Papers

Multi-source remote sensing image classification has attracted increasing attention due to the complementary spectral, structural, and geometric information. However, existing methods still suffer from two limitations: insufficient semantic contextual modeling and unreliable feature fusion caused by slight spatial misalignment. To address these issues, we propose a Semantic-Guided Fusion Network (SGFNet) for multi-source remote sensing image classification. Specifically, the Semantic Mixing Convolution Block (SMCB) is designed to dynamically generate semantic-aware convolution kernels according to contextual relationships among feature representations. In addition, the Frequency Modulated Fusion Block (FMFB) is introduced to perform cross-modal interaction in the frequency domain, which effectively alleviates the influence of slight spatial misalignment and improves complementary information fusion. Extensive experiments conducted on the Augsburg and Houston 2018 datasets demonstrate that the proposed SGFNet consistently outperforms several state-of-the-art methods. The codes are publicly available at https://github.com/oucailab/SGFNet .

Local learning trains each layer with its own auxiliary loss and no global backward pass, which makes layer updates structurally parallel. Two problems have kept it marginal: accuracy degrades as depth grows, and hyperparameters are fragile. We apply Muon-style spectral update geometry (momentum orthogonalization with spectral step scaling) to per-layer local updates, an intersection not previously studied. On CIFAR-10 MLP benchmarks with local linear heads, a single step-size setting is the best value in our tested grids from width 128 to 2048 and from depth 12 to 48, while local Adam requires re-tuning along both axes and still collapses at depth 48 (31.3 percent re-tuned per depth, 19 percent with its depth-12 setting transferred, vs 42.7 percent for the spectral update at its unchanged setting). At five seeds and width 512 the spectral update leads local Adam by a clear margin (48.9 +/- 0.5 vs 46.6 +/- 0.3). Prospectively specified controls attribute the transfer and most of the depth robustness to the spectral geometry itself rather than to any step-size rule on top of it. We additionally formulate the step size as a drift contract, lr = epsilon / RMS(input), which bounds each layer's weight-induced pre-activation change per step, conditioned on its current input. The contract yields a small gain over the best fixed learning rate where that baseline is measured, makes the step size interpretable, and provides a per-layer, input-conditioned drift bound that standard optimizers do not offer. We report one negative result: with RMSNorm and weight decay in the trunk, the stability benefit of spectral updates accrues to global rather than local training, so the local advantage concentrates precisely where normalization is absent.

We introduce a class of plurisubharmonic weights on \mathbb C^n and develop a theory of the associated weighted Fock spaces F_\varphi^p. The curvature assumptions are imposed on a \mathcal C^2-regularization at bounded distance from the original weight. Thus the original weight need not be smooth or strictly plurisubharmonic, and, even when it is of class \mathcal C^2, its complex Hessian eigenvalues need not be uniformly comparable. This provides a counterpart of Christ's doubling theory in several complex variables. We establish a global upper estimate with decay away from the diagonal and a uniform lower estimate near the diagonal for the weighted Bergman kernel. These estimates yield L^p bounds for the kernel functions, boundedness of the Bergman projection, and duality and complex interpolation for the associated Fock spaces. For a certain class of weights beyond the uniformly controlled curvature setting, we construct an integral solution operator for the \bar\partial equation and establish scale-adapted weighted L^p estimates for 1\leq p\leq\infty. As an application, for all 1\leq p,q<\infty, we characterize the boundedness and compactness of Hankel operators from F_\varphi^p to L_\varphi^q with possibly unbounded symbols in terms of weighted IDA spaces.

Reliable agricultural yield statistics are typically reported at coarse administrative scales, whereas modern geospatial machine learning methods require spatially explicit, pixel level supervision. This mismatch has limited the development of large-scale benchmarks for crop yield learning using multimodal Earth observation data. A reproducible benchmark, AgroBench, is presented for transforming publicly available U.S. county level crop yield statistics into weakly supervised pixel-level crop time series. Each crop pixel time series is paired with a county-level yield value as a weak supervisory signal rather than a directly measured pixel-level yield label. Our geospatial data generation pipeline integrates USDA crop yield statistics with crop-specific land cover masks, Sentinel 2 multispectral imagery, Sentinel-1 synthetic aperture radar observations, climatic variables, and terrain information to produce temporally aligned multimodal sequences describing individual crop pixels throughout the growing season. The resulting benchmark contains over 13 million observations from 788,654 unique crop pixels spanning 5,107 county year combinations across eight growing seasons (2017 to 2024) for five major U.S. crops. To facilitate standardized evaluation, we establish a crop yield prediction benchmark using a Leave-One-Year-Out evaluation protocol and provide baseline results using representative machine learning models. By releasing the complete data generation pipeline, benchmark dataset, and evaluation protocol, AgroBench provides a reproducible foundation for future research in weakly supervised learning, multimodal remote sensing, spatiotemporal modeling, and geospatial foundation models for agriculture.

