arXiv:2605.15625v1 Announce Type: new Abstract: We introduce ColPackAgent, an agent framework that autonomously runs Monte Carlo simulations of colloidal packing through a Model Context Protocol (MCP) tool server and an agent skill, whether as a standalone agent or inside an existing agent system. By harnessing the MCP server and agent skill, ColPackAgent executes a structured workflow for colloidal packing simulations, which are central to studies of phase behavior, self-assembly, and materials design. Without dedicated simulation tools and workflow instructions, general-purpose Large Language Model (LLM) agents tend to describe such workflows rather than execute them reliably. The MCP server exposes a custom-built colpack Python package that wraps HOOMD-blue hard-particle Monte Carlo, and the skill encodes a four-stage workflow contract. ColPackAgent can carry out the workflow interactively with human feedback, autonomously from an end-to-end prompt, or as autoresearch following a provided program file. We demonstrate the system in different modes with several colloidal packing simulation examples such as cube particles in 3D, a binary system of disks and capsules in 2D, and the 2D hard-disk freezing transition using autoresearch. We also compare model performance on this workflow across a panel of LLMs with 17 stage-specific prompts. This benchmark provides a stage-level check of how reliably different models follow the setup, planning, and analysis workflow. Together, these results show that pairing a domain Python package with MCP tools and a portable agent skill provides a practical route for turning a simulation toolkit into an agent-assisted research workflow.
Science Journals
arXiv:2605.15564v1 Announce Type: new Abstract: Generative models trained on public databases of protein structures, most of which have been determined by X-ray crystallography, now provide powerful priors for structure prediction. However, they are not readily conditioned on the measurements from a new crystallographic experiment, limiting their use for X-ray structure determination. In crystallography, the measured structure-factor amplitudes do not by themselves determine an electron density map or atomic structure because the associated phases are unobserved and must be inferred. Structure determination therefore remains an inverse problem in which candidate models must be both structurally plausible and consistent with measured diffraction data, often requiring substantial manual refinement by human experts. Emerging methods aim to incorporate experimental information more directly into predictive and refinement workflows. We present CrystalBoltz, a generative framework that casts crystallographic refinement as Bayesian inference over atomic structures and operates directly on structure-factor amplitudes. CrystalBoltz moves from unguided generation with a pre-trained prior over protein structures to experiment-guided posterior sampling, followed by atomic coordinate and B-factor refinement. Across multiple protein crystallography datasets, CrystalBoltz attains lower coordinate RMSD and lower R-factors than the strongest baselines considered, while reducing runtime by a factor of 33 relative to existing experimentally guided refinement.
arXiv:2605.15294v1 Announce Type: new Abstract: A DFA separates two disjoint languages $L_1$ and $L_2$ if it accepts every word in $L_1$ and rejects every word in $L_2$. Algorithms for active learning of small separating DFAs have many applications, e.g., for learning network invariants, learning contextual assumptions in compositional verification, learning state machines from large amounts of log data, and learning bug pattern descriptions. We propose a simple active learning algorithm, inspired by $L^{\#}$, that learns a minimal separating DFA for disjoint languages $L_1$ and $L_2$ if one exists. Experiments show that our algorithm significantly outperforms existing active learning algorithms on both randomly generated and industrial benchmarks.
arXiv:2605.15536v1 Announce Type: new Abstract: Previous imitation learning policies predict future actions at every control step, whether in smooth motion phases or precise, contact-rich operation phases. This uniform treatment is wasteful: most steps in a manipulation trajectory traverse free space and carry little task-relevant information, while a small fraction of \emph{key} steps around contacts, grasps, and alignment demand dense, high-resolution prediction. We propose a novel \emph{action relabeling} mechanism: at each timestep in a skip segment, we replace the behavior cloning target with the action at the entrance of the next key segment, enabling the policy to leap over redundant steps in a single decision. The resulting \textbf{Skip Policy (SkiP)} dynamically leaps over skip segments and intensively refines actions in key segments, within a single unified network requiring no learned skip planner or hierarchical structure. To automatically partition demonstrations into key and skip segments without manual annotation, we introduce \emph{Motion Spectrum Keying} (MSK), a fast, task-agnostic procedure that detects local motion complexity from action signals. Extensive experiments across 72 simulated manipulation tasks and three real-robot tasks show that SkiP reduces executed steps by $15$--$40\%$ while matching or improving success rates across various policy backbones. Project page: \texttt{https://pgq18.github.io/SkiP-page/}.
