arXiv:2607.05751v1 Announce Type: new Abstract: We revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include: (1) a new $\widetilde{O}(n^{3/2})$-bit protocol for computing a maximum matching in general graphs. While the same upper bound can be obtained by simulating the classic algorithms of Micali-Vazirani and Gabow, our protocol is conceptually simple and avoids the intricacies of finding a maximal set of shortest augmenting paths; (2) a new $\widetilde{O}(n)$-bit protocol for negative-cycle detection and negative-weight single-source shortest paths. Our protocol simplifies that of Blikstad et al. by replacing a long chain of reductions with a more direct approach based on vertex potentials; (3) a combinatorial $\widetilde{O}(n)$-bit protocol for computing a maximum matching in bipartite graphs, obtained by reinterpreting the near-linear communication protocol of Blikstad et al. through a discretized analysis. Together, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.
Science Journals
arXiv:2607.06329v1 Announce Type: new Abstract: In Numerical Algebraic Geometry (NAG) isolated solutions of polynomial systems are usually computed by tracking a solution curve defined by a homotopy equation. The tracking problem becomes especially challenging close to a singular root (the ``endgame'' regime). Existing approaches include power series endgames, Cauchy endgames, and various methods that regularize the system via dual-space-based {\em deflation}. We make the following contributions. (1) For corank-1 systems we introduce a new ``Arclength Endgame'' which combines the idea of the classical {\em pseudo-arclength continuation method} with the estimation of the Puiseux series of the curve. We formally prove that it has a superlinear rate of convergence in some neighborhood of the root. The method uses only evaluations of the system and its Jacobian, whereas previous techniques with proven superlinear convergence (such as deflation) require computing additional derivatives of the system. (2) For systems with a larger corank we propose a heuristic ``Lifted Arclength Endgame'', which shows promising experimental results. (3) A key step in our approach (as well as in the standard power series endgame) is estimating the Puiseux series of the curve, which is characterized by fractional exponents $k_i/c$ for $i\ge 1$ together with associated coefficients. Previous work addressed only estimating the ratio $k_1/c$. We present a new method for that which empirically appears to be more stable than previous methods, and also show how to estimate $k_i/c$ for $i\ge 2$.
arXiv:2607.05761v1 Announce Type: new Abstract: Modern data-driven marketing relies on large amounts of consumer data, yet collecting such data can be costly, time-consuming, and difficult to scale. This research examines whether large language models (LLMs) can be used to generate synthetic consumer data for projective techniques, a set of methods designed to elicit consumer associations, emotions, wants, and needs. We test LLM-generated responses across multiple projective tasks, LLMs, prompting strategies, and temperature settings, and compare them with human responses from a primary research study on perceptions of city tourism destinations. Human and LLM responses were analyzed using linguistic measures, diversity and concentration metrics, topic models, and top-term analyses. The results show substantial overlap between human and LLM responses in broad topics and associations, but also important differences in style, linguistic structure, and the way diversity is generated. Recommendations are given on how to best utilize LLMs for generating synthetic consumer data, how model and prompt choices shape response quality, and on recognizing the limitations of LLM synthetic consumer data generation.
arXiv:2607.05762v1 Announce Type: new Abstract: Scientific results produced by LLM generated analysis code must be understandable and reproducible. However, uncertainty can arise at different stages of the process, both in the original natural language specification and in the generated implementation. As a result, even executable code may not provide a clear understanding of which quantities are being computed or which assumptions determine the final results. To address this challenge, we introduce quantity grounded semantic differencing, a multi-agent framework for analyzing and comparing scientific programs generated by LLMs. The framework assigns code generation, execution, tracing, and validation to separate agents, allowing it to reconstruct how key output quantities are produced and to identify differences between the intended analysis and the implemented code. We also introduce a module that inspects ambiguities in the initial user instruction and suggests alternative rewrites before code generation. Its modular design enables application to different scientific domains by replacing domain specific resources while preserving the same workflow. We validate the framework on representative collider physics analyses. The results demonstrate that the modular task decomposition enhances both transparency and reliability relative to the previous single prompt approach, while enabling substantially smaller models to execute the complete workflow.
