arXiv:2511.08226v2 Announce Type: replace
Abstract: In order to achieve Continual Learning (CL), the problem of catastrophic forgetting, one that has plagued neural networks since their inception, must be overcome. The evaluation of continual learning methods relies on splitting a known homogeneous dataset and learning the associated tasks one after the other. We argue that most CL methods introduce a priori information about the data to come and cannot be considered agnostic. We exemplify this point with the case of methods relying on pretrained feature extractors, which are still used in CL. After showing that pretrained feature extractors imply a loss of generality with respect to the data that can be learned by the model, we then discuss other kinds of a priori information introduced in other CL methods. We then present the Online Patch Redundancy Eliminator (OPRE), an online dataset-compression algorithm that discards information through two explicit, input-space criteria. With a classifier that was randomly initialized at test time, OPRE's performance matches reported state-of-the-art online continual-learning methods on CIFAR 10 and CIFAR-100 without any pretrained feature extractor, and outperforms GDumb at an identical memory budget-while making only minimal and interpretable assumptions about the data to come. We frame these results as an empirical, information-theoretic perspective on continual learning.
Science Journals
arXiv:2604.18072v2 Announce Type: replace-cross
Abstract: Quantum gases confined in reduced dimensions have enabled the observation of many exotic quantum phenomena. While existing experiments primarily focus on homonuclear systems, we report here on the efficient preparation of a quasi-two-dimensional (2D) heteronuclear quantum degenerate mixture of ultracold $^{23}$Na and $^{87}$Rb. We describe the design of the vacuum system and detail the experimental procedures for preparing the 2D quantum mixture. The designed apparatus has several unique features, including compact and modular 2D-MOT sources, a science chamber that accommodates various lattice geometries, a precision in-vacuum electrode assembly, and high-resolution imaging for both atomic species. After loading the dual-species condensate into a single layer of a vertical optical lattice, we prepare a 2D gas mixture and observe quantum immiscibility in the in-situ equilibrium density profiles. The observed density profiles agree well with mean-field theories. The apparatus provides a versatile platform for investigating several interesting problems, including quantum impurities, quantum droplets, or polar molecules in low dimensions.
arXiv:2604.20899v2 Announce Type: replace-cross
Abstract: Scalable synthesis remains the gate between MOF discovery and industrial deployment, as scale-up know-how is fragmented across disparate reports. We introduce ScaleMOF, a literature-mined dataset and a positive-unlabeled learning strategy that fine-tunes large language models. Achieving 93.5% accuracy, this proof-of-concept serves as a literature-grounded ranking tool prioritizing plausible scale-up candidates.
arXiv:2511.08583v2 Announce Type: replace
Abstract: Developing efficient and accurate visuomotor policies poses a central challenge in robotic imitation learning. While recent rectified flow approaches have advanced visuomotor policy learning, they suffer from a key limitation: After iterative distillation, generated actions may deviate from the ground-truth actions corresponding to the current visual observation, leading to accumulated error as the reflow process repeats and unstable task execution. We present Selective Flow Alignment (SeFA), an efficient and accurate visuomotor policy learning framework. SeFA resolves this challenge by a selective flow alignment strategy, which leverages expert demonstrations to selectively correct generated actions and restore consistency with observations, while preserving multimodality. This design introduces a consistency correction mechanism that ensures generated actions remain observation-aligned without sacrificing the efficiency of one-step flow inference. Extensive experiments across both simulated and real-world manipulation tasks show that SeFA Policy surpasses state-of-the-art diffusion-based and flow-based policies, achieving superior accuracy and robustness while reducing inference latency by over 98%. By unifying rectified flow efficiency with observation-consistent action generation, SeFA provides a scalable and dependable solution for real-time visuomotor policy learning. Code is available on https://github.com/RongXueZoe/SeFA.
