Papers

Physics-Informed Neural Networks (PINNs) have emerged as an important class of numerical methods for solving partial differential equations (PDEs). However, during the late-stage optimization process, further parameter updates often yield diminishing accuracy improvements while increasing computational costs. To address this issue, this paper proposes a Physics-Informed Error Field Learning (PIEFL) framework for PINNs. Unlike conventional approaches that continuously approximate the solution field using a single network, PIEFL introduces an auxiliary error network after the primary network achieves satisfactory accuracy and shifts the learning objective from the solution field to the error field. By deriving error control equations under physical constraints, the error network learns the discrepancy between the current approximation and the exact solution, and the learned error correction is combined with the primary prediction to improve solution accuracy. The proposed framework avoids continuous optimization of the entire solution space and focuses computational resources on correcting existing prediction errors. Moreover, PIEFL requires no modification to the primary network architecture, making it compatible with existing PINN models and applicable as a general post-training optimization strategy. Numerical experiments on representative PDEs demonstrate that PIEFL achieves higher solution accuracy under the same computational budget, validating its effectiveness in improving the performance of PINNs.

Vision-language models such as LLaVA-1.5-7B often hallucinate objects absent from the image when generating captions. We ask whether an interpretability diagnosis of this failure can guide a targeted fix, and we measure what that fix actually changes. We rank attention heads by how much their image attention drops around hallucinated object words, then screen the shortlist by ablating candidate heads and measuring the change in hallucination-token log probability, yielding a 32-head set. We restrict two interventions to these heads: a head-sliced LoRA adapter and an inference-time grounding controller. On 400 held-out COCO images, the combined method lowers CHAIRs (the fraction of captions with a hallucinated object) from 0.370 to 0.230 and CHAIRi (the fraction of hallucinated object mentions) from 0.156 to 0.096 (p < 0.001, paired sign-flip tests). Two controls sharpen attribution. A random-head LoRA control, matched layer-for-layer and trained identically, performs no better than the matched baseline on a separate 200-image control split, supporting the role of head selection rather than LoRA capacity. Under fixed decoding budgets, the CHAIR reduction persists and grows with budget (23% at 64 tokens to 58% at 128), arguing against a pure max-token or truncation artifact, although the method remains shorter and more conservative. The resulting behavior reduces unsupported object mentions while also lowering object recall (0.78 to 0.70). We present a diagnosis-to-intervention pipeline for object hallucination, and, more importantly, a controlled account of what acting on the diagnostic signal actually does: it localizes intervention sites with real, non-random leverage, reported as a behavioral profile rather than a single score.

In this essay I reflect on the status of three of the Millennium Prize problems: the Riemann Hypothesis, P vs. NP, and the solvability of the Navier-Stokes equations.

This note studies the geometry of full conformal prediction (FullCP) regions generated by an empirical energy-form pairwise score. Candidate-score convexity alone does not guarantee connected FullCP regions, even for empirical averages of losses convex in the candidate argument. For the energy-form score, each leave-one-out training comparison reduces exactly to a pairwise-dissimilarity sublevel condition. Under symmetry, a constant diagonal, a diagonal lower bound, and attainment of the associated Fréchet-type objective, all comparison regions share a minimizer; if they are convex, every nontrivial exact conformal region is star-shaped about that point. For power distances $\rho_\beta(x,y)=\|x-y\|^\beta$, this geometry holds for $\beta\ge1$, while the conventional energy score is strictly proper for $0<\beta<2$. For $d=1,\beta=1$, every nontrivial empirical-CRPS FullCP region is a nonempty closed interval (possibly $\mathbb R$ when $m=1$). For $1<\beta<2$ and $m\ge2$, explicit data-checkable derivative bounds give Lipschitz control of the radial exits and exact conformal radial function. Combined with directional root search and classical Lipschitz extensions, they yield certified inner and outer radial envelopes of width at most $\delta+2\widetilde Lh_{\mathcal U}$ and same-ray Hausdorff guarantees. An analytic two-dimensional example shows why preserving star-shaped but nonconvex geometry can matter. A staged two-dimensional study finds modest but systematic tightening of the generic certificate and frequent robust nonconvexity witnesses, with detected normalized radial departures typically small. The method is intended for low-dimensional multivariate outputs rather than high-dimensional scaling or runtime improvement.