arXiv:2607.05782v1 Announce Type: new Abstract: Converters-based systems like wind farms manifest themselves as control-intensive systems, where control-driven stability issues frequently occur, e.g., oscillations. Such issues are popularly studied via circuit impedance-based methods. However, given its implicit controller modeling trait, the impedance-based methods have limitations in system analysis and designs involving large-scale controllers. To address this issue, this paper presents a novel frequency domain modeling framework, as a perspective shift from the circuit to the control system. Since the obtained model features a multi-input-multi-output (MIMO) feedback control structure and explicit controller placement, it is termed the Generalized Feedback Control (GFC) model. GFC modeling is conducted for both single and multi-converter cases, and the resulting models are validated by frequency scan and stability test. Moreover, advantages of the GFC method in achieving interaction analysis and stability-oriented designs of multi-controllers are demonstrated by three application examples, further suggesting its great potential for being applied to the analysis and design issues of converter systems involving large-scale controllers.
arXiv:2607.05787v1 Announce Type: new Abstract: Synthesizing physically plausible human-scene interactions (HSI) remains a critical challenge in computer vision and the development of human avatars. Although recent generative models enable diverse motion synthesis, they suffer from an inductive bias referred to as semantic-geometric entanglement. Because spatial constraints often strongly correlate with specific actions in training data, monolithic models will learn the shortcut bias, aggressively overriding the semantic intent when faced with strict geometric cues. Furthermore, this entanglement exacerbates physical hallucinations, such as body-scene penetrations. To address these limitations, we propose DeSeG, a hierarchical framework that explicitly decouples semantic intent from geometric constraints. First, we introduce a Residual Semantic Planner that encodes textual instructions and canonicalized goal voxels into a compact latent space, enabling fine-grained semantic control independent of spatial trajectories. Second, we propose a physics regularized diffusion executor that incorporates differentiable repulsive potential fields directly into the diffusion objective, enforcing collision-aware motion generation. Extensive experiments on the Lingo dataset demonstrate that DeSeG achieves state-of-the-art performance, reducing mean scene penetration by 47% and improving semantic alignment by 29% over the SOTA baselines.
arXiv:2607.06335v1 Announce Type: new Abstract: Diffusion models generate high-quality images, but their inference cost comes from two sources: large denoising networks and repeated denoising steps. Existing compression pipelines usually attack these costs separately. Pruning reduces the network, but most pruning methods still rely on a long post-pruning retraining stage to recover a many-step sampler. Step distillation reduces the number of denoising steps, but it usually assumes a student that can already follow the teacher well enough to receive useful distillation gradients. This paper asks whether post-pruning retraining can be replaced by step distillation. We find that the direct replacement fails: after pruning an EDM2-XS teacher, starting SiDA from the pruned checkpoint produces unusable samples. We introduce a short teacher-alignment repair stage as a bridge between pruning and step distillation. The bridge matches the pruned generator to the teacher on noisy real-image latents, then hands the repaired checkpoint to one-step distillation. On ImageNet-512, the original EDM2-XS baseline uses 124.713M parameters and 63 network evaluations, reaching an FID of 3.53. With a suitable distillation objective, our 20% pruned one-step generator uses 98.826M parameters and one network evaluation, reaching an FID of 3.12. With 30% pruning, the model uses 88.029M parameters and one network evaluation, with an FID of 4.26.
