interventions that are highly needed in causality research in many domains.

Variational Quantum Algorithms (VQAs) have been extensively researched for applications in Quantum Machine Learning (QML), Optimization, and Molecular simulations. Although designed for Noisy Intermediate-Scale Quantum (NISQ) devices, VQAs are predominantly evaluated classically due to uncertain results on noisy devices and limited resource availability. Raising concern over the reproducibility of simulated VQAs on noisy hardware. While prior studies indicate that VQAs may exhibit noise resilience in specific parameterized shallow quantum circuits, there are no definitive measures to establish what defines a shallow circuit or the optimal circuit depth for VQAs on a noisy platform. These challenges extend naturally to Variational Quantum Classification (VQC) algorithms, a subclass of VQAs for supervised learning. In this article, we propose a relative entropy-based metric to verify whether a VQC model would perform similarly on a noisy device as it does on simulations. We establish a strong correlation between the average relative entropy difference in classes, transpilation circuit depth, and their performance difference on a noisy quantum device. Our results further indicate that circuit depth alone is insufficient to characterize shallow circuits. We present empirical evidence to support these assertions across a diverse array of techniques for implementing VQC, datasets, and multiple noisy quantum devices.

Large Language Models are increasingly being considered for deployment in safety-critical military applications. However, current benchmarks suffer from structural blindspots that systematically overestimate model capabilities in real-world tactical scenarios. Existing frameworks typically ignore strict legal constraints based on International Humanitarian Law (IHL), omit edge computing limitations, lack robustness testing for fog of war, and inadequately evaluate explicit reasoning. To address these vulnerabilities, we present WARBENCH, a comprehensive evaluation framework establishing a foundational tactical baseline alongside four distinct stress testing dimensions. Through a large scale empirical evaluation of nine leading models on 136 high-fidelity historical scenarios, we reveal severe structural flaws. First, baseline tactical reasoning systematically collapses under complex terrain and high force asymmetry. Second, while state of the art closed source models maintain functional compliance, edge-optimized small models expose extreme operational risks with legal violation rates approaching 70 percent. Furthermore, models experience catastrophic performance degradation under 4-bit quantization and systematic information loss. Conversely, explicit reasoning mechanisms serve as highly effective structural safeguards against inadvertent violations. Ultimately, these findings demonstrate that current models remain fundamentally unready for autonomous deployment in high stakes tactical environments.

We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle ($<$5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

Host-acting agents promise a convenient interaction model in which users specify goals and the system determines how to realize them. We argue that this convenience introduces a distinct security problem: semantic under-specification in goal specification. User instructions are typically goal-oriented, yet they often leave process constraints, safety boundaries, persistence, and exposure insufficiently specified. As a result, the agent must complete missing execution semantics before acting, and this completion can produce risky host-side plans even when the user-stated goal is benign. In this paper, we develop a semantic threat model, present a taxonomy of semantic-induced risky completion patterns, and study the phenomenon through an OpenClaw-centered case study and execution-trace analysis. We further derive defense design principles for making execution boundaries explicit and constraining risky completion. These findings suggest that securing host-acting agents requires governing not only which actions are allowed at execution time, but also how goal-only instructions are translated into executable plans.

Multi-agent discussions have been widely adopted, motivating growing efforts to develop attacks that expose their vulnerabilities. In this work, we study a practical yet largely unexplored attack scenario, the discussion-monitored scenario, where anomaly detectors continuously monitor inter-agent communications and block detected adversarial messages. Although existing attacks are effective without discussion monitoring, we show that they exhibit detectable patterns and largely fail under such monitoring constraints. But does this imply that monitoring alone is sufficient to secure multi-agent discussions? To answer this question, we develop a novel attack method explicitly tailored to the discussion-monitored scenario. Extensive experiments demonstrate that effective attacks remain possible even under continuous monitoring, indicating that monitoring alone does not eliminate adversarial risks.

