arXiv:2605.12509v2 Announce Type: replace Abstract: Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order graph formalisms extend this framework by incorporating multiway, hierarchical, temporal, multilayer, recursive, and tensor-based interactions, thereby providing more expressive representations of complex systems. This book presents a comprehensive overview of mathematical notions that can be used to model higher-order networks. It surveys foundational concepts, extensional frameworks, and newly introduced formalisms, with an emphasis on their structural principles, relationships, and modeling roles. The aim is to provide a unified perspective that helps readers compare diverse higher-order network models and identify appropriate tools for theoretical study and practical applications. This book is Edition 2.0. It mainly includes the addition of several concepts, as well as corrections and improvements of typographical errors and explanations.
Science Journals
arXiv:2605.15451v1 Announce Type: new Abstract: We obtain the viscous and diffusive fundamental solution for monochromatic internal waves in a uniformly stratified medium and for anisotropic Brinkman flow. These solutions take the form of single integrals with logarithmic singularities, and can be computed numerically in an efficient manner for possible use in boundary integral methods. Far-field asymptotic results are obtained, giving solutions valid far from and inside a ``beam'' corresponding to the internal wave angle in the internal wave case, consistent with Thomas & Stevenson (1972). For Prandtl numbers $\text{Pr} \gtrsim O(1)$, the wave field is given by a superposition of wave- and Stokeslet-like terms. Unlike previous studies, a uniform asymptotic expansion of the wave-field for $\text{Pr} \gtrsim O(1)$ can be computed rigorously. Density diffusion attenuates the wave amplitude as to $(1+\text{Pr}^{-1})^{-2/3}$ and broadens the beam width according to $(1+\text{Pr}^{-1})^{1/3}$. Evanescent waves in a stratified medium and anisotropic Brinkman flows have similar behaviour. Anisotropic Brinkman flow is purely real, dominated by a single circulation cell. As anisotropy increases, the flow becomes increasingly confined to the direction with least resistance. The stratified evanescent wave field has near-vertical cells in its real part, and a dominant single circulation cell in its imaginary part.
arXiv:2605.16187v1 Announce Type: new Abstract: Most deployed WAN Traffic Engineering (TE) systems use a logically centralized controller that periodically gathers traffic demands, runs a TE optimization or heuristic, and then programs the network. At scale, these solutions can be sub-optimal, and can take minutes to react to demand changes or failures. In this paper, we introduce OnlineTE, a system that reacts immediately to demand changes and failures, and delivers near-optimal solutions within seconds of a change. OnlineTE builds on the theory of optimization decomposition to devise scalable, near-optimal, distributed TE solvers for path-based MLU and Max-flow problems. In OnlineTE, each switch solves part of the optimization, and a central coordinator orchestrates the progress of the switches. As such, a switch can trigger a re-optimization as soon as it notices a demand change or failure, enabling high reactivity. OnlineTE scales to large WANs, and its compute requirements are well below the capabilities of modern WAN switches. It also enables a new opportunity, edge-based TE, which can utilize resources more efficiently than today's path-based approaches. On a testbed emulation of a 750-node WAN topology, OnlineTE can outperform the state-of-the-art by up to an order of magnitude.
arXiv:2505.23678v3 Announce Type: replace Abstract: While reinforcement learning (RL) over chains of thought has significantly advanced language models in tasks such as mathematics and coding, visual reasoning introduces added complexity by requiring models to direct visual attention, interpret perceptual inputs, and ground abstract reasoning in spatial evidence. We introduce ViGoRL (Visually Grounded Reinforcement Learning), a vision-language model trained with RL to explicitly anchor each reasoning step to specific visual coordinates. Inspired by human visual decision-making, ViGoRL learns to produce spatially grounded reasoning traces, guiding visual attention to task-relevant regions at each step. When fine-grained exploration is required, our novel multi-turn RL framework enables the model to dynamically zoom into predicted coordinates as reasoning unfolds. Across a diverse set of visual reasoning benchmarks--including SAT-2 and BLINK for spatial reasoning, V*bench for visual search, and ScreenSpot and VisualWebArena for web-based grounding--ViGoRL consistently outperforms both supervised fine-tuning and conventional RL baselines that lack explicit grounding mechanisms. Incorporating multi-turn RL with zoomed-in visual feedback significantly improves ViGoRL's performance on localizing small GUI elements and visual search, achieving 86.4% on V*Bench. Additionally, we find that grounding amplifies other visual behaviors such as region exploration, grounded subgoal setting, and visual verification. Finally, human evaluations show that the model's visual references are not only spatially accurate but also helpful for understanding model reasoning steps. Our results show that visually grounded RL is a strong paradigm for imbuing models with general-purpose visual reasoning.