arXiv:2607.06364v1 Announce Type: new Abstract: Mapping cloud security controls to technical metrics is currently a manual process. This paper proposes domain adaptation of Sentence Transformer models to automate it. We build a training corpus of 3,499 semantic pairs from five European security standards and a set of technical metrics, then expand it via back-translation and LLM-based paraphrasing to up to 13,996 samples across four scenarios. We fine-tune five architectures and evaluate their performance on two independent tasks: control-to-metric and cross-standard controls association. All fine-tuned models outperform their zero-shot baselines. On the control-to-metric task, the best model gains up to 23 nDCG@10 points, while on the cross-standard control task, \textit{multi-qa-mpnet-dot-v1} under back-translation reaches 0.870 nDCG@10. The results show that in-domain training data is a primary driver of performance for the considered case studies.
arXiv:2607.06380v1 Announce Type: new Abstract: Characterization of the decomposition products of energized Criegee intermediates is essential for assessing their impact on the chemical evolution of the atmosphere. Here, a generic and microscopically resolved approach is used to determine the molecular fragmentation pathways and products for CF$_3$CHOO. They include, among others, direct formation of CO$_2$ + CHF$_3$ (HFC-23), HF + CO$_2$ + CF$_2$, and fragmentation routes that are not evident from static reaction path calculations alone. The computed probability for formation of HFC-23 of 14 \% qualitatively agrees with a value of $(7.9^{+0.4}_{-0.2})$ \% from recent measurements, given the differences in the two approaches. Non-statistical dynamics is found for almost all decomposition pathways and the simulations show that excess energy can redirect reaction outcomes away from minimum-energy pathways. The results highlight the power of machine-learned PESs to elucidate multi-step reaction mechanisms of atmospherically relevant intermediates beyond traditional Master equation/electronic structure approaches to provide molecular-level understanding of the role of dynamics.
arXiv:2607.06385v1 Announce Type: new Abstract: We propose an inverse biomechanical design framework for sectorial customized corneal crosslinking in keratoconus. The cornea is modeled as an anisotropic reduced shell with spatially varying crosslinking-induced stiffening, enabling the optimization of localized treatment patterns rather than uniform irradiation profiles. Numerical simulations show that sectorial stiffening can redistribute curvature, reduce localized steepening, and improve corneal regularity in decentered keratoconus models while preserving biomechanical plausibility. These results support the use of patient-specific computational planning for customized crosslinking protocols and provide a basis for future integration with corneal tomography and programmable ultraviolet delivery systems.
arXiv:2607.05397v1 Announce Type: new Abstract: Agent systems increasingly execute rather than advise. When an AI agent queries regulated data, invokes effectful tools, and mutates persistent state, correctness is not captured by whether a terminal output looks plausible. The operative questions are whether each step was authorized under a contract, whether the recorded history is tamper-evident, and whether the trajectory can be reconstructed deterministically. We formalize this as runtime proof of execution. An execution is a triple $x = (C, T, R)$: a contract $C$, an Execution Causal Event Stream (ECES) $T$, and a replay context $R$. A well-formedness predicate and five validator-checkable invariants form the PoE validity predicate. Five semantic guarantees describe authorization, path compliance, null effect on deny, history integrity, and replayability. We prove soundness under explicit cryptographic and deployment assumptions: any PPT adversary that produces a PoE-valid execution violating a semantic guarantee yields a signature forgery, a hash collision, or a quantified deployment-failure event. The Prime Execution Model (PEM) separates planning, enforcement, effect, and recordkeeping into distinct authority planes; a lemma reduces trace completeness to Effector-exclusive credentialing. An Execution Attestation Certificate is issued only when PoE = 1. In a single-node TypeScript prototype, PoE adds approximately 2.7 ms on a minimal flow and 4.4% overhead on concurrent batch workloads; a standard eight-event trace compresses to approximately 1.1 KB; injected Gateway-bypass and trace-mutation attacks are rejected. PoE does not replace consensus, TEEs, or zkVMs; it binds authorization, effect, history, and replay into a single runtime-checkable object so that governed execution becomes attestable under contract.
