arXiv:2605.16157v1 Announce Type: new Abstract: This paper explores epistemic realizability, a form of realizability in which the property that a piece of data constitutes evidence for a logical proposition is semi-decidable. In this framework, each proposition A is assigned a verifier} program that checks whether a datum X is a realizer for A, and a dual generator program that behaves as a generic realizer for X. We propose epistemic realizability interpretations for minimal logic, second-order intuitionistic logic, and higher-order intuitionistic logic, proving that each system is sound and complete under the proposed semantics.
Science Journals
arXiv:2605.16213v1 Announce Type: new Abstract: Sorting is a fundamental operation across numerous computational domains. Traditionally, this process involves transferring data from main memory to a processing unit for sorting, followed by writing the sorted data back to memory. This conventional approach incurs substantial latency and energy overheads due to the extensive data movement between memory and processing components. To mitigate these overheads, this paper introduces novel architectures for executing sorting operations directly within the memory fabric, eliminating the need for off-chip data transfer. To our knowledge, this work represents the first exploration of in-memory sorting using 6T SRAM. The proposed architecture is designed to operate on data represented in the standard weighted binary radix format commonly used in digital systems. The proposed architecture achieves a significant 3.4x reduction in latency compared to memristor-based IMC sorting.
arXiv:2605.15459v1 Announce Type: new Abstract: The minima of modern neural network loss functions are typically not isolated, rather they form connected components of reparameterization invariant solutions on the training data. Analytically characterizing these solutions is a hard problem, but sampling approaches are feasible. By construction, existing methods either spread over low-loss regions, and thus do not sample reparameterization invariant solutions exactly, or are inherently local, which limits exploration of other minima valleys. We propose sampling such reparameterization invariant models using a dynamical system based on kinetic energy, subject to a gravitational pull and a friction term that dissipates energy from the system. Our proposed sampler, DiMS, is guaranteed to sample exactly from the minimum level sets and depends on physically motivated hyperparameters which allows control over the exploration capabilities of the sampler. We consider uncertainty quantification in Bayesian inference as the motivating problem and observe improved performance compared to previously proposed approaches.
arXiv:2605.15363v1 Announce Type: new Abstract: Accurate forecasting of residual Physical Resource Blocks (PRBs) is critical for proactive network slice provisioning, energy-efficient operation, and spectrum-aware decision making in cellular systems, where residual PRBs serve as a practical proxy for short- and medium-term spectrum availability. Existing PRB prediction methods typically rely only on historical PRB values and are trained independently per carrier or sector, limiting their ability to capture cross-carrier dependencies and providing no measure of forecast uncertainty. Moreover, point forecasts alone are insufficient for robust spectrum-aware control under highly variable traffic conditions. This paper proposes PRB-RUPFormer, a recursive unified probabilistic Transformer for residual PRB forecasting. The proposed model jointly processes multivariate KPI time series using temporal, seasonal, and carrier-aware embeddings, preserving inter-metric temporal coupling during recursive rollout and stabilizing long-horizon forecasting. A single shared model is trained across all carriers and sectors of an eNB, enabling efficient learning of joint traffic dynamics with low computational overhead. Forecast uncertainty is captured through quantile-based prediction intervals, providing confidence-aware estimates of future PRB availability. Evaluations on six months of commercial LTE network data from multiple U.S. locations demonstrate median MAE below 0.05 and hit probabilities above 0.80 for both one-day and seven-day recursive forecasts. These probabilistic predictions directly support spectrum-aware RAN functions such as dynamic carrier activation, congestion avoidance, and proactive spectrum sharing, making the proposed framework well-suited for dynamic spectrum access scenarios.
