Papers

Weight-only post-training quantization (PTQ) relies heavily on reconstruction loss minimization to preserve model quality at low precision. We show that the weights favored by minimizing this loss need not yield better model performance on new tasks. In fact, we find that lower reconstruction loss can even degrade model performance on the same calibration data. Our analysis further shows that weights with lower reconstruction loss on calibration data can have higher loss than other weights when the distribution of input activations changes. Motivated by these observations and our analysis, we propose Distributionally Robust Quantization (DRQ), a post-hoc refinement process that minimizes worst-case reconstruction loss over a constrained set of input activation distributions. DRQ refines the integer codes representing quantized weights within the existing quantization grid, keeping quantization parameters and inference operators unchanged. Extensive experiments show that DRQ improves models quantized by six representative PTQ methods, including AWQ, GPTQ, and ParoQuant, and delivers gains across both dense and mixture-of-experts large language models. These results establish DRQ as a general post-hoc refinement framework for weight-only PTQ, achieving better downstream performance without adding inference overhead.

Qudits provide a larger local Hilbert space than qubits and have recently attracted interest as building blocks for efficient fault-tolerant quantum computation (FTQC). In this work, we extend many-hypercube (MHC) codes, high-rate concatenated quantum codes, from qubits to qudits of prime dimension $q$. We construct the level-2 and level-3 MHC codes with parameters $\left[\!\left[6^2,4^2,2^2\right]\!\right]_q$ and $\left[\!\left[6^3,4^3,2^3\right]\!\right]_q$, respectively, and generalize the level-by-level minimum-distance (LLMD) decoder originally proposed for the qubit MHC codes. In a qudit $X$-error model, we evaluate the code-capacity performance of the qudit MHC codes for dimensions up to $q=13$. We find that the error threshold increases monotonically with the local dimension $q$, reaching $10.0\%$ for $q=13$, nearly double the value of $5.1\%$ for qubits. Furthermore, for sufficiently large local dimensions, we observe a pronounced waterfall regime in which the logical error rate decreases substantially faster than expected from conventional distance-based estimates. To understand the origin of the observed qudit advantage, we analyze the decoding performance in terms of the entropy of the underlying $q$-ary noise channel. This analysis reveals a competition between the increased syndrome information available at larger $q$ and the simultaneous growth of the typical physical error weight at fixed entropy. These results demonstrate that higher-dimensional quantum systems can substantially improve the performance of high-rate concatenated quantum codes and motivate further development of qudit-based FTQC architectures.

Collaborative Edge Computing (CEC) is an efficient computing paradigm that enables neighboring edge servers to share computational resources with each other. Although CEC can enhance resource utilization, it still suffers from duplicate computations because nearby end-users often offload tasks with similar inputs. To improve system efficiency, the computation results of previously executed tasks can be cached and reused by subsequent tasks. However, time-varying task popularity and arrival rates require caching and scheduling decisions to adapt to demand changes, while frequent cache updates incur additional costs. To address this issue, this paper develops a two-timescale computation reuse algorithm for CEC networks. We formulate an optimization problem that jointly considers weighted response time and cache update cost, with result caching decisions determined at the frame level and workload scheduling, cache searching, and computational resource allocation adjusted at the slot level. Using recent workload observations, we construct a frame-level surrogate problem and decompose it into a caching subproblem and a scheduling subproblem. For the caching subproblem, we introduce marginal storage efficiency and incorporate cache update costs into a bisectionbased algorithm. Under bounded normalized marginal sensitivity, the algorithm achieves a near-optimal objective value for the single-BS caching subproblem when individual result sizes are small relative to the cache capacity and the relaxed solution is sufficiently accurate. For the scheduling subproblem, we utilize projected gradient descent and backtracking with warm starts across consecutive slots. Numerical results demonstrate consistent performance gains over benchmark schemes across diverse network and workload settings.

