Search arXiv⌕ Search

arXiv subjects

Peng Zhang

Publications and source records attributed to Peng Zhang.

At least 37 records · Page 2Linked to original sources
arXiv2026

GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research

We present GenLimitLib, a source-aligned Lean 4 library for language generation in the limit. Introduced by Kleinberg and Mullainathan at NeurIPS 2024, language generation in the limit studies a theoretical question motivated by LLMs: how to generate valid new strings from observed examples. This young and rapidly evolving field offers a natural testbed for studying large-scale formalization. GenLimitLib contains formal developments for 30 papers. It extracts shared definitions and reusable proof components while preserving paper-specific assumptions and statements, and records relationships across papers. In this way, GenLimitLib provides a concrete and structured view of the literature. We show through mathematical case studies and LLM experiments how our library can support both human mathematical research and AI-assisted research. Our Library: https://github.com/pengzhang91/generation-in-the-limit-lib.

cs.LG↗
arXiv2026

Probabilistic Symbolic-Distillation Model of Droplet Collision for Spray Simulation at High Ambient Pressures

Droplet collision governs droplet population dynamics in many chemical engineering processes, such as spray drying, spray cooling, agricultural spraying, and combustion. Existing analytical models impose deterministic, pairwise boundaries between collision outcomes, whereas machine-learning classifiers lack the explicit functional form required of analytical collision submodels. In this study, we develop a probabilistic symbolic-distillation model using nearly forty thousand experimental events spanning eight regimes and five dimensionless parameters, including over five thousand data for ambient pressure up to 50 atm. A machine-learning teacher learns the joint outcome-probability landscape from these data, and symbolic regression subsequently distils it into eight class-specific expressions that jointly define a coupled analytical model. The resulting analytical field replaces abrupt regime switching with finite-width fuzzy boundaries. It outperforms the evaluated conventional analytical boundary models and reveals that their main limitation is the inability of zero-width boundaries to represent gradual probability transitions. The "biased-dice" sampling scheme provides a statistically consistent and practically convenient model implementation for Eulerian-Lagrangian spray simulation.

physics.flu-dyn↗
arXiv2026

Enantiomer-specific pumping of chiral molecules in high-$J$ rotational states

Enantiomer-specific state transfer (ESST) based on electric-dipole transitions has attracted considerable interest in the studies of manipulating molecules with electromagnetic fields. It also holds promise as a powerful tool for enantiomer detection and separation. To date, experimental demonstrations of ESST have focused mainly on molecules in the lowest rotational angular-momentum states, namely, $J=0$ and $J=1$. Realistic molecular samples, however, may contain appreciable populations in higher-$J$ rotational states, making it desirable to develop ESST schemes applicable to such states. Nevertheless, one cannot derive such schemes via a simple and straightforward extension of existing low-$J$ schemes, because higher-$J$ manifolds contain more magnetic sub-levels and involve more complicated networks of electric-dipole transitions. Here, we propose an ESST scheme for chiral molecules involving the $J=1$ and $J=2$ rotational states. Specifically, our scheme is based on enantiomer-specific pumping driven by three linearly polarized microwave fields and one laser beam. Under this scheme, one enantiomer is pumped into an enantiomer-specific dark state within a sub manifold with $J=1,2$, whereas the other enantiomer is dissipatively pumped out of this manifold. Our strategy can be extended to systems involving rotational states with even higher angular momenta.

quant-ph↗
arXiv2026

Beyond the Beam: Constructive Repair and Candidate Completion for Generative Recommendation

Generative recommenders retrieve items by generating identifiers, but a valid identifier can remain outside the beam after catalog expansion. This raises two connected questions: which failures can identifier assignment repair, and how should retrieval proceed beyond the initial beam? We characterize assignment repair with a fixed generator and retained old identifiers. Output-invariance certificates identify failures shared by all admissible assignments. Under a common effective prefix, coupled support and ranking constraints give the exact feasible interval of new-item counts for target recovery. Building on this characterization, Beyond the Beam (BB) obtains minimum-replacement repairs through an integral flow formulation, selects a shared map and adapts the generator. At inference, generative likelihood and collaborative evidence define one score for ranking, candidate priority and stopping. Retained prefix bounds guide candidate completion and certify its global Top-$K$ when the stopping condition is met. Exhaustive finite-catalog evaluation confirms construction in every feasible case. Across three Amazon Reviews categories and three random seeds, the full T5 procedure improves mean Recall@10 by 15.5--46.3% and NDCG@10 by 15.2--44.4% over the best-performing evaluated generative baseline for each dataset and metric. Matched controls show that shared construction and adaptation improve new-target ranking and certification efficiency on Beauty and Toys. Combined scoring and candidate completion improve NDCG@10 across all three datasets with both T5 and decoder-only LC-Rec.