arXiv:2605.15362v1 Announce Type: new Abstract: Half a billion citation edges extracted from 100.7 million Ukrainian court decisions reveal that judicial citation structure encodes legal domain boundaries without supervision and predicts future legislative importance with near-perfect accuracy. We construct the first large-scale citation graph from the complete EDRSR registry (99.5 million full texts, 1.1 TB), extracting 502 million citation links across six types via regex on commodity hardware in approximately 5 hours, with precision of 1.00 on a 200-decision validation sample (95% Wilson CI: [0.982, 1.000]). Three principal findings emerge. (1) The degree distribution follows a power law (alpha = 1.57 +/- 0.008), placing the Ukrainian court network near the EU Court of Justice and below the US Supreme Court, with hub articles cited by millions of decisions. (2) Louvain community detection on the co-citation projection recovers legal domain boundaries (civil, criminal, administrative, commercial) with modularity Q = 0.44-0.55 and temporal stability (NMI = 0.83-0.86 across periods), constituting an automatically constructed legal ontology grounded in judicial practice. (3) Citation features predict top-1000 articles with AUC = 0.9984, substantially outperforming a naive frequency baseline (P@1000 = 0.655); temporal dynamics detect legislative regime changes as phase transitions and the 2022 invasion as a citation entropy spike (H: 11.02 -> 13.49) with emergent wartime legislation nodes. The citation-derived ontology is operationalized as the domain layer of a workflow memory system for LLM-assisted legal analysis, connecting to the ontology-controlled paradigm. The extraction pipeline, analysis code, and aggregated statistics are released as open data.
arXiv:2605.15357v1 Announce Type: new Abstract: A complete model of the motion of a quadcopter along a smooth spatial trajectory is presented. Based on the model, a robust algorithm is proposed for controlling a quadcopter using measurements of linear coordinates and yaw angle. By introducing additional integrators, a dynamic control algorithm with a simplified controller tuning methodology is obtained. The control law is synthesized within the geometric approach, and its stability is proven. A realizable output-feedback version using an extended observer is also given. The results enable coordinated trajectory following in three-dimensional space despite unmeasured disturbances and incomplete state information.
arXiv:2605.15381v1 Announce Type: cross Abstract: Non-bonded interactions govern structure, stability, and function across a wide range of solid-state materials, yet their chemical origins are often difficult to resolve from total energies alone. Here we generalize absolutely localized molecular orbital energy decomposition analysis to quantify and interpret non-bonded interactions within and between solids at the density functional theory level. Across molecular crystals, moir\'e heterobilayers, and layered perovskite heterostructures, this framework separates lattice-formation energies, interlayer binding energies, and band-structure changes into chemically intuitive contributions from frozen interactions, polarization, and charge transfer. The analysis reveals how dispersion controls polymorph stability in pharmaceutical crystals, how local stacking modulates interlayer coupling in MoS2/WSe2, and how alkali-cation substitution switches the quantum-well character of layered perovskite heterostructures. By connecting emergent solid-state properties to microscopic interaction mechanisms, this framework provides a chemically transparent basis for understanding and designing complex materials.
arXiv:2605.15356v1 Announce Type: new Abstract: Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive importance sampling provides a natural localization tool: its evolving proposal distribution progressively identifies the failure-relevant region. Motivated by this observation, we propose a surrogate-assisted adaptive importance sampling framework that refines the surrogate locally along the evolving proposal, rather than over the entire input space. The surrogate combines an encoder with a neural network, providing a low-dimensional latent representation for both prediction and sample selection. At each adaptive iteration, candidates drawn from the current proposal are selected by a greedy latent-space rule balancing proximity to the estimated failure boundary and sample diversity. The selected samples are evaluated by the high-fidelity model and used to refine the surrogate, which then guides the subsequent cross-entropy-type adaptive proposal update. We establish one-step proposal stability bounds under local surrogate errors, together with surrogate-induced misclassification and finite-sample estimation error bounds. Numerical experiments on multimodal benchmarks and PDE-driven rare-event problems up to 100 dimensions show that the proposed method achieves accuracy comparable to true-model adaptive importance sampling while requiring substantially fewer high-fidelity evaluations.
