Papers

Given a large corpus, the questions one might ask can vary – from "When was the first human heart transplant?" to "What are all the contradictory claims in this literature?" – but what makes some questions more challenging than others? In this work, we define a notion of Corpus Task Complexity (CTC) that characterizes tasks by how their difficulty grows with corpus size; for instance, a retrieval query only requires a single linear pass over a corpus, while finding contradictions requires checking a quadratically growing set of claim pairs. Observing that prior work has largely only studied tasks whose difficulty grows linearly with corpus size, which we call low CTC tasks, we introduce 10 new tasks belonging to a class of high CTC whose difficulty grows quadratically or more in corpus size. We find that high-CTC tasks not only grow much more challenging on average at longer contexts for LCLMs, they reverse many modeling conclusions drawn solely from low-CTC evaluations. For instance, efficient block-sparse and hybrid attention approaches consistently match full attention performance on low-CTC tasks, but degrade much more on high-CTC tasks. Large-corpus high-CTC reasoning thus remains an open challenge as full attention is too costly to scale, motivating future research on these tasks. We release our code, data, and 22-task suite (CTC-Bench), to facilitate future research in this area.

Spin-orbit coupling (SOC) plays a central role in modern condensed matter physics and is crucial for the development of spin-based devices and quantum technologies. In particular, the interplay between Rashba SOC (R-SOC), arising from structural inversion asymmetry, and Dresselhaus SOC (D-SOC), due to bulk inversion asymmetry, significantly influences spin coherence and manipulation in two-dimensional and topological systems. Disentangling these SOC components is essential for spintronics, superconducting spintronics, or topological superconductivity. In this study, we experimentally investigate in-plane low-bias conductance anisotropy in epitaxial Fe/MgO/V/MgO/Fe/Co junctions under varying temperature and magnetic field conditions. By applying a theoretical model that accounts for distinct R-SOC and D-SOC contributions, we interpret the observed anisotropy as a reliable method to disentangle these effects. Comparison between experiment and theory reveals a 5 % contribution of D-SOC to total SOC, attributed to periodic interfacial lattice mismatch defects confirmed by high-resolution scanning transmission electron microscopy (STEM). Our findings offer a practical approach to isolate interfacial SOC components in superconducting spintronic systems with implications for engineering in spintronic and quantum devices, and provide further evidence of superconducting spin-triplet pairing in Fe/MgO/V-based superconductor/ferromagnet heterostructures.

We study large-overtone quasi-normal modes of a massive scalar field in a four-dimensional Schwarzschild de-Sitter black hole in the presence of a wall placed at the static sphere. Dirichlet boundary condition is imposed at the wall. At leading order the quasi-normal modes with large overtones scale as $n$ for $n\gg 1$ and are inversely proportional to the bouncing time. We analyze correction terms up to $n^{-1}$ order in the asymptotic expansion.

Nonlinear contacts and friction strongly influence the vibration response of assembled structures, but their accurate numerical treatment is computationally demanding. The harmonic balance method is widely used to compute periodic steady-state responses, yet the required alternating frequency-time scheme becomes costly for nonsmooth and hysteretic nonlinearities and must be repeated throughout the nonlinear solution process. Here we show that this procedure can be replaced by neural networks that directly map displacement Fourier coefficients to nonlinear force coefficients and provide the corresponding Jacobian through automatic differentiation. The surrounding solver and continuation algorithms remain unchanged for the computation of frequency response curves. The neural networks exclusively learn individual nonlinear elements rather than complete system responses. Physics-based nondimensionalization and phase normalization facilitate the learning process and enable a single trained network to cover a wide range of parameter combinations. Building on the cubic spring, unilateral spring, and Jenkins elements considered here, the approach points toward a reusable library of nonlinear-element surrogates that can be combined in arbitrary number and location within a mechanical system. By bypassing the iterative force evaluation in time domain, the method offers favorable computational scaling for high-resolution analyses and systems with many nonlinear elements.