arXiv:2505.12601v2 Announce Type: replace Abstract: As large language models (LLMs) grow in scale and specialization, routing--selecting the best model for a given input--has become essential for efficient and effective deployment. While recent methods rely on complex learned routing strategies, their dependence on disparate training data and evaluation setups makes comparison and generalization difficult. In this work, we revisit LLM routing through the lens of simplicity. We show that a well-tuned k-Nearest Neighbors (kNN) approach not only matches but often outperforms state-of-the-art learned routers across diverse tasks. To support systematic evaluation, we introduce a suite of standardized routing benchmarks spanning instruction-following, question-answering, and reasoning tasks, as well as the first multi-modal routing dataset involving visual inputs. Our findings reveal that the locality properties of model performance in embedding space enable simple non-parametric methods to achieve strong routing decisions with lower sample complexity than parametric approaches. This challenges the prevailing trend toward sophisticated architectures and highlights the importance of thoroughly evaluating simple baselines before investing in complex solutions. To support reproducibility and further exploration, we will release all benchmarks and code upon publication.
arXiv:2506.01732v3 Announce Type: replace Abstract: Large Language Models (LLMs) are pre-trained on large amounts of data from different sources and domains. Such datasets often contain trillions of tokens, including large portions of copyrighted or proprietary content, which raises questions about the legal use of such models. This underscores the need for truly open pre-training data that complies with data security regulations. In this paper, we introduce Common Corpus, the largest open dataset for LLM pre-training. The data assembled in Common Corpus are either uncopyrighted or under open licenses, totaling about two trillion tokens. The dataset contains a wide variety of languages, ranging from the high-resource European languages to some low-resource languages rarely represented in pre-training datasets. In addition, it includes a large amount of code data. The diversity of data sources in terms of covered domains and time periods opens up the paths for both research and entrepreneurial needs across diverse areas of knowledge. In this paper, we present the detailed provenance of data assembling and the details of dataset filtering and curation. We train two small language models on Common Corpus and find that they perform comparably to other models of their size, indicating that our dataset is suitable for multilingual pretraining. Common Corpus represents a key contribution to the ecosystem for open science research on Large Language Models.
arXiv:2605.15290v1 Announce Type: new Abstract: Hyperparameter transfer across model architectures dramatically reduces the amount of compute necessary for tuning large language models (LLMs). The maximal update parameterization ({\mu}P) ensures transfer through principled mathematical analysis but can be challenging to derive for new model architectures. Building on the spectral feature-learning view of Yang et al. (2023a), we make two advances. First, we promote spectral norm conditions on the weights from a heuristic to the definition of feature learning, and as a consequence arrive at the Complete-P depth and weight-decay scalings without recourse to lazy-learning. Second, we consider a modified spectral norm that preserves the valid scaling law of network weights when weight matrices are not full rank. This enables (to our knowledge, the first) derivation of {\mu}P scalings for grouped-query attention (GQA). We demonstrate the efficacy of our theoretical derivations by showing learning rate transfer across the GQA repetition hyperparameter as well as experiments regarding transfer over weight decay.