Large Reasoning Language Models (LRLMs) enable multi-step reasoning for robotic task planning, but continued reasoning can overwrite valid intermediate plans or leave constraint violations unresolved, reducing planning reliability and wasting inference-time computation. We develop an inference-time monitor that exposes and verifies intermediate plans without disrupting the original decoding trajectory. Building on this monitor, we propose SafeInferCom, a formal verifier-guided framework that preserves valid intermediate plans and directs error correction during generation. Experiments across multiple LRLMs and planning domains reveal reasoning-response inconsistency and limited self-correction under one-shot inference. SafeInferCom improves planning success and accelerates error correction relative to one-shot inference. When combined with iterative refinement, it further improves success while reducing token usage compared with refinement alone. We additionally evaluate SafeInferCom in VirtualHome and provide a real-world robotic-arm demonstration.

Preclinical models poorly predict human drug efficacy, particularly in neurological disorders. Neural activity offers a uniquely rich source of translational information because it captures high-dimensional variation in nervous-system function that can be measured in both animals and humans. However, its high dimensionality makes it difficult to distinguish conserved disease-related features from variation arising from species, recording modality and experimental context. Here, we test whether shared neural dynamics can be identified directly from electrophysiology data by learning representations organized by biological state rather than species. We develop a dual-rule contrastive learning framework that aligns corresponding mouse and human states while preserving separation between distinct phenotypes. This framework recovered conserved sensory-response structure across species and, in epilepsy, resolved distinct relationships between three mouse models and heterogeneous human patient populations. When treated animals were projected into a frozen cross-species representation, drug-induced movement towards the human-aligned healthy state retrospectively tracked known clinical efficacy across ten model-drug combinations including a disease-specific detrimental effect. The framework also identified shared disease-associated neural dynamics between Fmr1-knockout mice and human 16p11.2 copy-number variant carriers despite differences in genetic aetiology and recording modality. Together, these findings show the potential of cross-species neural representation learning to map heterogeneous human disease onto experimentally tractable preclinical states and assess whether interventions restore human-relevant circuit function.

An ideal robot grasp is firm enough to securely handle an object, yet gentle enough to avoid damaging it. Achieving this balance requires knowledge of the object's material properties, such as its mass, elasticity, and surface friction. These properties, however, are seldom precisely known a priori. In this work, we propose a visuotactile approach to estimating material properties in real time, during the process of grasping. Our method uses these estimated properties to determine the minimum grasp force required to handle the object. We contribute a new dataset of real-world objects (fruits and vegetables) with measured physical properties (shape, mass, elasticity, and friction), which we use to construct our force estimation model via simulations. We experimentally validate our approach to grasp force control using a robot with a parallel-jaw gripper. We demonstrate our system's ability to gently grasp a wide variety of objects, in each case adapting to their unique physical properties.

Building upon the foundations laid by our previous work, this paper introduces Arena 5.0, the fifth iteration of our framework for robotics social navigation development and benchmarking. Arena 5.0 provides three main contributions: 1) The complete integration of NVIDIA Isaac Gym, enabling photorealistic simulations and more efficient training. It seamlessly incorporates Isaac Gym into the Arena platform, allowing the use of existing modules such as randomized environment generation, evaluation tools, ROS2 support, and the integration of planners, robot models, and APIs within Isaac Gym. 2) A comprehensive benchmark of state-of-the-art social navigation strategies, evaluated on a diverse set of generated and customized worlds and scenarios of varying difficulty levels. These benchmarks provide a detailed assessment of navigation planners using a wide range of social navigation metrics. 3) Extensive scenario generation and task planning modules for improved and customizable generation of social navigation scenarios, such as emergency and rescue situations. The platform's performance was evaluated by generating the aforementioned benchmark and through a comprehensive user study, demonstrating significant improvements in usability and efficiency compared to previous versions. Arena 5.0 is open source and available at https://github.com/Arena-Rosnav.