cs.IR↗
arXiv2026

Sound Constructive Refinement from Production Envelopes to Executable Manufacturing Schedules

Production planning and execution systems can interpret capacity, compatibility, material, and timing commitments differently. We treat this semantic boundary as a constructive refinement problem in which a rolling-horizon planner emits a machine-day production envelope - an explicit contract fixing production, order-fulfillment, mold-state, inventory, outsourcing, and unmet-demand commitments - and a constructive procedure refines it into order-machine-day allocations. The procedure maintains fulfillment, production, and capacity residuals. A zero fulfillment residual certifies that the allocation preserves the envelope's capacity, compatibility, and delivery-window semantics; a nonzero residual records the product, machine, mold, date, and quantity that blocked realization. Under divisible quantities, exact arithmetic, shared allocation semantics, no additional admissibility filter, and a matched-progress condition, the procedure discharges all fulfillment residuals; stricter execution policies are diagnostic extensions rather than completeness tests. We evaluate a factory-provided anonymized instance with 37 product types, 150 orders, and 8.35 million requested units, a 5,400-run synthetic matrix, and dynamic shocks. Under explicitly declared accessory-supply, initial-inventory, effective-capacity, due-window, divisible-allocation, and mold-state assumptions, the industrial scenario reports 100% on-time delivery, no shell outsourcing, and 1.9-4.6% changeover-driven capacity loss. Under a strict in-house accessory interpretation, the same data expose a load ratio of 8.0763 and nonzero residuals. The synthetic matrix locates the load boundary of the guarantee.

cs.CE↗
arXiv2026

Fast-Slow Thinking RM: Efficient Integration of Scalar and Generative Reward Models

Reward models (RMs) are critical for aligning Large Language Models via Reinforcement Learning from Human Feedback (RLHF). While Generative Reward Models (GRMs) achieve superior accuracy through chain-of-thought (CoT) reasoning, they incur substantial computational costs. Conversely, Scalar Reward Models (SRMs) offer efficiency but suffer from limited performance and adaptability in complex scenarios. We introduce Fast-Slow Thinking Reward Models (F/S-RM), a hybrid RM architecture inspired by Dual Process Theory. It trains a single model to integrate two distinct reward paradigms: scalar-style first-token pairwise judgment (fast thinking) and CoT-based judgment (slow thinking), regulated by a dual-confidence activation mechanism that determines when to activate slow thinking. Under hybrid inference, F/S-RM achieves state-of-the-art accuracy with an average score of 84.3 across benchmarks, while reducing token consumption by 22.5%.

cs.CL↗
arXiv2026

Optimal Measurement Selection for Certifiable Voltage Monitoring in Power Distribution Systems

Maintaining consumer-end voltages within mandated limits is a central task in operating power distribution systems. Rising penetration of distributed generation, electric vehicles, and flexible loads complicates this task, while a scarcity of real-time measurements leaves distribution networks largely unobservable. Operators commonly monitor a few bellwether meters, which indicate operational health but certify nothing about the unmeasured buses. This work asks how to select measurements that are reported in real time and can certify network-wide voltage-limit compliance. We first illustrate the geometry of the measurement values that certify voltage safety at unmeasured nodes. Building on this geometry, we formulate a bilevel optimization that selects measurements to maximize certification capability, introducing a novel safety-violation metric with favorable monotonicity properties. We derive a strong-duality-based single-level reformulation and two scenario-reduction schemes with quantifiable suboptimality. Numerical tests on the SCE 56-bus system corroborate the superior certification capability and computational efficiency of the proposed approach.