Published experience with neural surrogates in derivative-free optimisation is contradictory: the same family of models that cuts the evaluation count of one solver leaves another unchanged, or makes it worse. We show that the contradiction dissolves once three factors are stated, and that these, rather than the fit accuracy a training curve reports, are what delimit when a learned local model pays. Role: a surrogate that proposes candidates the true objective must still approve helps, while one that replaces a gradient the solver depends on hurts. Radius: a model fitted to an optimisation path is reliable only inside a bounded neighbourhood, and its error neither vanishes as that neighbourhood shrinks nor survives its growth. Room: a surrogate can only accelerate progress the base method is still able to make. We formalise radius-aware local generalisation, relate it to the classical fully linear condition, and test each factor with the surrogate class, training pipeline and base method held fixed. Over 117 benchmark instances safeguarded assistance raises the instances solved to high accuracy from 67 to 84 while gradient replacement lowers them to 65; removing the gradient term from the training loss cuts surrogate acceptance from 0.703 to 0.148; and 1000 paired comparisons over ten noise levels show no noise threshold, only a base method that stops early. The same factors bound the gain: a model-based trust-region solver, which leaves little room, drops from 88 to 86 when the identical surrogate is attached, and released interpolation software stays ahead at 103, and on a Monte-Carlo inventory model repairing the acceptance interface is worth 10.40 cost units against 0.00 for the surrogate.

AI coding assistants generate Infrastructure as Code, yet no work has examined whether this code meets security requirements. This matters because security smells in infrastructure code propagate to deployed systems, producing infrastructure that is insecure and untrustworthy. We evaluate 16 AI models generating Ansible roles for Apache Tomcat v10 and MongoDB v7, analysing 278 Ansible roles against CIS benchmarks. Without security guidance, all 16 AI models produced code containing security smells, resulting in vulnerable infrastructure that fails compliance verification and underperforms code written by human developers. We introduce an approach integrating Ansible best practices and CIS benchmarks into prompts through an extended CO-STAR framework, enabling security smell prevention during synthesis rather than detection after deployment. When this approach is applied, 4 out of 16 models generate compliant code, with the leading model achieving 95%-100% CIS compliance, a fourfold improvement over humans at 23%-43%, with overall code quality improving by 19%-49%. The remaining 12 models fail not because they cannot generate code but because they cannot follow instructions with multiple constraints. For capable models, the approach requires no retraining and can be adopted through system prompts.

Recent advances in artificial intelligence (AI) have sparked growing interest in its use for mathematical research. While some view this as a major opportunity for discovery, others have raised concerns about its impact on traditional research practices. Despite extensive debate, empirical evidence on how AI is actually being used in mathematics remains limited. To address this gap, we collected all 32,944 arXiv submissions posted between March 1 and August 20, 2026, whose primary or secondary categories included Mathematics. We identified 3,575 submissions that explicitly disclosed author use of AI, of which 1,712 involved at least one substantive mathematical contribution. Our analysis reveals several broad patterns. First, disclosed AI use increased sharply over the study period, with substantive use growing from 1.39% of Mathematics submissions in March to 14.09% through August 20. Second, substantive AI use is highly uneven across fields: Combinatorics has the largest number of such papers, while Metric Geometry has the highest substantive-use rate. Third, substantive AI use is geographically concentrated: under weighted author counts, the United States and China together account for about two-thirds of the recognized country weight. Fourth, AI is already being applied to open research problems: among 717 named open-problem records associated with substantive use, 71% are labeled as fully resolved based on the authors' descriptions, with proofs of the conjectured statement more common than counterexamples or disproofs. Finally, AI-system use is also highly concentrated, with OpenAI systems appearing most frequently, followed by Anthropic. Together, these findings suggest that AI-assisted mathematics is expanding rapidly but remains at an early and uneven stage of adoption.

Vision-Language-Action (VLA) models encode visual observations as flat 2D patch tokens that carry no intrinsic geometric structure, and augmenting them with dense monocular depth injects per-pixel scalar values that encode neither surface orientation nor geometric confidence. This leaves the policy with limited structured spatial reasoning for action prediction. We propose GaussVLA, a Mamba-based VLA that incorporates two custom modules: Gaussian Spatial Tokenizer (GST) to lift frozen semantic and depth features into compact 3D Gaussian tokens, pools geometrically salient regions with learned queries, and Depth-Aware Chain-of-Thought (DA-CoT) that performs structured, non-autoregressive geometric reasoning under language and flow-time conditioning. Across both simulation and real-world evaluations, GaussVLA demonstrates strong spatial-manipulation performance while remaining parameter-efficient. On LIBERO, it achieves 93.5% average success and 100.0% success on the Spatial suite with only 200M parameters, improving over SpatialVLA by 19.7% relative average success while remaining significantly more parameter-efficient.