The microscopic origin of magnetism in CeFe$_2$ has remained unresolved for almost forty years, where polarized-neutron diffraction and x-ray magnetic circular dichroism infer markedly different Ce $4f$ spin and orbital moments, that also are in disagreement with theory. We show here that within a relativistic multi-impurity DFT+DMFT framework, where the Fe $3d$ states are treated by spin-polarized T-matrix fluctuation exchange and Ce $4f$ orbitals by a bath-coupled configuration-interaction solver, this long standing problem is resolved. This level of theory is exclusive in reproducing magnetic moments (spin and orbital) for both the Ce and Fe atoms, yielding a total moment in agreement with the measured saturation moment. The theory put forth here is much closer to the atom specific moments reported from XMCD, compared to values from polarized-neutron diffraction. The occupation $\langle n_f\rangle=0.85$ and charge variance $\delta n_f^2=0.27$ establish substantial valence fluctuations, while the spectral function simultaneously recovers significant weight at the Fermi level together with separate incoherent structures. These results identify bath-mediated polarization and configuration mixing as the essential ingredients governing the electronic structure and magnetism of CeFe$_2$.

Text image super-resolution (TSR) aims to recover visually faithful and readable text under unknown degradations. Existing diffusion-based methods typically rely on multi-step prediction of either the high-resolution image or its text prior, resulting in prohibitive computational cost and inference latency. More critically, an erroneous text prior may be repeatedly injected into the denoising process, causing image and text predictions to reinforce each other and progressively amplify an early recognition error into a sharp yet semantically incorrect character. To address these limitations, we propose TOLA, a Text-aware One-step Latent Adaptation framework without iterative image-text diffusion. TOLA consists of two key modules. First, a confidence-weighted text conditioning module constructs the semantic condition only once and suppresses unreliable OCR predictions before they contaminate image reconstruction. Second, a lightweight latent residual correction module explicitly estimates and corrects the structured residual errors to recover missing or distorted stroke details. Extensive experiments demonstrate our state-of-the-art performance across all evaluation metrics on both CTR-TSR-Test ($\times 4$) and RealCE-200 benchmarks. It is worth noting that our TOLA consistently surpasses existing diffusion-based TSR methods by at least 2.72 dB in PSNR on CTR-TSR-Test.

We derive an explicit Faber-Walsh representation for the planar conductivity problem with finitely many disjoint inclusions of general shape and independently chosen positive conductivities. Walsh's lemniscatic map gives a conformal coordinate without smallness or wide-separation assumptions. The field expansion is expressed through Faber-Walsh polarization tensors, which we relate to the complex contracted generalized polarization tensors by a triangular change of basis. For analytic interfaces, we prove conformal continuation and absolute and uniform convergence of the Walsh-Grunsky series near the boundary to obtain explicit factorizations of the Neumann-Poincaré operator and the Faber-Walsh polarization tensors. These factorizations separate canonical interaction, which can remain nonzero even when all Grunsky coefficients vanish, from conformal deformation, while retaining the componentwise conductivity dependence in a coupled resolvent. For harmonic polynomial incident fields, we prove geometric convergence of outgoing truncations with exact coefficients on compact subsets of fixed exterior branch domains. Numerical comparisons with independent boundary-integral solutions illustrate the representation for heterogeneous, asymmetric, and nearly touching configurations.

Target speech extraction (TSE) typically trains a separate extractor per cue, and visual-cue systems often need corruption-matched training to remain robust under visual frame corruption. We show that one autoregressive LLM backbone, TSE-Omni, can serve both temporally synchronous cues (lip movements, co-speech gestures) and asynchronous cues (enrollment audio, text). TSE-Omni is driven by next-token prediction: each step predicts target speech semantic tokens from its own past outputs, which we term self-enrollment, forming a continuous target-speech context initialized by the enrollment cue (asynchronous audio or text, or a short visual prefix). This enables audio-visual compensation: the model uses synchronized visuals when intact and its token history when visual frames are missing. Under clean visuals, TSE-Omni matches strong discriminative and generative baselines (SpeechBERTScore 0.81 on VoxCeleb2 and 0.89 on LRS3 zero-shot) with higher DNSMOS. On the same VoxCeleb2 test set, after a 2 s clean visual start, removing the remaining visual frames leaves SpeechBERTScore at 0.81. It remains usable under sparse overlap and multi-speaker interference, and supports streaming inference. Project page: https://alexwxwu.github.io/tseomni-main/.

