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  • 2606.0005
    Common cyclic subfields of degree p division algebras over complete discrete valuation fields
    吴正尧
    Let $A,B$ be degree-$p$ division algebras over a complete discrete valuation field with $\ind(A\otimes B)<\ind(A)\cdot\ind(B)$. We study the existence of common cyclic maximal subfields of $A$ and $B$ in two complementary settings. In characteristic $\neq p$ (with $\mu_p\subset F$), we classify the common subfields via the Faddeev exact sequence on the Brauer group, giving explicit criteria in the unramified, mixed, and both-ramified valuation regimes, and prove a norm intersection formula. In characteristic $p$, we prove that when the residue field has trivial $p$-torsion Brauer group, every pair of degree-$p$ $p$-algebras shares the common Artin--Schreier splitting field $K(\wp^{-1}(\pi))$. For general non-Henselian fields, we identify structural obstructions in both settings.
    🤖 AI Theoretical
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  • 2510.0027
    From Knowledge Tree to Knowledge Forest: Harnessing Chemical Understanding with Machine Learning and Artificial Intelligence
    The 2024 Physics and Chemistry Nobel Prizes to machine learning (ML) and artificial intelligence (AI) breakthroughs marked “Year 1 of AI for Science,” underscoring their transformative role in physical sciences. Yet data are not the same as understanding—a distinction central to chemistry, which has long relied on concepts such as bond, aromaticity, and reactivity as scaffolds for understanding and explanation. Building on our recent perspectives (ACS Phys. Chem. Au 2024, 4, 135–142; J. Chem. Theory Compt. 2025, DOI: 10.1021/acs.jctc.5c01299), this article explores how ML/AI can become engines of chemical understanding. We introduce a quintet of chemical knowledge—ontology, epistemology, theory, concept, and understanding—and develop the metaphors of the Knowledge Tree and Knowledge Forest to show how diverse epistemologies interact and recursively enrich one another. Case studies on aromaticity, catalysis, orbital-free density functional theory, and protein folding illustrate how ML features, when interpreted as conceptual roots, yield fruits of understanding. Contrasting multiscale modeling with hierarchical modeling, we argue that ML enables emergent, concept-driven integration across levels. Cultivating this plural and hierarchical ecosystem may guide theoretical chemistry toward its next breakthroughs, resolving Dirac’s dilemma not by brute force but by forests of concepts that transform data into enduring understanding.
    👤 Human Position
    🎯 ICAIS2025 Accepted Paper
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  • 2608.0011
    Latent-Space Planning with JEPA World Models The Role of Action-Sensitivity and True-Position Evaluation in MiniGrid
    Ankit Jha
    World models based on Joint-Embedding Predictive Architectures (JEPA) promise sample-efficient, action-conditioned planning by predicting future representations rather than raw observations. However, an encoder–predictor pair can trivially collapse to representations that are easy to predict but insensitive to the agent's actions, in which case planning objectives defined purely in latent space can appear to succeed while producing incoherent real-world trajectories. In this work we study latent-space Cross-Entropy Method (CEM) planning with JEPA world models on two MiniGrid navigation tasks of increasing difficulty — FourRooms and DoorKey-6x6 — and introduce a true-position evaluation protocol that scores plans against the agent's actual environment state rather than latent distance. We compare a Simple GRU predictor against a FiLM-modulated GRU with an inverse-dynamics auxiliary head (FiLM+InvDyn) across five random seeds per condition. The Simple GRU predictor achieves modest, statistically significant gains on FourRooms (27.6% ± 15.3%, p = 0.0224) but fails on the harder DoorKey task (−4.4% ± 59.6%, p = 0.8899). Augmenting the predictor with FiLM conditioning and an inverse-dynamics loss raises performance to 43.4% ± 24.1% (p = 0.0227) on FourRooms and 77.2% ± 14.2% (p = 0.0004) on DoorKey. We trace this gap to an action-sensitivity ratio that improves from 0.11 in a historical, latent-space-evaluated checkpoint to 3.40 in the current model, and we show that effective representational rank collapses from 4.28 to 1.98 (out of 256 dimensions) between the easier and harder task. Our results argue that action-sensitivity, not merely representation quality, is the binding constraint for latent-space planning, and that true-position evaluation is necessary to detect this failure mode. Keywords: world models, self-supervised learning, JEPA, VICReg, latent-space planning, model predictive control, MiniGrid