Suikinkutsu are partially concealed acoustic devices traditionally installed adjacent to stone water basins (tsukubai) in Japanese temple gardens. While previous research has examined their physical acoustics and cultural significance, computational methods for documenting and comparing their acoustic characteristics remain underexplored. This exploratory study introduces a computational framework for analyzing suikinkutsu using spectral and temporal audio features extracted from field recordings. Rather than estimating the physical geometry of individual suikinkutsu, the framework characterizes their acoustic profiles using a multidimensional set of computational descriptors, enabling systematic comparisons between recordings across different sites and installations. Audio recordings from nine suikinkutsu located at temples, shrines, and gardens in the Kansai region of Japan were analyzed using a feature-extraction pipeline that incorporates Fast Fourier Transform (FFT), Mel-Frequency Cepstral Coefficients (MFCCs), Root Mean Square (RMS) energy, spectral centroid, spectral bandwidth, and spectral contrast. The extracted features indicate that, although the suikinkutsu share broadly similar spectral and timbral characteristics, each exhibits a measurably distinct acoustic profile; a supplementary analysis of within-site and between-site variability suggests these profiles reflect a bounded range of characteristic resonant behaviour rather than a fixed acoustic signature. The proposed framework provides one of the first computational approaches for systematically characterizing and comparing suikinkutsu, contributing a practical foundation for future research and the digital preservation of this distinctive form of Japanese environmental design.

Dense associative memory (DAM) provides an energy-based framework for memory retrieval with close connections to attention mechanisms in modern artificial intelligence. Despite growing interest in differential privacy for AI, the privacy of DAM retrieval dynamics remains relatively unexplored. In this paper, we develop a differential privacy framework for log-sum-ReLU (LSR) dense associative memory, whose finite-support retrieval dynamics pose distinctive challenges for privacy-preserving computation. We propose the Boundary-Responsive Adaptive Correction Evolution (BRACE) algorithm, a differentially private retrieval mechanism for LSR-DAM that adaptively corrects boundary-sensitive perturbations to control their cumulative effect over the retrieval trajectory. In theory, we prove that our method is minimax optimal by deriving dimension-independent terminal and full-trajectory retrieval error rates, with optimal dependence on the inverse temperature and, in the growing-horizon regime, the retrieval horizon. We further establish central limit theorems that enable uncertainty quantification for private retrieval by characterizing its asymptotic distribution and the additional variability introduced by privacy. Numerical experiments compare our proposed method with baseline differential privacy approaches and evaluate its retrieval accuracy. Together, our results provide a theoretical foundation for optimal privacy-preserving retrieval and uncertainty quantification in energy-based associative memory systems.

Low-dimensional magnetic systems have received significant interest due to their high scalability and energy efficiency for future electromagnetic applications. However, low-dimensional magnetism at finite temperature is subject to Mermin-Wagner fluctuations, which make its realization highly challenging. Here, we propose structural modulation in the thin-film structure of an orthoferrite system to achieve a high low-dimensional magnetic response at room temperature. ErFeO3 epitaxial thin film with atomically precise thickness control demonstrates that the magnetic response at 300 K can be significantly enhanced compared to its bulk counterpart. The magnetic response reaches its maximum value of 3.7 MuB/f.u. for the 2 nm-thick epitaxial film. The characteristic domain structure resulting from epitaxial strain and orbital reconstruction at the surface, both arising from the thin film geometry, has been proposed as the microscopic origin of the giant magnetization enhancement. We show that magnetic ordering can indeed be realized in the 2D limit, with deliberate structural control of orthoferrite systems.

Diffusion and autoregression (AR) have long been seen as different categories of generative models, with diffusion specialising in continuous fields and AR specialising in discrete tokens. Recent work seeks to combine the advantages of the two models, and each hybrid fixes its decoding schedule by design. In this paper, we ask whether the performance of decoding schedules of one model can be predicted before decoding at a fixed number of steps. We describe diffusion, AR, and models in between as paths on one corruption lattice, and define the cost of a schedule as the dependence its parallel steps discard. The cost shows that the fewest steps of a zero-cost schedule are set by the geometry of the data, in the same way for tokens and for continuous fields. In particular, for data that are Markov on a graph and dependent along its paths, the fewest steps equal the graph's treedepth, which is logarithmic in the length of a sequence and linear in the side length of a grid. With fewer steps than the treedepth, every schedule pays a positive cost, whose ranking we predict before decoding with a kernel of pairwise dependence estimated from pretrained weights. Across text generation, image generation, and video generation, we verify most of the predictions about the rankings of different schedules under different metrics and benchmarks. This work therefore provides a design principle for decoding for future AR models, diffusion models, and anything in between. Our code is available at https://github.com/TSUITUENYUE/The-Lattice-of-Transition-Laws.

