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01.
arXiv (CS.AI) 2026-06-12

EPIG: Emotion-Based Prompting for Personalised Image Generation

arXiv:2606.13247v1 Announce Type: new Abstract: Text-to-image diffusion models have achieved impressive results in synthesizing high-quality images from natural language prompts. However, commonly used prompting strategies remain relatively generic, limiting the model's ability to accurately express emotional intent and nuanced affective attributes. This work proposes EPIG, a method that enhances emotional expressiveness at the prompt level prior to image generation. Grounded in psychologically informed emotion representations (valence-arousal) and leveraging structured, role-aware prompt enrichment, EPIG enriches emotion-related components of prompts without modifying or retraining the image generation backbone. The resulting emotion-aware prompts guide the generative process toward more emotionally coherent visual outputs, with particular effectiveness in controlling arousal. EPIG is lightweight, training-free, and well suited for resource-constrained and personalized image generation scenarios. Experimental results on a benchmark of 10 diverse prompts show that EPIG reduces mean arousal error compared to strong baselines, including naive insertion and LLM-based prompt expansion, with reductions of 14% and 12%, respectively. These improvements are statistically significant. EPIG also preserves valence alignment and semantic consistency, as measured by CLIPScore and supported by ablation studies. The effect is more pronounced on prompts containing explicit subjects such as humans, children, or animals, where the reduction reaches 17%, highlighting the subject-sensitive behavior of the proposed method.

02.
medRxiv (Medicine) 2026-06-12

Crimean-Congo haemorrhagic fever virus transmission: exploring perceptions of human-animal-tick interactions across six districts in Uganda

Crimean-Congo haemorrhagic fever virus (CCHFV) causes a viral zoonotic disease transmitted through tick bites and direct contact with infected blood or tissue of infected animals. Socio-ecological and behavioural risk factors for CCHFV exposure in Uganda remain poorly understood, which can lead to the omission of key risk factors in quantitative survey design and limit our wider understanding. In this study, we explored human-animal-tick interaction transmission risks in Uganda. We conducted 24 focus group discussions (FGDs) and 31 key-informant interviews (KIIs) across six environmentally and socio-ecologically diverse districts, between October 2023 and March 2024. Study sites were selected using K-prototype analysis, which combined environmental and socio-ecological variables to identify distinct clusters within Uganda. FGDs were conducted separately with groups of community leaders, men, women and teenagers with stratified purposive sampling. Medical doctors, veterinarians, traditional healers, district surveillance officers, and herdsmen were individually interviewed as key informants and purposively sampled. Data were transcribed and translated into English, and analysed thematically using iterative categorisation in NVivo 14. Most participants reported tick bites, some as frequently as every day. Close contact with animals was common, including sleeping next to them in the same building, largely due to concerns about animal theft. Less frequent but notable practices included slaughtering animals for consumption or sacrifice and interactions with wild animals during hunting. Slaughtering and butchering an animal which was sick or had died was reportedly performed by participants in most districts. Plucking and roasting engorged ticks was a practice described in the Kaabong and Arua districts of Northern Uganda. These practices and behaviours highlight potential key risks of CCHFV transmission and underscore the need for future studies to address specific behaviours, to quantify if, and to what extent, they present an exposure risk. Further work should include underlying reasons for the behaviours, which would help ensure that culturally appropriate interventions are targeted.

03.
arXiv (CS.CV) 2026-06-12

Modality-Aware Feature Matching in Visual and Vision-Language Applications: A Comprehensive Survey

Feature matching is a cornerstone task in computer vision, essential for applications such as image retrieval, stereo matching, 3D reconstruction, and SLAM. This survey comprehensively reviews modality-based feature matching, exploring traditional handcrafted methods and emphasizing contemporary deep learning approaches across various modalities, including RGB images, depth images, 3D point clouds, LiDAR scans, medical images, and vision-language interactions. Traditional methods, leveraging detectors like Harris corners and descriptors such as SIFT and ORB, demonstrate robustness under moderate intra-modality variations but struggle with significant modality gaps. Contemporary deep learning-based methods, exemplified by detector-free strategies like CNN-based SuperPoint and transformer-based LoFTR, substantially improve robustness and adaptability across modalities. We highlight modality-aware advancements, such as geometric and depth-specific descriptors for depth images, sparse and dense learning methods for 3D point clouds, attention-enhanced neural networks for LiDAR scans, and specialized solutions like the MIND descriptor for complex medical image matching. Cross-modal applications, particularly in medical image registration and vision-language tasks, underscore the evolution of feature matching to handle increasingly diverse data interactions.