We propose a novel method to measure the strength and isospin dependence of short-range correlations (SRCs) in nuclei with their collisions at relativistic energies. Since nucleons in the high-momentum tail (HMT) induced by SRCs have large transverse velocities, we find that measuring the yield ratio of free spectator neutrons at large to small transverse distances detected by Zero-Degree Calorimeter (ZDC) array may probe the fraction of nucleons in the HMT. In addition, measuring the yield ratio of ZDC neutrons in central $^{96}$Zr+$^{96}$Zr to $^{96}$Ru+$^{96}$Ru collisions at large transverse distances may probe the isospin dependence of the HMT and SRCs. Compared to traditional scattering experiments, our study illustrates that relativistic heavy-ion collisions may serve as an alternative way of measuring SRCs in colliding nuclei with less final-state interactions.

In this paper, the 3D scheme of the fuel code ALCYONE is applied to a database consisting of more than 50 base irradiations and ramp tests performed on rods with UO 2 , MOX or Cr-doped UO 2 fuels and Zy4 or M5__ cladding tubes with burn-ups up to 70 GWd/tU. The ability of the 3D scheme to predict the behaviour of a single fuel pellet -cladding element situated at the maximum Linear Heat Rate (LHR) during ramp testing is demonstrated by comparing the following experimental and calculated data: residual clad diameter after base irradiation and ramp test, height of inter-pellet and mid-pellet ridges after base irradiation and ramp test, dish filling after ramp test. In the second part of the paper, 3D simulations that catch the stress -strain localization at the triple point are presented. It is shown that the stress-strain concentration occurs only at the end of the power transient and is quickly relaxed by pellet and clad creep.

Camera-LiDAR fusion has become a prevailing paradigm for 3D object detection in autonomous driving. However, existing fusion detectors often establish strong inter-modality dependencies by decoding object queries from tightly coupled multimodal representations. Under corrupted driving conditions, such dependencies make the detector vulnerable to unreliable modalities, where degraded observations may interfere with reliable modality-specific evidence and lead to suboptimal predictions. Moreover, modality reliability can vary across both global driving scenes and individual object queries, requiring adaptive fusion decisions at a finer granularity. To bridge this gap, we reformulate robust camera-LiDAR fusion as a scene-aware branch routing problem and propose SARFusion, a robust 3D object detector. Instead of producing detections from a single fused representation, SARFusion decouples object-query decoding into three parallel reasoning branches: a camera branch, a LiDAR branch, and a camera-LiDAR fusion branch. Guided by a Scene Reliability Prior estimated from the global driving context, SARFusion further incorporates object-level evidence to route each query to the most suitable branch. This query-wise routing strategy alleviates harmful cross-modal interference while preserving the benefits of multimodal fusion when complementary cues are trustworthy. On the nuScenes test set, SARFusion achieves strong performance with 72.5 mAP and 74.4 NDS. Extensive analyses demonstrate its robustness under challenging conditions, including sensor corruptions and environmental changes.

The minimum cycle mean problem (MCM) on weighted digraphs is the problem of finding the minimum value of the cycle mean, that is, the ratio of the cost to the length, over all cycles. Despite its wide range of applications to discrete event systems, the parametric counterpart of the MCM has received relatively little attention in the literature, unlike other parametric problems in network optimization. In this paper, we consider the linear parametric MCM, where all edges $e$ have cost $a(e)-b(e)t$ with parameter $t$. We propose an algorithm to solve the linear parametric MCM in $O((m+n\log n)n^2W)$ time, where $n$ is the number of vertices, $m$ is the number of edges, and $W$ is the maximum absolute value of the coefficients $b(e) \in \mathbb{Z}$. The central technique of the proposed method is the algorithm for the parametric shortest path problem. The MCM is closely related to spectral theory in the tropical semiring, where the “$\min$” operation is regarded as addition and “$+$” as multiplication. By exploiting the connection between them, we provide a method to compute the eigenvalues and eigenvectors of tropical parametric matrices.