Reconstructing complete, scene-aligned 3D objects from casual images requires integrating sparse, uncertain observations and inferring surfaces hidden by occlusions. We present GATOR, a generative and agentic framework that recovers textured object assets and their scene-relative pose from one or more images. Our local modality mixer couples patch-aligned RGB, target-mask, and pointmap features before cross-view reasoning, preserving scene context while distinguishing the target from its surroundings. Text-guided semantic conditioning complements these spatial cues with category names and object captions through stage-specific adapters for structure, geometry, and appearance generation. The generated asset initializes a multimodal agent, providing instance-specific geometry and pose for targeted structural and texture refinement through an observation-guided edit-render-review loop. Across synthetic objects, cluttered tabletops, and indoor scenes, GATOR achieves strong geometric and appearance fidelity while recovering scene-relative pose from sparse observations. Time-budget comparisons and scene-level simulation further demonstrate the reconstruction efficiency and simulation readiness. Project page: https://research.nvidia.com/labs/lpr/gator/

KV-cache quantization and linear attention are two representative approaches to tackling the storage and computational costs of Transformers. KV-cache quantization compresses individual KV entries into discrete codes but retains all entries, whereas linear attention recurrently aggregates multiple historical KV contributions into a fixed-size continuous state but can introduce interference. This contrast raises the question of whether per-KV compression and multi-KV aggregation can be bridged within a single mechanism for efficient attention. We identify RAM-Net as such a bridge through soft assignments over a discrete address space. These assignments determine recurrent updates to the continuous slot state associated with each address. Under a restricted RAM-Net construction, we prove that soft address assignments extend hard quantized matching to a separable read-write overlap that locally approximates full-attention similarity and supports recurrent aggregation. These connections further enable Transformer-to-RAM-Net weight migration through a new path based on a soft-quantized intermediate construction. Across nine pretrained Transformer models from 0.3B to 7B parameters, RAM-Net recovers an average of 87.1% of the teachers' accuracy gains over random guessing across six commonsense and knowledge tasks using only a 500M-token budget per model.

Long-term Time Series Forecasting (LTSF) tasks, which leverage the current data sequence as input to predict the future sequence, have become increasingly crucial in real-world applications such as weather forecasting and planning of electricity consumption. However, state-of-the-art LTSF models often fail to achieve prediction output alignment for the same timestamps across lagged input sequences. Instead, these models exhibit low output alignment, resulting in fluctuation in prediction outputs for the same timestamps, undermining the model's reliability. To address this, we propose AliO (Align Outputs), a novel approach designed to improve the output alignment of LTSF models by reducing the discrepancies between prediction outputs for the same timestamps in both the time and frequency domains. To measure output alignment, we introduce a new metric, TAM (Time Alignment Metric), which quantifies the alignment between prediction outputs, whereas existing metrics such as MSE only capture the distance between prediction outputs and ground truths. Experimental results show that AliO effectively improves the output alignment, i.e., up to 58.2% in TAM, while maintaining or enhancing the forecasting performance (up to 27.5%). This improved output alignment increases the reliability of the LTSF models, making them more applicable in real-world scenarios.

Interlayer coupling controls the electronic properties of layered van der Waals transition metal dichalcogenides. We investigate light-induced control of the interlayer spacing through orbital-selective excitation in trilayer 1T'-WSe2 and 1T'-WS2. Real-time time-dependent density functional theory simulations show that the interlayer spacing contracts or expands depending on whether chalcogen p-orbital density is depleted from or accumulated in the interlayer region. Effective Lindblad models coupled to the lattice dynamics reproduce these contrasting responses with simplified dynamics. A single effective excited state captures the cosine-like displacive motion in trilayer 1T'-WSe2, whereas the shift of the equilibrium spacing in trilayer 1T'-WS2 requires two excited states with different electron-phonon couplings and relaxation channels. Static calculations at varied interlayer spacings indicate that these spacing changes modify the electronic gaps and could access different electronic phases. These results connect orbital redistribution, carrier relaxation, and interlayer breathing motion, and establish orbital-selective optical excitation as a route to tuning the electronic properties of layered materials.