Self-supervised learning (SSL) has become an effective approach for learning visual representations without manual annotations. Among SSL approaches, contrastive learning has been widely used for visual representation learning. However, existing contrastive SSL methods have focused primarily on image-level or pixel-level representation learning, while region-level representation learning remains less explored. We propose SPARC, a region-level contrastive learning framework that leverages superpixels to establish explicit correspondence between augmented image views. SPARC introduces a region contrastive branch that performs superpixel-based feature pooling and optimizes a region-level contrastive objective jointly with a global image-level objective. Under identical settings, SPARC consistently outperforms previous methods such as MoCo-v2 and DenseCL, achieving improvements of up to +9.79 mIoU for semantic segmentation and +4.88 AP for object detection. Ablation studies further demonstrate that region-level objectives produce the strongest performance. Thus, region-level contrastive learning is an effective approach for improving self-supervised visual pretraining for dense prediction tasks. Code repository can be accessed at https://github.com/xRIPEIx/SPARC.

Large language models (LLMs) are increasingly used to simulate human survey responses and behavioral reactions, yet unreliable simulations can mislead social science conclusions. However, existing evaluations focus on end-to-end scores, leaving it unclear how different aspects of the simulation process interact to determine reliability. We propose ReliMap, which decomposes LLM-based human behavior simulation into three structured layers and evaluates reliability at both the individual level (R1) and population level (R2) across three configuration dimensions: model capacity, profile completeness, and population coverage. Through experiments across four simulation tasks and eleven LLMs, we find that all models exhibit substantial distributional bias without profile conditioning. Profile conditioning reduces this bias with diminishing returns. Larger models benefit more, and attribute informativeness matters more than quantity. Critically, R1 gains do not reliably transfer to R2–individual and population-level reliability can move in opposite directions. At the population layer, increasing coverage reduces variance but not systematic bias, with R2 stabilizing at around 50-100 individuals. These findings highlight that reliable simulation cannot be achieved by optimizing any single layer in isolation, but requires coordinated improvement across all three.

In this work, we establish a criterion for classifying elliptic curves that have no solutions in the set of positive integers. In particular, we prove that if $E: y^2 = Ax^3 + Bx^2 + Cx + D$ is an elliptic curve where $A$, $B$, $C$, and $D$ are coefficients of the curve, and $p$ is a prime number where $p \equiv 1 \pmod{4}$, and $(x,y)$ is a positive integer point, then if $$ -3A + C \equiv -1 \pmod{4}, $$ $$ A - B + C \equiv -1 \pmod{4}, $$ and $$ p^2 = A - B + C - B, $$ then there are no positive solutions for the curve $E$, where $E(\mathbb{Z}^{+}) = \varnothing$. Furthermore, we generalize this criterion by incorporating techniques from linear algebra. Specifically, we introduce a matrix construction to establish the nonexistence of positive integer solutions for a family of elliptic curves.

Post-quantum cryptography (PQC) acceleration has been studied for CPUs and FPGAs, yet GPGPUs - dominating high-throughput computing - remain unexplored for PQC hardware integration as a functional unit. We present what is, to our knowledge, the first such integration: the Vortex Post-Quantum Crypto Unit (PCU) on the open-source Vortex RISC-V GPGPU. The PCU implements a 256-point NTT over Kyber (q=3329) and Dilithium (q=8380417) moduli in 134 logic cells (73 LUT4 + 61 CCU2C) - the smallest reported NTT accelerator by logic-cell count, 2.8x smaller than the next smallest design. It achieves 228.78 MHz on Lattice ECP5 and 299.8 MHz place-and-route on Xilinx Artix-7, and passes 253 functional tests across 7 suites. On Vortex SimX, it achieves 42.6x acceleration over GPU ALU execution, projecting to roughly 36x speedup on RTL. Synthesized to ASAP7 7nm, the NTT datapath occupies 96.53 um^2 (post-route) at 702 MHz. This work establishes a foundation for integrating PQC hardware acceleration into general-purpose parallel computing.