We find that language models can transfer capabilities through task-unrelated text. Post-training typically improves language models using task-specific data. Prior work on subliminal learning shows that information about these updates can pass through unrelated generations, but has largely focused on traits or preferences using extensive teacher outputs. We introduce Active Taskless Distillation (ATD), which achieves capability transfer using only a single word from the teacher per prompt. ATD probes the behavioral shadow of post-training by selecting prompts where the teacher and student's shared public ancestor is nearly indifferent between two ordinary words. A student initialized from this ancestor learns solely from the resulting prompt-word pairs, without target-task examples, teacher logits, or teacher parameters. In the primary coding experiment with Qwen2.5-1.5B, 5,664nses yield a 5.34 pp gain on HumanEval+ over an exact nuisance-matched control thadisrupts prompt-resperiments showtransfer in scientific knowledge, commonsense reasoning, and reading comprehensins across additional model generations, sizes, and families. Functional analyses show that the learned sid composable, andthat its strength tracks the teacher's update strength.

Integer maps are discrete dynamical systems defined on the natural numbers. In this paper, we investigate the dynamics of the shifted Alladi-Erd{\H o}s map, a one-parameter family of integer maps in which each composite number is mapped to the sum of its prime factors, while each prime is mapped to $n+A$, where $A \in \mathbb{N}$ is a fixed shift parameter. By systematically exploring the parameter space for $2 \leq A \leq 10^5$, we uncover a rich bifurcation structure characterized by the emergence, disappearance, and reorganization of attractor cycles as the shift parameter varies. We find that although several attractors may coexist for a given value of $A$, for most values of $A$, almost all natural numbers belong to the basins of only two dominant attractors. Using elementary number theoretic arguments, we explain the observed bifurcation diagram. We further characterize the attractor cycles and quantify the distribution of their basin sizes across the parameter space. Our results reveal an unexpectedly rich landscape of arithmetic dynamics arising from a remarkably simple integer map. %and provide a systematic characterization of how attractors and their basins evolve as shift parameter is varied.

In this work, we study the one-dimensional regression problem under random design and Gaussian errors. Our framework is very general: we make no prior assumptions about the design (which may be nonstationary and exhibit short or long-range dependence), nor do we assume that the errors are homoscedastic. We examine in detail the cases where the error process exhibits short or long-range dependence. We adopt a least-squares penalized strategy using piecewise polynomials to estimate the regression function, following the framework of Baron, Birgé and Massart [1999]. We derive explicit penalties, up to calibration constants, to obtain adaptive estimators for which we establish risk bounds. Since these penalties depend on the dependence properties of the error process, which are unknown in practice, we propose several adaptations of the dimension jump calibration algorithm to make our procedures fully data-driven.

End-to-end event extraction remains challenging for large language models as it requires simultaneous identification of event triggers, classification of event types, and extraction of schema-grounded argument spans. We present EAGER, a reinforcement learning framework for generative event extraction that combines fine-grained verifiable rewards with Schema-Contrastive Advantage Estimation to alleviate advantage collapse under sparse binary rewards. Our reward design explicitly targets structural validity, extraction accuracy, groundedness, coverage, over-generation, and span precision. Experiments across seven benchmark datasets show that EAGER consistently outperforms prompting, supervised fine-tuning, and prior reinforcement learning baselines, achieving a substantial improvement over the strongest prior method. Results demonstrate that task-aligned verifiable rewards and contrastive advantage estimation substantially improve structured extraction.

This data article provides the datasets, symbolic derivations, and scripts used to reproduce master diagrams, stationary-phase spectra, windowed first-order coherence functions, and quantum-noise stability maps for strongly chirped dissipative solitons of the cubic-quintic complex Ginzburg-Landau equation in normal and anomalous group-delay dispersion regimes. The repository includes node-regularized normal-dispersion spectra and energies; small-parameter expansions of the branch roots; cavity-map gain-loss update relations; Airy uniformization at the normal-dispersion spectral edge; anomalous-dispersion spectra and coherence calculations; and processed tables for plotting and stability analysis. OriginLab projects are accompanied by open-format .csv/.txt numerical tables to support reuse without proprietary plotting software. Data and code repository: https://doi.org/10.5281/zenodo.22690899.