eess.SY↗
arXiv2026

Machine Learning Accelerated Plasma Simulation through Physics Guided Time Jumps

We present a machine-learning-accelerated plasma simulation scheme that combines learned time jumps with ordinary physics evolution. A neural network corrects a low-cost physics forecast over multiple time steps, while the original solver reconstructs the state and advances it between jumps through short reanchoring intervals. The scheme is implemented in PASCHEN-1D, a one-dimensional drift-diffusion-Poisson solver, achieving up to $4.70 \times$ CPU rollout speedup relative to the ordinary solver for nanosecond pulsed nitrogen discharges. The simulations capture pre-breakdown evolution, rapid sheath formation, expansion and collapse under pulsed-voltage excitation, and post-pulse afterglow. Bulk densities and electric fields agree closely with the ordinary-solver reference, while cathode sheath width, gap voltage, and discharge current reproduce the principal temporal features. The largest spatial discrepancies occur in the cathode sheath during fast transients. A sweep of the physics-reanchoring duration reveals a trade-off between accuracy, acceleration, and numerical stability over the tested 500 ns simulation interval. A model trained on simulations with 1000 grid points also shows useful transfer to 500- and 1500-point meshes without retraining. These results demonstrate a practical route to accelerating plasma simulations by augmenting an established physics solver with machine learning.

physics.plasm-ph↗
arXiv2026

Droop-Aware Foundation Model Power Flow

This paper develops a droop-aware extension of the GridFM power systems foundation model, embedding droop gains and frequency/voltage deadband parameters as per-bus node features to enable control-aware AC power-flow analysis. Existing power-flow datasets encode only static electrical features, conflating operating points from qualitatively different control regimes; this work resolves that gap by exposing droop and deadband parameters as structured node features, with deadband discontinuities handled through a smooth tanh approximation that preserves solver differentiability. A transformer-based graph neural network is pre-trained on masked reconstruction and fine-tuned on the resulting control-aware datasets. The framework is validated against PSCAD electromagnetic-transient simulations on a two-bus system (0.11% maximum steady-state error) and cross-validated against an independent PyPower droop solver on the IEEE 24-bus RTS. On the 24-bus system the surrogate attains R2 = 0.9996 for active generation and 0.0015 p.u. voltage-magnitude RMSE; scalability is confirmed on the IEEE 300-bus system (0.0036 p.u. RMSE, R2 = 0.9841 for voltage magnitude across 299,700 predictions). A three-mode control study further shows that the deadband widens the control-error distribution while leaving total droop compensation unchanged, establishing deadband width as an actionable node-level design feature.

cs.ET↗
arXiv2026

Convective Heat Transfer Optimization for Liquid Cooling Plates Driven by Field Synergy and Fractal Geometry

The rapid development of liquid-cooled data centers has imposed imperative demands on the performance of liquid cooling plate. The density-based topology optimization (TO) is an effective approach to resolving the growing thermal-hydraulic performance requirements of liquid cooling plate. However, existing TO methods can hardly optimize convective heat transfer directly which is the intrinsic heat transfer mechanism, due to the highly complex and evolving structural topologies, varying flow and temperature fields, making it extremely challenging to explicitly describe the heat transfer coefficient and heat transfer area during TO process. A convective heat transfer topology optimization (CTO) method is proposed in this study, where the iteratively evolving heat transfer coefficient is explicitly depicted by the field synergy theory in the thermal objective, and directly described by the velocity and temperature fields without relying on specific geometry. Combined with the explicit depiction of heat transfer area by the fractal geometry theory, a CTO framework is built for a direct optimization of convective heat transfer under both the laminar and turbulent flow conditions. The CTO tends to generate more hierarchical and directional structural topologies in optimization results, which is conducive to reducing low-velocity stagnation zones and improving flow direction in branched channels, achieving enhanced synergy and thermal-hydraulic performance in the optimized liquid cooling plates. Compared with the TO results without incorporation of field synergy theory, the CTO can reduce average temperature rise by 20% while improving the Nusselt number by 15% under laminar flow conditions, and reduce maximum temperature rise by 10.2% and pressure drop by 25% under turbulent flow conditions.

physics.app-ph↗
arXiv2026

Dynamic Feature-Embedding Communication via Codebook Distillation for Federated Recommendation

Federated recommendation systems commonly protect user privacy by keeping user parameters on local devices, while exchanging item parameters for collaborative model training. However, such item parameters usually model items independently and suffer from both efficiency and effectiveness challenges, making communication costs grow with the item space and limiting cross-item generalization and robustness to noisy feedback. To address these limitations, we propose to model items via shared latent feature embeddings for communication. Residual Quantization (RQ) provides a natural way to instantiate this communication by representing each item with a short sequence of discrete code IDs, i.e., Semantic IDs (SIDs). However, directly applying centralized and static RQ-based recommendation to federated learning is non-trivial due to 1) private and biased historical interactions and 2) evolving collaborative information. We propose RQFedRec, an RQ-based federated recommendation framework for dynamic feature-embedding communication. To construct globally aligned codebooks without accessing private interactions, RQFedRec introduces an information distillation module. Each client first learns item embeddings that encode local collaborative information from private interactions, and then distills such information into feature-indexed codebooks under globally shared SIDs, making sparse and biased local signals more compatible with server aggregation. To adapt to evolving collaborative information, RQFedRec introduces a self-refining SID update module that dynamically refines global SID assignments from aggregated codebooks. Extensive experiments demonstrate that RQFedRec improves recommendation performance and reduces communication costs without relying on semantic information, while further benefiting from public semantics when available. Code is available at https://github.com/Mingzhe-Han/RQFedRec.

