arXiv subjects

Jia Liu

Publications and source records attributed to Jia Liu.

At least 73 records · Page 4Linked to original sources

arXiv2026

Coordinate-wise Polyhedral Method for Eliciting Multivariate Linear Utility and Univariate Nonlinear Utility Functions

In this paper, we propose a coordinate-wise polyhedral method (CPM) for cutting polyhedra with theoretical guarantees of convergence. Unlike the existing polyhedral method, which designs pairwise comparison queries by solving coupled optimization problems and performs cuts subsequently, CPM specifies coordinate-wise cuts in advance and then designs corresponding pairwise comparison queries by solving a linear system of equations. Under this framework, we show that CPM reduces the diameter of the polyhedron at a linear convergence rate. Moreover, we extend CPM to a univariate piecewise-linear utility function by representing it with its increment vector over consecutive breakpoints. We show that the Kantorovich distance between the true utility function and the estimated one obtained by CPM decreases at a linear convergence rate. Further, we extend the CPM to general nondecreasing Lipschitz continuous utility functions by piecewise-linear approximation (PLA). We introduce an adaptive-breakpoint strategy to avoid direction errors caused by PLA. We prove that the set of piecewise-linear utility functions corresponding to the ambiguity set of increment vectors converges to the true utility function as the number of queries increases, and derive an explicit bound for the approximation. Finally, to evaluate the performance of CPM, we conduct a series of numerical experiments. The results demonstrate comparable convergence to the standard polyhedral method in the case of linear multivariate utility functions. For nonlinear univariate utility functions, CPM achieves stable convergence to the true utility function, in line with the theoretical findings.

math.OC↗

arXiv2026

Centrifugal-corrected harmonic oscillator model for spherical proton emitters

In the present work, we propose an improved harmonic oscillator model to systematically evaluate the proton radioactivity half-lives in spherical nuclei, incorporating centrifugal potential effects. By fitting the experimental data, the centrifugal parameter $d = 0.143$ for the correction term $dl(l+1)$ and nuclear potential depth $V_0 = 62.4$ MeV are obtained. The model integrates the relativistic mean field (RMF) theory with the BCS method based on the DD-ME2 force to determine spectroscopic factors $S_p$. Moreover, by verifying the linear relationship between the logarithm of the normalized width $\log_{10}{γ^2}$ and fragmentation potential $V_{frag}$, the connection between nuclear structure and tunneling dynamics is confirmed, and an analytical expression for the adjustable parameter $d$ corresponding to the centrifugal potential is derived as $d^{\rm{Ae}}$ $\approx$ 0.167. Compared with $d^{\rm{Ae}}$, the modified model based on $d$ yields results in better agreement with experimental half-lives, and is able to control the error of the experimental data within a factor of 2.4. Furthermore, the extended improved model is used to predict the half-lives of some possible proton radioactivity candidates in NUBASE2020 that are energetically allowed or have been observed but not yet quantified. This work improves the accuracy of proton radioactivity studies and provides a robust theoretical framework for future nuclear structure research.

nucl-th↗

arXiv2026

Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations

This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators. While standard ReLU networks achieve minimax-optimal rates in the $L^2(P)$ norm for various nonparametric regression tasks, we establish a theoretical lower bound demonstrating that least-squares ReLU estimators can suffer from the curse of dimensionality in their uniform convergence behavior. Motivated by the need for reliable uniform guarantees in downstream tasks requiring worst-case reliability, we address this limitation by analyzing smoothly activated DNNs (smooth DNNs), encompassing both feedforward and residual structures. We establish novel pseudo-dimension bounds, non-asymptotic approximation guarantees, and Hölder-norm bounds for the approximators of these models. Leveraging these results, we derive non-asymptotic uniform convergence rates for smooth DNN estimators across multiple statistical contexts, including Huber, least-squares, quantile, and logistic regression. We prove that smooth DNNs can mitigate the {curse of dimensionality} in uniform convergence by adaptively exploiting the low-dimensional hierarchical composition structure of the target function. Supported by both simulation studies and a real-world application, our results position smooth DNNs as a theoretically grounded and practically viable alternative to ReLU networks for statistical learning tasks requiring uniform guarantees.

cs.LG↗

arXiv2026

From Live to Recording: Consumer Demand and Response to Price Across the Livestreaming Lifecycle