An audio language model is a black box in a specific way: we see what it says, never what it works out on the way there, and chain-of-thought monitoring helps only if the model writes its reasoning down. Reading a base Qwen3-Omni with a logit lens at the audio-token positions, we find that the answer to a spoken question becomes legible - in words - in the model's middle layers, before it emits any token. Five findings follow. (1) The readout carries concepts in neither the question, the options, nor the model's own transcription: on a clip whose verbatim transcription is empty garbling, it reconstructs Watergate and scandal, passes through the role president, and resolves to Nixon - a hidden multi-hop chain, read with no chain-of-thought. (2) The content is language-agnostic: one audio-inferred concept surfaces in several scripts at once, and 38% of top-1 readouts are Chinese on English inputs. (3) It is paralinguistic: given the same clip as audio and as the model's own emotion-free caption, the audio mind forms the sound source, speaker role, or affect that the caption discards, and answers correctly more often. (4) The audio-driven signal is absent at the input, turns on about a tenth of the way into the network, separates most cleanly from the text prior in the middle band (35-80% of depth), and activation patching shows it is causally used and committed before the last fifth of the layers. (5) Deleting single layers maps the pipeline: reading the sound in is localized to the entry layers and answer delivery to the output layer, while retrieval is distributed across the interior. Throughout, a waveform-swap control - identical text, only the sound changed - isolates the audio-driven signal from a prior over the printed options. This is a qualitative account of what an audio model works out before it speaks: the quantities are controls, not benchmark scores.

LLM agents routinely include privacy-sensitive data (PSD) in tool call arguments beyond what the invoked tools require, crossing trust boundaries to third-party services on every invocation. A controlled measurement on three production LLMs (GPT-4o, Claude 3.5 Sonnet, Llama-3.3-70B) shows that 81–88% of tool calls include unnecessary PSD under default prompts; explicit privacy instructions still leave 36–76% over-sharing. Existing defenses gate calls (allow/block) or label flows (information-flow control) but cannot rewrite argument values, and PII detection tools miss implicit PSD like “Memorial Sloan Kettering” (a hospital name that implies a diagnosis). We present \system{}, a middleware that intercepts tool calls and rewrites their arguments to the minimum data necessary for tool functionality, combining schema-aware necessity analysis with four operations: removal, generalization, substitution, and truncation. Live validation on 307 tool calls across the three LLMs above reduces privacy cost by 81.2–92.0% at 100% argument-level task validity (TOST equivalence $p{<}0.001$ at $\Delta{=}1.0$); on 25 unannotated Model Context Protocol (MCP) schemas, by 79.0% with no minimum\_necessary metadata. An optional LLM content-necessity layer strips task-irrelevant PSD from otherwise-necessary free-text fields, raising live-LLM reduction to 85.1–95.6% and author-schema reduction from 71.1% to 90.9%. Median latency is 1.77\,ms.

Data-driven methods are widely used in landslide susceptibility mapping (LSM) because they can effectively model the complex relationships between landslides and geo-environmental conditions. Existing data-driven approaches generally follow two types of data representations. Pixel-based models focus solely on the geo-environmental characteristics of a specific landslide but neglect the influence of its surrounding environment. Patch-based models incorporate surrounding spatial context but may include pixels with weak or no spatial relevance to the target landslide location. To address this limitation, this study proposes a Local-Geo and Spatial Context Fusion (LGSCF) strategy, which synergises the geo-environmental characteristics of landslide points with their corresponding spatial context through a feature-wise modulation mechanism. We tested the LGSCF strategy by integrating it into several representative convolutional neural network (CNN) architectures, creating nine different LGSCF-based models. The primary study area covers approximately 2644 km2 across Jenai and Sinyi Townships in Nantou County, Taiwan, and the dataset comprises 5332 landslide samples and an equal number of non-landslide samples. The results show that LGSCF-based models consistently outperform their corresponding baselines, achieving F1-scores up to 87.09% and AUC values up to 0.9472. Furthermore, the susceptibility maps produced by LGSCF-based models show that known landslides are more accurately concentrated in "very high" susceptibility zones with fewer misclassifications. These findings demonstrate that our fusion strategy can significantly improve the accuracy of landslide susceptibility mapping.

Decompilation has become a foundational technique in software engineering and security analysis, and it is now advancing through the integration of modern machine learning (ML) approaches. This article presents a systematic review of decompilation studies published over the past decades and develops a comprehensive taxonomy of methodologies employed in contemporary research. We further examine trends in evaluation metrics, tools, and benchmarks used to assess state-of-the-art approaches. Our review reveals key challenges, such as the lack of reliable ground truth and the absence of standardized benchmarks, which hinder rigorous comparison. Finally, we outline future research directions.