arXiv:2605.15689v1 Announce Type: new Abstract: Fine-grained image recognition classifies subcategories such as bird species or car models. While state-of-the-art (SOTA) models are accurate, they are often too resource-intensive for deployment on constrained devices. Knowledge distillation addresses this by transferring knowledge from a large teacher model to a smaller student model. A key challenge is selecting the right teacher, as it heavily impacts student performance. This paper introduces a teacher selection metric, \textbf{Ratio 1-2}, based on teacher prediction ratios. Extensive analysis of over one thousand experiments across 3 students, 8 teachers, and 8 datasets under 4 training strategies demonstrates that our metric improves teacher selection by 18\% over previous methods, enabling small student models to achieve up to 17\% accuracy gains. Experiment codebase is available at: \href{https://github.com/arkel23/FGIR-KD-Teacher}{https://github.com/arkel23/FGIR-KD-Teacher}.
arXiv:2605.15217v1 Announce Type: new Abstract: Instruction-tuned language models exhibit behavioural fairness in high-stakes decisions while retaining biased associations in their internal representations. However, whether these suppressed representations can affect model outputs - and whether such causal potency is symmetric across demographic groups - remains unknown. We investigate the use of open-weight models for mortgage underwriting using matched applications that differ only in racially-associated names and reveal a critical disconnect: models show no output-level bias, yet retain and amplify demographic representations across model layers. Through activation steering and novel cross-layer interventions, we demonstrate that this suppressed information is decision-relevant: when reinjected at critical layers, it produces near-complete decision reversals. Critically, this latent bias is asymmetric - steering interventions affect decisions in one demographic direction, while producing minimal effects in reverse - and susceptible to adversarial prompt engineering and parameter-efficient fine-tuning. These findings demonstrate that behavioural audits focused on outputs are insufficient: fair outputs can mask exploitable internal biases. They also motivate dual-layer testing frameworks combining output evaluation with representational analysis for AI governance in high-stakes decisions.
arXiv:2601.21798v2 Announce Type: replace Abstract: Large Language Models(LLMs) have revolutionized text generation and multimodal perception,but their capabilities in 3D content generation remain underexplored. Existing methods compromise by producing either low-resolution meshes or coarse structural proxies, failing to capture finegrained geometry natively. In this paper, we propose CG-MLLM, a novel Multi-modal Large Language Model (MLLM) capable of 3D captioning and high-resolution 3D generation in a single framework. Leveraging the Mixture-ofTransformer architecture, CG-MLLM decouples disparate modeling needs, where the Token-level Autoregressive (TokenAR) Transformer handles token-level content, and the Block-level Autoregressive (BlockAR) Transformer handles blocklevel content. By integrating a pre-trained visionlanguage backbone with a specialized 3D VAE latent space, CG-MLLM facilitates long-context interactions between standard tokens and spatial blocks within a single integrated architecture. Experimental results show that CG-MLLM significantly outperforms existing MLLMs in generating high-fidelity 3D objects, effectively bringing high-resolution 3D content creation into the mainstream LLM paradigm. Beyond generation, we further observe that learning to produce 3D content transfers back to perception, strengthening the model's image-based 3D understanding.
arXiv:2605.15542v1 Announce Type: new Abstract: GUI agents powered by Multimodal Large Language Models (MLLMs) have demonstrated impressive capability in understanding and executing user instructions. However, accurately grounding instruction-relevant elements from high-resolution screenshots cluttered with irrelevant UI components remains challenging for existing approaches. Inspired by how humans dynamically adjust their perceptual scope to locate task-related regions on complex screens, we propose DRS-GUI, a training-free dynamic region search framework for GUI grounding that can be seamlessly integrated into existing MLLMs. DRS-GUI introduces a lightweight UI Perceptor that performs three human-like perceptual actions (Focus, Shift, and Scatter) to progressively explore the interface and generate region proposals. To dynamically schedule these actions, we further design an Action Planner based on Monte Carlo Tree Search (MCTS). A region quality reward is employed to evaluate and select the highly instruction-relevant region, efficiently pruning redundant UI elements. Experiments demonstrate that DRS-GUI yields a 14\% improvement on ScreenSpot-Pro for general and GUI-specific MLLMs (Qwen2.5-VL-7B and UGround-V1-7B), significantly enhancing grounding performance and generalization.