04.
arXiv (quant-ph) 2026-06-19

Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series

arXiv:2605.21597v2 Announce Type: replace Abstract: We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

05.
arXiv (CS.AI) 2026-06-16

CogGuard: Cognitive and Operational Profiling for Proactive Warning in Edge Intelligent Services

arXiv:2606.15199v1 Announce Type: new Abstract: Proactive warning is an important capability for edge intelligent services, where the system predicts whether a subject will successfully complete an incoming task under strict latency and privacy constraints. Such prediction depends on both long-term static attributes and short-term dynamic states derived from historical interaction logs. Recent Large Language Models (LLMs) offer strong long-context reasoning for constructing structured profiles from these logs, but existing solutions face two challenges for edge deployment: (1) profiling methods are typically domain-specific and lack a reusable abstraction across service scenarios, and (2) fine-tuning alignment models on heterogeneous edge clusters incurs high synchronization overhead due to the variance in input sequence lengths. To address these challenges, we propose CogGuard, a proactive-warning framework for edge intelligent services. CogGuard decouples offline LLM-based profile construction from online Small Language Model (SLM)-based score prediction through a shared static-dynamic profile-to-score pipeline, and instantiates it in two representative scenarios: educational performance warning and operational task outcome warning. For efficient profile construction, we design scenario-specific profiling methods with prefix-aligned KV-cache reuse to reduce repeated encoding overhead. For edge-side model alignment, we propose a length-aware distributed fine-tuning strategy with contrastive regularization to mitigate workload imbalance on heterogeneous clusters. Experiments on education and operation datasets show that CogGuard reduces profile construction time by up to 48% and distributed fine-tuning time by 19%, while achieving MAEs of 13.4 and 5.9, respectively, on 100-point-scale warning tasks. In the largest educational setting, CogGuard reduces prediction error by 15.4% compared with the strongest baseline.

06.
arXiv (CS.CL) 2026-06-18

ScholarSum: Student-Teacher Abstractive Summarization via Knowledge Graph Reasoning and Reflective Refinement

Abstractive summarization plays a crucial role in enabling efficient understanding of scientific literature, yet it inherently demands both linguistic fluency and factual faithfulness. Existing approaches often fail to reconcile these two requirements. Extractive methods rely on rigid sentence splicing that disrupts macro-level logical coherence, while large language model (LLM)-based generative approaches, despite mastering linguistic fluency, exhibit limited factual consistency. In this work, we propose ScholarSum, a hierarchical reflective graph-based framework that emulates a student-teacher writing process for fluent and faithful scientific summarization. ScholarSum first organizes the document into a hierarchical knowledge graph by segmenting it into semantically coherent units, whose multi-layered community structure captures global logic and macro-level themes. Guided by this global structure, the student generates an initial draft, which is subsequently refined through fine-grained evidence retrieval. To ensure factual consistency, a teacher-like reviewer then iteratively examines the draft, identifies unsupported content, and prompts targeted re-retrieval and rewriting until the summary meets rigorous quality standards. Extensive experiments demonstrate that ScholarSum significantly outperforms previous baselines in terms of both completeness and faithfulness. Our code is available at https://github.com/Xiaoyu-Tao/ScholarSum.

07.
arXiv (CS.CV) 2026-06-11

CellNet – Localizing Cells using Sparse and Noisy Point Annotations

Counting living cells is an important step in many biological research workflows. Our collaborators at the Wellcome Sanger Institute study vital genes in humans via large scale saturation genome editing screening, which requires repeatedly counting cells a great number of times. Computer Vision based automation is crucial for high throughput and resource efficiency. In this work, we develop a regression-based deep learning computer vision algorithm to detect and count cells in phase-contrast microscopy images. To reduce annotation effort, which in practice often becomes a bottleneck, we focus on counting cells only using sparse point annotations, which are fast and easy to acquire. By comparison to state-of-the-art 0-shot methods, we show that regression-based counting is a promising alternative in low data regimes. Through developing methods to automatically count living cells in microscopy images, we contribute to valuable research on the human genome. The code is available at https://github.com/beijn/cellnet.