Hourly precipitation forecasting involves several distinct statistical challenges, including spatially varying predictor-precipitation relationships, a strongly imbalanced precipitation distribution, and progressive degradation of precipitation event skill with increasing lead time. We develop a spatiotemporal forecasting framework that addresses these challenges through three complementary components: explicit geographic representation, event-aware learning for imbalanced precipitation, and weak asymmetric regularization derived from the atmospheric water budget. The physical information is treated as an asymmetric constraint rather than as an additional prediction target, designed to discourage physically unsupported precipitation attenuation without replacing the data-driven forecast. Experiments using ERA5 data across regional, enlarged domain, and spatial subset settings show that explicit geographic information improves spatial field prediction, while event-aware learning provides the most consistent gains in detecting moderate and heavy precipitation events. Physical regularization has a more selective effect, mainly reducing systematic underprediction over the enlarged domain while improving longer lead precipitation event prediction in the spatial subset experiment. These results indicate that the benefit of physical guidance depends on the available data regime and becomes most apparent when data-driven precipitation information deteriorates with increasing lead time.

We study non-vanishing modulo primes of critical values of $L$-functions over imaginary quadratic fields twisted by Coates–Wiles characters. For a parallel weight two Hecke eigenform over an imaginary quadratic field, we prove that a positive proportion of Coates–Wiles characters have nonzero integral $L$-values modulo each prime in a positive-density set. The argument constructs automorphic symbols in parabolic homology with integral coefficients and expresses the critical values through their pairings with parabolic cohomology classes. A vertical family of additive averages of these pairings recovers Fourier coefficients and force the module generated by symbols to have full rank. We transfer this full-rank property to non-vanishing modulo primes. This extends the homological strategy of Kim–Sun from classical modular curves to arithmetic orbifolds, while addressing the unit obstructions specific to the imaginary quadratic setting.

We study gradient Ricci solitons whose potential functions have level hypersurfaces with parallel second fundamental form. We show that such a soliton is locally a multiply warped product of a one-dimensional base and Einstein fibers, with potential function depending only on the base. Thus, locally, this condition characterizes the multiply warped structure that occurs in many classical constructions of Ricci solitons. We further prove that the same local structure follows for any gradient Ricci soliton if just one regular level hypersurface has parallel second fundamental form and parallel intrinsic Ricci tensor. As an application, we prove that a complete nonsteady gradient Ricci soliton with constant scalar curvature is rigid as soon as one regular level hypersurface has this property. In particular, the conjecture of Cao holds for gradient shrinking Ricci solitons with this property. We also prove that a complete gradient shrinking Ricci soliton whose regular level hypersurfaces have parallel second fundamental form and at most one nonzero principal curvature is rigid, without any assumption on the scalar curvature.

Functional generalized linear models provide a flexible framework for relating a scalar response to functional and scalar predictors, but their conventional formulation requires specification of the response distribution and is typically developed for a single population. We propose a semiparametric functional generalized linear model for multi-population data that leaves the baseline response distributions unspecified and links them across populations through a density ratio model. The proposed framework accommodates both functional and scalar predictors while borrowing information across related populations. We develop a maximum empirical likelihood estimation procedure and use penalized B-spline approximations to estimate the functional coefficients. A cross-validation procedure based on a kernel-smoothed empirical likelihood density estimator is introduced to select the smoothing parameters. Simulation studies show that borrowing information through the density ratio structure can improve estimation efficiency relative to fitting each population separately, and that the proposed semiparametric method remains competitive when a parametric Gaussian model is correctly specified while providing substantial robustness when it is misspecified. We illustrate the method using county-level soybean yield data from Kansas, with daily temperature curves and irrigation levels as predictors.