arXiv:2601.21702v3 Announce Type: replace Abstract: We consider Representation Misdirection (RM), a class of large language model (LLM) unlearning methods that achieve forgetting by redirecting the forget-representations, that is, latent representations of forget-samples, toward a target vector. Despite being important, the roles of the target vector used in RM, however, remain underexplored. Here, we approach and revisit RM through the lens of the Linear Representation Hypothesis. Specifically, if one can identify a one-dimensional representation corresponding to a high-level concept, the Linear Representation Hypothesis enables linear operations on this concept vector within the forget-representation space. Under this view, we hypothesize that, beyond forgetting, machine unlearning via RM elicits controllable emergent side behaviors and stronger side capabilities corresponding to the high-level concept. Our hypothesis is empirically validated across a wide range of tasks, including behavioral control (e.g., controlling unlearned models' truthfulness, sentiment, refusal, and language) and capability enhancement (e.g., improving unlearned models' in-context learning (ICL) capability). Our findings reveal that this phenomenon could be either a hidden risk if misused or a mechanism that can be harnessed for developing unlearned models that require stronger capabilities and controllable behaviors.
arXiv:2605.16003v1 Announce Type: new Abstract: Autoregressive video diffusion models enable open-ended generation through local attention and KV caching. However, existing training-free long-video optimization methods mainly focus on stable extension under a single prompt, making them difficult to handle interactive scenarios involving prompt switching, old scene forgetting, and historical scene recall. We identify the core bottleneck as the functional entanglement of historical KV states: stable anchors and recent dynamics are handled by the same cache policy, leading to outdated background contamination, delayed response to new prompts, and loss of long-range memory. To address this issue, we propose Echo-Forcing, a training-free scene memory framework specifically designed for interactive long video generation with three core mechanisms: (1) Hierarchical Temporal Memory, which decouples stable anchors, compressed history, and recent windows under relative RoPE; (2) Scene Recall Frames, which compresses historical scenes into spatially structured KV representations to support long-term recall; and (3) Difference-aware Memory Decay, which adaptively forgets conflicting tokens according to the discrepancy between old and new scenes. Based on these designs, Echo-Forcing uniformly supports smooth transitions, hard cuts, and long-range scene recall under a bounded cache budget. Extensive evaluations on VBench-Long further demonstrate that Echo-Forcing achieves the best overall performance in both long-video generation and interactive video generation settings. Our code is released in https://github.com/mingqiangWu/Echo-Forcing
arXiv:2601.20761v2 Announce Type: replace Abstract: In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty associated with the current state estimate as data are acquired incrementally. To this end, the proposed framework augments existing QST techniques by associating current point estimates of the state with confidence sets that are guaranteed to contain the true quantum state with a user-defined probability. The methodology is grounded in recent statistical advances in anytime-valid confidence sequences. Numerical results confirm the theoretical coverage properties of the proposed anytime-valid QST.
arXiv:2605.15288v1 Announce Type: new Abstract: The Electron-Ion Collider (EIC) is a next-generation particle accelerator facility designed to probe the fundamental structure of matter such as the origins of nucleon mass, spin, and the dynamic behavior of quarks and gluons within nucleon and nucleus. As the electromagnetic calorimeter in the barrel region, the Barrel Imaging Calorimeter (BIC) is tasked with precise energy measurements of electrons and photons as well as efficient separation of these particles from background pions. The BIC integrates Pb/SciFi sampling layers and AstroPix silicon pixel sensors for three-dimensional shower imaging. The Korean group has actively contributed through silicon chip testing, module assembly, prototype development, beam test, readout system design, and detailed simulations. This presentation highlights the recent progress and plans for the R\&D of the Barrel Imaging Calorimeter in Korea.