Finite state machine (FSM) and behavior trees (BT) are widely adopted behavioral modeling paradigms for autonomous intelligent systems. While functionally equivalent and inter-convertible in principle, existing transformation methods between FSM and BT face major challenges in preserving behavioral completeness and avoiding model complexity explosion. To overcome these issues, we propose an LLM-driven unified conversion framework that enables automatic, efficient, and semantically consistent transformation between FSM and BT. Specifically, a novel loop execution BT structure is designed for LLM to accurately capture the loop structure in FSM, thereby preserving behavioral completeness. To mitigate the state explosion problem in BT-to-FSM conversion, a depth compression strategy is introduced with LLM prompt to eliminate redundant control nodes, complemented by differentiated hierarchical conversion rules that collectively reduce the number of required sub-FSM. Simulation experiments in multiple autonomous decision-making scenarios demonstrate that the proposed framework enables an accurate and automated bidirectional conversion between FSM and BT. Furthermore, it significantly enhances the scalability and maintainability of generated models compared to traditional approaches, providing a practical solution for behavior model conversion in consumer-grade autonomous intelligent systems such as service robots, game agents, and smart home devices

For binary matroids \(M,N\) representable over a common field \(\F\), the Kronecker product of their \(\F\)-representations defines a matroid \(T_{\F}(M,N)\) independent of the chosen representations. We classify when this represented tensor product is regular, cographic, graphic, or binary. For simple nonfree factors, regularity holds exactly when, up to interchange, one factor is a cactus matroid and the other is outerplanar, or one is a triangular cactus matroid and the other is series–parallel. Cographicity holds exactly in the first case. For simple factors with nonempty ground sets, graphicity holds exactly when one factor is free and the other is graphic. For fixed factors, regularity, cographicity, and graphicity are independent of the common representation field, although the isomorphism type may vary with its characteristic. Products of at least three simple nonfree factors are nonregular.

Valley Hall effect is a signature effect in the field of valleytronics, and recent studies have pushed this effect into the nonlinear regime. Here, we reveal a previously unexplored type of nonlinear valley Hall effect which arises from a valley Berry curvature dipole (vBCD) mechanism. We show this nonlinear valley Hall effect is forbidden for conventional time-reversal-connected valleys, but is supported in the class of valleytronic systems featuring time-reversal-invariant valleys. The candidate layer groups and detailed symmetry constraints on vBCD are obtained. It shows the nonlinear valley Hall response, as well as the nonlinear charge Hall response, can be well controlled by tuning the driving field direction. We demonstrate our proposal in an effective model study and in a concrete material example, strained Nb$_{3}$SBr$_{7}$, by first-principles calculations. The nonlocal transport signature of this vBCD induced nonlinear valley Hall effect is also discussed.

Lip synchronization aims to generate visual lip dynamics that align precisely with speech audio. Despite the high generation quality of diffusion models, they often struggle in complex scenarios and suffer from prohibitive inference latency, limiting real-world deployment. We present ComplexSync, a unified diffusion-based framework that enables real-time, high-fidelity lip sync under complex conditions. First, we introduce a dual-stream joint training strategy to mitigate information leakage from reference frames while preserving natural dynamics. Second, we develop a distillation-based acceleration scheme for single-step denoising, achieving a throughput of over 70 FPS. Third, we propose a relational alignment loss that leverages structural priors from Vision Foundation Models (VFMs) to enhance robustness against complex scene factors. Furthermore, we present the first benchmark specifically designed for complex lip synchronization, comprising over 200 challenging video sequences and specialized metrics. Extensive experiments demonstrate that ComplexSync achieves state-of-the-art performance across both standard and complex scenarios while enabling real-time inference.

Dense metric depth from cameras is essential to real-world 3D applications, yet achieving accuracy, faithful surface geometry, and fast inference simultaneously remains challenging. Monocular foundation models provide rich, transferable geometric priors but lack reliable metric scale, while depth-completion networks recover metric depth at the cost of geometric fidelity, cross-domain robustness, or speed. We present FounRef, a training-free method that aligns a frozen monocular foundation prior with sparse metric anchors to produce dense metric depth. FounRef is modular by design: its depth prior, anchor source, and refinement solver can each be replaced independently. We instantiate FounRef with MoGe-2 and LiDAR anchors. FounRef validates each anchor against the prior's dense depth prediction, rejecting inconsistencies caused by cross-sensor misalignment that geometry-only filters cannot detect. It then applies global and local metric corrections through a structure-preserving solver, retaining the prior's fine-grained geometry. FounRef requires no task-specific training and operates out of the box across unfamiliar cameras and scenes. On out-of-domain data, it delivers up to 24% lower depth error, 92% lower surface-normal noise, and almost 15x faster inference than DMD3C, a state-of-the-art depth-completion network. By decoupling metric alignment from geometry prediction, FounRef provides an accurate, geometrically faithful, and efficient approach to dense metric depth that can directly benefit from future advances in foundation models and metric sensors.