Livestreaming has evolved into a thriving industry where creators can directly monetize and engage with their audiences and followers. In practice, creators and platforms typically concentrate their marketing efforts on the period leading up to the livestream. However, livestreaming events naturally transition into recorded formats once the event concludes, creating potential "residual" opportunities for monetization. This study systematically examines consumer demand for live events throughout the entire livestream life-cycle, using data from a large livestreaming platform that allows consumers to purchase the recorded version of a paid live event after the livestream ends. We find that the demand is surprisingly more price-sensitive during the pre-livestream period compared to the post-period. This is partly driven by two mechanisms: consumer self-selection (infrequent consumers who may have missed the live events exhibit a higher willingness to pay for recorded versions) and quality uncertainty (consumers face higher uncertainty in event quality during the pre-period than in the post-period). Our findings generate implications for the pricing and targeting strategies in livestreaming markets.

stat.ML↗

arXiv2026

On strong spaceability of continuous functions and fractal dimensions

Given $s\in(1,2]$, define $$H_s[0,1]=\{f\in C[0,1]:{\dim}_HG_f([0,1])=s\}$$ and $$\overline{B}_s[0,1]=\{f\in C[0,1]:\overline{\dim}_BG_f([0,1])=s\}.$$ The main goal of this paper is to study the $(α,β)$-lineability/spaceability of the sets $H_s[0,1]$ and $\overline{B}_s[0,1]$. As a principal result, we prove that $H_s[0,1]$ is $(p,\mathfrak{c})$-spaceable for $p=1,2$ and also $(n,n+m)$-lineable for any $m,n\in\mathbb{N}$. This partially answers a question raised by Liu et al. concerning the Hausdorff dimension of graphs of continuous functions. Furthermore, for a cardinal number $α$, we prove that $\overline{B}_s[0,1]$ is $(α,\mathfrak{c})$-spaceable if and only if $α<\aleph_0$. This completely resolves an open question raised by Liu et al. concerning the upper box dimension of graphs of continuous functions.

math.FA↗

arXiv2026

FIRM: Federated In-client Regularized Multi-objective Alignment for Large Language Models

Aligning Large Language Models (LLMs) with human values often involves balancing multiple, conflicting objectives such as helpfulness and harmlessness. Training these models is computationally intensive, and centralizing the process raises significant data privacy concerns. Federated Learning (FL) offers a compelling alternative, but existing Federated Multi-Objective Optimization (FMOO) methods face severe communication bottlenecks as their reliance on transmitting multiple gradients to a server is unscalable for large models. We introduce FIRM (Federated In-client Regularized Multi-objective alignment), a novel algorithm that achieves both client disagreement drift mitigation and communication efficiency. In FIRM, each client locally solves a regularized multi-objective optimization problem. By directly mitigating client disagreement drift through in-client regularization, our method eliminates the need for the multi-gradient transmissions common in prior works. Consequently, clients need only to transmit a single set of adapted parameters, maintaining high communication efficiency. We prove that our algorithm converges to Pareto-stationary points and, to our knowledge, provide the first finite-time convergence guarantees for this federated multi-objective alignment setting. Empirically, we show that FIRM leads to smoother training dynamics, reduced client disagreement drift, and improved reward trade-offs compared to baselines. We further propose a method to incorporate a preference over the objectives and report empirical Pareto plots, demonstrating that FIRM can smoothly adapt trade-offs between objectives in response to specified preferences.

cs.LG↗

arXiv2026

Attosecond soft X-ray pulses generated by chirp-dispersed manipulation in an XFEL reveal nonlinear core-electron dynamics in neon

Free-electron lasers have demonstrated their capability of generating intense attosecond X-ray pulses, which are the key to studying electron dynamics at their natural time scale and in specifically targeted electronic states, but come at the expanse of complicated generation schemes and stochastic pulse shapes. Here, we demonstrate a novel and simple operation concept based on the manipulation of the electron-bunch chirp-dispersion and working with the full 4.5 MHz repetition rate at the European XFEL in Germany. With a high-fidelity single-shot temporal characterisation, we detect X-ray pulses with durations of down to 200 attoseconds and peak powers reaching into the terawatt regime at ~1 keV photon energy. As a direct application, we present simultaneous measurements of nonlinear X-ray-matter interaction via time-resolved electron spectroscopy. Using the derived temporal pulse information and restricting the durations to a regime where individual X-ray pulses are shorter than the single-core-hole life time in neon atoms, we reveal an otherwise hidden peak-intensity dependence in the nonlinear dynamics of double-core-hole formation. Our results open the field of attosecond science to the investigation of electronic processes not only in the ground state but also in systems driven far off their equilibrium. They shed light on highly transient intermediate steps in complex electronic dynamics and thus promise to help build the conceptual bridge between fundamental physical processes and chemical photo-reactions.