Scalar field theories of modified gravity are strongly constrained by the absence of detectable long range fifth forces in laboratory and Solar System environments. The chameleon mechanism addresses this problem by making the equilibrium value and effective mass of the scalar field dependent on the ambient matter density. In this work, we investigate an effective phenomenological extension of the chameleon framework in which the scalar potential contains an additional quadratic environmental contribution characterized by a density dependent background frequency. This background frequency is distinct from the frequency of scalar perturbations and parametrizes unresolved environmental effects beyond the conventional matter coupling. For an inverse power law scalar potential, we derive the modified equilibrium configuration and identify a frequency dominated regime in which the environmental contribution controls the density dependence of the field. Linear perturbations about the environmental minimum obey a Klein Gordon dispersion relation with a density-dependent effective mass, and the absence of tachyonic instability requires a positive environmental coupling. We further derive analytical consistency conditions associated with frequency dominance, thin shell screening, fifth-force suppression, and the weak field approximation. Numerical illustrations for representative parameter choices demonstrate how the modified density scaling can enhance fifth-force suppression relative to the conventional chameleon case.

Flat loss landscapes have long been linked to better generalization in neural networks. However, its role as a causal mechanism for generalization is less established. Grokking provides an unique testbed to understand this distinction: models are prone to fit observed data using non-generalizing structure and remain in that regime for prolonged periods, transitioning to generalization only under particular training conditions. In this work, we study whether flat loss landscapes can act as a driving mechanism in this transition. While recent work has argued for flatness as a necessary geometric condition for this transition, we find that biasing training toward flatter solutions using sharpness-aware minimization (SAM) is insufficient to reliably induce this transition, despite producing flatter solutions. However, when SAM is paired with mechanisms that drive generalization such as weight decay, an interesting property emerges: SAM can accelerate the transition to generalizing solutions by up to 4x at the epoch-level. We theoretically untangle this relationship between SAM and weight decay using a minimal interpolating two-layer ReLU model with both memorizing and generalizing solutions. We show that even in this simple setup, flatness alone cannot distinguish a memorizing solution from a generalizing one, while weight decay favors generalizing solutions. However, under a local stability analysis, there exists a window where a memorizing interpolant is locally stable under gradient descent but unstable under SAM in the low-norm regime, which can explain SAM's ability to accelerate this transition. Overall, our results provide a more interpretable account of the role of flatness in driving generalization, especially in settings where models are vulnerable to minimizing loss through learning non-generalizing structure.

Representation structure is crucial for understanding Vision Transformer (ViT) architectures and their generalization behavior. However, prior studies neither isolate nor analyze module-level features nor investigate how their interactions contribute to performance estimation. In this work, we conduct the first rigorous analysis of feature information across diverse architectural scales, empirically uncover the relationship between ViT representation and generalization behavior, and leverage these insights to guide efficient ViT design. Our contributions are fivefold: Across diverse architectural scales, 1) We identify feature collapse at initialization, which leads to redundancy, and propose a reduction scheme to mitigate this issue. 2) We quantify feature information using entropy and the minimum eigenvalue, demonstrating that these metrics serve as reliable indicators for generalization prediction. 3) We show that feature in the token space provides a more faithful representation than those in embedding space. 4) We discover an unexpected finding: features produced by linear submodules within ViT layers are critical for the prediction of generalization performance. 5) Our proposed proxy improves the correlation ranking by 18-48% over prior baselines and can effectively identify ViT architectures that achieve higher accuracy at lower or comparable computational cost.

We study quantitative stability for the fractional Schrödinger equation $(-\Delta)^s u+u-|u|^\alpha u=0$ near finite sums of widely separated positive ground states. For every $n\ge1$, $0<s<1$, and Sobolev-subcritical exponent $\alpha>0$, we estimate the $H^s$ distance to the family of such sums in terms of the $H^{-s}$ norm of the equation's residual. The optimal rate changes at $\alpha=n/[2(n+2s)]$, with a logarithmic correction at the threshold. Above the threshold the rate is $t^{(n+2s)/(n+2s+1)}$; below it the exponent is $[(1+\alpha)(n+2s)-n/2]/(n+2s+1)$. The proof combines uniform invertibility away from the translation modes with precise interaction estimates and a weighted correction of the approximate configuration. This correction resolves the translation interactions even when the nonlinearity has a small exponent. We also construct nonnegative configurations that attain these rates. The estimates quantify the effect of the algebraic decay of fractional ground states on stability.