cs.IR↗
arXiv2026

FedHUR: Learning Hierarchical Utility-Guided Client Relations for Personalized Federated Recommendation

Federated recommendation enables collaborative model training while keeping user interaction data on local clients. A central problem in federated recommendation is how to aggregate useful information across clients for personalized recommendation. Existing personalized aggregation methods usually construct client relations from predefined parameter-based assumptions, such as parameter similarity or complementarity, and use these relations to determine aggregation weights. However, such methods construct a single global relation, which is insufficient to capture the hierarchical and multi-granularity nature of user relations in recommendation. Moreover, these predefined relations cannot directly reflect whether the related clients can improve prediction performance after aggregation. To address these limitations, we propose FedHUR, a federated recommendation framework for learning hierarchical utility-guided client relations. FedHUR takes item-item filters as the object for relation construction and aggregation. Specifically, it first aggregates and clusters each client's local information to obtain global hierarchical information. Each client computes hierarchical utility signals based on its local information and the global hierarchical information, indicating which collaborative information is useful for improving its prediction. The server uses these utility signals to retrieve clients that are useful to that client for further personalized aggregation. Extensive experiments on five real-world datasets show that FedHUR consistently outperforms existing federated recommendation baselines, demonstrating the effectiveness of hierarchical utility-guided client relation learning. Code is available at https://github.com/Mingzhe-Han/FedHUR.

cs.IR↗
arXiv2026

Search for neutrinoless quadruple beta decay of $^{136}$Xe in PandaX-4T detector

The observation of neutrinoless quadruple beta decay (0$ν$4$β$) in the absence of neutrinoless double beta decay (0$ν$2$β$) has been argued to provide a strong indication that neutrinos are Dirac particles. We report a search for 0$ν$4$β$ decay of $^{136}\text{Xe}$ using a total $^{136}\text{Xe}$ exposure of 148.4 kg$\cdot$yr, collected during the commissioning and the first science runs of the PandaX-4T experiment. No significant excess of events over the background is observed. A lower limit on the 0$ν$4$β$ decay half-life of $^{136}\text{Xe}$ is set at 6.01 x $10^{24}$ yr at the 90% confidence level. This result establishes the most stringent constraint on this process in xenon, demonstrating the unique capability of the PandaX-4T detector in probing lepton number violation and shedding light on the fundamental nature of neutrinos.

nucl-ex↗
arXiv2026

Spatial-Code-Domain Grouped Index Modulation: Fluid-Antenna-Assisted System Design and BER Performance Analysis

Fluid antenna systems (FASs) provide reconfigurable spatial resources within compact apertures. In this paper, we introduce code-domain grouped index modulation (CGIM) and its spatial-code-domain extension, termed SCGIM, for FA-assisted transceivers. CGIM partitions the available orthogonal spreading codes into multiple subsets and jointly maps information onto their in-phase and quadrature indices and constellation symbols. In an Rx-FAS-assisted single-input multiple-output (SIMO) link, group-wise despreading separates the orthogonal code groups for parallel detection, while receive-port selection provides spatial diversity. SCGIM further associates interleaved Tx-FA port subsets with the code subsets, with the Tx-FAS conveying spatial-index information and the Rx-FAS providing selection diversity in a multiple-input multiple-output (MIMO) link. For SCGIM, we develop maximum-likelihood (ML), staged greedy (GD), and cross-domain index message-passing (CD-IMPD) detectors. CD-IMPD exchanges soft information over a cycle-free factor graph to account for the coupling between the spatial and code indices, requiring only one inward and one outward message pass. For CGIM, the BER is derived from the joint decision regions of the despread-domain observations and averaged over the Rx-FAS selected-gain distribution under Rayleigh, Nakagami-m, and additive white Gaussian noise channels. For SCGIM, an average-BER approximation is derived from a full-pair union bound using the selected-gain density ratio and exponentially tilted quadratic-form Laplace transforms. Simulation results validate the BER analysis and show that the proposed schemes achieve lower BER and higher throughput than the considered IM schemes, while CD-IMPD achieves near-ML BER performance with lower detection complexity.