arXiv:2607.06402v1 Announce Type: new Abstract: Images tell us what a scene looks like, but rarely what it would feel like to be there. While recent datasets pair visual scenes with electronic-nose measurements, aligning smell signals with images remains challenging because many olfactory cues arise from contextual environmental factors that are not directly visible in pixels. We introduce SCENT, a multimodal framework that uses language guidance as a semantic bridge between vision and olfaction. Our approach leverages Vision-Language Models (VLMs) to generate scene descriptors capturing objects, environmental context, and plausible ambient smell cues suggested by the visual scene. These descriptors provide semantic guidance for learning olfactory representations. We train a smell encoder that maps electronic-nose signals into a shared embedding space aligned with both visual and textual representations, and introduce a languageguided latent decomposition that separates object-specific odors from contextual environmental contributions. Experiments on the New York Smells dataset demonstrate that SCENT significantly improves crossmodal retrieval compared to vision-only baselines, achieving state-of-theart performance on smell-to-image and smell-to-text retrieval tasks. In addition, our framework produces interpretable olfactory representations that enable the disentanglement of complex smell mixtures. Our results reveal the importance of contextual semantic information for grounding olfactory perception in multimodal learning and pave the way for future research in this area.
arXiv:2607.06407v1 Announce Type: new Abstract: The XAI community has studied a wide range of queries and scores for explaining predictions of ML models. From a data management perspective, this proliferation of explanation notions calls for declarative query languages in which such notions can be specified, combined, and analyzed uniformly. In this paper, we develop such a framework for Boolean models. We first revisit FOIL, an interpretability query language for black-box models, and show that it has two fundamental limitations: it cannot express central optimality-based explanation queries, and its evaluation problem over decision trees is hard for every level of the polynomial hierarchy. We then introduce ExplAIner, a query language based on FOIL with an extended vocabulary and a layered structure. We show that ExplAIner can express a broad family of explanation notions, including abductive, contrastive, feature-based, and distance-based queries. We also prove that the evaluation problem for each query in ExplAIner belongs to the Boolean hierarchy over every class of Boolean models for which some basic predicates can be evaluated in polynomial time. In particular, that property holds for deterministic and decomposable Boolean circuits. Finally, we introduce Opt-FOIL, an optimization-oriented fragment of ExplAIner for computing explanations that are minimal with respect to strict partial orders, and prove that its evaluation problem is in $\mathrm{FP}^{\mathrm{NP}}$ under the same tractability assumptions. These complexity results have a direct algorithmic consequence: a fixed ExplAIner query can be evaluated with a fixed number of calls to a SAT solver, while a notion of explanation specified in Opt-FOIL can be computed with a polynomial number of such calls. This is particularly relevant in formal XAI, where SAT solvers have been successfully used to compute explanations for several classes of ML models.
arXiv:2607.06408v1 Announce Type: new Abstract: Robust remote verification of identity documents relies on analyzing faint, transparent security features like Optically Variable Devices (OVDs), or "holograms", within user-captured videos under uncontrolled conditions. Current systems, however, face critical limitations: existing methods often treat video frames in isolation, neglecting the intrinsic dynamic nature of OVDs and leaving systems vulnerable to swapping attacks, or focus on general holographic presence and lack the ability to verify specific OVD types. Moreover, the economic infeasibility of frame-by-frame video annotation makes supervised training impractical. In this work, we introduce two novel approaches for verifying the dynamic behavior of transparent OVDs protecting the holder's portrait, specifically designed for open-set scenarios where attack types are unknown during training. We demonstrate that these approaches can be trained without any attack samples in a self-supervised setting, surpassing previous state-of-the-art methods on public datasets while adhering strictly to industrial constraints. Our results confirm that modeling temporal dynamics is essential for defeating sophisticated attacks under realistic conditions, and underscores the promise of sequence modeling and anomaly detection for OVD verification. Code is available at https://github.com/EPITAResearchLab/pouliquen.26.icdar.