arXiv:2605.15455v1 Announce Type: new Abstract: Chatbot behavior is often opaque to users, as responses can shift unpredictably across a conversation, drifting toward sycophancy, toxicity, or other unsafe responses. This can leave users vulnerable, either being misled by overly agreeable AI or manipulated by a harmful chatbot that no longer behaves as intended. To address this, we introduce multi-turn neural transparency, an interface that surfaces an LLM's internal neural activations in real time to help users anticipate and recognize how behaviors change across turns. We construct behavioral vectors for six personality traits using methods from mechanistic interpretability, identifying directions in activation space that correlate with trait expression ($R^2 \geq 0.9$) via contrastive system prompts, and visualize trait expression using a sunburst and drift panel that updates at each turn. In a randomized controlled study (N = 246), participants predicted trait expression from a system prompt alone, then rated observed behavior after interacting with the chatbot for both assistant and role-play personas. We find that participants without visualization struggled to accurately evaluate traits (RMSE $\approx$ 0.6-0.7), while the inclusion of neural transparency significantly improved both anticipation and evaluation compared to no visualization (d = -0.34 to -0.49). The multi-turn dynamic visualization additionally outperformed the static single-turn visualization on holistic evaluation of model behavior (d = -0.32). Transparency also reduced overconfidence: participants without visualization grew more confident despite no gain in accuracy. These findings suggest that surfacing internal model representations to everyday users is a meaningful step toward more transparent and informed human-AI interaction.
arXiv:2512.09673v3 Announce Type: replace Abstract: Equivariant neural networks encode the intrinsic symmetry of data as an inductive bias, which has achieved impressive performance in wide domains. However, the understanding to their expressive power remains premature. Focusing on 2-layer ReLU networks, this paper investigates the impact of enforcing equivariance constraints on the expressive power. By examining the boundary hyperplanes and the channel vectors, we constructively demonstrate that enforcing equivariance constraints could undermine the expressive power. Naturally, this drawback can be compensated for by enlarging the model size -- we further prove upper bounds on the required enlargement for compensation. Surprisingly, we show that the enlarged neural architectures have reduced hypothesis space dimensionality, implying even better generalizability.
arXiv:2605.15701v1 Announce Type: new Abstract: Memory data are ubiquitous in Large Language Model (LLM)-based agents (e.g., OpenClaw and Manus). A few recent works have attempted to exploit agents'memory for improving their performance on the question-answering (QA) task, but they lack a principled mechanism for effectively modeling how memory data evolves over time and retrieving memory data effectively, leading to poor performance in memory utilization. To fill this gap, we present H-Mem, a novel memory mechanism via a hybrid structure that can not only effectively model the evolution of agent memory over a long period of time, but also provide an efficient memory retrieval approach. Particularly, H-Mem builds a temporal and semantic tree structure that allows the short-term memory data to evolve progressively into long-term memory data, where the latter provides summarized information about the former, while simultaneously constructing a knowledge graph to capture the relationships between entities in memory. Moreover, it offers an effective memory retrieval approach by exploiting the hybrid structure of the tree and graph structures. Extensive experiments on three agent memory benchmarks show that H-Mem achieves state-of-the-art performance on the QA task.
arXiv:2601.21028v2 Announce Type: replace Abstract: AI-generated media is radically changing the way content is both consumed and produced on the internet, and in no place is this potentially more visible than in sexual content. AI-generated sexual content (AIG-SC) is increasingly enabled by an ecosystem of individual AI developers, specialized third-party applications, and foundation model providers. AIG-SC raises a number of concerns from older debates about the line between pornography and obscenity to newer debates about fair use and labor displacement (in this case, of sex workers), and has spurred new regulations to curb the spread of non-consensual intimate imagery (NCII) created using the same technology used to create AIG-SC. However, despite the growing prevalence of AIG-SC, little is known about its creators, their motivations, and what types of content they produce. To inform effective governance in this space, we conducted an in-depth study to understand what AIG-SC creators make, along with how and why they make it. Interviews with 28 AIG-SC creators, ranging from hobbyists to entrepreneurs to those who moderate communities of hundreds of thousands of other creators, revealed a wide spectrum of motivations, including sexual exploration, creative expression, technical experimentation, and in a handful of cases, the creation of NCII.