Neural networks provide expressive representations for scientific computing. However, even sufficiently expressive networks can suffer training failure in weak-gradient regimes, limiting their practical use in quantum many-body physics and ab initio quantum chemistry. Here we derive an unbiased direct gradient estimator and introduce the adaptive minimum-variance phase (AMVP) estimator for neural-network variational optimization. By improving the signal-to-noise ratio of weak gradients, these methods enable reliable scientific calculations where training previously failed, while substantially reducing computational cost. The framework enables compact networks to outperform larger and fine-tuned default standard-estimator models with over an order of magnitude less GPU time on correlated flux models, and ultimately exceed the density matrix renormalization group (DMRG) accuracy. It further achieves chemical accuracy in N$_2$ bond breaking and, for the first time, in heavy-element I$_2$ with explicit spin-orbit coupling. These results demonstrate that gradient-estimator design expands the capabilities of neural-network variational methods for accurate scientific computing.

Although tens of thousands of two-dimensional (2D) crystals are now known, the nanotubes they can form are usually constructed for individual materials, using procedures derived for graphene. Here, we develop a general theory of the rolling construction for arbitrary 2D crystals and implement it in \ntbuilder{} (NanoTube Builder), an open-source library with desktop and web interfaces. We express the size of the exact unit cell of a tube through the reduced form of a single rational number built from the lattice metric, which explains why triangular and square lattices always close with small cells, whereas rectangular, centered rectangular, and oblique lattices can require cells larger by many orders of magnitude. The optimal approximate cells are the best rational approximations of a second number, so that a cell small enough for first-principles calculations can be chosen with a controlled departure from periodicity, as in the biphenylene network, where such a cell is eight orders of magnitude smaller than the exact one. The 17 plane groups reduce to seven distinct chirality maps once rolling is taken into account, the rolling sense of layers without a horizontal mirror defines distinct tubes, and bonds formed or broken by curvature are detected pair by pair against the flat layer. The same framework assembles multiwalled tubes whose walls share one axial period, periodic bundles, and strained or twisted structures that remain periodic. Applied to 46,403 distinct 2D systems, it produced a public catalog of 20,334,372 nanotubes, of which 57.1% show no bond change upon rolling. All structures can be exported directly as input for first-principles and molecular dynamics codes.

Let $f_{0,1,4}(n)$ denote the number of partitions of $n$ into parts congruent to 0, 1 or 4 modulo 5 with each part used at most twice, and let $f_{0,2,3}(n)$ be defined analogously for parts congruent to 0, 2 or 3 modulo 5. We prove that for every prime $p \equiv 3 \pmod 4$ there are explicit non-negative integers $a(p)$ and $b(p)$, determined by $20a(p) \equiv -9$ and $20b(p) \equiv -1 \pmod{p^2}$, such that $f_{0,1,4}(p^2m + a(p))$ and $f_{0,2,3}(p^2m + b(p))$ are congruent modulo 3 to $f_{0,1,4}(m)$ and $f_{0,2,3}(m)$ when $p \equiv \pm 1 \pmod 5$, and to $f_{0,2,3}(m)$ and $f_{0,1,4}(m)$ when $p \equiv \pm 2 \pmod 5$. By quadratic reciprocity the two functions are preserved exactly when 5 is a quadratic residue modulo $p$, and interchanged otherwise. The smallest cases are $f_{0,1,4}(9m) \equiv f_{0,2,3}(m)$ and $f_{0,2,3}(9m+4) \equiv f_{0,1,4}(m)$. The proof reduces each generating function modulo 3 to the square of a Rogers-Ramanujan-type theta function by means of $(1-x)^{\ell} \equiv 1-x^{\ell} \pmod{\ell}$ and the Jacobi triple product, and then dissects the resulting binary quadratic form using the fact that $-1$ is a quadratic non-residue modulo $p$. As corollaries we obtain, for each such $p$, a congruence with exceptions on a progression of modulus $p$, and an infinite family of self-similarity congruences on progressions of modulus $p^{dn}$ with $d = 2$ or $d = 4$ and constants $9(p^{dn}-1)/20$ and $(p^{dn}-1)/20$.