arXiv:2607.06416v1 Announce Type: new Abstract: This paper systematically analyzes the relationships among the $dq$-domain, $\alpha\beta$-domain, and sequence-domain representations used in small-signal impedance modeling of voltage-source converters (VSCs). It is shown that the AC impedance matrix expressed with $dq$-complex and $\alpha\beta$-complex variables leads to different formulations in the sequence domain. The study demonstrates that asymmetric systems exhibit different physical phenomena in the rotating and stationary reference frames; therefore, the transformations between these frames are not physically consistent in such cases. It is also demonstrated that the so-called modified sequence-domain impedance is equivalent to the universal impedance model in the frequency domain. The analysis clarifies several notational inconsistencies found in the literature. Finally, a physical interpretation is presented highlighting the implications of using stationary and rotating reference frames for stability analysis of power converters.
arXiv:2607.06420v1 Announce Type: new Abstract: Visual counting is a fundamental pillar of multimodal intelligence, requiring a seamless integration of fine-grained grounding and spatial reasoning. While Multimodal Large Language Models (MLLMs) have achieved remarkable success in qualitative scene understanding, their quantitative precision remains a significant bottleneck, often characterized by persistent numerical hallucinations. Existing counting benchmarks primarily focus on basic perception in simplified contexts, failing to capture the complex failure modes that emerge under logical constraints or adversarial conditions. To address these limitations, we introduce HoloCount, a holistic and diagnostically rich benchmark structured around a three-level hierarchical taxonomy. HoloCount evaluates MLLMs across: (1) Semantic Counting, focusing on atomic and property-based enumeration; (2) Analytical Counting, assessing logical composition through spatial and set-based reasoning; and (3) Robustness Testing, probing model integrity against adverse scenarios and grounded counter-priors, such as high-density scenes and linguistic biases. Through an exhaustive evaluation of over 20 state-of-the-art MLLMs, we reveal a critical performance gap: even top-tier models degrade significantly as tasks transition from perception to complex analytical reasoning and adverse scenarios. Our findings provide a systematic landscape of current MLLM counting capabilities and offer a roadmap for developing more grounded and reliable multimodal systems. The dataset is available at https://mm-mvr.github.io/HoloCount/.
arXiv:2607.06437v1 Announce Type: new Abstract: Roaming reactions are organized not by potential-energy saddles but by transition states that are unstable invariant objects in phase space, periodic orbits in the two degrees of freedom studied here. To ask what controls roaming, we modify the Chesnavich model of a barrierless ion--molecule dissociation: its orientation-dependent angular hindrance is replaced by a transverse-stiffness ridge whose angular frequency peaks at an interior radius, and the classical dynamics are studied at a fixed energy just above the dissociation threshold. Comparing two ensembles that differ only in this angular interaction (same radial channel, energy, and inward initial conditions) isolates its effect. The ridge gates entry into the inner well, cutting inner capture from $57\%$ to $15\%$ and returning most of the incoming flux directly to reactants; it does not eliminate roaming but relocates it outward, suppressing it inside the ridge and switching it on farther out. The model retains analogues of the original model's three transition states (tight, free-rotor, and outer orbiting orbits), which we locate as unstable periodic orbits. The tight orbit spans a dividing surface that coincides, within numerical accuracy, with the variational minimum-flux surface, and it carries no barrier along the reaction coordinate: a deep entropic bottleneck placed at an interior radius by the stiffness maximum. Its entropic character is shared with the original model. Strength-matched monotone controls show that the gating tracks the hindrance strength at the bottleneck radius; what the interior maximum supplies is placement, concentrating that strength where it gates most effectively. The trajectories it admits roam nonstatistically, with nonexponential gap-time distributions: the entropic bottleneck governs how much is captured, not the dynamics that follow.