arXiv:2605.15355v1 Announce Type: new Abstract: Spiking neural networks (SNNs) are biologically inspired energy-efficient models that use sparse binary spike-based communication between neurons, making them attractive for resource-constrained edge devices. Federated learning enables such devices to train collaboratively without sharing raw data. In time-series applications, edge devices often collect data at different time resolutions due to hardware and energy constraints. This temporal heterogeneity poses a fundamental challenge for federated learning: parameters learned at one temporal resolution do not necessarily transfer directly to another, which might result in the naive federated averaging being ineffective. Targeting SNNs and, more broadly, deep networks with stateful neurons, we propose a federated learning framework that addresses this temporal resolution mismatch. We investigate how neuron parameters learned from data at different temporal resolutions and model aggregation should be integrated. We evaluate the proposed framework across two SNN-native benchmark datasets (SHD and DVS-Gesture) under a range of resolution heterogeneity scenarios. Our results show that the proposed adaptation methods can substantially recover accuracy lost due to temporal mismatch, hence enabling each client to train at their local temporal resolution while remaining compatible with the global model.
arXiv:2605.15365v1 Announce Type: new Abstract: Communicating using only a limited vocabulary is a common but challenging cognitive phenomenon, requiring an ideal communicator to plan carefully to optimize for intelligibility while circumventing a constrained lexicon. In this work, we investigate how humans respond to a broad array of questions under variable vocabulary limitations, consisting of only 250 highly frequent words at the most restrictive. We provide theoretically motivated comparisons to greedy and globally optimal sampling algorithms using Sequential Monte Carlo inference with large language models. Humans generally resemble greedy sampling more than globally optimal sampling, though more skilled humans are more likely to backtrack and revise -- a non-greedy behavior. An observed human pattern of leaning on semantically light words in high-constraint settings falls out of both greedy and globally optimal sampling. We discuss the results and their broader implications for resource-rational cognition, psycholinguistics, L2 communication, and language impairments.
arXiv:2602.20630v4 Announce Type: replace Abstract: Keypoint-based matching is a fundamental component of modern 3D vision systems, such as Structure-from-Motion (SfM) and SLAM. Most existing learning-based methods are trained on image pairs, a paradigm that fails to explicitly optimize for the long-term trackability of keypoints across sequences under challenging viewpoint and illumination changes. In this paper, we reframe keypoint detection as a sequential decision-making problem. We introduce TraqPoint, a novel, end-to-end Reinforcement Learning (RL) framework designed to optimize the \textbf{Tra}ck-\textbf{q}uality (Traq) of keypoints directly on image sequences. Our core innovation is a track-aware reward mechanism that jointly encourages the consistency and distinctiveness of keypoints across multiple views, guided by a policy gradient method. Extensive evaluations on sparse matching benchmarks, including relative pose estimation and 3D reconstruction, demonstrate that TraqPoint significantly outperforms some state-of-the-art (SOTA) keypoint detection and description methods.The code will be available at https://github.com/xiaomi-research/traqpoint.
arXiv:2605.02689v2 Announce Type: replace Abstract: Long-term time series forecasting requires models that simultaneously capture rapid oscillations, medium-range periodicities, and slowly evolving macro-trends from a fixed look-back window. Existing lightweight MLP-based models typically operate on a single temporal resolution, limiting their ability to explicitly model patterns at multiple scales. We propose MSMixer, a channel-independent multi-scale MLP architecture that addresses this limitation through three complementary innovations: (i) three parallel scale branches at down-sample factors {1x, 4x, 16x} with independent MLP blocks, (ii) a learnable softmax gate that dynamically weighs branch outputs, and (iii) a DLinear complementary shortcut that provides full-window trend and seasonality context. MSMixer contains only 112K parameters at H=96 and runs at O(T) complexity. Evaluated on four ETT benchmarks with standard chronological splits and three random seeds, MSMixer achieves the lowest average MSE (0.357) among lightweight models, outperforming DLinear (0.386, -7.4%) and NLinear (0.365, -2.1%), winning 12 of 16 configurations. Against five Transformer-based baselines from the literature, MSMixer achieves best or second-best MSE in 9 of 16 configurations while using 5x fewer parameters than PatchTST. Ablation and sensitivity analyses confirm the complementary contributions of the multi-scale branches and the DLinear shortcut.