    👤 Human Empirical
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  • 2510.0052
    Conformal Prediction as Bayesian Quadrature for Risk Control
    In this paper, we present a novel framework that leverages Bayesian quadrature for conformal prediction to achieve rigorous, data-conditional, and distribution-free risk guarantees, addressing the challenge of controlling predictive risk in high-stakes, black-box settings. Our approach constructs an upper bound on the expected loss by integrating over the quantile function of the loss distribu- tion, where, given calibration losses ℓ1 , . . . , ℓn , we define the aggregated loss Pn+1 as L+ = i=1 Ui ℓ(i) with Dirichlet random variables Ui ∼ Dir(1, . . . , 1) and ℓ(n+1) = B, thereby ensuring that the condition Pr(L+ ≤ α) ≥ β is met. Our contributions include a principled derivation that recovers well-known conformal methods such as Split Conformal Prediction (SCP) and Conformal Risk Control (CRC) as special cases, while introducing a novel high posterior density (HPD) rule that exploits the full posterior of L+ . We rigorously validate our method on synthetic binomial loss and heteroskedastic regression tasks, where experimental results indicate that methods based solely on the posterior mean (CRC) or uniform concentration bounds (RCPS) often yield either overly optimistic or conservative decisions, whereas our HPD rule achieves risk control with zero empirical failure rate and improved utility. For example, in the binomial experiment, while SCP selects an average λ of 0.596 with a 61.6% failure rate, HPD selects λ ≈ 0.970 with a 0% failure rate, and a similar trend is observed in regression tasks with test risks decreasing from 0.512 for SCP to 0.067 for HPD. These findings, summarized in Table 1, confirm that our Bayesian quadrature reformulation not only provides a more interpretable statistical characterization of conformal risk but also adapts effectively to calibration sample size and confidence level tuning, thus offering a robust solution for high-stakes decision-making.
    🤖 AI Methodology
    🎯 ICAIS2025 Accepted Paper
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  • 2510.0057
    Adaptive Prompt-Enhanced Score Matching for Partially Observed Data
    Adaptive prompt-enhanced score matching for partially observed data addresses the challenging problem of recovering score functions from datasets with significant missing entries, where traditional imputation methods or naı̈ve score estimators often fail to achieve reliable parameter recovery and structural inference. In our work, we consider both marginal Importance-Weighted (Marg-IW) and marginal Variational (Marg-Var) approaches to estimate the score function, using a surrogate mean squared error loss. here sθ (x) is the estimated score computed as −P(x − µ) and strue (x) = −Ptrue (x − µtrue) with Ptrue representing the true precision matrix. This formulation inherently accounts for the missingness mechanism, typically modeled as MCAR with a missing rate of 30%, and is further stabilized via techniques such as log-sum-exp and gradient clipping. Our contributions include the integration of a meta-learning prompt generator, which dynamically selects key hyperparameters (e.g., sample size r ∈ {5, 10, 50}, number of inner-loop steps L, learning rates 1×10−2 , 5×10−3 , 1×10−3 , and truncation parameters) to optimize convergence behavior across a diverse set of synthetic datasets including multivariate Gaussians, ICA-inspired models, and sparse Gaussian graphical models (GGMs) with star graph structures. Experimental results demonstrate significant improvements: for instance, in the Gaussian experiment the loss reduced from 9.687 at iteration 50 to 0.094 at iteration 300 and the corresponding parameter error decreased from 3.033 to approximately 2.030, while in the GGM case, the ROC AUC improved from 0.219 to 0.97, thereby confirming our method’s efficacy in both parameter estimation and structure recovery under partial observations. These empirical validations underscore the relevance of adaptive score matching in high-dimensional and complex data regimes, set against the inherent difficulties of handling missing data and ensuring numerical stability in the estimation process, and pave the way for future extensions to accommodate MNAR scenarios and diffusion-based denoising score matching frameworks.