Architecture views are essential for software architecture documentation, yet their manual creation is labor intensive and often leads to outdated artifacts. As systems grow in complexity, the automated generation of views from source code becomes increasingly valuable. Goal: We empirically evaluate the ability of LLMs and agentic approaches to generate architecture views from source code. Method: We analyze 340 open-source repositories across 13 experimental configurations using 3 LLMs with 3 prompting techniques and 2 agentic approaches, yielding 4,137 generated views. We evaluate the generated views by comparing them with the ground-truth using a combination of automated metrics complemented by human evaluations. Results: Prompting strategies offer marginal improvements. Few-shot prompting reduces clarity failures by 9.2% compared to zero-shot baselines. The custom agentic approach consistently outperforms the general-purpose agent, achieving the best clarity (22.6% failure rate) and level-of-detail success (50%). Conclusions: LLM and agentic approaches demonstrate capabilities in generating syntactically valid architecture views. However, they consistently exhibit granularity mismatches, operating at the code level rather than architectural abstractions. This suggests that there is still a need for human expertise, positioning LLMs and agents as assistive tools rather than autonomous architects.

The computational demands of modern AI services are increasingly shifting execution beyond centralized clouds toward a computing continuum spanning edge and end devices. However, the scale, heterogeneity, and cross-layer dependencies of these environments make resilience difficult to maintain. Existing fault-management methods are often too static, fragmented, or heavy to support timely self-healing, especially under noisy logs and edge resource constraints. To address these limitations, this paper presents NeSy-Edge, a neuro-symbolic framework for trustworthy self-healing in the computing continuum. The framework follows an edge-first design, where a resource-constrained edge node performs local perception and reasoning, while a cloud model is invoked only at the final diagnosis stage. Specifically, NeSy-Edge converts raw runtime logs into structured event representations, builds a prior-constrained sparse symbolic causal graph, and integrates causal evidence with historical troubleshooting knowledge for root-cause analysis and recovery recommendation. We evaluate our work on representative Loghub datasets under multiple levels of semantic noise, considering parsing quality, causal reasoning, end-to-end diagnosis, and edge-side resource usage. The results show that NeSy-Edge remains robust even at the highest noise level, achieving up to 75% root-cause analysis accuracy and 65% end-to-end accuracy while operating within about 1500 MB of local memory.

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable Hilbert spaces, exploiting the invariance property of covariance kernels under the group of isometries of the manifold. The identification of these measures with infinite-product Gaussian measures is then obtained via the eigenfunctions of the Laplace-Beltrami operator on the manifold. The involved time-varying angular spectra constitute the key tool for dimension reduction in the implementation of this regression approach, adopting a suitable truncation scheme depending on the functional sample size. The simulation study and synthetic data application undertaken illustrate the finite sample and asymptotic properties of the proposed functional regression predictor.

This paper addresses the challenge of improving information retrieval from semi-structured eXtensible Markup Language (XML) documents. Traditional information retrieval systems (IRS) often overlook user-specific needs and return identical results for the same query, despite differences in users' knowledge, preferences, and objectives. We integrate external semantic resources, namely a domain ontology and user profiles, into the retrieval process. Documents, queries, and user profiles are represented as vectors of weighted concepts. The ontology applies a concept-weighting mechanism that emphasizes highly specific concepts, as lower-level nodes in the hierarchy provide more precise and targeted information. Relevance is assessed using semantic similarity measures that capture conceptual relationships beyond keyword matching, enabling personalized and fine-grained matching among user profiles, queries, and documents. Experimental results show that combining ontologies with user profiles improves retrieval effectiveness, achieving higher precision and recall than keyword-based approaches. Overall, the proposed framework enhances the relevance and adaptability of XML search results, supporting more user-centered retrieval.

In this paper, we explore a joint source and reconfigurable intelligent surface (RIS)-assisted channel encoding (JSRE) framework for multi-user semantic communications, where a deep neural network (DNN) extracts semantic features for all users and the RIS provides channel orthogonality, enabling a unified semantic encoding-decoding design. We aim to maximize the overall energy efficiency of semantic communications across all users by jointly optimizing the user scheduling, the RIS's phase shifts, and the semantic compression ratio. Although this joint optimization problem can be addressed using conventional deep reinforcement learning (DRL) methods, evaluating semantic similarity typically relies on extensive real environment interactions, which can incur heavy computational overhead during training. To address this challenge, we propose a truncated DRL (T-DRL) framework, where a DNN-based semantic similarity estimator is developed to rapidly estimate the similarity score. Moreover, the user scheduling strategy is tightly coupled with the semantic model configuration. To exploit this relationship, we further propose a semantic model caching mechanism that stores and reuses fine-tuned semantic models corresponding to different scheduling decisions. A Transformer-based actor network is employed within the DRL framework to dynamically generate action space conditioned on the current caching state. This avoids redundant retraining and further accelerates the convergence of the learning process. Numerical results demonstrate that the proposed JSRE framework significantly improves the system energy efficiency compared with the baseline methods. By training fewer semantic models, the proposed T-DRL framework significantly enhances the learning efficiency.