arXiv:2511.14282v2 Announce Type: replace Abstract: Deep neural networks achieve outstanding performance across vision and language tasks, yet their large parameter counts limit deployment in resource-constrained settings. One-shot pruning reduces model size without retraining, but models trained with standard objectives often suffer substantial accuracy drops under aggressive sparsity. Prior work mitigates this drop along two directions: regularizers such as $\ell_1$ and DeepHoyer that shape the weight distribution during training, and pruning-robust optimizers such as SAM, CrAM, and S$^2$SAM that flatten the loss landscape. However, existing regularizers either shrink all weights uniformly ($\ell_1$) or induce scale-invariant sparsity (DeepHoyer), without concentrating weight energy onto a small set of informative parameters. We propose a Weight Concentration Regularizer (WCR), a training-time regularizer that amplifies the magnitude of a small subset of parameters while driving the remainder toward zero, so that magnitude pruning predominantly removes parameters with negligible functional contribution. We provide a convergence analysis and evaluate WCR on LLM fine-tuning, image classification, and medical segmentation, demonstrating consistent improvements in pruning robustness across architectures and compatibility with existing pruning-robust optimizers.
arXiv:2605.15889v1 Announce Type: new Abstract: Security in cloud computing has become a major concern due to several factors such as layered cloud architectures, dynamic environments, and exposure to unseen or zero-day attacks. Moreover, intrusion detection systems (IDS) typically operate at specific layers and rely heavily on machine learning models, which often perform well in experimental settings but fail to sustain performance in real cloud deployments. In this work, we implement a confidence-aware multilevel intrusion detection system using reinforcement learning tailored for cloud environments. The system secures three distinct layers: network, host, and hypervisor. Machine learning models at each layer detect known attack patterns, while prediction confidence distinguishes reliable decisions from uncertain outcomes. Within the multi-gate flow, low-confidence events pass through a learned-threshold confidence gate (Gate-1), followed by a Chroma memory-matching gate (Gate-2), with unresolved events escalated to a large language model (LLM) for semantic analysis and explanation. Final attack promotion at Gate-3 uses calibrated LLM confidence or weighted-fusion fallback, while uncertain events are retained in a review bucket to avoid forced classification. Generated explanations and confirmed knowledge are stored in ChromaDB to support future analysis and retraining. The approach is first evaluated using static thresholds, establishing a baseline for comparison. Results show that the proposed system learns adaptive thresholds and reduces LLM escalation by 58.78%, lowering cost while maintaining strong performance (88.68% accuracy, 85.29% precision, 84.72% recall, 85.00% F1). The network and hypervisor layers achieve 98.02% and 97.08% accuracy, demonstrating a balanced and efficient detection system.
arXiv:2601.19923v2 Announce Type: replace Abstract: As Large Language Models (LLMs) evolve into the core of Web-based autonomous agents and complex Web Information Systems, their ability to faithfully translate natural language into rigorous structured formats has become paramount, as this capability is critical for Web API invocation and data exchange. However, evaluating this structural fidelity in Web-native payloads remains a challenge: traditional text metrics fail to capture topological consistency in semi-structured Web data, while manual evaluation is prohibitively costly. To address this, we propose Structure-BiEval, a novel self-supervised framework for quantitative, annotation-free assessment tailored for Web data engineering. By leveraging deterministic Intermediate Representations, our framework effectively decouples structure from content, utilizing Content Semantic Accuracy and Normalized Tree Edit Distance as precise metrics. We empirically benchmark 15 state-of-the-art LLMs across dual Web structural topologies, namely Hierarchical Data (Web backend payloads) and Tabular Data (Web frontend presentation). The results reveal substantial variability in structural performance, including cases where mid-sized models unexpectedly outperform larger counterparts in Web data formatting. Furthermore, our findings show that deep recursive nesting poses a consistent challenge for Web agents across varying parameter scales.