arXiv:2605.15775v1 Announce Type: new Abstract: Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious, domain-specific cues (``shortcut learning''), which limits generalization to unseen domains after deployment. In this paper, we address this limitation through continual learning of domain-invariant representation. We introduce a broad class of CL methods that sequentially learn representations capturing invariant structures across domains. Our methods are motivated by the observation that such invariant structures often preserve the underlying causal mechanisms, which can reduce the risk of overfitting to domain-specific cues and thus offer better out-of-domain generalization. Our proposed CL methods combine replay-based training with a tailored sequential invariance alignment to learn -- and preserve -- invariant structures over time. We evaluate our methods under a deployment-oriented protocol that measures performance on unseen target domains. Across six benchmark and real-world datasets spanning vision, medicine, manufacturing, and ecology, our methods consistently outperform existing CL baselines in terms of generalization to unseen target domains. As an ablation, we further show that na\"ive extensions of sequential training with existing domain-invariant representation learning (DIRL) methods provide only limited benefits. To the best of our knowledge, this is the first work to develop domain-invariant representation methods for CL.
arXiv:2605.16054v1 Announce Type: new Abstract: Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are fundamental to environment transitions, reward structures, and high-level agent behavior. Explicitly modeling these hidden processes is essential for both precise dynamics modeling and effective decision-making. In this paper, we propose a unified framework that explicitly incorporates latent dynamic inference into generative decision-making from minimal yet sufficient observations. We theoretically show that under mild conditions, the latent process can be identified from small temporal blocks of observations. Building on this insight, we introduce Ada-Diffuser, a causal diffusion model that learns the temporal structure of observed interactions and the underlying latent dynamics simultaneously, and furthermore, leverages them for planning and control. With a modular design, Ada-Diffuser supports both planning and policy learning tasks, enabling adaptation to latent variations in dynamics, rewards, and latent actions. Experiments on simulated control and robotic benchmarks demonstrate its effectiveness in accurate latent inference and adaptive policy learning.
arXiv:2605.15487v1 Announce Type: new Abstract: Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.
arXiv:2605.16161v1 Announce Type: new Abstract: This paper presents a novel architecture utilizing a 10T SRAM cell for XNOR-based in-memory computing, aimed at mitigating the extensive routing challenges typically encountered in conventional in-memory computing systems. By integrating a full adder between in-memory multiplication cells, the proposed design achieves a 50% reduction in routing complexity. The architecture performs multiply-accumulate (MAC) operations using XNOR computation optimized for binary neural networks (BNNs). Additionally, a 14T-based full adder is employed to construct an N-bit ripple carry adder in the adder tree, significantly reducing the area compared to traditional 28T-based CMOS designs. The 10T SRAM XNOR computation further enhances the latency for MAC operations. The proposed approach reduces the latency and area overhead, improving the overall hardware's area efficiency by 2.67x compared to the state-of-the-art.
arXiv:2605.13521v2 Announce Type: replace Abstract: We introduce the multilingual Granite Embedding R2 models, a family of encoder-based embedding models for enterprise-scale dense retrieval across 200+ languages. Extending our English-focused R2 release, these models add enhanced support for 52 languages and programming code, a 32,768-token context window (a 64x expansion over R1), and state-of-the-art overall performance across multilingual and cross-lingual text search, code retrieval, long-document search, and reasoning retrieval datasets. The release consists of two bi-encoder models based on the ModernBERT architecture with an expanded multilingual vocabulary: a 311M-parameter full-size, and a 97M-parameter compact model built via model pruning and vocabulary selection that achieves the highest retrieval score of any open multilingual embedding model under 100M parameters. The full-size also supports Matryoshka Representation Learning for flexible embedding dimensionality. Both models are trained on enterprise-appropriate data with governance oversight, and released under the Apache 2.0 license at https://huggingface.co/collections/ibm-granite, designed to support responsible use and enable unrestricted research and enterprise adoption.