arXiv:2605.16133v1 Announce Type: new Abstract: Technical Debt (TD) refers to the long-term costs incurred when developers prioritize short-term delivery over quality-improving work. Architectural Technical Debt (ATD) arises when architectural decisions (e.g., technology choices, patterns, or decomposition) prioritize near-term progress over future maintainability and evolvability. Because ATD affects a system's core structure and propagates through architectural dependencies, it is often more expensive and disruptive to remediate than localized code-level debt. Although ATD has been widely studied, an important but underexplored aspect of repayment is who performs it. Prior work provides limited empirical evidence on repayment responsibility in ATD and its relationship to time-to-fix. We empirically study self-fixed ATD, where the introducer also repays the debt, and contrast it with non-self-fixed ATD in large Apache open-source projects. We reconstruct ATD lifecycles by tracing Jira artifacts to version-control history to identify introduction and repayment points and attribute developer roles. We address three research questions on the prevalence of self-fixed ATD, time-to-fix differences between self-fixed and non--self-fixed items, and how factors related to code change and collaboration metrics relate to repayment speed. Using descriptive statistics, non-parametric tests, and survival analysis, we show that self-fixed and non--self-fixed ATD exhibit distinct repayment dynamics and differences in how changes are shared on ATD-affected files. In particular, non--self-fixed ATD is more likely to remain unresolved longer when changes are spread across many developers. These results provide actionable guidance for maintainers to identify high-risk ATD items and to reduce handoff costs by increasing introducer involvement when possible and documenting the design rationale during repayment.
arXiv:2510.05676v2 Announce Type: replace Abstract: Graph-based methods are becoming increasingly popular in machine learning due to their ability to model complex data and relations. Insurance fraud is a prime use case, since fraudulent claims are often the result of organised criminals that stage accidents or the same persons filing erroneous claims on multiple policies. One challenge is that graph-based approaches struggle to find meaningful representations of the data because of the high class imbalance present in fraud data. In addition, insurance graphs are heterogeneous and dynamic, given the changing relations among people, companies and policies. As a result, gradient-boosted tree approaches on tabular data still dominate the field. Therefore, we present a novel inductive graph gradient boosting machine (G-GBM) for supervised learning on heterogeneous and dynamic graphs. G-GBM combines the class-imbalance robustness of gradient boosting with heterogeneous graph information encoded through interpretable path-level feature concatenations, while preserving access to the original tabular feature space. In addition, the explicit representation of neighbourhood information enables transparent SHAP-based explanations at the metapath and feature level. We demonstrate G-GBM for insurance fraud detection on an open-source and a real-world, proprietary dataset, and find that G-GBM performs on par or better than the state-of-the-art. The associated insurance fraud dataset is publicly released to facilitate reproducibility.
arXiv:2605.15464v1 Announce Type: new Abstract: Post-training has become a crucial step for unlocking the capabilities of large language models, with reinforcement learning (RL) emerging as a critical paradigm. Recent RL-based post-training has increasingly split into two paradigms: reinforcement learning from human feedback (RLHF), which optimizes models using human preference signals in target domains, and reinforcement learning from verifiable rewards (RLVR), which operates in verifier-backed environments. The latter has dominated recent reasoning-oriented post-training because it delivers stronger gains and higher efficiency on domain-specific tasks (e.g., reasoning). However, although in-domain RL training achieves promising performance, it still requires a substantial amount of GPU compute, which remains a major barrier to broad adoption. In this work, we study the generalization ability of RLHF learned from scratch from a small set of interactions in open-ended environments, and investigate whether the conversational abilities it explicitly acquires can implicitly transfer to downstream tasks such as mathematical reasoning and code generation, namely GRLO. Specifically, on Qwen3-4B-Base backbone, GRLO improves the average performance across all domains from 24.1 to 63.1 with only 5K prompts and 22.7 GPU hours, requiring about $46\times$ less data and $68\times$ less compute than a strong in-domain RLVR baseline. The resulting model is even competitive with Qwen's released post-trained models which required a much larger training cost. Notably, a subsequent in-domain RLVR stage brings only selective gains, mainly on harder competition-math benchmarks. We hope GRLO offers a simple and efficient recipe for building broadly capable post-trained models. Our code and data will be available at: \href{https://github.com/SJY8460/GRLO}{https://github.com/SJY8460/GRLO}.