The preprint arXiv:2609.04176 (Z.-W. Sun, 3 September 2026) claims a proof that Catalan's constant $G$ is irrational: it constructs for each $B$ a number $\hat q_B$ from weighted tails of the series and asserts that, if $G=a/q$, the integer $N_B=q^S H_B^{\min}\hat q_B$ satisfies $0<|N_B|<1$ for large $B$ (its Theorem 9.1). We report four exact computations. First, the printed proof of the rank theorem (Theorem 2.1) carries $T_i$ where its own recurrence requires $T_{i+1}$; the slip is repairable, and the statement is verified exactly at 44 parameter pairs with $S\le 4$, $B\le 30$. Second, with the paper's definitions and the worst-case denominator, attained at an explicit rational $a/q$, a lower bound for the quantity the derivation of Theorem 9.1 controls equals $+1.49$ to $+1.79\,B^2$ at eighteen indices $20\le B\le 119$, where the derivation claims at most $-0.00966\,B^2+o(B^2)$. Third, the paper's own denominator bound (Corollary 5.2) holds in every tested instance and is nearly sharp, so the discrepancy lies in the asymptotic ledger of Sections 6-9. Fourth, an exact identity locates it: the prime 2 contributes $v_2(F_D)\log 2=(2\log 2+o(1))B^2$ to the quantity, because the positive part at 2 vanishes while $|\hat q_B|$ carries the full power of 2 in $F_D$; no display in the ledger carries a term of this order, and Remark 9.3 assigns it to the derivation of the odd-prime constant $c_{\rm odd}=0.006$ without showing how. At the tested parameters the odd-prime layers agree with the paper's constants to within about $0.1\,B^2$, and the remainder of the discrepancy is the size of the residual minor at those indices. These computations test the paper's bounding method, which is uniform in $(a,q)$; they show that the published derivation does not justify the claimed estimate, so the proof of the main theorem is incomplete. Nothing is concluded about the irrationality of $G$.

This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fundamentally changes in the bilinear settings, how recent theory addresses finite-sample learning and control, and how these ideas connect to broader themes in nonlinear control, representation learning, and data-driven decision making. For learning, we emphasize tools that are particularly useful in the bilinear settings, such as one-sided Bernstein's inequality for dependent and heavy-tailed covariates, blocking arguments, and martingale concentration for input-dependent noise. We then apply these tools to obtain finite-sample learning guarantees for fully observed bilinear systems, partially observed bilinear systems, and linear systems with bilinear observations. For control, we discuss quadratic control from bilinear observations, where the classical separation principle fails, and review tractable approaches based on belief-space receding horizon control. We also cover stabilization of bilinear dynamics under state feedback using semi-definite programming, LMI relaxations, sum-of-squares methods, and Koopman-based lifting. We conclude by discussing connections to reinforcement learning and machine learning, and some open problems in combined learning and control of bilinear systems.

We prove the irreducibility conjecture for Legendre polynomials proposed by Stieltjes: for every integer $j\geq 1$, both $P_{2j}(x)$ and $P_{2j+1}(x)/x$ are irreducible over the rational numbers. The proof proceeds by contradiction. Starting from a hypothetical nontrivial factorization, we remove the zero root from $P_n$ when present, multiply by a suitable constant, and express the resulting polynomial as a product of two integral polynomials $A(x^2)$ and $B(x^2)$. We then construct the resultant and its odd part, $R=\operatorname{Res}_t(A,B), \mathcal{R}=\frac{|R|}{2^{v_2(R)}}.$ Put $k=\operatorname{deg} A\leq\operatorname{deg} B$ and $m=\lfloor n/2\rfloor$. Using the classical auxiliary polynomial $U_n$ and the differential identity $(1-x^2)(P_n'U_n-P_nU_n')=1-P_n^2,$ together with orthogonality, divisibility properties of the coefficients, and a least-common-multiple estimate, we obtain an upper bound for $\mathcal{R}$. On the other hand, the Legendre differential equation gives a lower bound for the absolute value of the derivative of $AB$ at each root of $A$. We use Chebyshev polynomials and Hadamard's inequality to bound the product of the squared pairwise differences of these roots, and combine this with estimates for the leading coefficients and the power of $2$ in $R$ to obtain a lower bound for $\mathcal{R}$. These estimates yield $m\log4-\log\frac{4(m+1)^2}{\sqrt m} <\frac{\log\mathcal R}{k} <(m+\sqrt{2n-1})\log3 (n\ge64).$ For every $n\ge256$, the lower bound strictly exceeds the upper bound, giving a contradiction. Combining this with established irreducibility results and explicit integer comparisons for the remaining degrees proves irreducibility in every degree.