Traffic management in emerging megacities requires real-time analytics over thousands of CCTV video streams under latency, bandwidth, compute and energy constraints. We present TrafficFab, an autonomic edge–cloud testbed for AI-driven traffic management, designed to validate a representative slice of a megacity deployment. TrafficFab combines RTSP stream emulation, heterogeneous edge inference using DNNs, cloud-based nowcasting and forecasting using Spatio-Temporal Graph Neural Network (ST-GNN), and continual model adaptation through foundation-model (FM)-assisted Federated Learning (FL). Its autonomic control enables fine-grained scale-out/in of edge inference through energy- and migration-aware scheduling, elastic scale-up/down of GNN forecasting on public clouds, and periodic adaptation of the DNN on edge accelerators and private cloud, without centralized video collection. We evaluate TrafficFab on a Bangalore-city inspired deployment, spanning Raspberry Pis, Jetson accelerators, GPU fogs, private cloud servers, and cloud VMs, sustaining real-time analytics for $\approx 400$ live camera streams (10% of Bangalore) and analytically characterize larger setups. The results demonstrate that TrafficFab offers a practical validation-scale platform for closed-loop traffic analytics, short-term operational decision support, and longer-horizon planning analyses in megacity scales.

Mining before validation allows miners to extend a newly received block before completing its validity checks, giving them a head start in the race for the next block reward. This head start, however, comes with a security risk: rejecting one invalid block also discards the honest work built on it, an effect missed when validation is treated as instantaneous. We quantify this risk in a model of Nakamoto consensus with bounded network delay and a validation-time bound independent of processing load. We establish an explicit threshold on adversarial mining power below which honest miners' fully validated chains continue to grow and agree on a stable history with high probability over any fixed observation period. We also construct an attack that repeatedly draws honest mining onto invalid branches. When the adversary produces more than one block on average during the allowed validation time, the attack can eventually remove a target block at any fixed initial confirmation depth. Combined with ordinary private mining, this attack yields a matching asymptotic bound in the fully decentralized regime, where each honest miner has negligible mining power. The results show how validation latency limits the security of mining before validation, beyond the constraint imposed by network delay.

Virtual cells are evolving from single-task predictive models toward programmable biological simulation systems, yet heterogeneous data, models, and validation evidence still lack a unified organizational framework. Here, we present PRAXIS-VirtualCell, a modular framework that organizes biological data, predictive models, perturbations, adapters, execution environments, and validation evidence to enable reproducible and auditable virtual experiments. The system supports cross-species tasks spanning Escherichia coli, Saccharomyces cerevisiae, and human K562 cells, while using biological contracts and evidence-aware execution to distinguish supported predictions from extrapolation and abstention. By further integrating agentic orchestration, PRAXIS-VirtualCell automatically translates natural-language questions into traceable virtual experiments, providing a unified runtime foundation for trustworthy and scalable Virtual Cell systems.

The fidelity of image reconstruction from projections in linear inverse problems, such as tomography, is critically dependent on the synergistic interaction between frequency-domain filtering and spatial-domain interpolation. However, a physical model that can quantitatively describe how these two components cascade interact in the frequency domain and ultimately determine image quality is still lacking to this day. Here, we introduce a unified frequency-domain model that conceptualizes the combined effect of filtering and interpolation in the filtered backprojection (FBP) algorithm as a cascaded modulation process. This model demonstrates that the effective reconstruction spectrum is determined by the original projection data being sequentially modulated by the frequency responses of the filter and the interpolation kernel. Comprehensive numerical simulations and synchrotron radiation CT experiments validate the model, confirming its power to explain the performance hierarchy of classical filter-interpolation pairs under both ideal and noisy conditions. The model successfully predicts key performance characteristics, including spatial resolution and structural fidelity, thereby elucidating the physical principles behind the efficacy of specific combinations. This work establishes a generalizable theoretical foundation for analyzing cascaded systems in linear inverse problems, moving the practice of algorithm selection in computational imaging from empiricism to a principled, physics-based paradigm.