At redshift z<1, the $\Lambda$CDM paradigm predicts that $\sim$40-50% of baryons reside in the warm-hot intergalactic medium (WHIM) within cosmic web filaments. Characterizing the physical state and distribution of this dominant baryonic component is crucial for a complete picture of baryon evolution in the low-redshift Universe. However, directly observing the WHIM has been challenging due to its low density and high temperature and ionization state. Absorption-line spectroscopy offers a promising approach, particularly through analyses of broad Ly-$\alpha$ absorbers (BLAs; Doppler parameter b>40 km/s) and OVI absorbers. This work focuses on probing WHIM signatures by analyzing the incidence rates of these tracers in and around putative cosmic web filaments connecting massive galaxy clusters. We use far-ultraviolet (FUV) absorption spectroscopy from HST/COS along ten QSO sightlines at z<1, selected for their proximity in projected distance and velocity to cluster pairs. We focus on absorption features of WHIM tracers (BLAs and OVI) and cold-gas tracers (narrow Ly-$\alpha$ absorbers, or NLAs; b<40 km/s), which are used as a control sample for colder gas. We measure excess incidence rates for total HI, NLAs, BLAs, and OVI within a rest-frame $\Delta v=\pm1000$ km/s and an impact parameter $\Delta d<3$ Mpc relative to the field expectation, and find that the excesses of BLAs and OVI are about twice those of NLAs. Additionally, the covering fractions of BLAs and OVI appear larger by factors of $\sim$1.7 and 1.8, respectively, than in a random field control sample, whereas the NLA covering fraction is consistent with the random expectation. The larger relative excess of WHIM tracers compared to cold-gas tracers near independent cluster pairs indicates the prevalence of warm-hot gas in these environments, representing a potential signature of WHIM detection in inter-cluster filaments.

Let $\mathcal{H}$ be the separable, infinite-dimensional complex Hilbert space. In the first paper of this series, we introduced, by means of the Rosenblum operators, the shift representation operators $K_x=\sum_{n=0}^{\infty}T^nx\otimes e_n$, which relate an operator $T$ with $r(T)<1$ to the unilateral shift $S$ and reveal its hidden analytic structure. In this paper we replace the pair $(H^2,S)$ by the Sobolev disk algebra $R(\mathbb{D})$ and the multiplication operator $M_z$, whose canonical left inverse $B$ plays the role of $S^*$, and study the two-parameter family $K_{x,y}=\sum_{n=0}^{\infty}T^nx\otimes B^{*n}y$. We prove that $T\in B(R(\mathbb{D}))$ with $r(T)<1$ is intransitive whenever there exist a nonzero vector $g$ and a nontrivial $M_z$-invariant manifold $\mathcal{M}$ such that $f(T)g$ has a zero in the closed unit disk for every $f\in\mathcal{M}$; the proof explicitly constructs a nontrivial invariant subspace of $T$. We further introduce the ideal property and show that every intransitive operator on $\mathcal{H}$ is unitarily equivalent to an operator on $R(\mathbb{D})$ with this property, so that the Invariant Subspace Problem for arbitrary operators reduces to a problem about a concrete function algebra. Applications include a characterization of intransitivity through the rationality of the generating function $\sum_{n=0}^{\infty}\langle T^n\xi,\eta\rangle z^n$ and new results on Pearcy's problem. Our main application is Halmos's third problem, which has remained open for more than fifty years: we reduce it to invertible operators with conjugate bi-geometric form, and we prove that $T^{-1}$ is intransitive for every invertible $T$ admitting a nontrivial projection $P$ with $PTP=TP$ and $PT(I-P)$ of rank one. Finally, we exhibit tridiagonal operators that are intransitive and admit infinite decreasing chains of invariant subspaces.

Dynamic sparse attention limits the KV pages selected by each query, but a small support does not necessarily yield efficient GPU work. Query unions share page loads and populate Tensor Core tiles; their cost depends on which queries are grouped together. We present PageWeaver, an execution design that uses selected-page affinity to assemble query groups while preserving each query's original support and complete output ownership. A bounded GPU search produces query IDs, and an ID-aware two-CTA kernel consumes them without materializing reordered Q tensors or cross-page partial outputs. A direct KV-page union implementation provides a complementary design study of nonlocal reuse and reduction cost. With FP8 KV throughout, the H200 Union8 implementation achieves a 1.70x geometric-mean complete-call speedup over the measured FlashInfer path on six captures. Online regrouping further lowers latency by 3.26-7.66% on five selected 64K-context captures. Whole-model prefill throughput is 7.88-14.36% above the tested native path; the incremental regrouping benefit is smaller, with observed median gains of 0.47-0.73% at 32K/64K and regressions at 8K. A B300 comparison identifies cases where preparation cost and a stronger native kernel remove the advantage. These results separate execution-group reuse from the complete cost of exploiting it online.