arXiv:2511.12810v2 Announce Type: replace
Abstract: Camouflaged object detection is an emerging and challenging computer vision task that requires identifying and segmenting objects that blend seamlessly into their environments due to high similarity in color, texture, and size. This task is further complicated by low-light conditions, partial occlusion, small object size, intricate background patterns, and multiple objects. While many sophisticated methods have been proposed for this task, current methods still struggle to precisely detect camouflaged objects in complex scenarios, especially with small and multiple objects, indicating room for improvement. We propose a Multi-Scale Recursive Network that extracts multi-scale features using a Pyramid Vision Transformer backbone and combines them with specialized Attention-Based Scale Integration Units, thereby enabling selective feature merging. For more precise object detection, our decoder recursively refines features by incorporating Multi-Granularity Fusion Units. A novel recursive-feedback decoding strategy is developed to enhance the model's understanding of global context, thereby helping it overcome the challenges of this task. By jointly leveraging multi-scale learning and recursive feature optimization, our proposed method achieves performance gains, successfully detecting small and multiple camouflaged objects. Our model achieves state-of-the-art results on two benchmark datasets for camouflaged object detection and ranks second on the remaining two. Our code, model weights, and results are available at https://github.com/linaagh98/MSRNet.
arXiv:2607.08689v1 Announce Type: new
Abstract: The naming choices of powerful rulers encode millennia of cultural, political, and institutional influences. Consequently, the long-term onomastic dynamics within some of the most powerful dynasties cannot be explained by simple mechanisms such as frequency-dependent reinforcement or random name reuse. Here, we propose a minimal model that encapsulates these influences in a single highly stochastic variable, prestige, and assume that name selection is driven by the prestige accumulated by previous rulers bearing the same name within each dynasty. Using an extensive dataset spanning ten dynasties, we show that the model reproduces the pronounced inequalities in name frequencies, the long-term persistence of dominant names, and the abrupt rises in popularity observed in historical records. Our results suggest that the naming traditions of powerful rulers preserve institutional memory through reinforcement while remaining sensitive to rare historical events that can reshape the hierarchy of names across generations.
arXiv:2606.08872v2 Announce Type: replace
Abstract: We consider the fair division problem of indivisible chores and resolve the long-standing open problem for the existence of EFX (envy-free up to any item) allocations with additive cost functions. We show that, even for tri-valued additive cost functions, for every $n\geq 4$, there exists an instance with $n$ agents where no EFX allocation exists. Our counterexample only uses three types of chores and two types of agents. The numbers of types for chores and agents are both tight: an EFX allocation is known to exist for one type of agents (i.e., with identical cost functions) or two types of chores.
We then consider bi-valued instances. We show that, for every $n\geq 4$, there exists an instance with $n$ agents where every EFX allocation is not Pareto-optimal. This is also the first example showing the incompatibility of EFX and Pareto-optimality when the costs of items are positive: existing examples showing the incompatibility of EFX and Pareto-optimal exploit items with $0$ costs. Our result shows such an example exists even for bi-valued instances. The number of agents $n$ is also tight: for $n\leq 3$, it is known that EFX is compatible with Pareto-optimality. Finally, we also show that an EFX allocation is guaranteed to exist for $n=4$.
arXiv:2607.08691v1 Announce Type: new
Abstract: Repository-level code generation requires implementing target functions while accounting for complex cross-file dependencies and project-specific conventions. Existing retrieval methods predominantly rely on lexical, structural, or semantic similarity, often overlooking repository functions that implement similar procedural logic despite differing in identifiers or application domains. We propose ProjAgent, a repository-level code generation system that introduces procedural similarity as an explicit retrieval signal. ProjAgent decomposes the target function into intermediate reasoning steps and employs an agentic workflow to retrieve repository functions that exhibit similar procedural behavior at each step. The retrieved procedural context is integrated with conventional semantic retrieval to construct a richer repository context for code generation. ProjAgent further incorporates a conservative static-analysis feedback loop that iteratively repairs generated code using compiler and static-analysis feedback. Evaluated on REPOCOD, ProjAgent achieves 41.14% Pass@1, outperforming existing retrieval-based baselines. These results demonstrate that procedural similarity is an effective and previously unexplored retrieval dimension for repository-level code generation.
arXiv:2607.08694v1 Announce Type: new
Abstract: In this paper, we introduce nonstandard versions of multistep multistage methods. While proving the convergence of these schemes, we also define nonstandard general linear methods. We show that the nonstandard methods can attain the same order as their standard counterparts while preserving certain qualitative properties (e.g., boundedness) for all positive step sizes. These results are also demonstrated by some numerical experiments.