Modern AI and HPC accelerators increasingly expose dataflow features: software-visible mechanisms for data movement and overlap, such as inter-core communication through the on-chip network and intra-core asynchronous pipelining. These features shift scheduling responsibility from hardware to the compiler, and because placement, movement, and synchronization become software-visible, they also make the performance of static schedules predictable. Yet high performance on such hardware still relies on vendor-engineered kernel libraries or profile-based auto-tuning, whose embedded expert knowledge transfers poorly across architectures and algorithms. We present Loom, a tuning-free symbolic compiler framework for tile-based SPMD programs on spatial dataflow architectures. The central idea is to treat tile-based SPMD compilation as a hardware-explicit static optimization problem. Loom enumerates discrete spatial-mapping and communication candidates while keeping value parameters, such as tiling factors and pipeline knobs, symbolic within each candidate. From an explicit hardware description, it derives symbolic legality constraints and latency expressions, formulates one CP-SAT problem per schedule candidate, and jointly solves inter-core dataflow, intra-core asynchronous scheduling, and block sizes at compile time. On two Tenstorrent generations, Wormhole and Blackhole, Loom matches or exceeds the vendor-optimized TTNN library on GEMM, Flash Attention, and Flash Decode, out of the box and without per-shape profiling or profile-based platform-specific schedule tuning. These results suggest that hardware-derived symbolic compilation provides a retargetable alternative to profiling-based tuning for spatial dataflow architectures while remaining interpretable by keeping optimization decisions traceable to source-level symbols.

This paper investigates entire classical separable variable radial solutions to a class of parabolic k-Hessian equations -u_t (sigma_k(lambda(D^2u)))^alpha = f(|x|)g(t), where the right-hand side consists of positive continuous functions. Without assuming that -u_t is positively bounded, we extend previous work for the equations whose right-hand side is 1 to more general cases, including cases where the right-hand side terms are bounded and periodic. By employing the method of Euler's broken line, we obtain the existence and nonexistence results. Furthermore, we obtain the precise asymptotic power exponent.

Full-duplex spoken dialogue requires simultaneous listening and speaking at sub-second latency, under conversational timing and cognitive demands that change moment to moment. Yet current models mostly impose static operating points, lacking a systematic mechanism for adaptive decisions. We present AdaptDuplex, which extends Qwen3-Omni with such a mechanism, co-designed across three layers. A compact token-level protocol represents every window as a canonical sequence, trains dual-stream alignment through a bounded text lead over speech, and exposes every behavioral decision as an explicit token for training-free runtime control via logits bias. Adaptive mechanisms dynamically predict among discrete window durations and augment direct response as needed with non-blocking cognitive consolidation and multi-flight external reasoning. A progressive pipeline introduces these behaviors through a three-stage Thinker curriculum, then Talker-only and joint SFT, with GRPO as a preliminary increment. On Full-Duplex-Bench v1 and v1.5, AdaptDuplex outperforms DuplexOmni on 18 of 21 comparable turn-taking, overlap-behavior, and timing metrics and MiniCPM-o 4.5 on 19 of 22, with gains in both interaction decisions and response timing. On human-recorded HumDial-FDBench, it attains the top Final score (69.6) of the compared duplex models.

Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models ($\Pi$GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of $\Pi$GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one $\Pi$GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform $\Pi$GDM at its nominal setting, even when the latter is given the true noise level, by up to 14 dB depending on the operator, and to match the ground-truth-calibrated $\Pi$GDM oracle within 0.1 dB. (ii) FB-GDM is robust when the forward operator, the noise level, or the image distribution changes: it stays close to a per-problem $\Pi$GDM oracle throughout and does not exhibit the hallucinations observed with DPS, whereas DPS substantially degrades at a fixed scale and $\Pi$GDM stays competitive only if it is re-tuned against the ground truth for each new problem. When the prior is applied to images outside its training set, this re-balancing between data and prior keeps FB-GDM faithful where a fixed face-prior guidance can otherwise hallucinate.