Large language models (LLMs) hallucinate numerical values when generating high-stakes meteorological text, posing risks for weather communication. We present AFDBench, an AI meteorologist that generates professional Area Forecast Discussions (AFDs) by reasoning through structured AI weather forecast data from Google's WeatherNext 2. We introduce AFDBench, the first benchmark for evaluating generative meteorological reasoning, comprising 7,732 expert written discussions from 13 National Weather Service (NWS) offices paired with real AI weather forecast inputs, and three complementary metrics: Met-Align (numerical accuracy), Style-Align (professional dialect adherence), and Input-Grounding (fidelity to source weather data). Zero-shot evaluations reveal that open-source LLMs achieve low Style-Align (~0.33) and moderate Input-Grounding (~0.88), failing to write in the professional NWS register or faithfully use their input data. We apply Group Relative Policy Optimization (GRPO) with domain-specific rewards targeting temperature accuracy, synoptic correctness, and format compliance. On 1,033 held-out samples from two unseen NWS offices, GRPO nearly doubles Style-Align from 0.318 to 0.619 and improves Input-Grounding from 0.881 to 0.940, demonstrating that reinforcement learning teaches a 7B-parameter model to write like a professional meteorologist and faithfully interpret AI weather data.

Action-conditioned world models increasingly serve as learned simulators for robotic policy improvement, yet their reliability rests on an unverified assumption: generated futures faithfully reflect the consequences of arbitrary valid actions. Systematic evaluation against action-specific ground truth remains limited beyond expert demonstrations. To address this gap, we introduce WorldEcho, which evaluates action following over a broader action distribution through visual integrity and SE(3) end-effector trajectory alignment. Our diagnosis shows that expert-trained models perform better on demonstrated actions but struggle with off-expert trajectories, producing motion inconsistent with the commanded actions or visually invalid rollouts. To mitigate these failures, we propose WorldSync, which broadens action coverage, grounds intermediate video representations in action-induced robot dynamics through an Action-Forcing Expert, and aligns predicted and ground-truth changes under action interventions. Experiments show that WorldSync reduces integrity-gated error on RoboTwin and, when used for iterative policy improvement, yields higher success rates in simulation and on real robots.

World action models (WAMs) improve robot control by modeling how observations evolve, but generating future observations at test time incurs substantial latency. Fast-WAM removes this process for efficiency; however, our matched implementations show lower generalization for Fast-WAM than for future-aware alternatives, especially with scarce robot demonstrations and in out-of-distribution scenarios. To bridge this gap, we introduce **LAWA**, a WAM architecture that uses compact latent actions as an operational representation of future intentions, enabling efficient test-time future imagination without generating future observations. Specifically, a discrete tokenizer enhanced by action-free pre-training produces manipulation-centric codebook targets. LAWA jointly denoises a continuous latent state anchored to these targets with executable action chunks while omitting the future-video branch at inference. On RoboCasa, LAWA achieves state-of-the-art average success rates of 65.6% and 80.8% in the few-shot and full data settings, improving over the matched Fast-WAM baseline by 9.6 and 4.5 points, respectively. It also preserves the performance level of the matched Joint-WAM variant while requiring 42.9% lower inference latency. LAWA also demonstrates competitive zero-shot robustness on LIBERO-Plus and superior performance on real-world tasks. These results show that future imagination need not be discarded: retaining it with compact latent actions yields an effective trade-off among performance, generalization, and latency. Code and models will be released.

Generative models are commonly ranked by Fréchet Inception Distance (FID) and Kernel Inception Distance (KID), yet FID's first-two-moment summary can miss distributional differences, and a reported scalar gap alone is not a calibrated test against sampling variation. FID's moment restriction has concrete consequences: on ImageNet, visually unrecognizable images optimized only to match the reference Inception mean and covariance obtain FID $24.7$ versus $58.6$ for held-out real images (lower is better). Moreover, FID and KID are scalar discrepancies that are unchanged when the two samples are exchanged and therefore do not encode the direction of a dispersion change: under-dispersion, as can occur in mode collapse, versus over-dispersion. We introduce ZID (Z-resolved Integrated Diagnostic), which combines six standardized location- and dispersion-sensitive arms from a rank graph (RISE) and Gaussian kernels (GPK at two bandwidths). Rather than asking one scalar to serve incompatible roles, ZID reports three linked outputs: an index for ranking departure magnitude, a permutation $p$-value for testing distributional equality, and a signed dispersion readout for diagnosis. In controlled experiments, ZID detects a broad range of departures, and its score tracks increasing severity along the corresponding sweeps, including cases in which FID is flat or reversed. On DiT-XL/2 and SiT-XL/2 guidance sweeps, ZID detects departure from real data, and its signed readout labels the high-guidance diversity collapse as under-dispersion.