arXiv:2511.18940v3 Announce Type: replace
Abstract: Cross-subject motor imagery decoding remains a fundamental challenge in EEG-based brain-computer interfaces due to substantial inter-subject variability. Recent approaches have leveraged Riemannian geometry by representing EEG signals as covariance matrices on the symmetric positive definite (SPD) manifold. However, existing methods primarily focus on manifold-based representations while largely overlooking subject-specific variations in covariance dispersion and orientation. In this work, we address these challenges through geometry-aware congruence transformations and propose three complementary models: (i) Discriminative Congruence Transform (DCT), (ii) Deep Linear DCT (DLDCT), and (iii) Deep DCT-UNet (DDCT-UNet). The proposed models are evaluated both as manifold alignment modules for downstream classifiers and as end-to-end discriminative architectures optimized via cross-entropy with a custom logistic regression head. Experiments on challenging cross-subject motor imagery benchmarks demonstrate consistent improvements in transductive decoding performance, achieving 2-3% higher accuracy than strong baselines. These results highlight the effectiveness of geometry-aware congruence learning for mitigating inter-subject variability in EEG decoding.
arXiv:2511.19032v2 Announce Type: replace
Abstract: Visual corruptions can change vision--language model (VLM) behavior in ways that top-1 accuracy does not capture. A model may keep the same answer while losing distributional support, or improve accuracy through unstable wrong-to-correct changes. We introduce Bench-C, a controlled multiple-choice testbed for studying these effects. It selects semantically diverse samples whose predictions respond to corruption, and evaluates them under 19 corruption types and five severity levels. To measure how corruption changes the option distribution, we introduce the Robustness Alignment Score (RAS), which combines confidence-correctness alignment with uncertainty direction. We further separate originally correct samples from originally wrong samples, and track whether changes are temporary or persistent across severity. Experiments across 13 VLMs reveal a counterintuitive pattern: mild corruptions can improve top-1 accuracy while degrading prediction structure. These failures include silent degradation, erroneous overconfidence, and severity-dependent persistence. Bench-C therefore supports robustness evaluation that goes beyond final answers and attributes where reliability changes occur. Code and data are available at https://github.com/xiangjieSui/Bench-C.
arXiv:2606.17595v2 Announce Type: replace-cross
Abstract: Collective stress generation in cellular monolayers is a key phenomenological process governing coordinated migration and emergent multicellular dynamics. We employ a generic active nematics model to investigate stress generation and its associated properties. By analyzing the maximal principal stress and its correlation with the nematic director across different activity strengths, we find that the principal stress aligns perpendicular (parallel) to the nematic director for extensile (contractile) activity. In the turbulent regime, we identify a rotation-invariant scalar measure of the in-plane deviatoric stress whose zero-level contour coincides with the locations of all $\pm 1/2$ topological defects (both nematic and principal stress defects) are localized. This feature is robust and remains unchanged with variations in both the magnitude and nature (extensile or contractile) of activity. Our findings thus open up a new route to probe the spatial alignment from the mechanical and rheological properties of confluent cell layers, where stress measurements are more accessible than detailed cell shape or size characterisation.
arXiv:2511.20644v2 Announce Type: replace
Abstract: Spatial reasoning is a critical capability for intelligent robots, yet current vision-language models (VLMs) still fall short of human-level performance in video-based spatial reasoning. This gap mainly stems from two challenges: a semantic-geometric misalignment that prevents consistent 3D understanding, and the absence of persistent memory to retain 3D representation and understanding across frames. To address these limitations, we present VLM$^2$, a Vision-Language Model with persistent Memory for spatial reasoning with a view-consistent, 3D-aware representation purely from 2D videos. Specifically, we incorporate a dual-memory module consisting of a working memory that operates as a sliding window to focus on immediate context, and an episodic memory that consolidates and stores critical information across frames. This design enables bounded and efficient spatial reasoning under a fixed computational cost. Extensive experiments on multiple benchmarks show that VLM$^2$ achieves state-of-the-art performance among video-based models, significantly advancing the frontier of visual-spatial intelligence.
arXiv:2606.30388v3 Announce Type: replace-cross
Abstract: Delayed generalization (\ie~grokking) refers to the phenomenon in which a neural network fits its training data early in training but only begins to generalize after a prolonged delay, often through an abrupt transition. Despite extensive empirical study, its underlying mechanism remains poorly understood. In this work, we first theoretically characterize a shell--core topological configuration of the reachable solution space induced by Adam's optimization dynamics with weight-shrinkage regularization, supported by empirical evidence. This optimization-induced topological configuration gives rise to grokking. In model's parameter space, random initialization solutions concentrate on a thin outer spherical shell, enclosing another spherical shell of memorization solutions, which in turn contains a core corresponding to the generalization solutions. Leveraging stopping-time theory, we then analyze the geometry of this topological configuration and the solution transition time at which optimization trajectories escape the memorization manifold and first reach the boundary of the generalization manifold. Our theoretical analysis derives grokking scaling laws for the learning rate, batch size, and $\ell_2$ regularization coefficient, which are further validated through experiments and shown to recover results from prior literature.