    🤖 AI Methodology
    🎯 ICAIS2025 Accepted Paper
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  • 2603.0004
    Correcting hybrid density functionals to model Y6 and other non-fullerene acceptors
    Tom Ward, Isabel Creed, Tim Rein, Jarvist Moore Frost
    Recently developed fused-ring organic electron-acceptors such as Y6 have strong oscillator strength, good charge-carrier transport and low bandgaps. They therefore have enormous current technical application to optoelectronic devices, such as solar cells. Due to the large number of atoms involved in representative aggregates of these materials, we need an efficient electronic structure method to model them. Standard density functional theory poorly describe charge-transfer states, and were developed for vacuum calculations of individual molecules. In this work we tune a range-separated hybrid functional for Y6. We characterise representative dimers of the solid-state and show that Y6 dimers show the extensive solvatochromic effects are due, in part, to oscillator strength borrowing. We provide an explanation for the short optimally tuned range-separation parameter, based in the Penn model for the frequency dependent dielectric of a semiconductor. We caution that standard range-separated hybrids are less accurate than global hybrids for these, and similar, materials. We show how reducing the range-separation length improves the accuracy of standard functionals, without an involved tuning process.
    👤 Human Theoretical
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  • 2608.0017
    QuantumFerryV2B: Weather-Robust Quantum-AI Control for Ferry-Port Vehicle-to-Building Energy Systems
    Yifan Wang
    Battery-electric ferry ports are emerging as demanding nodes in maritime electrification: one shore transformer must deliver megawatt-scale charging in minute-long berth windows while serving terminal buildings, refrigerated cargo, electrified equipment, and cold-weather battery limits. We introduce QuantumFerryV2B, a real-data-grounded Quantum-AI framework that controls this coupled system as one weather-robust, thermally aware Vehicle-to-Building (V2B) problem rather than isolated charging, building, or battery subproblems. The framework combines a three-region benchmark, a physics-based energy and battery-thermal evaluator, a chance-constrained P90 weather reserve learned by a SciML surrogate, a QPU-ready QUBO day-ahead scheduler with deterministic feasibility repair, and a physics-shielded variational quantum circuit (VQC) controller. The benchmark uses Entur ferry timetables, Danish AIS traces, Washington State Ferries GTFS schedules, Open-Meteo weather and marine fields, NREL/OEDI port-load profiles, CALCE low-temperature lithium-ion data, EnergyPlus terminal simulation, and OpenModelica battery-thermal validation. Across Norway, Denmark, and the USA, coordinated scheduling cuts peak demand by 52.5--56.1\% and operating cost by 33.0--38.5\% relative to uncontrolled opportunity charging. Thermal preconditioning is necessary in cold-wave cases; the SciML P90 reserve converts brittle point-optimal schedules from 45--70\% held-out feasibility to 98--100\% robust feasibility at below 2.5\% cost premium. The QUBO scheduler matches the exact optimizer on demand peak, while the physics-shielded VQC sustains zero missed departures under IBM Heron-r2-class hardware noise with 16x slower parameter growth than a matched neural network. QuantumFerryV2B provides a reproducible benchmark and deployable Quantum-AI control architecture for robust ferry-port electrification.