physics.optics↗

arXiv2026

PowLU: An Activation Function for Stable Pre-Training of LLMs

In contemporary large language models (LLMs), the swish-gated linear unit (SwiGLU) activation function is widely adopted to regulate the information flow and introduce non-linearity. For large positive inputs, SwiGLU approximates the quadratic function $x^2$, providing strong nonlinearity and expressive capacity. However, this property also causes numerical instability as the input or model scale increases, particularly in low-precision LLM training. The main reason is its approximate quadratic amplification, which enlarges the output range and exacerbates outliers. To address this issue, we propose a stable activation function, Power Linear Unit (PowLU), for large-scale LLM pre-training. Specifically, PowLU employs a rational power function to achieve adaptive nonlinearity, thereby improving representation ability and enabling stable training in spike regions. Moreover, we provide theoretical justification for several key properties of PowLU. Scaling law experiments confirm that the performance is consistent across model sizes, and further experimental results with the Ling architecture (7.9B and 124B total parameters) demonstrate that PowLU achieves competitive results against SwiGLU and SwiGLU-Clip in large-scale training of LLMs. In addition, the experimental results also show that PowLU effectively improves the scalability of the large-scale training of LLMs.

cs.CL↗

arXiv2026

A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level strong convexity assumption, which significantly restricts their applicability to modern machine learning problems of growing complexity. In this paper, we make the first attempt to extend BLO to the multi-task setting under a relaxed lower-level general convexity (LLGC) assumption. To this end, we reformulate the multi-task bilevel learning (MTBL) problem with LLGC into an equality constrained multi-objective optimization (ECMO) problem. However, ECMO itself is a new problem that has not yet been studied in the literature. To address this gap, we first establish a new Karush-Kuhn-Tucker (KKT)-based Pareto stationarity as the convergence criterion for ECMO algorithm design. Based on this foundation, we propose a weighted Chebyshev (WC)-penalty algorithm that achieves a finite-time convergence rate of $O(ST^{-\frac{1}{2})$ to KKT-based Pareto stationarity in both deterministic and stochastic settings, where $S$ denotes the number of objectives, and $T$ is the total iterations. Moreover, by varying the preference vector over the $S$-dimensional simplex, our WC-penalty method systematically explores the Pareto front. Finally, solutions to the ECMO problem translate directly into solutions for the original MTBL problem, thereby closing the loop between these two foundational optimization frameworks.

cs.LG↗

arXiv2026

Wess-Zumino-Witten Interactions of Axions: Three-Flavor

We present a complete Lagrangian describing axion interactions with pseudoscalar and (axial-)vector mesons within the three light-flavor quark framework. This formulation incorporates both the standard chiral Lagrangian and the full Wess-Zumino-Witten (WZW) term. By including instanton effects associated with the anomalous $U(1)_A$ symmetry, we demonstrate that physical observables remain invariant under arbitrary chiral phase rotations of the quark fields. This comprehensive Lagrangian provides a robust and consistent framework for exploring axion phenomenology through its interactions with mesons and gauge bosons. As a demonstration, we compute the decay widths of GeV-scale axions into various mesonic final states for several benchmark axion models.

hep-ph↗

arXiv2026

Relax: An Asynchronous Reinforcement Learning Engine for Omni-Modal Post-Training at Scale

Reinforcement learning (RL) post-training has proven effective at unlocking reasoning, self-reflection, and tool-use capabilities in large language models. As models extend to omni-modal inputs and agentic multi-turn workflows, RL training systems face three interdependent challenges: heterogeneous data flows, operational robustness at scale, and the staleness -- throughput tradeoff. We present \textbf{Relax} (Reinforcement Engine Leveraging Agentic X-modality), an open-source RL training engine that addresses these challenges through three co-designed architectural layers. First, an \emph{omni-native architecture} builds multimodal support into the full stack -- from data preprocessing and modality-aware parallelism to inference generation -- rather than retrofitting it onto a text-centric pipeline. Second, each RL role runs as an independent, fault-isolated service that can be scaled, recovered, and upgraded without global coordination. Third, service-level decoupling enables asynchronous training via the TransferQueue data bus, where a single staleness parameter smoothly interpolates among on-policy, near-on-policy, and fully asynchronous execution. Relax achieves a 1.20$\times$ end-to-end speedup over veRL on Qwen3-4B on-policy training. Its fully async mode delivers a 1.76$\times$ speedup over colocate on Qwen3-4B and a 2.00$\times$ speedup on Qwen3-Omni-30B, while all modes converge to the same reward level. Relax supports R3 (Rollout Routing Replay)~\cite{ma2025r3} for MoE models with only 1.9\% overhead, compared to 32\% degradation in veRL under the same configuration. It further demonstrates stable omni-modal RL convergence on Qwen3-Omni across image, text, and audio, sustaining over 2{,}000 steps on video without degradation. Relax is available at https://github.com/rednote-ai/Relax.