arXiv:2607.00504v2 Announce Type: replace-cross
Abstract: Centralized hydrothermal planning models determine generation schedules and electricity spot prices based on inflow forecasts in audited-cost power systems, such as those prevalent in Latin America, and provide operational benchmarks and decision support in hydro-dominated competitive electricity markets. Consequently, biased forecasts can propagate directly into both operational decisions and market outcomes. This paper studies how persistent optimistic inflow-forecast bias propagates through the Brazilian hydrothermal power system and market. For a stylized hydrothermal model, we show analytically that optimistic bias weakly reduces water values and weakly increases first-stage hydro discharge relative to the unbiased optimum, thereby lowering reservoir storage and postponing thermal commitment. Using official Brazilian planning and operational data, we provide empirical evidence consistent with this mechanism. We then conduct a controlled SDDP experiment to compare policies trained under biased and bias-corrected inflow-forecast processes, evaluating both under the same bias-corrected inflow scenarios. The policy trained under biased forecasts produces lower reservoir levels, delayed dry-season thermal dispatch, sharper spot-price peaks, higher reliability risk, and higher expected operating costs. Finally, we show that these distortions increase the price-quantity risk for hydropower producers and reduce their willingness to contract. The results indicate that inflow-forecast bias is not merely a statistical forecasting problem, but can be a source of operational inefficiency, reliability risk, and distorted market incentives in hydro-dominated power systems. We argue that the insights and policy implications drawn in this paper may be relevant beyond Brazil to other hydro-dominated systems and electricity markets that are increasingly reliant on energy storage.
arXiv:2606.10358v3 Announce Type: replace
Abstract: Learning Bayesian network (BN) structure from sparse discrete data is hard: when each instance records only a few variables, most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure. Imperfect domain knowledge, expressible as a weighted directed knowledge graph (KG), is often available. KG-SoftMAP encodes such a KG as a finite-strength, confidence-weighted edge prior and maximizes a MAP objective that adds this logit-form prior to the BDeu score. With an informative but imperfect KG, KG-SoftMAP recovers partial directed structure even at observation rate rho=0.05, with directed F1 (DF1) of 0.19-0.32 across benchmarks. At higher observation rates within this sparse grid, DF1 reaches 0.44-0.66 at rho=0.20 and 0.46-0.64 at rho=0.40. Across the same three rates, KG-SoftMAP without the KG prior averages DF1 0.00, 0.19, and 0.21. Stress tests that corrupt, remove, or blur the KG signal, together with checks on LLM-extracted graphs beyond canonical benchmarks, show that recovery rises and falls with KG quality. On three real sparse educational datasets without ground-truth DAGs, we evaluate prediction, calibration, and KG-consistency. On Short Answer Feedback (SAF), KG-SoftMAP+VE reaches Fail-class F1 0.75 versus 0.78 for logistic regression while also providing an inspectable concept graph, calibrated Fail probabilities, and posterior queries from partially observed concept evidence. The remaining datasets sharpen the operating picture: weak heuristic KG signal leaves prediction unchanged, while an independent expert ontology moves the learned graph toward expert relatedness.
arXiv:2607.08698v1 Announce Type: new
Abstract: We examine educational YouTube videos through multimodal metadata, such as transcripts, titles, thumbnails, and viewer comments, to investigate how ChatGPT is framed across creator groups and how those framings relate to audience response and platform reach. Little is known about how large language models are presented to learners in informal, creator-driven public discourse. Following PRISMA, we selected 52 videos for analysis. We identified three structurally distinct discourse groups: (G1) videos that positioned ChatGPT as a conceptual scaffold for thinking, (G2) videos oriented toward retrieval practice and skill-building, and (G3) videos that framed ChatGPT as a tool for output generation. Epistemic Network Analysis revealed statistically significant group differences with large effect sizes. Multimodal metadata consistently reflected these distinctions across transcript discourse, titles, and thumbnails. Viewers of learning-oriented content described ChatGPT as a thinking partner or tutor, whereas viewers of output-oriented content raised concerns about over-reliance, surface-level learning, and cognitive offloading. G3 achieved comparable platform reach to G2, yet with substantially weaker learning-oriented framing. This may suggest that output-oriented content competes for visibility despite lower pedagogical depth. These findings reveal a structural tension in self-directed AI learning: content that prioritizes quick outputs reaches far more learners than content that promotes deep engagement. This gap raises critical questions about whose vision of AI literacy scales and what learners are actually left with.