08.
arXiv (CS.CV) 2026-06-16

Multi-view feature High-order Fusion for Space Weak Object Detection and Segmentation

Weak objects are common in images and videos of space applications. However, it is hard to learn proper representations from their limited appearance information. Inspired by multi-view learning, we develop simple multi-view attentions, treating their outputs as multi-view features. We also propose a multi-view feature high-order fusion method (MHF) to aggregate more accurate and richer features of weak objects. Our MHF extends the commonly used low-order feature fusion method to higher orders. It enhances the model's capacity to capture relevant and complementary information about weak objects. This is achieved by introducing high-order multi-view features perception and a recursive task-contribution gated selection of multi-view features. The new operation is highly flexible and customizable. It is compatible with various variants of multi-view feature representations. We conduct extensive experiments on two newly constructed space science datasets and an open, large-scale satellite video dataset. Our MHF serves as a plug-and-play module and significantly improves various vision transformers and convolution-based detection and segmentation models. We achieve all state-of-the-art accuracies on both tasks across three datasets. Our MHF can be a new basic module for visual modeling that effectively represents weak objects in terms of multi-view learning. The code will be available at https://github.com/Kingdroper/MHF.

09.
arXiv (quant-ph) 2026-06-12

Multi-entropy in heavy local quenches

arXiv:2606.12526v1 Announce Type: cross Abstract: We study the time evolution of tripartite entanglement in heavy local quenches in two-dimensional holographic conformal field theories. Our diagnostic is the genuine multi-entropy of adjacent intervals, computed from both bulk and boundary perspectives. A perturbative bulk analysis shows that the first-order small-mass perturbation around the vacuum geodesic network cancels identically at any time after the quench. In the fully back-reacted geometry, a vacuum-subtracted genuine multi-entropy arises from a mismatch between the winding selected by the trivalent geodesic network and the windings selected independently by the pairwise geodesics. In the sharp quench limit, the time dependence of genuine multi-entropy is kinematically fixed to logarithms of rational functions of time and is independent of the heavy operator dimension. The CFT calculation reproduces the same formula within the heavy-light vacuum block approximation, where the branch choice in the heavy-background uniformization map corresponds to the winding selection in the bulk. These results indicate that, in this setup, the genuine multi-entropy is controlled by global saddle selection, rather than by a local energy response or quasiparticle propagation.

10.
arXiv (CS.LG) 2026-06-15

Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems

arXiv:2606.14079v1 Announce Type: new Abstract: We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces. We instantiate the method as Deep Spectral Encoder (DSE), an operator-based latent state-space model in which a time-invariant neural encoder implements learnable nonlinear feature maps from observations, and these features define Markovian latent states whose temporal evolution and observation mapping are described by the transfer and observation operators, respectively. Functional canonical correlation analysis in a learnable Galerkin-projected feature space provides state coordinates from past and future observations, and the two linear operators are estimated on the state coordinates as ridge-regularized closed-form solutions that coincide with Galerkin projections of the associated covariance operators. On this representation, we generalize sequential Bayesian filtering and Koopman spectral mode decomposition in feature space. Experiments on several scenarios show stable and superior performance with sequential Bayesian filtering and dynamic mode decomposition baselines even under noise and partial observability.

11.
arXiv (CS.LG) 2026-06-15

Binary Black Hole Parameter Estimation with Hybrid CNN-Transformer Neural Networks

arXiv:2606.13941v1 Announce Type: cross Abstract: The detection of gravitational waves has revolutionized our ability to explore fundamental aspects of the Universe. Traditionally, modeled gravitational-wave signals have been identified using template-based matched filtering, followed by coincidence analysis across multiple detectors in the signal-to-noise ratio time series. Recent advances in Machine Learning and Deep Learning have sparked growing interest in their application to both signal detection and parameter estimation. In this study, a hybrid Deep Learning strategy is proposed that leverages the effectiveness of Transformer encoders alongside well-established Convolutional Neural Network architectures in an attempt to estimate the intrinsic and extrinsic parameters of non-precessing binary black hole systems. The primary focus of this work is point estimation, producing single best-fit values for each parameter rather than full posterior distributions. This method is evaluated on both simulated signals embedded in Gaussian noise and real gravitational-wave events, and it demonstrates strong predictive performance and robustness across key astrophysical parameters.