arXiv:2607.06440v1 Announce Type: new Abstract: Recent text-to-image models such as DALLE-3 excel at following diverse prompts yet remain blind to individual aesthetic preferences. We study personalized image generation, where models must align outputs with a user's implicit visual preferences based on a few historically preferred images and a short prompt. To this end, we introduce PIPBench, the first profile-inclusive benchmark for evaluating personalized image generation. We further propose a novel data construction pipeline that leverages psychological and demographic profiling dimensions for both real-user data collection and scalable agent-based data generation. Using PIPBench, we conduct a thorough evaluation of representative line of methods. Our experiments reveal key limitations in existing methods, suggesting new challenges and opportunities for personalized text-to-image synthesis. Project page: https://wuyuhang05.github.io/PIPBench/
arXiv:2607.06468v1 Announce Type: new Abstract: We introduce EgoPolice, a carefully curated dataset of real, egocentric police-civilian interactions, sourced from publicly available body-worn camera videos. We select police-civilian action labels that are critical for police behavioral research and annotate them at a second-by-second granularity. The videos feature rapid and irregular camera motion, dense human interactions, and rare high-stakes events, making the dataset a challenging benchmark for motion-robust and context-aware egocentric perception. We provide two different tasks, classification and multiple-choice question-answering, and benchmark both open-source and closed-source models. We find that even the best video models like Gemini 2.5 Pro still struggle to accurately predict high-risk actions such as "Weapon Out". Beyond serving as a benchmark, EgoPolice provides a foundation for developing models capable of identifying events of interest in large-scale body-worn camera video repositories, enabling more efficient downstream human review.
arXiv:2607.06505v1 Announce Type: new Abstract: GitHub hosts hundreds of millions of public repositories, but the platform exposes no native mapping from repositories to standardized industry sectors. This gap limits empirical work on the geography of innovation, the industrial composition of open-source production, and the diffusion of new technologies across economic sectors. We present NAICS-GH, a publicly released corpus of 6,588 GitHub repositories drawn from source pools covering the United States, the European Union, and Australia, each labeled with a 2-digit sector from the North American Industry Classification System (NAICS 2022). Labels are produced by a retrieve-and-verify pipeline that combines BAAI/bge-large-en embeddings, FAISS retrieval, and GPT-4.1 rubric scoring. The pipeline narrows about 1.37 million source repositories to 31,178 candidate repository-sector pairs and retains 6,588 high-confidence labels with score at least 8. Re-running the retrieval pipeline end to end reproduces the candidate set to within 0.03 percent. On a 2,421-repository human-validated random sample, the released labels attain 96.98 percent precision, with Wilson 95 percent confidence interval [96.23, 97.59]. We benchmark six pretrained encoders on the released corpus; RoBERTa-large reaches 86.45 percent F1 and 86.35 percent accuracy on a held-out 20 percent test set. The dataset, Croissant metadata, pipeline code, prompts, and fine-tuned checkpoint are released under CC-BY-4.0 and MIT licenses.
arXiv:2607.06514v1 Announce Type: new Abstract: We present FootsiesGym, an open-source environment for learning in a non-trivial two-player, zero-sum, imperfect-information game. Built on HiFight's minimalist 2D fighting game Footsies, it isolates the cyclic, non-transitive strategic interactions of fighting game neutral play while remaining simple enough for efficient analysis. We provide a vectorized simulator that enables high-throughput training on standard hardware, making the environment accessible and reproducible. We describe the design of the environment, benchmark several reinforcement learning algorithms, and discuss open research directions it enables. The code is available at https://github.com/como-research/FootsiesGym.