    🤖 AI Application
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  • 2609.0010
    预测编码网络在语言建模中的样本效率、机制不可达性与测量纪律:一项单卡架构研究
    邓克瑜
    我们报告预测编码网络(PCN)与 Transformer 在语言建模上的系统性对照研究,并给出两者的混合架构。核心发现六项:(1)误差流变体的优势随数据稀缺单调放大(至 +84%),参数轴呈倒 U(峰位 ≈1025 tokens/param),带外预测成功;(2)纯 PCN 在 101M 对称调优终判中落败 33.7%,失败机制锁定为优化动力学内禀失稳;(3)混合架构(12TF+12PCN,96M)预训练 PPL 63.18±0.22,反超纯 Transformer 36%(p≈0),优势经 330-354M 外推保持,500M 判决揭示 V 形压缩曲线与「优雅饱和墙 vs 灾难墙」对照;(4)适应优势经预注册判据两次诚实收窄:从「性能独占」到「零配置鲁棒性」(PEFT 22 格网格),再到「TF 相对」;(5)**终判**:把 PCN 头移植到官方 Gated DeltaNet 骨干,冷启动能力可迁移但流式不稳,且纯 GDN 自身适应全协议安全、同参数同预算预训练 PPL 29.74±0.13(为 TF 的 3.35×)——delta 规则家族同时占据预训练与适应两个生态位,终端架构选择的最终答案由此改写;(6)**理论遗产**:PCN 梯度适应在形式上就是施加于权重的 delta 规则(与 Widrow-Hoff 1960 及 GDN 状态更新三实例同构),但三臂实证反向证伪「梯度自熄灭⟹适应安全」——有效变量是 Adam 逐坐标归一化对梯度-更新的解耦。端侧验证两级:研究原型(纯 CPU 2240 tok/s、20 秒冷启动 +85%)与生产级运行时(llama.cpp/GGUF 数值等价 0.015%、Q4+W_res 豁免 +0.10%、75.8MB、503 tok/s)。全部七起测量偏差由预设协议捕获。PCN 研究据此封存,路线移交 GDN 底座的五属性新项目。
    👤 Human Empirical
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  • 2610.0031
    he Dual Bottleneck: A Composition Law for Judge Reliability and Generator Capability in Self-Evolving Agents
    LI HAO
    Self-evolving agents—systems that iteratively generate tasks, solve them, and dis- till experience—have shown promise in code generation and mathematical reason- ing. Existing work predominantly focuses on the judge (the evaluator providing feedback), assuming that reliable judges suffice. Through 2,400 controlled experi- ments on Z3 constraint-solving tasks, we uncover a second, equally critical bottle- neck: the generator (the LLM authoring new tasks). We formalize the Dual Bottle- neck as a composition law on error budgets: 1−∆global t = (1−∆gen t )(1−∆valid t ), verified to machine precision (1.11e-16) on 2,400 real-API rounds. The law im- plies that the generator and judge bottlenecks share one budget: a condition with large ∆gen t needs a more reliable judge for the same overall tolerance. If ∆gen t alone exceeds the budget, no judge reliability can compensate. We empirically measure τc ≈ 0.55 on Level 1 tasks using the real DeepSeek V4 Flash API, and derive the parameter-free formula τc =√︁ 1 − 2∆max t . We identify a pseudo- difficulty trap: when the difficulty controller upgrades to Level 2/3, the LLM’s task-generation validity collapses from ∼89% to <10%, causing the system to spin without progress. We propose a four-layer constraint generation framework that restores validity to 100% at L1, 73.8% at L2, and 83.8% at L3 on real API.
    🤖 AI Theoretical
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  • 2511.0002
    Battery-Sim-Agent: Leveraging LLM-Agent for Inverse Battery Parameter Estimation
    Parameterizing high-fidelity ``digital twins'' of batteries is a critical yet challenging inverse problem that hinders the pace of battery innovation. Prevailing methods formulate this as a black-box optimization (BBO) task, employing algorithms that are sample-inefficient and blind to the underlying physics. In this work, we introduce a new paradigm that reframes the inverse problem as a reasoning task, and present \textsc{Battery-Sim-Agent}, the first framework to deploy a Large Language Model (LLM) agent in a closed loop with a high-fidelity battery simulator. The agent mimics a human scientist's workflow: it interprets rich, multi-modal feedback from the simulator, forms physically-grounded hypotheses to explain discrepancies, and proposes structured parameter updates. On a systematically constructed benchmark suite spanning diverse battery chemistries, operating conditions, and difficulty levels, our agent significantly outperforms strong BBO baselines like Bayesian optimization in identifying accurate parameters. We further demonstrate the framework's capability in complex long-horizon degradation fitting tasks and validate its practical applicability on real-world battery datasets. Our results highlight the promise of LLM-agents as reasoning-based optimizers for scientific discovery and battery parameter estimation.
    👤 Human Methodology
    🎯 ICAIS2025 Accepted Paper
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