12.
arXiv (CS.AI) 2026-06-17

Patients With Personality: Realistic Patient Simulation through Controlled Diversity and Selective Disclosure

arXiv:2606.17441v1 Announce Type: cross Abstract: Simulating realistic patient interactions is a key requirement to testing clinical applications of LLMs at scale without time-consuming and expensive user studies. However, existing approaches often lack realism and controllability, often oversharing information unprompted, and failing to capture the wide variability of patient behavior. Here, we introduce PatientsWithPersonality (PWP), a patient simulation framework that generates realistic yet diverse virtual patient responses through explicit personality parametrization over a latent patient state. Grounded in HEXACO, a six-dimensional personality space used to quantify and parameterize human behavioral traits, our approach enables fine-grained control over conversational style, cooperativeness, and information disclosure within a unified framework. In a clinician evaluation, PWP is judged nearly as realistic as recorded human actors and clearly ahead of prior simulators, while being flagged as "too informative" far less often. Conditioning on HEXACO axes yields personas whose configured traits are recoverable by both clinicians and an autorater, span a substantially wider behavioral footprint than the closest baseline, and prevent oversharing. Altogether, our framework paves the way for more accurate and informative LLM benchmarking through our realistic and steerable patient simulator.

13.
arXiv (CS.LG) 2026-06-18

FinP: Fairness-in-Privacy in Federated Learning by Addressing Disparities in Privacy Risk

arXiv:2502.17748v4 Announce Type: replace Abstract: Federated Learning (FL) inherently mitigates mass data centralization risks; however, its privacy protections are not equally distributed - leaving vulnerable individuals disproportionately exposed to sophisticated privacy attacks. Crucially, statistical heterogeneity in human-centric FL environments often results in an inequitable distribution of privacy risks, particularly affecting those whose sensitive attributes or behaviors make them outliers. To address this critical gap, we introduce FinP, a novel framework designed to formalize and enforce fairness-in-privacy by mitigating disproportionate client vulnerability to Source Inference Attacks (SIA). FinP operationalizes a two-pronged defense strategy that tackles both the symptoms and root causes of privacy disparity, ensuring that no group of clients bears an excessive privacy burden. It combines a server-side adaptive aggregation mechanism, which dynamically weights client contributions based on their estimated privacy risk, with a client-side regularization technique to curb localized overfitting that drives unique data memorization. Extensive empirical evaluations on FEMNIST, Human Activity Recognition (HAR), and CIFAR-10 datasets demonstrate that FinP effectively aligns privacy fairness with primary task utility. Notably, FinP successfully mitigates SIA risks and reduces disparities in privacy exposure, establishing that strong fairness-in-privacy guarantees need not compromise model utility. Ultimately, FinP establishes equitable privacy protections by reducing vulnerability disparities by up to 57.14%, while preserving global model utility within a marginal +/- 1.75% of standard federated baselines.

14.
arXiv (CS.AI) 2026-06-12

PI-Hunter: Automated Red-Teaming for Exposing and Localizing Prompt Injections

arXiv:2606.12737v1 Announce Type: cross Abstract: Large Language Models (LLMs) are rapidly evolving into agentic systems that interact with external tools and environments, introducing new security risks such as indirect prompt injection attacks through untrusted external sources. Existing defenses mainly focus on blocking malicious content at inference time, and current red-teaming methods primarily optimize attack success. As a result, developers have limited visibility into how latent prompt injections emerge and propagate through agents. We propose PI-Hunter, an automated agentic auditing framework for proactive vulnerability exposure in LLM agents. PI-Hunter constructs realistic source-aware test cases and iteratively evolves them through feedback-driven exploration to induce agents to retrieve and reveal latent malicious instructions embedded within external environments. Extensive experiments across multiple benchmarks, agent architectures, attacks, and defenses demonstrate that PI-Hunter substantially improves vulnerability exposure and attack-surface coverage over strong automated red-teaming baselines, while remaining effective under existing prompt injection defenses.