Vision-Language-Action (VLA) models have emerged as foundational models for next-generation robotics. High VLA inference throughput is critical for meeting the control-rate requirements of robots. VLA models comprise two phases, a vision-language model (VLM) and an action head, that can be decoupled and executed asynchronously and concurrently across independent robot requests. Through a detailed characterization of four state-of-the-art VLAs, we observe that GPUs are severely underutilized in VLA inference as the Cooperative Thread Array (CTA) scheduler of GPU is unable to fully overlap the two independent phases of VLA execution. We identify that this inefficiency is caused by head-of-line blocking in the hardware thread-block dispatcher. We demonstrate that prior scheduling frameworks do not address the challenges posed by VLA concurrency. First, the independent phases across different robot requests each comprise numerous kernels, and at any given time, there are different combinations of kernels that are executed in parallel. This makes static or ahead-of-time scheduling policies largely ineffective. Second, many of the action-head operators are short-running kernels and there are numerous such kernels. This leaves no headroom for online profiling or preemption-based mechanisms. To address these challenges, we present KerColle, a lightweight GPU scheduling framework that leverages online Streaming Multiprocessor (SM) utilization and individual kernel resource requirements to intelligently and dynamically co-schedule kernels to efficiently overlap the two phases of execution by (1) mitigating head-of-line blocking, and (2) co-scheduling kernels with complementary resource requirements. We demonstrate in simulation, across two GPU architectures, for 4 state-of-the-art VLA models, that KerColle delivers throughput gains of up to $28\%$.

We define a rank-two extension $\mathcal{H}^{(2)}$ of the spherical $\mathcal{H}$-transform, together with its associated transform $\mathcal{R}^{(2)}$. For sums, both transforms are additive. The transform $\mathcal{R}^{(2)}$ yields a $4\times4$ formula for the average product of two hermitized resolvents, and hence for off-diagonal eigenvector overlaps, recovering the Ginibre, elliptic, and bi-invariant formulas. We also treat correlated pairs of matrices, and obtain overlaps between their eigenvectors or singular vectors.

This research addresses the challenge of limited material recycling in wood recycling processes by leveraging artificial intelligence (AI)-based dimensionality reduction. Our study explores the application of convolutional neural networks (CNNs) in multi-channel hyperspectral imaging (HSI), extending beyond RGB channels to over 200 spectral channels. Dimensionality reduction within this context involves streamlining the feature space for AI system training and inference. Focusing on explainable AI (XAI) methods, this paper contributes to a broader research initiative, presenting a solution framework that enhances the sustainability and efficiency of wood recycling processes.

Generalizable robot manipulation requires predicting how a scene will evolve, identifying where interactions are feasible, and determining how to act. Action-labeled robot videos directly supervise control but are costly and limited in diversity, whereas egocentric human videos capture diverse interactions but lack robot actions and differ in embodiment and appearance. We introduce AffordanceWAM, an affordance-aware generative World Action Model that represents object-centric spatiotemporal affordance through Scalar Affordance and Affordance Heatmap, within the generated future World. This representation grounds visual prediction in task-relevantant objects and interaction regions for action generation, and provides shared interaction targets across human and robot videos. Built on a pretrained video diffusion Transformer, AffordanceWAM uses separately parameterized World and Action Experts, coupled through Masked Joint Self-Attention, to jointly predict future RGB observations, Scalar Affordance fields, Affordance Heatmaps, and continuous robot actions under a unified flow-matching objective. Human videos supervise all three future-World streams, whereas robot trajectories additionally provide action supervision, enabling transfer without human action labels or retargeting. Experiments on RoboCasa, CALVIN ABC$\rightarrow$D, and real-world manipulation demonstrate consistent gains over RGB-only and robot-data-only baselines. Under fixed robot supervision, RoboCasa performance improves monotonically as affordance-annotated human video scales. These results support affordance as an effective interface for both vision-language-action learning and human-to-robot transfer.

Using ideas of Digne and recent work of Gaitsgory–Rozenblyum–Varshavsky, we show that Lusztig induction commutes with (a minor variant of) the Glauberman correspondence for large prime degree field extensions. This allows one to reduce the Mackey formula in Deligne–Lusztig theory to the case of “large” base fields, in which case the result is due to Bonnafé.

We prove Stieltjes' common root conjecture: Legendre polynomials of distinct degrees have no common nonzero root. We construct an auxiliary polynomial and show that, for the relevant power of two $q\ge2$, the edge of slope $1/q$ in its $2$-adic Newton polygon has horizontal length less than $3q$. If a common nonzero root existed, Newton polygon theory and the Legendre differential equation would force the same edge to have horizontal length at least $3q$, yielding a contradiction.