arXiv:2605.15726v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards (RLVR) has emerged as a scalable paradigm for improving the reasoning capabilities of large language models. However, its effectiveness is fundamentally limited by exploration: the policy can only improve on trajectories it has already sampled. While increasing the number of rollouts alleviates this issue, such brute-force scaling is computationally expensive, and existing approaches that modify the optimization objective provide limited control over what is explored. In this work, we propose NudgeRL, a framework for structured and diversity-driven exploration in RLVR. Our approach introduces Strategy Nudging, which conditions each rollout on lightweight, strategy-level contexts to induce diverse reasoning trajectories without relying on expensive oracle supervision. To effectively learn from such structured exploration, we further propose a unified objective, which decomposes the reward signal into inter- and intra-context components and incorporates a distillation objective to transfer discovered behaviors back to the base policy. Empirically, NudgeRL outperforms standard GRPO with up to 8 times larger rollout budgets, while outperforming oracle-guided RL baseline on average across five challenging math benchmarks. These results demonstrate that structured, context-driven exploration can serve as an efficient and scalable alternative to both brute-force rollout scaling and feasibility-oriented methods based on privileged information. Our code is available at https://github.com/tally0818/NudgeRL.
arXiv:2605.15728v1 Announce Type: new Abstract: Category-level 6D object pose estimation is typically formulated as a multi-category joint learning problem with fully shared model parameters. However, pronounced geometric heterogeneity across categories entangles incompatible optimization signals in shared modules, resulting in gradient conflicts and negative transfer during training. To address this challenge, we first introduce gradient-based diagnostics to quantify module-level cross-category contention. Building on results of diagnostics, we propose DecomPose, a difficulty-aware decomposition framework that mitigates optimization contention via: (1) difficulty-aware gradient decoupling, which groups categories using a data-driven difficulty proxy and routes each instance to a group-specific correspondence branch to isolate incompatible updates; and (2) stability-driven asymmetric branching, which assigns higher-capacity branches to structurally simple categories as stable optimization anchors while constraining complex categories with lightweight branches to suppress noisy updates and alleviate negative transfer. Extensive experiments on REAL275, CAMERA25, and HouseCat6D demonstrate that DecomPose effectively reduces cross-category optimization contention and delivers superior pose estimation performance across multiple benchmarks.
arXiv:2605.15848v1 Announce Type: new Abstract: Conversational interfaces powered by large language models (LLMs) are widely used for ideation and analysis, yet their linear structure limits exploration of alternatives and management of long-running interactions. We present CanvasConvo, a conversational interface concept that transforms linear chat into a branching conversation tree embedded in a spatial canvas. CanvasConvo enables users to explore what-if scenarios by branching directly from conversational content, supporting parallel development of alternative directions. These branches are visualized on a canvas while remaining integrated with a familiar chat interface, allowing users to switch between linear and non-linear interaction. Features such as timeline-based navigation, automatic tagging and summarization, and context-aware controls (e.g., goals, reusable prompts) support structured interaction and continuity. We evaluated CanvasConvo in a 5-7 day field study with 24 participants. Our findings highlight how non-linear conversational structures support exploratory workflows and different interactions in LLM-based work.
Decentralized LoRA augmented transformer with multi-scale feature learning for secured eye diagnosis
arXiv:2505.06982v3 Announce Type: replace Abstract: Accurate and privacy-preserving diagnosis of ophthalmic diseases remains a critical challenge in medical imaging, particularly given the limitations of existing deep learning models in handling data imbalance, data privacy concerns, spatial feature diversity, and clinical interpretability. This paper proposes a novel Data efficient Image Transformer (DeiT) based framework that integrates context aware multiscale patch embedding, Low-Rank Adaptation (LoRA), knowledge distillation, and federated learning to address these challenges in a unified manner. The proposed model effectively captures both local and global retinal features by leveraging multi scale patch representations with local and global attention mechanisms. LoRA integration enhances computational efficiency by reducing the number of trainable parameters, while federated learning ensures secure, decentralized training without compromising data privacy. A knowledge distillation strategy further improves generalization in data scarce settings. Comprehensive evaluations on two benchmark datasets OCTDL and the Eye Disease Image Dataset demonstrate that the proposed framework consistently outperforms both traditional CNNs and state of the art transformer architectures across key metrics including AUC, F1 score, and precision. Furthermore, Grad-CAM++ visualizations provide interpretable insights into model predictions, supporting clinical trust. This work establishes a strong foundation for scalable, secure, and explainable AI applications in ophthalmic diagnostics.