Smart glasses are evolving from capture and display accessories into first-person intelligence platforms that connect human perception, persistent context, and digital or physical action. Their on-body viewpoint aligns with the wearer's vision, audition, motion, and hand-object interaction, but must operate under tight energy, thermal, privacy, and feedback constraints. Despite rapid progress in augmented reality, egocentric vision, multimodal models, human-computer interaction, and embodied intelligence, the literature remains fragmented across devices, tasks, and benchmarks. The key challenge is not whether a model can recognize, answer, remember, or act in isolation, but whether a complete system can sustain a reliable, temporally valid, correctable, and governable perception-state-interaction-action loop. This survey is \textit{the first to systematically study smart glasses through such a unified framework}. We formalize first-person data flow and constrained task utility, characterize devices along eight verifiable hardware capability axes, organize the literature around seven interdependent foundational capabilities, and introduce an L0-L5 framework spanning capture, reactive perception, contextual assistance, persistent state, governed action, and embodied coupling. Across nine application scenes, we connect tasks with datasets, systems, products, stakeholders, failure consequences, and evidence gaps. We further present a nine-dimensional deployment framework, a claim-conditioned evaluation protocol, and an evidence ladder from controlled measurement to longitudinal field validation and audit. Together, these elements make smart glasses more comparable, deployable, and reproducibly evaluated, while outlining a roadmap toward trustworthy first-person intelligence.

Recursive self-improvement (RSI) remains hard in long-horizon tasks, where growing histories obscure the task state and misalign skill invocation. We introduce Recuris, a recursive Experiential-Working Memory architecture for long-horizon agent harnesses, in which Working Memory tracks task progress and guides skill selection from Experiential Memory, grounding skill use in current needs rather than the full history. This coupling also turns execution into structured evidence that localizes failures to specific memory components. Across tasks, a fixed Meta-Agent turns that evidence into localized, validation-gated updates to Skill Memory that reshape execution and yield new evidence, forming a bounded recursive memory-evolution loop. Across four long-horizon benchmarks and ten models, Recuris improves task success in 35 of the 37 completed model-benchmark pairs, carrying frontier models to SOTA-level task success: on tau-bench it adds +17.8 points to GPT-5.6 Sol and +15.6 to Claude Opus 5, taking Opus 5 to 87.9%, and +16.6/+13.5 points on Qwen3.6-27B/35B on SkillFlow. The advantage widens as the interaction horizon grows, to +32.2 points on the longest tasks, and common long-horizon failures fall by up to 80%. These results position recursively evolving memory as a scalable foundation for RSI, enabling agents to continuously transform accumulated experience into increasingly effective long-horizon behavior. Code: https://github.com/Gen-Verse/Recuris

Group-relative reinforcement learning waits for sibling rollouts of the same prompt, which is costly for long and variable tool-use trajectories. Single-stream Policy Optimization (SPO) removes this dependency with a persistent prompt-level value estimate, but its recipe whitens one advantage per trajectory before optimizing a token-mean actor loss. We show that trajectory centering generally does not center the token-weighted quantity consumed by the actor, and fix the mismatch by standardizing terminal-outcome advantages under the action-token measure. We additionally organize prompt evidence by the policy event that generated it rather than learner receipt order. Across matched runs on ALFWorld at two model scales and on Math-TIR, SPO++ improves online learning efficiency over SPO. A paired ablation identifies action-token-measure normalization as the strongest tested component.

Affine modular linear hashing is one of the simplest classical hash families. For a prime $p > u$, the hash function is obtained by choosing $s,t$ uniformly from $\mathbb{Z}_p$ and mapping each key $x \in \{0,\ldots,u-1\}$ to one of $n$ bins by $h(x) = [(sx+t) \bmod p] \bmod n$. Despite its simplicity, the maximum load of linear hashing remains poorly understood. For $n$ keys hashed into $n$ bins, the best known upper bound is $O((n \log n)^{1/3})$, whereas the best known lower bound is only $\Omega(\log n / \log\log n)$. We prove a lower bound of $\exp(\Omega(\log n / \log\log n))$ for universes of size $n^{1+o(1)}$. Surprisingly, there is a key set for which this load holds not just in expectation, but for every random seed. The proof is driven by two simple reductions: one transfers lower bounds from a real version of linear hashing to modular linear hashing, and the other transfers arithmetic Kakeya constructions to real hashing. We further show that, for sufficiently large $p$, the expected maximum loads in the modular and real settings are essentially the same, giving an alternative route to an $n^{1/3+o(1)}$ upper bound. Finally, we show that any uniform subpolynomial upper bound for either setting would imply a polynomial-length arithmetic Kakeya conjecture and hence the Kakeya conjecture for upper Minkowski dimension.