Black-Box Optimization (BBO) is often applied in several engineering fields and can utilize an advancement of numerical measure- ments and simulation technologies. It deals with the optimization func- tions, where an analytical description is unavailable. It relies on meth- ods that require only an input point in the search space, paired with its corresponding objective function value, obtained through non-analytical means, e.g., sensors, experiments, or simulations. Common approaches include evolutionary optimization and other metaheuristics. Since BBO methods rely solely on objective function values, they typically require many evaluations, which becomes problematic when evaluating the ob- jective function is time-consuming or expensive. This leads to using surrogate-based optimization which evaluates selected true objective val- ues and trains a regression model to approximate the objective function across the search space. Surrogate-assisted black-box optimization is a small-data learning problem because the optimizer must approximate an expensive objective function from limited evaluations. Surrogate models act as data-efficient regressors, guiding the search toward promising or informative points under a restricted evaluation budget. In this paper, a new surrogate model using artificial neural networks, called Adaptive- Fidelity Nexus Covariance Matrix Adaptation Evolution Strategy (AFN- CMA-ES), is proposed for the selective evaluation of objective functions. The experimental results show its competitive performance compared to state-of-the-art surrogate-assisted BBO methods.

Universality in nonlinear nonequilibrium systems is typically expressed through scaling laws that render macroscopic behavior insensitive to microscopic details. Whether this universality survives when periodic forcing and nonlocal dissipative memory act simultaneously remains an open question in driven open dynamics. Here, we demonstrate that barrier-crossing processes in periodically driven dissipative systems are governed not merely by modified exponential scaling, but by an explicit two-parameter universal response function. Within a semiclassical instanton framework incorporating Floquet modulation and Ohmic environmental coupling, the tunneling exponent factorizes into a system-dependent static contribution and a universal function of two dimensionless control parameters: normalized driving frequency and dissipation strength. This factorization arises from the combined modification of a single saddle-point trajectory and introduces no additional independent scaling variables. Weak-to-moderate dissipation acts as a smooth dynamical renormalization of the effective action, preserving the saddle-point structure and enabling controlled analytical expansion. In the high-frequency regime, the response exhibits universal dynamical averaging, while an explicit integral representation establishes a continuous adiabatic to Floquet crossover. Direct numerical evaluation of the nonlocal instanton action confirms that the normalized tunneling exponent exhibits a universal dependence on the driving parameters across different model systems. These results identify driven dissipative barrier crossing as a distinct two-parameter universality class within nonlinear nonequilibrium dynamics and provide a predictive functional framework for response phenomena in driven systems with memory.

Visual graph reasoning requires answering graph-theoretic questions directly from graph images, where graph topology and state are conveyed visually rather than given in symbolic form. Despite recent progress of vision-language models (VLMs), current approaches to visual graph reasoning still fail on simple visual graph problems. This reveals a fundamental limitation of existing approaches: they prioritize final-answer supervision over the intermediate recovery of an explicit graph representation that preserves graph topology and state from visual input. To address this limitation, we propose VGCompiler, a compilation-centric paradigm for visual graph reasoning via knowledge compilation. VGCompiler organizes reasoning around two compilers: a representation compiler that recovers a structure-preserving intermediate graph representation from visual input, and an operation compiler that compiles query intent under the recovered graph state into an executable graph operation. Specifically, we build VGCompiler on Qwen3-VL-8B and train it with reinforcement learning guided by a layered reward over executability, compiled graph validity, representation quality, and operation quality. VGCompiler uses a frozen observer to summarize graph and question conditions into lightweight signatures, enabling archive retrieval and code reuse across similar regimes. Experiments on three benchmarks GVLQA, VisionGraph, and VGCURE, show that Qwen-VGCompiler, built on an 8B backbone, surpasses the strongest closed-source VLM baseline by 28.9% and the strongest code-based baseline by 23.7%, while maintaining high efficiency. We further evaluate VGCompiler on three real-world domains, including metro routing, logistics delivery, and network fault assessment, where it generalizes across heterogeneous visual graphs and domain-grounded tasks.