Standard theories trace information asymmetry to privately held information, heterogeneous signals, or costly information acquisition. We identify a distinct mechanism: otherwise identical rational agents observing a common Markov state at asynchronous times can hold different predictive distributions because their information differs in age. When the transition kernel separates information ages, independent Bernoulli observation arrivals make such divergence recur infinitely often almost surely, even with identical arrival probabilities. When agents instead choose costly updating intensities, independent update realizations can regenerate heterogeneous information ages among ex ante identical agents. In a stationary Gaussian AR(1) environment, the consequences depend on common staleness as well as the age gap: holding the gap fixed, older information raises individual uncertainty while reducing expected squared forecast disagreement and the value of certifying relative freshness. This generates stale consensus: low disagreement despite high uncertainty. With multiple ordered ages, costly certification supports partial-unraveling equilibria in which fresher types certify and sufficiently stale types pool. Under geometric information ages, more frequent updating weakly lowers the smallest and largest equilibrium disclosure cutoffs wherever positive-certification equilibria exist. The framework has implications for credit, insurance, financial markets, and multi-agent AI.

We derive the pressureless Euler-Maxwell system as a semiclassical limit from the Maxwell-Schrödinger equation. The method relies on studying a quantum modulated energy accounting for the self-consistent magnetic effects. Crucially, a correction is incorporated in the quantum modulated energy as to enable to close the Grönwall estimate provided a smallness assumption on the initial data is imposed. This is the first result on the semiclassical limit of the Maxwell-Schrödinger equation avoiding any regularization or conditional uniform in $\hbar$ bounds on the wave

3D object removal aims to remove target objects from reconstructed scenes and complete the geometry and appearance of occluded regions. Existing NeRF- and 3DGS-based methods typically inpaint 2D images to guide 3D completion. However, complex multi-object layouts limit the surrounding context visible in each view, making 2D inpainting prone to artifacts. Inconsistent completions across views also introduce conflicting supervision and blurry reconstructions. We propose 3D Gaussian Multi-Object Removal via Texture-Space Inpainting (3DTexMOR). Our key idea is to perform inpainting in a unified texture space shared by all views. By combining complementary observations, this space provides richer context for recovering missing regions and promotes cross-view appearance consistency. We aggregate multi-view observations into texture maps, inpaint the missing regions, and reproject the completed maps into camera views to supervise Gaussian scene completion. To avoid the influence of view-dependent highlights and reflections, we decompose appearance and aggregate view-independent intrinsic attributes instead of RGB colors. We further introduce geometrically regularized Gaussian completion to constrain the geometry of the completed regions. Extensive experiments demonstrate visually plausible completions and state-of-the-art multi-object removal performance, improving PSNR by 5.8 dB and reducing LPIPS by at least 22% compared with existing methods.

Automatic music transcription (AMT) is limited by the scarcity of audio recordings paired with precise symbolic annotations. Synthetic data can provide supervision at scale, but it remains unclear whether effective transfer depends on realistic score structure or broad timbral coverage. We study these factors separately through an online sampler–renderer pipeline. A unified corruption sampler ranges from unmodified MIDI clips through partial corruption to deeply randomized note-event distributions. The renderer converts these events to audio while independently controlling instrument and timbral coverage. A fixed transcription model is trained jointly on offline recordings and newly rendered examples. Controlled ablations reveal an asymmetry between the two factors: moderate corruption of the note-event distribution does not impair transfer and can improve it, whereas broader renderer-side timbral support consistently improves out-of-domain generalization under a fixed note-event distribution. Finally, online-rendered examples complement real and existing synthetic data in a strong combined-data regime. These results suggest that synthetic AMT data should prioritize coverage of note-level attributes and their timbral realizations over realistic joint score structure.