Lipschitz constants are a standard way to quantify the sensitivity of neural networks to small input perturbations, but computing them is difficult even for shallow ReLU networks. We study this problem for two-layer input-convex neural networks (ICNNs), a restricted architecture where nonnegative output weights enforce convexity. Computing the $L_p$-Lipschitz constant for these networks is equivalent to maximizing the dual norm over a zonotope. While $L_1$- and $L_\infty$-norm maximization on zonotopes admit fixed-parameter and polynomial-time algorithms, respectively, the parameterized complexity of the remaining $L_p$-norms was open. We prove that, for every fixed $p\in (1,\infty)\cap \mathbb{Q}$, maximizing the $L_p$-norm over a zonotope in $\mathbb{R}^d$ is W[1]-hard with respect to the dimension $d$. Moreover, our hardness results imply that brute-force enumeration algorithms are essentially optimal for this problem under the Exponential Time Hypothesis. By duality, the same hardness results hold for computing the $L_p$-Lipschitz constant of two-layer ReLU ICNNs. Our proof first establishes the result for the $L_2$-norm and then transfers the construction to arbitrary fixed $p\in (1,\infty)\cap\mathbb{Q}$ using a suitable Taylor approximation. These results resolve the corresponding questions regarding the parameterized complexity status for zonotope norm maximization and two-layer ICNN Lipschitz constants. Our paper resolves an open problem posted at COLT'25. There are several independent concurrent papers resolving the same problem. Our paper prioritizes a clear exposition of the underlying mathematics and conceptual intuitions behind the proof. Additionally, we explicitly describe our research process including the use of LLMs.

Multi-task vehicle routing problem (VRP) solvers seek to handle multiple VRP variants within a single unified model, avoiding the need to train a separate model for every variant. In spite of recent progress, current approaches remain limited on two fronts. On the training side, reinforcement learning suffers from reward-scale disparities and shrinking advantage signals as policies improve, whereas preference optimization stagnates once sampled tours become near-identical and thus fundamentally limited by the quality of the policy's own generated solutions, leaving both paradigms with weak supervision as training progresses. On the architecture side, existing fully shared encoders entangle constraint-dependent representations across heterogeneous variants, which limits generalization. We address these gaps with two model-agnostic contributions. First, we propose Preference Optimization with Locally Augmented Refinement (POLAR), a novel training algorithm that applies a local search refinement pass to the best decoded tour before forming preference pairs, yielding much more informative pairwise margins. Second, a Progressive Layered Extraction (PLE) encoder routes each encoder layer through one shared expert and a set of task-specific experts via a gating mechanism, progressively separating common routing structure from constraint-specific encodings. Through extensive experiments on various VRP variants, we show that POLAR and PLE together elevate the current state-of-the-art among neural multi-task solvers. We reduce the average gap to reference solutions by 21.3% relative to the strongest published baseline on 16 in-distribution variants, and outperform prior neural methods on 27 out of 32 unseen variants. Ablation studies confirm the efficacy of each contribution, showing that both improve cross-problem generalization across multiple backbone model architectures.

Marginalized importance weighting evaluates a target policy by reweighting offline state-action samples with its discounted occupancy ratio, characterized by an adjoint Bellman equation. Existing minimax, primal-dual, and fitted fixed-point estimators can leave residual occupancy-balance violations because of function-class approximation, regularization, or incomplete optimization. These violations are difficult to diagnose and reduce because the objectives generally lack a direct supervised validation loss for hyperparameter tuning, model selection, and early stopping. We introduce isotonic Bellman calibration, a one-dimensional, model-agnostic post-processing method that reduces these violations while preserving the ranking information in any initial occupancy-ratio estimate. The method corrects the estimate's scale and shape by applying fitted occupancy-ratio evaluation (FORE) over a one-dimensional class of nondecreasing transformations. We characterize Bellman calibration as a conditional fixed-point property equivalent to occupancy-balance against every test function of the calibrated ratio. More generally, we derive a calibration-refinement bound showing that any fitted ratio with small calibration error performs nearly as well as the best post-processing based on its fitted values. For isotonic Bellman calibration, we establish finite-sample calibration guarantees and a KL oracle inequality relative to the best monotone transformation of the initial estimate. Consequently, isotonic Bellman calibration achieves small calibration error and KL risk within statistical error of the best monotone correction, with guarantees for downstream target-occupancy functionals, including policy-value estimation.