cs.CL↗

arXiv2026

Detecting low left ventricular ejection fraction from ECG using an interpretable and scalable predictor-driven framework

Low left ventricular ejection fraction (LEF) frequently remains undetected until progression to symptomatic heart failure, underscoring the need for scalable screening strategies. Although artificial intelligence-enabled electrocardiography (AI-ECG) has shown promise, existing approaches rely solely on end-to-end black-box models with limited interpretability or on tabular systems dependent on commercial ECG measurement algorithms with suboptimal performance. We introduced ECG-based Predictor-Driven LEF (ECGPD-LEF), a structured framework that integrates foundation model-derived diagnostic probabilities with interpretable modeling for detecting LEF from ECG. Trained on the benchmark EchoNext dataset comprising 72,475 ECG-echocardiogram pairs and evaluated in predefined independent internal (n=5,442) and external (n=16,017) cohorts, our framework achieved robust discrimination for moderate LEF (internal AUROC 88.4%, F1 64.5%; external AUROC 86.8%, F1 53.6%), consistently outperforming the official end-to-end baseline provided with the benchmark across demographic and clinical subgroups. Interpretability analyses identified high-impact predictors, including normal ECG, incomplete left bundle branch block, and subendocardial injury in anterolateral leads, driving LEF risk estimation. Notably, these predictors independently enabled zero-shot-like inference without task-specific retraining (internal AUROC 75.3-81.0%; external AUROC 71.6-78.6%), indicating that ventricular dysfunction is intrinsically encoded within structured diagnostic probability representations. This framework reconciles predictive performance with mechanistic transparency, supporting scalable enhancement through additional predictors and seamless integration with existing AI-ECG systems.

cs.LG↗

arXiv2026

Supermassive Primordial Black Holes from a Catalyzed Dark Phase Transition for Little Red Dots

JWST has revealed an abundant population of compact, low-metallicity "Little Red Dots" (LRDs) at high redshift, challenging conventional scenarios in which supermassive black holes (SMBHs) grow from stellar-mass seeds. We consider a scenario in which the SMBHs are instead supermassive primordial black holes (SMPBHs), formed directly in a decoupled, subdominant dark sector undergoing a first-order phase transition. Unlike conventional stochastic phase transitions, our mechanism is based on the catalysis by domain walls (DWs): most of the Universe completes the transition rapidly, while rare long-lived false-vacuum domains survive because of DW statistics and collapse into PBHs. This mechanism naturally yields SMPBH seeds with masses up to $M_{\rm PBH}\sim \mathcal{O}(10^{10}) M_\odot$, whose abundance can account for the observed LRD population. It also avoids the usual tensions with phase transition completion, $ΔN_{\rm eff}$, and large curvature perturbations. The dark phase transition simultaneously generates an ultra-low-frequency stochastic gravitational-wave background peaking near the pulsar-timing-array range, providing a test of this dark-sector origin of LRDs.

hep-ph↗

arXiv2026

PRBench: End-to-end Paper Reproduction in Physics Research

AI agents powered by large language models exhibit strong reasoning and problem-solving capabilities, enabling them to assist scientific research tasks such as formula derivation and code generation. However, whether these agents can reliably perform end-to-end reproduction from real scientific papers remains an open question. We introduce PRBench, a benchmark of 30 expert-curated tasks spanning 11 subfields of physics. Each task requires an agent to comprehend the methodology of a published paper, implement the corresponding algorithms from scratch, and produce quantitative results matching the original publication. Agents are provided only with the task instruction and paper content, and operate in a sandboxed execution environment. All tasks are contributed by domain experts from over 20 research groups at the School of Physics, Peking University, each grounded in a real published paper and validated through end-to-end reproduction with verified ground-truth results and detailed scoring rubrics. Using an agentified assessment pipeline, we evaluate a set of coding agents on PRBench and analyze their capabilities across key dimensions of scientific reasoning and execution. The best-performing agent, OpenAI Codex powered by GPT-5.3-Codex, achieves a mean overall score of 34%. All agents exhibit a zero end-to-end callback success rate, with particularly poor performance in data accuracy and code correctness. We further identify systematic failure modes, including errors in formula implementation, inability to debug numerical simulations, and fabrication of output data. Overall, PRBench provides a rigorous benchmark for evaluating progress toward autonomous scientific research.