arXiv:2606.11408v2 Announce Type: replace
Abstract: Action chunking has become a standard design in modern robot policies, from diffusion/flow policies to vision-language-action models, where the policy predicts a sequence of actions and executes a fixed number of them instead of acting one step at a time. However, this paradigm relies on a key assumption: a fixed execution horizon. During chunk execution, the policy operates open-loop, which is particularly problematic for fine-grained manipulation tasks that require frequent replanning. In practice, the execution horizon is typically chosen through empirical tuning and is highly task-dependent. To this end, we propose Dynamic Execution Horizon Prediction (DEHP), an effective method that trains a lightweight execution-horizon prediction branch using online reinforcement learning while keeping the pretrained chunk policy completely frozen. This makes the method compatible with black-box chunk policies and isolates the effect of adapting the execution horizon from changes to the underlying action generator. Across our evaluations, DEHP improves the success rate of different high-precision and long-horizon manipulation tasks by a large margin. Our qualitative analysis further shows that DEHP predicts shorter execution horizons during fine-grained stages of the task and longer horizons during free-space motion. In this way, DEHP balances the efficiency of open-loop chunk execution with the reactivity of closed-loop single-step control. Project page: https://dehp-chunking.github.io/
arXiv:2607.08705v1 Announce Type: new
Abstract: Rapid advancements in video diffusion models and temporal editing tools have enabled the generation of highly realistic human-centric videos, posing unprecedented challenges to digital content forensics. Existing benchmarks primarily focus on either face-swapping or global text-to-video synthesis, overlooking the crucial dimensions of human-object or human-human interactions and multi-modal alignment. To address these limitations, we introduce HumanForge, a unified, large-scale, and multi-paradigm human-centric video forgery dataset. To construct and annotate this dataset without labor-intensive manual labeling or hallucinated monolithic prompts, we propose Gen2Anno, a modular active multi-agent pipeline built on LangGraph. Gen2Anno coordinates six specialized agents-ranging from source profiling to MoE-based reference analysis and closed-loop forensic verification-to generate over 18K high-fidelity video segments and produce structured, contrastive omni-annotations containing binary decisions, fine-grained artifact categories, and spatio-temporal localization. Extensive benchmarks using state-of-the-art traditional detectors and Large Multimodal Models (LMMs) demonstrate the significant challenges of zero-shot generalization and fine-grained reasoning on HumanForge. Code and dataset will be publicly released.
arXiv:2512.01803v3 Announce Type: replace
Abstract: Despite rapid advances in video generative models, robust metrics for evaluating visual and temporal correctness of complex human actions remain elusive. Critically, existing pure-vision encoders and Multimodal Large Language Models (MLLMs) are strongly appearance-biased, lack temporal understanding, and thus struggle to discern intricate motion dynamics and anatomical implausibilities in generated videos. We tackle this gap by introducing a novel evaluation metric derived from a learned latent space of real-world human actions. Our method first captures the nuances, constraints, and temporal smoothness of real-world motion by fusing appearance-agnostic human skeletal geometry features with appearance-based features. We posit that this combined feature space provides a robust representation of action plausibility. Given a generated video, our metric quantifies its action quality by measuring the distance between its underlying representations and this learned real-world action distribution. For rigorous validation, we develop a new multi-faceted benchmark specifically designed to probe temporally challenging aspects of human action fidelity. Through extensive experiments, we show that our metric achieves substantial improvement of more than 68% compared to existing state-of-the-art methods on our benchmark, performs competitively on established external benchmarks, and has a stronger correlation with human perception. Our in-depth analysis reveals critical limitations in current video generative models and establishes a new standard for advanced research in video generation.