Large Language Models (LLMs) increasingly generate code from natural-language prompts, making prompt engineering a key mechanism for shaping the security of generated software. Structured and security-oriented prompts are widely used to encourage safer code, yet their effects extend beyond whether detected weaknesses are simply present or absent. Using 424 security-sensitive Python tasks, we generate solutions with GPT-4o and LLaMA 3.1-8B under five prompt variants that progressively add structural and security guidance, and evaluate them with Bandit and CodeQL along two axes: generation compliance and security weakness prevalence, severity, and CWE distributions. Structured prompting substantially reduces refusals (e.g., GPT-4o invalid outputs drop from 338 of 424 to 37-52), enabling large-scale analysis, but security-oriented refinements do not consistently reduce overall weakness prevalence. For GPT-4o, stronger prompts primarily redistribute risk: high-severity findings fall (20.8% to 13.6%) while low-severity findings rise (32% to 43.5%); LLaMA shows weaker, less consistent shifts. We also observe security-driven semantic drift, where stricter prompts silently remove or rewrite explicitly requested unsafe constructs. Overall, prompt structure improves compliance but is an unreliable substitute for robust security controls in LLM-assisted development.

Let $G_q$ be an alphabet of size $q\geq2$. We determine the optimal asymptotic rate of generalized covering codes $C\subseteq G_q^n$, whose covering centers in $G_q^{t\times n}$ are constrained to the product form $C^t$. For every fixed integer $t\geq1$ and every $\rho\in[0,1]$, we prove that \[ \kappa_t(\rho,q)= \begin{cases} 1-H_{q^t}(\rho),&0\leq\rho<1-q^{-t},\\ 0,&1-q^{-t}\leq\rho\leq1, \end{cases} \] where $\kappa_t(\rho,q)$ denotes the minimum asymptotic rate $n^{-1}\log_q|C|$ among codes whose $t$-th covering radius is at most $\rho n$, and $H_{q^t}$ is the $q^t$-ary entropy function. When $q$ is a prime power, we prove that the same formula holds under the additional requirement that $C\leq\mathbb F_q^n$. Thus, both the product-form constraint and linearity are asymptotically cost-free: the resulting rate is the ordinary sphere-covering rate over an alphabet of size $q^t$. This extends the recent $t=2$ result of Elimelech and Schwartz for codes without a linearity constraint and the classical $t=1$ result of Cohen and Frankl for linear codes, thereby resolving both open problems posed by Elimelech and Schwartz. Our proofs are probabilistic and combine tools from information theory and probabilistic combinatorics, including the method of types, Janson's inequality, the second-moment method, and a structured alteration argument. Direct applications of Janson's inequality and the second-moment method are obstructed by highly dependent pairs of candidate error matrices. We overcome this obstruction by restricting the errors to a balanced exact-type class of optimal exponential size. Standard type-class estimates, together with Shearer's inequality, then give the required bounds on the number of error-matrix pairs whose selected rows have a prescribed difference.

Latent world models are inherently strong encoders that transform image pixel to latent embedding, yet existing world models still rely on online trajectory optimization for action planning: for every state-goal pair, an iterative optimizer is run from scratch to search for optimal action sequences, treating the world model as a black-box simulator. This approach pays the full iterative optimization cost anew at every replanning step and reuses no planning experience across queries. In this work, we ask whether planning itself can be amortized once a latent world model has been learned. We present LeFlow, which learns a reusable latent trajectory prior operating directly in the latent dynamics space from the world model. LeFlow recasts planning as conditional latent trajectory generation: a rectified-flow model imagines a future latent path between the current and goal embeddings, an inverse dynamics decoder turns latent transitions into action chunks, and the frozen world model verifies each candidate by autoregressive rollout. Across four major goal-conditioned pixel-control benchmarks, LeFlow replaces iterative action-space optimization with amortized latent planning and fixed-budget rollout selection, achieving consistent success-rate gains with an order-of-magnitude reduction in planning time. Our results argue that latent world models should support not only prediction but reusable planning priors. Our code is available at https://github.com/hsiangwei0903/LeFlow.