arXiv:2605.15397v1 Announce Type: new Abstract: Illegal gold mining in the Amazon rainforest causes deforestation, water contamination, and long-term ecosystem disruption, yet remains difficult to monitor at fine spatial scales. Satellite imagery supports large-scale observation, but often misses small mining-related structures and subtle land-cover transitions, especially under frequent cloud cover. We introduce ELDOR, a large-scale UAV benchmark for monitoring environmental and landscape disturbance from illegal gold mining in the rainforest. ELDOR contains manually annotated orthomosaic imagery covering over 2,500 hectares, with pixel-level semantic labels for both mining-related activities and surrounding ecological structures. With this unified annotation source, we establish four benchmark tasks: semantic segmentation, segmentation-derived recognition, direct multi-label classification, and class-presence recognition with vision-language models. Across these tasks, we compare generic and remote-sensing-specific segmentation models, vision foundation model-related segmentation methods, direct multi-label classification methods, and vision-language models under a controlled closed-set protocol. Results show that current methods still struggle with rare small-scale mining structures and fine-grained recovery classes, suggesting the need for context-aware and multimodal modeling. To support domain analysis and practical use, we further build an interactive explorer for domain experts that provides a unified interface for data exploration and model inference.
arXiv:2605.14205v2 Announce Type: replace Abstract: LLM-based web agents can navigate live storefronts, yet they often collapse to a single "average buyer" policy, failing to capture the heterogeneous and distributional nature of real buyer populations. Existing personalization methods rely on hand-crafted prompt-based personas that are brittle, difficult to scale, context-inefficient, and unable to faithfully represent population-level behavior. We introduce SimPersona, a novel framework that learns discrete buyer types from historical traffic and exposes them to LLM-based web agents as compact persona tokens. Given raw clickstreams, a behavior-aware VQ-VAE induces a discrete buyer-type space that captures the statistical structure of real buyer behavior and merchant-specific buyer population distributions. To provide behavior-specific guidance to LLM-based web agents, SimPersona maps each learned buyer type to a dedicated persona token in the LLM agent vocabulary and fine-tunes the agent with these tokens on real browsing traces. At inference, each synthetic buyer is assigned to a learned buyer type with a single encoder forward pass, requiring no retraining or store-specific prompt engineering. For population-level simulation, SimPersona samples buyer types from each merchant's empirical distribution over the learned VQ-VAE codebook and instantiates agents with the corresponding persona tokens, preserving merchant-specific buyer population distributions. Evaluated on $8.37$M buyers across $42$ held-out live storefronts, SimPersona achieves $78\%$ conversion-rate alignment with real buyers, exhibits interpretable behavioral variation across buyer types, and outperforms a baseline with $8\times$ more parameters on goal-oriented shopping tasks. We further release an open-source data pipeline that converts raw e-commerce event logs into buyer representations and agent-training traces.
arXiv:2605.14354v2 Announce Type: replace Abstract: We present a new computational framework for detecting and structuring manipulative political narratives. A task that became more important due to the shift of political discussions to social media. One of the primary challenges thereby is differentiating between manipulative political narratives and legitimate critiques. Some posts may also reframe actual events within a manipulative context. To achieve good clustering results, we filter manipulative posts beforehand using a detailed few-shot prompt that combines documented campaign narratives with legitimate criticisms to differentiate them. This prompt enables a reasoning model to assign labels, retaining only manipulative narrative posts for further processing. The remaining posts are subsequently embedded and dimensionality-reduced using UMAP, before HDBSCAN is applied to uncover narrative groups. A key advantage of this unsupervised approach is its independence from a predefined list of target categories, enabling it to uncover new narrative clusters. Finally, a reasoning model is employed to uncover the narrative behind each cluster. This approach, applied to over 1.2 million social media posts, effectively identified 41 distinct manipulative narrative clusters by integrating prompt-based filtering with unsupervised clustering.