arXiv:2606.14567v2 Announce Type: replace
Abstract: Nucleation is classically treated as a local process, yet whether coupling between neighboring sites governs activation and stability remains unexplored. Here we show bubble nucleation is fundamentally collective: sites separated by the hydrodynamic-boundary-layer scale activate more readily and resist deactivation under changing thermal loads, consistent with a non-local hydrodynamic shielding mechanism, whereby neighboring bubbles slow the intervening flow, suppress convective heat removal, and stabilize vapor embryos. Using surfaces with two independently tunable length scales, we isolate this near-wall coupling from a second collective process, coalescence between departing bubble clusters, which transitions through isolated, promotive, and excessive regimes as the departure diameter grows with heat flux. The dominant length scale thus shifts with operating conditions, from boundary-layer coupling near activation to departure-scale coupling once nucleation is established. These results establish a scale-dependent framework for collective nucleation and departure, broadly related to phase change processes on structured surfaces.
arXiv:2512.16558v3 Announce Type: replace
Abstract: Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN), a multiscale density-based clustering algorithm that replaces HDBSCAN*'s fixed minimum cluster size pruning of a mutual-reachability linkage hierarchy with a persistence-based cluster selection procedure. Effectively, PLSCAN identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. In concept, PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher median ARI, is less sensitive to changes in the number of mutual reachability neighbours, and has higher stability under resampling. Additionally, we compare PLSCAN's computational costs to $k$-Means++, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.
arXiv:2601.00473v4 Announce Type: replace
Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between the numerical/exact solutions of the Burgers' and Eikonal equations, and the same obtained via PINNs is presented. We show that PINN learning provides a different computational pathway compared to standard numerical discretization in approximating essentially the same underlying dynamics of the system. Within this framework, DNNs can be interpreted as discrete dynamical systems whose layer-wise evolution approaches attractors, and multiple parameter configurations may yield comparable solutions, reflecting the degeneracy of the inverse mapping. In contrast to the structured operators associated with finite-difference (FD) procedures, PINNs learn dense parameter representations that are not directly associated with classical discretization stencils. This distributed representation generally involves a larger number of parameters, leading to reduced interpretability and increased computational cost. However, the additional flexibility of such representations may offer advantages in high-dimensional settings where classical grid-based methods become impractical.
arXiv:2601.00549v2 Announce Type: replace
Abstract: The deployment of large-scale neural networks within the Open Radio Access Network (O-RAN) architecture is pivotal for enabling native edge intelligence. However, this paradigm faces two critical bottlenecks: the prohibitive memory footprint required for local training on resource-constrained gNBs, and the saturation of bandwidth-limited backhaul links during the global aggregation of high-dimensional model updates. To address these challenges, we propose CoCo-Fed, a novel Compression and Combination-based Federated learning framework that unifies local memory efficiency and global communication reduction. Locally, CoCo-Fed breaks the memory wall by performing a double-dimension down-projection of gradients, adapting the optimizer to operate on low-rank structures without introducing additional inference parameters/latency. Globally, we introduce a transmission protocol based on orthogonal subspace superposition, where layer-wise updates are projected and superimposed into a single consolidated matrix per gNB, drastically reducing the backhaul traffic. Beyond empirical designs, we establish a rigorous theoretical foundation, proving the convergence of CoCo-Fed even under unsupervised learning conditions suitable for wireless sensing tasks. Extensive simulations on an angle-of-arrival estimation task demonstrate that CoCo-Fed significantly outperforms state-of-the-art baselines in both memory and communication efficiency while maintaining robust convergence under non-IID settings.
arXiv:2606.17854v2 Announce Type: replace
Abstract: Wegner conjectured in 1965 that every finite family $\mathcal R$ of axis-parallel rectangles satisfies $\tau(\mathcal R)\le 2\nu(\mathcal R)-1$, where $\tau(\mathcal R)$ is the minimum number of piercing points and $\nu(\mathcal R)$ is the maximum size of a pairwise-disjoint subfamily. We disprove the conjecture by an explicit triangle-free family of $64$ rectangles with $\nu=16$ and $\tau\ge 32$.
More generally, for every $\varepsilon>0$, we construct triangle-free rectangle families for which the standard clique-LP relaxation for maximum independent set of rectangles has integrality gap at least $5/2-\varepsilon$. The same families satisfy $\tau(\mathcal R)\ge (5/2-\varepsilon)\nu(\mathcal R)$. We also prove that, on triangle-free rectangle families, this LP has gap at most $3$. Our approach gives an example with axis-parallel segments instead of rectangles with integrality gap tending to $2$. We also give a relatively small $4092$-rectangle triangle-free family with chromatic number $6$ improving the construction of Asplund and Gr\"unbaum (On a coloring problem, Mathematica Scandinavica, 1960) that required more than $10^8$ rectangles.