Accurate characterization of shallow cryosphere subsurface structures is critical for understanding snow and ice dynamics, evaluating environmental hazards, and informing climate-related decision making. Recent advances in unmanned aerial vehicles (UAVs) and compact radar instrumentation have enabled UAV-borne ground penetrating radar (GPR) as a non-contact alternative for subsurface sensing in these environments. By combining the safety-constrained mobility of unmanned aerial platforms with the penetration capability of radar, UAV-borne GPR facilitates rapid, wide-coverage and flexible surveys over snow and ice surfaces in cryosphere that are often inaccessible to traditional ground-based methods. This contribution reviews recent progress in UAV-borne GPR for cryosphere investigations, encompassing system architectures, operational strategies, and representative deployment practices. Furthermore, key data-processing methodologies are summarized for their roles in enhancing subsurface imaging and reconstruction fidelity. A case study from Mochou Lake in East Antarctica, illustrates these capabilities, yielding an ice-thickness estimation error of only 0.03 m when benchmarked against drilling measurements. Finally, the remaining challenges, particularly those associated with scanning coverage, real-time data processing, and detection accuracy, are discussed for future cryosphere applications.

Large language models have shown considerable potential for natural-language-driven parametric CAD modeling. However, a fundamental contradiction exists between their probabilistic generation and the deterministic requirements of CAD modeling, resulting in limitations in reliability, design-intent preservation, and geometric validity. Existing methods typically rely on large-scale annotated datasets, lack explicit modeling of design intent, and underutilize the deterministic capabilities of CAD kernels. To address these limitations, we propose ReliCAD, a unified framework that transforms uncertain LLM generation into reliable parametric CAD modeling. Through explicit design-intent modeling, ReliCAD converts user requirements into structured design specifications and explicitly models geometric relations, topological dependencies, and feature construction order. It then generates constraint-aware parametric instructions and invokes the CAD kernel through an Agent-ready API to perform geometric construction and constraint solving. ReliCAD further records runtime evidence and employs a verification-feedback mechanism to assess consistency between the generated model and the design specifications, enabling error localization and iterative repair. Experiments on the public HistCAD generation dataset and our multi-granularity CAD editing dataset demonstrate that ReliCAD significantly outperforms baseline methods, achieving 99.8% validity rate and 0.8753 IoU. ReliCAD provides a verifiable, repairable, and generalizable approach to natural-language-interactive CAD modeling.

For an infinite product P(q) = prod_{m>=1} (1-q^m)^{eps(m)} and real delta, write P(q)^delta = sum_{n>=0} c_delta(n) q^n. Schlosser and Zhou conjectured precise sign patterns for these coefficients, for several products and ranges of delta. We resolve four of their conjectures completely, in each case extending partial results already in the literature: those for the Goellnitz-Gordon product Q_8 = (q,q^7;q^8)_inf/(q^3,q^5;q^8)_inf (Conjecture 21), for Q_12 = (q,q^11;q^12)_inf/(q^5,q^7;q^12)_inf (Conjecture 24), and for the Borwein products G_7 and G_11 (Conjectures 20 and 23). Conjecture 23 is true. Conjecture 21 fails exactly on [beta, 8/3), where beta is approximately 2.66448; the threshold 8/3 is sharp, and the first counterexamples occur near n = 7.6 x 10^5. Conjecture 24 fails exactly on (delta_1, 0), where delta_1 = -0.64411... is a root of the 22nd coefficient polynomial. Conjecture 20 fails exactly on (delta_c, 5), where delta_c = 4.8735075853867342634... is a root of the 897th coefficient polynomial. All other stated ranges are proved. Parts of Conjecture 21 were settled independently by He and Li; what is new here is the range near delta = -1, where their threshold diverges. Each failure has the same mechanism: a leading circle-method amplitude vanishes, and a secondary term with the wrong sign overtakes it. The proofs are self-contained apart from classical facts. The cusp analysis is exact, via finite orbits of Weil representations; the Hardy-Ramanujan-Rademacher expansion is made fully explicit; and certified computations in exact and ball arithmetic handle the finite ranges and the degenerate regimes.

Few-shot learning research is predominantly evaluated on accuracy alone, with limited attention to the parameter and training-sample budgets required to reach that accuracy - a real constraint for practitioners without large-scale compute. We present an ultra-lightweight (22,249-34,917 parameter) spatial-relational architecture for few-shot image classification that combines fixed Gabor edge-energy guidance with a windowed, content-adaptive patch locator. Under a strictly matched, iso-episode-budget protocol (250 meta-training episodes, 5 canonical seeds, 600 evaluation episodes per seed), our architecture achieves 5-shot accuracy gains, consistent across all five seeds, over Prototypical Networks, Relation Networks, and MAML on both CIFAR-FS and MiniImageNet, while using 27-53% fewer parameters than any baseline. It also converges in fewer training episodes, generalizes better to an unseen fine-grained domain (CUB-200-2011 birds, zero retraining), and is more robust to 50% occlusion and 25% spatial translation than all three baselines. A series of falsification ablations - zeroing relational tokens at inference and retraining without them entirely - shows that the architecture's pairwise relational computation, while present, is not the primary driver of its performance; the content-adaptive patch locator is. We report this honestly, together with a capacity sweep showing a genuine accuracy plateau near 22-35k parameters, and release full seed-level results and checkpoint hashes for reproducibility.