cs.CL↗

arXiv2026

Eliciting Von Neumann-Morgenstern utility from discrete choices with response error

We develop a preference elicitation method for a Von Neumann-Morgenstern (VNM)-type decision-maker from pairwise comparison data in the presence of response errors. We apply the maximum likelihood estimation (MLE) method to jointly elicit the non-parametric systematic VNM utility function and the scale parameter of the response error, assuming a Gumbel distribution. We incorporate structural preference information known in advance about the decision-maker's risk attitude through linear constraints on the utility function, including monotonicity, concavity, and Lipschitz continuity. Under discretely distributed lotteries, the resulting MLE problem can be reformulated as a convex program. We derive finite-sample error bounds between the MLE and the true parameters, and establish quantitative convergence of the MLE-based VNM utility function to the true utility function in the sense of the Kolmogorov distance under some conditions on the lotteries. These conditions may have potential applications in the design of efficient lotteries for preference elicitation. We further show that the optimization problem maximizing the expected MLE-based VNM utility is robust against the response error and estimation error in a probabilistic sense. Numerical experiments in a portfolio optimization application illustrate and support the theoretical results.

math.OC↗

arXiv2026

Ultralight Scalar Dark Matter with Off-Diagonal Flavor Couplings

Ultralight dark matter can behave as a coherent background field and induce time-dependent modifications of Standard Model parameters. We study a scenario in which a real ultralight scalar $ϕ$ couples off-diagonally to down-type quarks, linking ultralight dark sectors to flavor physics. Working within an effective field theory, we diagonalize the quark mass matrix in a coherent $ϕ$ background and derive analytic expressions for oscillatory shifts in down-type quark masses and CKM parameters. These effects lead to signatures in both the classical regime, where $ϕ$ acts as a background field, and the quantum (particle) regime, where it contributes through on-shell production or off-shell mediation. Using precision flavor measurements, nuclear $β$ decays, atomic clocks, pulsar timing, and meson observables, we derive constraints on the flavor-violating couplings $λ_{ij}$ for $m_ϕ\sim 10^{-24}$--$10^{-12}\,\mathrm{eV}$, highlighting the complementarity of time-domain and flavor probes of ultralight dark sectors.

hep-ph↗

arXiv2026

On the number of non-cyclic subgroups of finite p-groups

Let $G$ be a finite $p$-group and $δ(G)$ denote the number of all non-cyclic subgroups of $G$. In this paper, an upper bound for $δ(G)$ is obtained. Furthermore, we prove that $δ(G)\leq δ(M_p(1, 1, 1) \times C_{p}^{n-3})$ (if $p=2$, then $δ(G)\leq δ(D_8\times C_{2}^{n-3})$), for any non-elementary abelian $p$-group $G$ of order $p^n$.

math.GR↗

arXiv2026

Scalable Text-Embedding-informed Cognitive Diagnosis of Large Language Models

Large language models (LLMs) have achieved remarkable performance on diverse benchmarks, yet existing evaluation practices largely rely on coarse summary metrics that obscure underlying reasoning abilities. In this work, we propose novel methodologies to adapt cognitive diagnosis models (CDMs) in psychometrics to LLM evaluation, enabling fine-grained diagnosis via multidimensional discrete capability profiles and interpretable characterizations of LLM strengths and weaknesses. First, to enable CDM-based evaluation at benchmark scale (more than 1000 items), we propose a scalable method that jointly estimates LLM mastery profiles and the item-attribute Q-matrix, addressing key challenges posed by high-dimensional latent attributes (K > 20), large item pools, and the prohibitive computational cost of existing marginal maximum likelihood-based estimation. Second, we incorporate item-level textual information to construct AI-embedding-informed priors for the Q-matrix, stabilizing high-dimensional estimation while reducing reliance on costly human specification. We develop an efficient stochastic-approximation algorithm to jointly estimate LLM mastery profiles and the Q-matrix that balances data fit with text-embedding-informed priors. Simulation studies demonstrate accurate parameter recovery. An application to the MATH Level 5 benchmark illustrates the practical utility of our method for LLM evaluation and uncovers useful insights into LLMs' fine-grained capabilities.

stat.ME↗