arXiv:2509.15267v2 Announce Type: replace Abstract: The costs of generative model compute rekindled promises and hopes for efficient data curation. In this work, we investigate whether recently developed autoguidance and online data selection methods can improve the time and sample efficiency of training generative diffusion models. We integrate joint example selection (JEST) and autoguidance into a unified code base for fast ablation and benchmarking. We evaluate combinations of data curation on a controlled 2-D synthetic data generation task as well as (3x64x64)-D image generation. Our comparisons are made at equal wall-clock time and equal number of samples, explicitly accounting for the overhead of selection. Across experiments, autoguidance consistently improves sample quality and diversity. Early AJEST (applying selection only at the beginning of training) can match or modestly exceed autoguidance alone in data efficiency on both tasks. However, its time overhead and added complexity make autoguidance or uniform random data selection preferable in most situations. These findings suggest that while targeted online selection can yield efficiency gains in early training, robust sample quality improvements are primarily driven by autoguidance. We discuss limitations and scope, and outline when data selection may be beneficial.
arXiv:2605.15999v1 Announce Type: new Abstract: This paper introduces a motion planning framework to plan morphology and trajectory for morphing quadrotors under extremely constrained environments. We develop a novel obstacle avoidance cost function for nonlinear model predictive control (MPC) that enables navigation through extremely narrow gaps under limited perception from a 2D LiDAR. Classical artificial potential field-based costs typically have a high cost in narrow passages, artificially blocking the navigable path. In contrast, we propose a smooth exponential obstacle cost that preserves low traversal cost within narrow gaps while maintaining strong collision avoidance behavior. The formulation avoids hard activation thresholds and introduces a cost reduction factor to reduce the cost within narrow passages. Direct use of 2D LiDAR measurements in MPC allows navigation around arbitrarily shaped obstacles. The method is embedded within an acados-based nonlinear MPC framework. Simulation and experimental results demonstrate successful traversal of narrow corridors where typical repulsive cost functions would fail. The approach provides a computationally efficient and practical solution for navigating through tight spaces while maintaining safety from the obstacles. While we are implementing the framework on the morphing quadrotors, the cost function formulation is general-purpose for any mobile robot application, and is not limited to the morphing quadrotors. The implementation code is available at \href{https://github.com/harshjmodi1996/morphocopter_mpc}{Github Repo} and a short video is available at \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/03/MPC_MorphoCopter_video.mp4}{Video Link}.
arXiv:2605.15356v1 Announce Type: new Abstract: Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive importance sampling provides a natural localization tool: its evolving proposal distribution progressively identifies the failure-relevant region. Motivated by this observation, we propose a surrogate-assisted adaptive importance sampling framework that refines the surrogate locally along the evolving proposal, rather than over the entire input space. The surrogate combines an encoder with a neural network, providing a low-dimensional latent representation for both prediction and sample selection. At each adaptive iteration, candidates drawn from the current proposal are selected by a greedy latent-space rule balancing proximity to the estimated failure boundary and sample diversity. The selected samples are evaluated by the high-fidelity model and used to refine the surrogate, which then guides the subsequent cross-entropy-type adaptive proposal update. We establish one-step proposal stability bounds under local surrogate errors, together with surrogate-induced misclassification and finite-sample estimation error bounds. Numerical experiments on multimodal benchmarks and PDE-driven rare-event problems up to 100 dimensions show that the proposed method achieves accuracy comparable to true-model adaptive importance sampling while requiring substantially fewer high-fidelity evaluations.
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:2605.15997v1 Announce Type: new Abstract: Recent progress in deep learning has significantly advanced CT image analysis, particularly for segmentation tasks. However, these advances are largely confined to image-level pattern recognition, with most methods lacking explicit anatomical or contextual reasoning. Large vision-language models introduce linguistic context into image analysis, yet most approaches typically focus on a single task, which is insufficient for clinical workflow analysis that requires multiple fine-grained types of analysis, such as anatomy detection and segmentation. In this paper, we propose a unified autoregressive framework that integrates language-guided visual reasoning into CT interpretation. Our method introduces task-routing tokens that trigger detection and segmentation heads conditioned on the hidden states of a large vision-language model, enabling coherent generation of visual outputs (e.g., masks and bounding boxes) and textual reasonings. To progressively enhance localisation accuracy and semantic clarity, we further design a "closer-look" mechanism that allows the model to perform progressive coarse-to-fine visits to regions of interest under refined fields of view. To support model training and evaluation, we curated a new multimodal CT dataset containing pixel-wise masks, bounding boxes, spatial prompts, and structured descriptions for visual objects constructed through an AI-assisted annotation process with human verification. Experiments on public benchmarks demonstrate consistent improvements over the SoTA, achieving up to 1.0% Dice on BTCV and 1.7% Dice on MosMed+, while additionally providing appearance reasoning outputs. The code and dataset will be available.