arXiv:2604.01573v2 Announce Type: replace-cross Abstract: We study the monotonicity of the cumulative dose response (cDR) for a class of incoherent feedforward motifs (IFFM) systems with linear intermediate dynamics and nonlinear output dynamics. While the instantaneous dose response (DR) may be nonmonotone with respect to the input, the cDR can still be monotone. To analyze this phenomenon, we derive an integral representation of the sensitivity of cDR with respect to the input and establish general sufficient conditions for both monotonicity and non-monotonicity. These results reduce the problem to verifying qualitative sign properties along system trajectories. We apply this framework to four canonical IFFM systems and obtain a complete characterization of their behavior. In particular, IFFM1 and IFFM3 exhibit monotone cDR despite potentially non-monotone DR, while IFFM2 is monotone already at the level of DR, which implies monotonicity of cDR. In contrast, IFFM4 violates these conditions, leading to a loss of monotonicity. Numerical simulations indicate that these properties persist beyond the structured initial conditions used in the analysis. Overall, our results provide a unified framework for understanding how network structure governs monotonicity in cumulative input-output responses.
arXiv:2605.16122v1 Announce Type: new Abstract: Diffusion-based image synthesis has made AI-generated images (AIGI) increasingly photorealistic, raising urgent concerns about authenticity in applications such as misinformation detection, digital forensics, and content moderation. Despite the substantial advances in AIGI detection, how to correct detected AI-generated images with visible artifacts and restore realistic appearance remains largely underexplored. Moreover, few existing work has established the connection between AIGI detection and artifact correction. To fill this gap, we propose GenShield, a unified autoregressive framework that jointly performs explainable AIGI detection and controllable artifact correction in a closed loop from diagnosis to restoration, revealing a mutually reinforcing relationship between these two tasks. We further introduce a Visual Chain-of-Thought based curriculum learning strategy that enables self-explained, multi-step ``diagnose-then-repair'' correction with an explicit stopping criterion. A high-quality dataset with large-scale ``artifact-restored'' pairs is also constructed alongside a unified evaluation pipeline. Extensive experiments on our correction benchmark and mainstream AIGI detection benchmarks demonstrate state-of-the-art performance and strong generalization of our method. The code is available at https://github.com/zhipeixu/GenShield.
arXiv:2604.08426v4 Announce Type: replace Abstract: With the growing demand for long-context LLMs across a wide range of applications, the key-value (KV) cache has become a critical bottleneck for both latency and memory usage. Recently, KV-cache offloading has emerged as a promising approach to reduce memory footprint and inference latency while preserving accuracy. Prior evaluations have largely focused on tasks that do not require extracting large amounts of information from the context. In this work, we study KV-cache offloading on context-intensive tasks: problems where the solution requires looking up a lot of information from the input prompt. We create and release the Text2JSON benchmark, a highly context-intensive task that requires extracting structured knowledge from raw text. We evaluate modern KV offloading on Text2JSON and other context-intensive tasks and find significant performance degradation on both Llama 3 and Qwen 3 models. Our analysis identifies two key reasons for poor accuracy: low-rank projection of keys and unreliable landmarks, and proposes a simpler alternative strategy that significantly improves accuracy across multiple LLM families and benchmarks. These findings highlight the need for a comprehensive and rigorous evaluation of long-context compression techniques.