arXiv:2605.14236v2 Announce Type: replace Abstract: Pairwise Ranking Prompting (PRP) elicits pairwise preference judgments from an LLM, which are then aggregated into a ranking, usually via classical sorting algorithms. However, judgments are noisy, order-sensitive, and sometimes intransitive, so sorting assumptions do not match the setting. Because sorting aims to recover a full permutation, truncating it to meet a call budget does not produce a dependable top-K. We thus reframe PRP reranking as active learning from noisy pairwise comparisons and show that active rankers are drop-in replacements that improve NDCG@10 per call in the call-constrained regime. Our noise-robust framework also introduces a randomized-direction oracle that uses a single LLM call per pair. This approach converts systematic position bias into zero-mean noise, enabling unbiased aggregate ranking without the cost of bidirectional calls.
arXiv:2504.18361v2 Announce Type: replace Abstract: Recent advances in image manipulation have enabled highly photorealistic content generation, but also lowered the barrier to arbitrary editing, raising concerns about multimedia authenticity and security. Existing Image Manipulation Detection and Localization (IMDL) methods mainly target splicing or copy-move forgeries, while benchmarks for inpainting-based manipulations remain limited. To bridge this gap, we present COCO-Inpaint, a comprehensive benchmark specifically designed for inpainting detection and localization, with three key contributions: 1) High-quality inpainting samples generated by six state-of-the-art inpainting models, 2) Diverse generation scenarios enabled by four mask generation strategies with optional text guidance, and 3) Large-scale coverage of 238,302 inpainted images with rich semantic diversity. Our benchmark is constructed to highlight intrinsic inconsistencies between inpainted and authentic regions, rather than superficial semantic artifacts such as object shapes. We further establish a rigorous evaluation protocol with three standard metrics to benchmark existing IMDL methods and reveal current trends and challenges.
arXiv:2605.15285v1 Announce Type: new Abstract: Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivatives are foundational open questions and delicate problems in nonlinear functional analysis. In this manuscript, we prove the first UATs of non-linear $k$-times differentiable operators between Banach spaces and their derivatives, uniformly on compact sets and in weighted Sobolev norms for general finite input measures, via OL architectures. Our results are the first complete generalizations of the corresponding influential classical results in [Hornik, 1991] to infinite-dimensional settings and OL. We discuss several open areas where DIOL and our UATs find applications: high-order accuracy in OL, fast constrained optimization in Banach spaces (e.g. optimal control of PDEs, inverse problems) and numerical methods for infinite-dimensional PDEs (e.g. HJB PDEs on Banach spaces from optimal control of PDEs, SPDEs, path-dependent systems, partially observed systems, mean-field control). We parameterize nonlinear operators via Encoder-Decoder Architectures, renowned classes in OL due to their generality, including classical architectures, such as DeepONets, Deep-H-ONets, PCA-Nets. Our results are based on four key features that allow us to prove UATs in full generality: (i) Approximation Properties of Banach spaces. (ii) $k$-times continuous differentiability in the sense of Bastiani (weaker than $k$-times continuous Fr\'echet differentiability). (iii) Natural compact-open topologies for UA; indeed, we show that UA in standard compact-open topologies induced by operator norms is violated even for Fr\'echet derivatives. (iv) Construction of novel weighted Sobolev spaces for the UA.