arXiv:2602.21536v2 Announce Type: replace Abstract: Retrospective MRI harmonization is limited by poor scalability across modalities and reliance on traveling subject datasets. To address these challenges, we introduce IHF-Harmony, a unified invertible hierarchy flow framework for multi-modality harmonization using unpaired data. By decomposing the translation process into reversible feature transformations, IHF-Harmony guarantees bijective mapping and lossless reconstruction to prevent anatomical distortion. Specifically, an invertible hierarchy flow (IHF) performs hierarchical subtractive coupling to progressively remove artefact-related features, while an artefact-aware normalization (AAN) employs anatomy-fixed feature modulation to accurately transfer target characteristics. Combined with anatomy and artefact consistency loss objectives, IHF-Harmony achieves high-fidelity harmonization that retains source anatomy. Experiments across multiple MRI modalities demonstrate that IHF-Harmony outperforms existing methods in both anatomical fidelity and downstream task performance, facilitating robust harmonization for large-scale multi-site imaging studies. Code is available at https://github.com/Idea89560041/IHF-Harmony.
arXiv:2505.21698v3 Announce Type: replace Abstract: Vision-language foundation models achieve promising performance in natural image classification, yet their direct application to medical imaging is limited by severe domain shifts, resolution mismatches, and the multi-label nature of clinical diagnosis. Training dedicated medical foundation models from scratch, however, is costly and data-intensive. Here, we propose MedBridge, a lightweight adaptation framework that opens a new direction in domain-gap mitigation by jointly combining domain alignment, resolution preservation, and multi-label reasoning via complementary VLM experts for medical image diagnosis. Specifically, MedBridge transforms pretrained VLMs into multi-view query encoders that inject a compact set of learnable query tokens into intermediate layers, enabling non-destructive domain alignment while preserving fine-grained pathological cues via multi-view high-resolution sampling. These query tokens further act as routing signals for a mixture-of-experts, dynamically integrating heterogeneous foundation models for multi-label reasoning without requiring a shared representation space. We evaluated MedBridge on five chest radiograph benchmarks in three key adaptation tasks. MedBridge demonstrates superior performance in both cross-domain generalization (out-of-distribution transfer) and in-domain specialization (same-distribution tuning) settings, yielding a significant 6-15% AUC improvement over state-of-the-art adaptation methods for multi-label thoracic disease diagnosis. Furthermore, MedBridge is model-agnostic and demonstrates broad extensibility across eight diverse VLMs (e.g., CLIP, LLaVA, Qwen-VL, MedGemma), highlighting its ability to flexibly adapt arbitrary foundation models into a powerful medical diagnostic tool. Our code will be released upon acceptance.
arXiv:2605.16058v1 Announce Type: new Abstract: In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy compared to traditional matrix methods. Under the star-M tensor framework, tensors can be decomposed in a matrix-mimetic way, including using the star-M SVD. This tensor SVD has optimality guarantees and has shown exceptional performance on specific types of data, but software implementations have been mostly limited to productivity-oriented languages. In this work, we present our development of a shared-memory parallel, high-performance solution designed to efficiently implement the underlying algorithms. This software will enable optimal compression of extensive scientific datasets, paving the way for enhanced data analysis and insights.
arXiv:2605.15774v1 Announce Type: new Abstract: Traditional Fully Homomorphic Encryption (FHE) schemes often suffer from prohibitive computational overhead and complex noise management. In this paper, we propose a novel symmetric FHE through a mechanism of plaintext fragmentation and dynamic interposition. Our approach is built upon a modular encryption foundation, c = mk + rp, which is naturally additive but typically limited by exponential noise growth during multiplication. To resolve this, we introduce an interposition framework where the plaintext is partitioned into multiple fragments across distinct logical positions. We introduce a dual-regulator system to govern the multiplication process; exponent regulators (t_i) redirect the product of fragments to a new target position, preventing the accumulation of secret key exponents, while coefficient regulators (d_i) normalize the resulting scalars. Security is established through a binding mechanism where exponents and coefficients are mutually dependent, shielding the secret key k from algebraic manipulation and substitution attacks.