arXiv:2604.26782v2 Announce Type: replace Abstract: This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games (MFG). We reformulate the game as a regenerative problem with deterministic cycles, which allows policy evaluation (PE), policy improvement (PI), and population measure estimation to be carried out cycle by cycle. Within this formulation, we approximate the population measure by a particle system and update it using a one-step random mapping induced by the Euler-Maruyama discretization of the state dynamics. This update transports a mini-batch of particles from one cycle to the next, avoiding sequential trajectory simulation over the entire time horizon at each iteration. The PE and PI subproblems are formulated through the relation between consecutive cycles, with adversarial training used for evaluation and averaged optimization used for improvement. The resulting method is efficient and scalable in high dimensions, as it avoids the direct solution of the coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, the full simulation of trajectories to estimate the population measure, the explicit computation of conditional expectations in policy evaluation, and pointwise optimization in policy improvement. Numerical experiments demonstrate that the proposed method effectively handles dimensions up to 10,000.
arXiv:2605.04336v2 Announce Type: replace-cross Abstract: We study a contest-theoretic model of adversarial investment in which an attacker and a defender allocate resources to AI-augmented capabilities across multiple attack surfaces. The attacker's investment operates through two channels: it amplifies offensive potency unconditionally and erodes defensive effectiveness conditionally, generating an adversarial discount that deepens endogenously with the defender's own investment. We derive a closed-form arms race ratio decomposing the relative marginal effectiveness of offensive and defensive investment into six structural primitives and establish equilibrium uniqueness and global convergence under a continuous best-response dynamic. The central result concerns signal cross-correlation, the degree to which threat intelligence on one surface informs detection on another. With full cross-correlation, the arms race ratio is independent of the number of attack surfaces: the attacker's structural advantage from surface proliferation is completely neutralized. Under the benchmark full-dilution case, without cross-correlation, per-surface defense effectiveness vanishes as the attack surface grows. Extending the analysis to heterogeneous defenders facing an attacker who targets by expected value, we argue that the model points to a dual inefficiency: overinvestment in private defense (a zero-sum redirective externality) and underinvestment in shared signal correlation (a public good). These formal results, together with public-good reasoning outside the base model, characterize when collective information aggregation can dominate private capability investment as the decisive margin in adversarial contests.
arXiv:2604.10785v2 Announce Type: replace-cross Abstract: For a connected simple graph $G$ on $n$ vertices with chromatic number $\chi$, the distance Laplacian matrix is $\DL(G)=\operatorname{diag}(\Tr_G(v_1),\dots,\Tr_G(v_n))-D(G)$, where $D(G)$ is the distance matrix and $\Tr_G(v)=\sum_{u\in V(G)} d_G(u,v)$ is the transmission. The eigenvalues of $\DL(G)$ are ordered as $\partial^{L}_1(G)\ge \partial^{L}_2(G)\ge \cdots \ge \partial^{L}_n(G)=0$. Building on the chromatic lower bound $\partial^{L}_1(G)\ge n+\ceil{n/\chi}$ and subsequent developments, we prove a \emph{color-class majorization principle}: if $(\ell_1,\dots,\ell_\chi)$ are the color-class sizes in an optimal $\chi$-coloring with $\ell_1\ge\cdots\ge\ell_\chi$, then the first $\ell_1-1$ distance Laplacian eigenvalues satisfy $\partial^{L}_i(G)\ge n+\ell_1$, for $1\le i\le \ell_1-1$. This gives sharp lower bounds on the number of eigenvalues above the chromatic threshold $b_\chi=n+\ceil{n/\chi}$, thereby refining distribution theorems of [Aouchiche and Hansen, Filomat, 2017] and [Pirzada and Khan LAA, 2021]. We further refine clique/independent-set based multiplicity results by deriving explicit chromatic criteria in terms of neighborhood compression, and we generalize the extremal problem for minimum $\partial^{L}_1$ at fixed chromatic number by characterizing the balanced complete multipartite minimizers. Finally, we present a Ky Fan type result, and complement-component consequences of the majorization principle.