arXiv:2607.06525v1 Announce Type: new Abstract: This paper introduces Crossroads, a smart contract layer for chain-abstracted assets. In Crossroads, assets from nearly any chain are represented on a single backend blockchain as ERC-20 tokens. As a result, any asset can participate in smart-contract-based exchange, lending, or privacy applications on a single unified platform. So while Crossroads offers cross-chain bridging, a common, partial approach to alleviating the fragmentation of the blockchain ecosystem today, this is just one service within Crossroads' general-purpose chain-abstraction model. Crossroads relies on key encumbrance: a threshold signing committee holds encumbered keys controlling assets on each integrated chain, signing transactions only as authorized by smart contracts on the backend blockchain. Asset movements are fee-efficient, as ownership changes are recorded on the backend blockchain and users may set the transaction fee for withdrawals. Crossroads enables permissionless, modular integration of new blockchains using pluggable oracles with flexible design options (zkBridge, TEE-based, hybrid). Asset deposits into Crossroads benefit from strong, chain-specific finalization guarantees, minimizing the risk of reorg attacks. Unlike existing bridges, however, third-party smart contracts in Crossroads can provide fast, optimistic access to funds before finalization completes. We prove that Crossroads satisfies soundness: given an honest quorum of signing committee members, any user can unilaterally generate a withdrawal transaction transferring their net balance to an account on an integrated blockchain. We implement a proof of concept across multiple public blockchains: Bitcoin, Ethereum, and Solana. We catalog a range of applications enabled by Crossroads, including universal wallets, cross-chain staking and lending, privacy-preserving payments, and private management of public blockchain assets.
arXiv:2607.06527v1 Announce Type: new Abstract: Multi-hop Question Answering over Knowledge Graphs faces a critical challenge: traditional retrieve-then-read pipelines break differentiability, preventing the retriever from learning to bridge the semantic gap where intermediate nodes lack lexical overlap with the query. To address this, we propose RSF-GLLM, a framework decoupling differentiable graph reasoning from answer generation. Our Recurrent Soft-Flow (RSF) module employs a GRU-guided query updater to propagate continuous relevance scores, utilizing a dynamic gating mechanism to traverse semantically dissimilar bridge nodes via structural cues. We introduce flow sparsity regularization to theoretically guarantee convergence from soft probabilities to discrete reasoning paths. These paths are extracted and textualized to fine-tune a Large Language Model (LLM), ensuring generation is grounded in factual topology. Experiments on WebQSP and CWQ demonstrate that RSF-GLLM achieves competitive performance with superior inference efficiency compared to LLM based computationally expensive approaches.
arXiv:2607.06532v1 Announce Type: new Abstract: Mixed-integer linear programming (MILP) instances used for solver development are hard to obtain when models come from private or application-specific pipelines. A generator must keep the structure that solvers and learned policies rely on. Existing general generators usually choose their generation unit from a formulation template, summary statistics, local graph edits, or blocks found after recombination. These units do not explicitly record how a local part of the MILP is coupled to the rest of the instance. We propose GraphBU, a graph-native generator whose basic unit is a local subproblem plus its interface. The method promotes coupling nodes into master constraints or boundary variables and uses the resulting block units for compatibility-checked replacement. The analysis focuses on the properties needed by this construction: promotion separates interfaces, replacement can preserve feasibility under an interface-slack condition, and the graph construction is invariant to row-column permutations. On MILP instances generation, this unit keeps graph statistics close to the source family, preserves feasibility on most datasets, and improves downstream Predict-and-Search training. Genrated by GraphBU, The average graph-statistical similarity was approximately 0.934, the average feasibility was approximately 96.7%, and the average increase in the main index of downstream PS was approximately 8.0%.
Quantum-inspired methods for finite-element discretizations of the high-dimensional Poisson equation
arXiv:2607.06533v1 Announce Type: new Abstract: In recent years, quantum linear system algorithms have been applied to partial differential equations (PDEs), particularly in high-dimensional settings, demonstrating an exponential speedup in dimension. Concurrently, randomized and quantum-inspired classical linear solvers have emerged, showing computational complexity comparable to their quantum counterparts in many application areas. In this paper, we investigate the applicability of these quantum-inspired classical algorithms to PDEs. We provide both upper and lower bounds on their computational complexity, proving that these methods cannot achieve exponential speedup in dimension for discretizations of high-dimensional Poisson problems. Our theoretical findings definitively demonstrate that quantum-inspired classical algorithms are not competitive with quantum algorithms for solving PDEs, confirming that quantum methods retain a significant advantage for high-dimensional problems.