As LLM capabilities have expanded, multi-agent communication has emerged as an increasingly active area of research. Prevailing protocols often adopt rigid structures that introduce coordination bottlenecks and can degrade as the number of agents increases. We introduce Proxifield, a round-adaptive multi-agent protocol with decentralized agent decision-making that constructs sparse communication graphs from the evolving semantic proximity of agents. Without model training or a centralized planner, Proxifield connects agents using four routing signals derived at inference time: direct address, information needs, plan alignment, and information complementarity. We compare Proxifield with two representative coordination baselines, a centralized Star protocol and a decentralized Shared Context protocol, across two domains: Drone Search and Rescue and the collective-reasoning benchmark HiddenBench. We first ablate base-model capability and find that, in both domains, the performance of Proxifield improves with model size (35B -> 397B parameter model) and Proxifield outperforms all baselines at the largest scale. As team size increases, Proxifield's task-reward advantage over Star widens from 5.4% at (N=5) to 53.0% at (N=25) and 59.5% at (N=50), while Shared Context consistently underperforms both protocols. Proxifield is also substantially more robust to permanent agent failure, retaining 73.6% of its no-failure task reward under the most severe condition, compared with 58.3% for Shared Context and 38.8% for Star. These results demonstrate that decentralized, semantically adaptive routing can improve the scalability and fault tolerance of multi-agent systems.

Massive KV caches can cause severe memory-bandwidth bottlenecks during long-context decoding. Sparse attention methods mitigate this problem, but often drop necessary context, leading to quality degradation. We introduce Elastic Threshold Attention (ETA), an end-to-end trainable architecture that rivals dense model quality under hardware-aligned block-sparse decoding. ETA predicts dynamic, contextual thresholds directly from query representations, adjusting context retention depending on the task at hand. To learn this policy from scratch while enabling near lossless KV cache pruning at inference time, we filter attention logits through a shifted SiLU gate during training. We show theoretically and empirically that this creates a smooth, near-uniform attention floor that neutralizes sub-threshold value contributions while simultaneously causing localized attention sinks on initial tokens to disappear. To materialize these advantages, we implement a fused inference-time kernel in Triton that screens KV blocks in $O(1)$ time using cached geometric-probabilistic bounds. Across language modeling, reasoning, and RULER benchmarks, our 1.45B ETA model matches or exceeds dense quality, outperforming alternative fast decoding methods (Quest, H$_2$O, NSA) while achieving higher sparsity levels. Our kernel also achieves up to $2.15\times$ end-to-end speedups over FlashAttention-2 at context lengths of up to $512$K tokens. Finally, we introduce an offline calibration algorithm for domain-specific deployments that freezes per-head constant thresholds, cutting attention compute by an additional 27% at no quality cost.

Multimodal embodied systems require translating human intentions into interpretable and coordinated behaviors across heterogeneous modalities. However, existing multimodal agents often rely on implicit representations, limiting controllability and cross-modal consistency. We present a hybrid multi-agent framework for interactive multimodal behavior simulation that bridges semantic reasoning and physical execution through a Unified Parameter Representation (UPR). LLM-based reasoning agents transform multimodal inputs into UPR, which encodes behavioral states and interpretable control parameters for simulation agents generating synchronized 3D motion, spatialized soundscapes, and environmental behaviors. We develop BirdsongChat as a prototype implementation of the proposed framework, using interactive avian behavior simulation as a testbed that tightly couples motion, vocalization, and environmental context. BirdsongChat is evaluated on text- and image-guided scenarios involving species, behaviors, affective states, environments, and multi-bird interactions. The system achieves normalized scores of 94.4% for cross-modal coherence, 100% for affective consistency, and 92.6% for generation consistency. These results demonstrate that an explicit intermediate representation effectively bridges semantic reasoning and physical execution, improving controllability and multimodal synchronization. The proposed framework thus offers a generalizable design principle for embodied AI systems requiring interpretable semantic-to-physical coordination across modalities, with potential applications in bio-inspired ecoacoustics, swarm robotics, virtual environments, and creative multimedia.