Based on some recent work of the author on stochastic approximation in non-markovian environments, the situation when the driving random process is non-ergodic in addition to being non-markovian is considered. Using this, we propose an analytic framework for understanding transformer based learning, specifically, the `attention' mechanism, and continual learning, both of which depend on the entire past in principle.

Composing coherent long-form music remains a significant challenge due to the complexity of modeling long-range dependencies and the prohibitive memory and computational requirements associated with lengthy audio representations. In this work, we propose a simple yet powerful trick: we assume that AI models can understand and generate time-accelerated (speeded-up) audio at rates such as 2x, 4x, or even 8x. By first generating a high-speed version of the music, we greatly reduce the temporal length and resource requirements, making it feasible to handle long-form music that would otherwise exceed memory or computational limits. The generated audio is then restored to its original speed, recovering the full temporal structure. This temporal speed-up and slow-down strategy naturally follows the principle of hierarchical generation from abstract to detailed content, and can be conveniently applied to existing music generation models to enable long-form music generation. We instantiate this idea in SqueezeComposer, a framework that employs diffusion models for generation in the accelerated domain and refinement in the restored domain. We validate the effectiveness of this approach on two tasks: long-form music generation, which evaluates temporal-wise control (including continuation, completion, and generation from scratch), and whole-song singing accompaniment generation, which evaluates track-wise control. Experimental results demonstrate that our simple temporal speed-up trick enables efficient, scalable, and high-quality long-form music generation. Audio samples are available at https://SqueezeComposer.github.io/.

We study the problem of learning a low-degree spherical polynomial of degree $k_0 = Θ(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network with augmented feature in this paper. Our main result is the significantly improved sample complexity for learning such low-degree polynomials. We show that, for any regression risk $\eps \in (0, Θ(d^{-k_0})]$, an over-parameterized two-layer neural network trained by a novel Gradient Descent with Projection (GDP) requires a sample complexity of $n \asymp Θ( \log(4/δ) \cdot d^{k_0}/\eps)$ with probability $1-δ$ for $δ\in (0,1)$, in contrast with the representative sample complexity $Θ(d^{k_0} \max\set{\eps^{-2},\log d})$. Moreover, such sample complexity is nearly unimprovable since the trained network renders a nearly optimal rate of the nonparametric regression risk of the order $\log({4}/δ) \cdot Θ(d^{k_0}/{n})$ with probability at least $1-δ$. On the other hand, the minimax optimal rate for the regression risk with a kernel of rank $Θ(d^{k_0})$ is $Θ(d^{k_0}/{n})$, so that the rate of the nonparametric regression risk of the network trained by GDP is nearly minimax optimal. In the case that the ground truth degree $k_0$ is unknown, we present a novel and provable adaptive degree selection algorithm which identifies the true degree and achieves the same nearly optimal regression rate. To the best of our knowledge, this is the first time that a nearly optimal risk bound is obtained by training an over-parameterized neural network with a popular activation function (ReLU) and algorithmic guarantee for learning low-degree spherical polynomials. Due to the feature learning capability of GDP, our results are beyond the regular Neural Tangent Kernel (NTK) limit.

Brain encoding and decoding aims to understand the relationship between external stimuli and brain activities, and is a fundamental problem in neuroscience. In this article, we study latent embedding alignment for brain encoding and decoding, with a focus on improving sample efficiency under limited fMRI-stimulus paired data and substantial subject heterogeneity. We propose a lightweight alignment framework equipped with two statistical learning components: inverse semi-supervised learning that leverages abundant unpaired stimulus embeddings through inverse mapping and residual debiasing, and meta transfer learning that borrows strength from pretrained models across subjects via sparse aggregation and residual correction. Both methods operate exclusively at the alignment stage while keeping encoders and decoders frozen, allowing for efficient computation, modular deployment, and rigorous theoretical analysis. We establish finite-sample generalization bounds and safety guarantees, and demonstrate competitive empirical performance on the large-scale fMRI-image reconstruction benchmark data.