arXiv:2605.15279v1 Announce Type: new Abstract: Piezoelectric resonators (PRs) have been seen as a competitive alternative to magnetic components. In PR-based converters, the motional current (in the LC series branch of the equivalent circuit) is vital for control proposes but cannot be measured directly. The difficulties to detect the zero-crossing points or to measure the amplitude of the motional current has been one of the most dominating obstacles that complicates the control strategies and limits the frequency range of the PR-based converters. This work discusses a ring-dot shaped piezoelectric transformer (PT) based motional current sensing method that provides current information with low-delay, low-loss and intrinsic isolation. It is physically proven that the proposed method is robust with various non-ideal factors of the piezoceramic and circuit implementation. Based on this, an event-driven control strategy is introduced, consisting of only a finite state machine, a PI loop, a low-speed ADC and several comparators. Experiments on a step-down PR-based converter verify that the proposed approach realize ZVS for all transitions within a switching cycle with reduced hardware and software resources, enhances stability and is capable of self-startup.
arXiv:2406.14930v5 Announce Type: replace-cross Abstract: The minimization principle $\textsf{MIN}(\triangleleft)$ studied in bounded arithmetic says that a strict linear ordering $\triangleleft$ on any finite interval $[0,\dots,n)$ has the minimal element. We shall prove that bounded arithmetic theory $\textsf{T}^1_2(\triangleleft)$ augmented by instances of the pigeonhole principle for all $\Delta^b_1(\triangleleft)$ formulas does not prove $\textsf{MIN}(\triangleleft)$.
arXiv:2605.15363v1 Announce Type: new Abstract: Accurate forecasting of residual Physical Resource Blocks (PRBs) is critical for proactive network slice provisioning, energy-efficient operation, and spectrum-aware decision making in cellular systems, where residual PRBs serve as a practical proxy for short- and medium-term spectrum availability. Existing PRB prediction methods typically rely only on historical PRB values and are trained independently per carrier or sector, limiting their ability to capture cross-carrier dependencies and providing no measure of forecast uncertainty. Moreover, point forecasts alone are insufficient for robust spectrum-aware control under highly variable traffic conditions. This paper proposes PRB-RUPFormer, a recursive unified probabilistic Transformer for residual PRB forecasting. The proposed model jointly processes multivariate KPI time series using temporal, seasonal, and carrier-aware embeddings, preserving inter-metric temporal coupling during recursive rollout and stabilizing long-horizon forecasting. A single shared model is trained across all carriers and sectors of an eNB, enabling efficient learning of joint traffic dynamics with low computational overhead. Forecast uncertainty is captured through quantile-based prediction intervals, providing confidence-aware estimates of future PRB availability. Evaluations on six months of commercial LTE network data from multiple U.S. locations demonstrate median MAE below 0.05 and hit probabilities above 0.80 for both one-day and seven-day recursive forecasts. These probabilistic predictions directly support spectrum-aware RAN functions such as dynamic carrier activation, congestion avoidance, and proactive spectrum sharing, making the proposed framework well-suited for dynamic spectrum access scenarios.
arXiv:2604.16925v3 Announce Type: replace Abstract: Cross-dose denoising for low-dose positron emission tomography (LDPET) has been proposed to address the limited generalization of models trained at a single noise level. However, neural networks trained on a specific dose level often fail to generalize to other dose conditions due to variations in noise magnitude and statistical properties. Conventional "one-size-for-all" models attempt to mitigate this variability but tend to learn averaged representations across noise levels, resulting in degraded performance. In this work, we analyze this limitation and show that standard training formulations implicitly optimize an expectation over heterogeneous noise distributions, causing the network to learn an averaged denoising mapping that cannot accurately model dose-specific noise characteristics. We propose a unified residual noise learning framework that estimates noise directly from low-dose PET images rather than predicting full-dose images. Experiments on large-scale multi-dose PET datasets from two medical centers demonstrate that the proposed method outperforms the "one-size-for-all" model, individual dose-specific U-Net models, and dose-conditioned approaches, achieving improved denoising performance. These results indicate that residual noise learning effectively mitigates the averaging effect and enhances generalization for cross-dose PET denoising.