15.
arXiv (CS.AI) 2026-06-18

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior

arXiv:2604.13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we argue that this delay reflects limited access to already learned structure rather than failure to acquire that structure in the first place. We study one-step Collatz prediction and find that the encoder organizes parity and residue structure within the first few thousand training steps, while output accuracy remains near chance for tens of thousands more. Causal interventions support the decoder bottleneck hypothesis. Transplanting a trained encoder into a fresh model accelerates grokking by 2.75 times, while transplanting a trained decoder actively hurts. Freezing a converged encoder and retraining only the decoder eliminates the plateau entirely and yields 97.6% accuracy, compared to 86.1% for joint training. What makes the decoder's job harder or easier depends on numeral representation. Across 15 bases, those whose factorization aligns with the Collatz map's arithmetic (e.g., base 24) reach 99.8% accuracy, while binary fails completely because its representations collapse and never recover. The choice of base acts as an inductive bias that controls how much local digit structure the decoder can exploit, producing large differences in learnability from the same underlying task.

16.
arXiv (CS.AI) 2026-06-16

Phantoms and Disclosures: a Causal Framework for Auditing Synthetic Data

arXiv:2606.16952v1 Announce Type: cross Abstract: The rapid adoption of generative AI and Large Language Models (LLMs) has spurred interest in synthetic data as a privacy-preserving alternative to sensitive real-world datasets. However, generating high-utility synthetic data often carries the risk of memorizing and regurgitating private information from the training corpus. In this work, we present a customizable empirical auditing framework designed to detect and explain such data disclosures. Our framework introduces a mechanism to distinguish between "true disclosures"-where the system directly reproduces a user's information-and "phantom disclosures''-where the system incidentally generates a user's data. By partitioning input data into training and holdout sets and applying rigorous statistical hypothesis testing, we determine if observed disclosures are consistent with strict privacy baselines, such as zero-learning or specific Differential Privacy (DP) bounds. Crucially, this approach requires no model access, no canary insertion, and no reference model training -only the synthetic output and a held-out control set. We demonstrate that this framework effectively functions as a membership inference attack, providing empirical lower bounds on privacy leakage that are tighter than prior data-based auditing methods. Our approach is model-agnostic, applies to any synthetic data generation mechanism, and requires orders of magnitude fewer computational resources than shadow-model or canary-based alternatives.

17.
arXiv (CS.CV) 2026-06-16

Multi-Modal Attention for Automated Disaster Damage Assessment Using Remote Sensing Imagery and Deep Learning

Timely and accurate disaster damage assessment is crucial for effective emergency response, resource allocation, and recovery. Traditional methods, which often rely on manual inspections or sparse data, are typically slow and error-prone. This paper introduces a novel framework leveraging remote sensing imagery and deep learning to automate building damage classification. Using pre- and post-disaster satellite imagery, our model categorizes buildings into four damage levels: no damage, minor damage, major damage, and destroyed. The core innovation is a multi-modal attention mechanism that fuses bi-temporal features to explicitly detect and assess structural changes. We employ a lightweight ConvNeXT-Tiny backbone to ensure efficient processing without compromising performance. Key contributions include: (1) a cross-attention module for multi-modal data fusion, (2) an optimized preprocessing pipeline for large-scale datasets, and (3) robust data augmentation techniques. Experiments on a large-scale disaster dataset demonstrate an overall classification accuracy of 94.90%. The model effectively discriminates between damage categories and remains resilient to incomplete data. This system significantly improves assessment speed and accuracy, aiding emergency responders in prioritizing interventions. This work advances automated disaster damage detection by integrating multi-temporal imagery with deep learning, offering a scalable solution for real-time response.

18.
arXiv (CS.AI) 2026-06-11

Mind the Perspective: Let's Reason Recursively for Theory of Mind

arXiv:2606.11724v1 Announce Type: new Abstract: Theory of Mind (ToM) reasoning requires inferring agents' beliefs from partial and asymmetric observations, which remains an open challenge for LLMs. Existing prompting-based approaches improve ToM reasoning through observable-event filtering or temporal belief chains, without explicitly modeling nested beliefs. We introduce RecToM, an inference-time framework for ToM reasoning that models nested beliefs via recursive perspective construction. RecToM constructs each character perspective from the preceding character perspective along the character chain specified by the question, reducing higher-order belief questions to actual-world questions within the final constructed perspective. We further provide a KD45 analysis showing that RecToM's perspective construction induces a well-formed belief modality beyond simple event filtering. Experiments on ToM benchmarks, including Hi-ToM, Big-ToM, and FanToM, across multiple LLM backbones show that RecToM consistently outperforms recent advanced approaches, achieving state-of-the-art performance. Notably, RecToM reaches 100\% accuracy on Hi-ToM with GPT-5.4 and Qwen3.5, a benchmark requiring higher-order ToM reasoning.