Social interaction can improve collective learning but also amplify early mistakes. We study this tension when the credibility of social information is generated by the sender's own decision process rather than fixed ex ante. Reinforcement-learning agents make binary choices through a drift–diffusion process that jointly determines choice, decision time, and confidence; decision confidence then becomes social credibility by weighting anticipatory influence and retrospective social learning. Under balanced community exposure, the anticipatory field admits an exact quotient representation. Its local Jacobian is a scalar decision-sensitivity term multiplying the community-coupling matrix, which yields a common-mode amplification threshold and an analytical role for cross-community permeability in damping relative community differences. Monte Carlo experiments show the corresponding non-monotone performance pattern: moderate transmission accelerates correction, whereas strong transmission can lock populations into wrong consensus; low permeability instead sustains disagreement. Ablations reveal a dual role for confidence: credibility-sensitive transmission amplifies social error, while confidence-dependent private learning stabilises it. The model yields testable predictions linking sender confidence to receiver behaviour conditional on accuracy.

Enterprise cybersecurity research draws on a wider range of methods than any single community routinely teaches. Researchers face a selection problem before they face a technical one: a study may simultaneously need a systematic review, a design-science artifact, a controlled detection experiment, an interview study, or an attack-graph model. This paper addresses that problem in two ways. First, it provides a narrative review and synthesis of methodological practices across a verified corpus of 151 works. We organise these practices into eleven methodology families, detailing for each what questions it answers, the strength of its supporting evidence, and its common failure modes. Second, we convert each family into an executable protocol comprising ordered steps, required instruments, evaluation criteria, common validity threats, and a reporting checklist. Every protocol is also visually mapped to make the sequence, decisions, and threats legible at a glance. We also treat contradictions in the literature as evidence. For example, reported rankings of intrusion-detection algorithms are wildly inconsistent across individually careful studies. We argue this pattern is most parsimoniously explained by variations in evaluation design rather than the algorithms themselves, as these studies differ in design dimensions known to shift results by more than the margins separating the algorithms. Ultimately, the evidence supports methodological pluralism disciplined by explicit validity reasoning. We conclude that researchers must match their evaluation design to the decision under study, triangulate technical against organisational evidence, explicitly state the population a result generalises to, and report the conditions under which the result would not hold.

Web agents that act from rendered pixels avoid the fragility and heavy token cost of reading a page's HTML or accessibility tree, but training them depends on large amounts of high-quality interaction trajectories, and how to produce such data at scale remains an open problem. Public datasets typically contain only a few thousand trajectories drawn from a fixed and narrow set of websites, and even recent automated synthesis pipelines stay bound to predefined site lists or tutorial sources, so the number of distinct websites the agent ever sees barely grows. We present BrowserForge, a framework that generates web interaction data at scale by driving many browser sandboxes in parallel over the open web. BrowserForge couples three components: an open-web sourcing stage that exposes the agent to hundreds of thousands of real, openly reachable websites; a sandbox cluster manager that schedules hundreds of concurrent browsers with high utilization; and a Proposer-Solver dual-agent loop that turns a raw page into an executable task and then collects a verified trajectory for it. A rule-plus-model cleaning pipeline removes failed runs and rewrites the surviving reasoning into a single unified chain-of-thought style. Page structure such as the accessibility tree is used only as a synthesis-time signal; the agent we train and release acts purely from the screenshot. The resulting corpus contains 203,238 trajectories, each collected from a distinct website, larger and more diverse than prior trajectory datasets. Fine-tuning a compact multimodal model on this corpus raises its success rate on the live Online-Mind2Web from 25.66% to 33.33% and consistently improves step accuracy on the static Multimodal-Mind2Web, with the gain growing as the corpus scales. Controlled analyses further confirm that open-web sourcing and broad website coverage are key contributors to the observed improvement.

Real-world data for knowledge graph question answering is often distributed across different organizations due to governance and data sovereignty constraints. While centralized systems exist, they cannot answer multi-hop questions when the required facts are split across vertically partitioned silos. In this paper, we propose FedV-KGQA, a framework for multi-hop reasoning over knowledge graphs in which organizations share entities but own disjoint sets of relations. Our approach combines local graph enrichment and knowledge graph embeddings to ensure raw triples and relation parameters never leave each silo, establishing a structural data boundary without requiring centralized graph access. We further introduce a topic entity anchoring mechanism that grounds questions in the correct graph neighborhood without any runtime inter-silo communication. We evaluate 12 model configurations across three benchmarks and show that FedV-KGQA performs strongly, remains close to centralized performance, generalizes to 3-hop reasoning, and is robust to embedding perturbations.