cs.IT↗
arXiv2026

ElderBench: Benchmarking Autonomous Mobile Agents for Older Adults

While autonomous mobile agents hold great potential for assisting older adults with smartphone usage, existing GUI benchmarks mainly rely on explicit, goal-oriented instructions and rarely capture the naturally occurring language patterns of older users, such as indirect speech, referential ambiguity, and under-specified requests. This mismatch between benchmark instructions and real-world elderly interactions may hinder reliable agent deployment. To address this gap, we present ElderBench, the first benchmark for evaluating mobile GUI agents in authentic elderly-oriented scenarios. ElderBench is constructed from 249 naturally elicited smartphone tasks collected from older adults across 20 applications. We first characterize the linguistic divergence between elderly instructions and existing GUI benchmark instructions from syntactic, semantic, and pragmatic perspectives. We then evaluate mainstream GUI agents and Vision-Language Models under both online and offline settings, revealing substantial performance degradation when handling elderly-oriented instructions. Through controlled instruction normalization, failure analysis, and fine-grained linguistic feature analysis, we further identify how elderly-specific language patterns contribute to agent failures. Our findings provide actionable design insights toward more adaptive, interpretable, and age-inclusive GUI agents for older adults.

cs.AI↗
arXiv2026

Embedding Single-Phase Grid-Forming Inverters in Three-Phase Unbalanced Power Flow

This letter introduces Grid-Forming Three-Phase Power Flow (GFM-3PF), an augmented Newton power flow framework for modeling single-phase grid-forming inverters (GFMs) in three-phase unbalanced networks. The contributions of this work are threefold: 1) developing a two-stage solution strategy based on positive-sequence initialization followed by three-phase phase-domain lifting for robust large-scale computation; 2) incorporating phase-domain unbalanced network modeling with controlled mutual coupling together with phase-dependent, frequency-sensitive load representation; and 3) embedding a single-phase GFM bus model directly into the three-phase unbalanced Newton power flow equations through a common droop-governed frequency state. GFM-3PF is validated on 3-bus, 33-bus, and 118-bus test systems, demonstrating its accuracy, robustness, and scalability.

cs.ET↗
arXiv2026

QSVT-Based Three-Phase Unbalanced Power Flow

This letter introduces QSVT-3PF, a quantum singular value transformation (QSVT) based solver for three-phase unbalanced power flow with embedded single-phase grid-forming inverter (GFM) operation. The contributions are threefold: 1) reformulating the Newton correction as a QSVT-compatible inverse problem using a normalized block-encoded phase-domain Jacobian; 2) introducing a regularized singular-value filter to improve robustness under ill-conditioned and stressed operating conditions; and 3) validating the proposed solver on an IEEE 5-bus system and the IEEE 123-node test feeder with single-phase GFM integration. Test results show that QSVT-3PF matches the classical Newton benchmark in residual convergence, voltage profile, and final operating point, demonstrating the feasibility of QSVT-3 for large, unbalanced distribution systems.

cs.ET↗
arXiv2026

DTD-VAE: Disentangled Temporal Dependencies VAE for Credit Risk Prediction

Evaluating customer creditworthiness is crucial for retail banking operations, as it impacts marketing strategies, customer relationship management, and credit risk control. Traditional methods often struggle to capture complex temporal dependencies and extract pertinent information from customer data, crucial for accurate risk assessment. Specifically, they fail to differentiate between temporal patterns indicative of credit risk and those reflecting general customer behavior or preferences, leading to suboptimal risk predictions. In this study, we introduce the Disentangled Temporal Dependencies Variational Autoencoder (DTD-VAE), an advancement over conventional VAE, designed to disentangle temporal dependencies and distinguish credit risk-related features from past customer preferences. The feature inference module of the DTD-VAE incorporates an autoregressive temporal dependency learning mechanism that adeptly captures the temporal dependencies among latent variables, enriching the model's comprehension of the inherent data structure. Furthermore, the feature generative module utilizes an element-wise gating mechanism that assigns independent weights to each dimension of the expert models, enabling a finer-grained disentanglement of latent variables, particularly those relevant to credit risk prediction. Extensive experiments on six real-world datasets demonstrate that the proposed framework consistently outperforms existing methods, achieving performance gains of 3.2%-4.86% in ROC-AUC and 6.41%-9.71% in Accuracy Ratio.

q-fin.RM↗