19.
arXiv (CS.LG) 2026-06-15

CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

arXiv:2606.14565v1 Announce Type: cross Abstract: Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather than local stress information, robust discovery typically requires multiple loading modes to constrain the multidimensional response. This is challenging for soft biological tissues, where repeated testing, damage, and sample variability limit reliable information from a single specimen. Here, we combine CANNs with the stress-unsupervised full-field discovery framework EUCLID to identify sparse hyperelastic laws directly from displacement fields and reaction forces in one heterogeneity-inducing loading case. CANN-EUCLID minimizes equilibrium imbalance with sparsity-promoting regularization selecting compact active terms, without local stress measurements or a prescribed law. We evaluate the approach on isotropic and anisotropic benchmarks with prescribed ground-truth laws. When the ground truth is representable by the chosen CANN basis, our method recovers the correct terms with near-exact accuracy, including exponential terms with embedded parameters. When it is not contained in the basis, the method retains shared terms and approximates missing contributions using available basis functions. Generalization depends strongly on sampled deformation states: exponential strain-stiffening terms can be recovered accurately when sufficiently probed, but can produce large extrapolation errors when the stiffening regime lies outside the sampled domain. Forward FE validation simulations show that the discovered behavior accurately replicates the ground truth. These results establish stress-unsupervised CANN discovery as a promising framework for interpretable full-field constitutive model identification.

22.
arXiv (math.PR) 2026-06-16

Malliavin Calculus for the stochastic Cahn-Hilliard equation driven by fractional noise

arXiv:2601.10490v2 Announce Type: replace Abstract: The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply Malliavin calculus to investigate the existence of a density for the stochastic solution $u$. In particular, we show that $u$ admits continuous paths almost surely and construct a localizing sequence through which we prove that its Malliavin derivative exists locally, and that its law is absolutely continuous with respect to the Lebesgue measure on $\bf R$, establishing thus that a density exists. A key contribution of this work is the analysis of the stochastic integral appearing in the mild formulation: we derive sharp estimates for the expectation of the $p$-th power ($p \geq 2$) of the $L^{\infty}(D)$-norm of this stochastic integral as well as for the integral involving the $L^{\infty}(D)$-norm of the operator associated with the kernel appearing in the integral representation of the fractional noise, all of which are essential for this study.

24.
arXiv (CS.LG) 2026-06-17

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

arXiv:2503.05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key foundational topics are introduced, including finite-dimensional representations of function spaces, singular-value decomposition, and sampling from infinite-dimensional function spaces. Beyond forward modeling, the review discusses the use of neural operators as surrogate models within a Bayesian inverse-problem framework, including prior specification, forward-map approximation, and posterior computation. The performance of the three neural-operator architectures is evaluated on in-distribution samples, out-of-distribution samples, and Bayesian inference tasks. The review also discusses challenges related to prediction accuracy and generalization, outlining emerging strategies such as residual-based error correction and multi-level training. The review concludes by positioning neural operators within broader scientific-computing workflows and by identifying directions for reliable, scalable operator learning.

25.
arXiv (CS.LG) 2026-06-12

Generative Modeling of Bach-Style Symbolic Music: A Comparative Study of Autoregressive, Latent-Variable, and Adversarial Approaches

arXiv:2606.13626v1 Announce Type: cross Abstract: We study generative modeling of Bach-style symbolic piano music using a shared MIDI corpus and three model families: autoregressive LSTMs with attention, latent-variable models including recurrent VAEs and vector-quantized VAEs, and generative adversarial networks. We compare their ability to model polyphonic note sequences, learn useful latent representations, and generate stylistically coherent compositions. Our experiments show that the autoregressive LSTM with attention produces the most musically coherent samples, while vector quantization helps mitigate posterior collapse and yields more structured outputs than conventional recurrent VAEs. The adversarial approach captures local pitch patterns but remains difficult to train and generalizes less reliably to Bach's style. These results highlight the relative strengths and failure modes of autoregressive, latent-variable, and adversarial approaches for symbolic music generation.