arXiv subjects

Na Zhang

Publications and source records attributed to Na Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Joint Distributional Copula Regression for Insurance Claim Frequency and Severity via Boosting

In this paper, we introduce a model-based boosting approach for fitting structured additive distributional copula regression models for bivariate responses, with particular emphasis on jointly modeling insurance claim frequency and severity. The approach uses regression-type base learners, such as linear terms and splines with low degrees of freedom. It builds on generalized additive models for location, scale, and shape (GAMLSS), which extend generalized additive models (GAMs) by allowing multiple distributional parameters, rather than only the conditional mean, to depend on covariates. The structured additive predictors make the model inherently interpretable, offering greater transparency and auditability than black-box approaches. These features are particularly relevant in regulated actuarial settings and applications requiring explainable artificial intelligence. By estimating the entire conditional joint distribution, the framework also enables insurance practitioners to examine conditional quantiles, tail behavior, and prediction intervals of risks. The copula component captures dependence between claim frequency and severity and allows practitioners to investigate how this dependence varies with policyholder characteristics, potentially improving predictive performance. Moreover, by incorporating modern machine-learning techniques, specifically boosting, the proposed model improves prediction accuracy while retaining interpretability. We assess the proposed framework using both simulated and real data. The results demonstrate its ability to recover the true covariate effects on the marginal distributional parameters and the dependence structure, select informative variables, and achieve predictive performance competitive with standard benchmark models. We also illustrate how to interpret the fitted model.

stat.ML↗

arXiv2026

Linear Self-Symmetries of Inverse-Based S-boxes: Generic Rigidity and Applications

Finite-field inversion is a basic nonlinear building block in the design of S-boxes for symmetric cryptography. In inverse-based S-boxes, finite-field inversion is often combined with linear or affine layers that may preserve or destroy algebraic symmetries of the inverse function. We study how often nontrivial linear self-symmetries remain as the outer invertible linear transformation varies over $GL_n(\mathbb F_2)$. Using the classification of two-sided linear equivalences of inversion, we reduce the problem to semilinear conjugacy and centralizer estimates. We obtain matching upper and lower bounds for the probability that a nontrivial linear self-symmetry remains, and these bounds determine its leading quadratic exponent. This exponent is governed by the smallest prime divisor of the extension degree. Thus the decay rate depends on the arithmetic of the field extension and not only on its dimension. As cryptographic applications, we provide a practical rigidity criterion, prove that the full AES S-box has no nontrivial linear self-symmetry, and illustrate the broader relevance of the framework through ARIA and Vision.

cs.CR↗

arXiv2026

Longitudinal fMRI reveals multi-network reconfiguration and a recurrent frontoparietal shift across rest and task states during adult aging

Functional connectivity changes across adult aging, but most evidence is cross-sectional, and covariance-based connectivity depends on blood oxygenation level dependent (BOLD) fluctuation amplitude. Covariance decline can reflect changing fluctuation amplitude, and its interpretation may depend on whether normalization uses signal amplitude or includes estimated noise. It is also unclear which longitudinal changes recur across brain states. We analyzed 852 adults (baseline age 36-89 years) from the Aging Adult Brain Connectome with repeated functional MRI (fMRI) during rest, inhibitory control, associative memory, and visual-motor processing (2,220 sessions; median follow-up 5.5 years). Baseline age and elapsed follow-up were modeled separately. Ten cortical networks were tested jointly across states, and covariance was normalized either by released signal amplitude or by a candidate total amplitude reconstructed from released signal and noise amplitudes. Native common covariance declined by 7-11% per 5 years, while signal pair amplitude declined by 9% on average across states, significantly more than estimated noise pair amplitude. Under signal normalization, the relative balance among networks reconfigured over follow-up and differed across states, and the frontoparietal network shifted positively relative to the other nine networks in all four states, by 5-8% per 5 years. The estimated common trajectory was near zero under signal normalization but declined by 4-7% per 5 years under candidate total normalization. The network reconfiguration and the positive frontoparietal-relative direction persisted under both. Within-person coupling between the frontoparietal shift and fluid cognition was not detected. Adult aging thus combines normalization-dependent overall change with a state-dependent redistribution among networks that includes a recurrent frontoparietal shift.

q-bio.NC↗

arXiv2026

Basis Rigidity of the AES S-box and Generic Rigidity of Inversion under Affine Transformations

The AES S-box is constructed from finite field inversion followed by a fixed affine transformation. Since inversion possesses intrinsic Frobenius symmetries among its coordinate realizations, we study how these basis symmetries are altered by outer affine transformations. We first develop a deterministic rigidity criterion for transformed inversion and apply it to the AES S-box. This shows that the linear part of the AES S-box affine transformation alone makes the transformed inversion map basis rigid. We then investigate the corresponding generic problem when the outer invertible linear transformation varies. The existence of a nontrivial linear stabilizer is reduced to a conjugacy problem for semilinear candidates arising from two sided linear equivalences of inversion, which we characterize in terms of relative norms and Frobenius orbits. We also determine the dimensions of the associated centralizer algebras exactly. These structural results imply that, for a uniformly chosen outer linear transformation, the probability that the linear stabilizer is nontrivial is bounded by $2^{-Ω(n^2)}$, with sharper finite dimensional bounds obtained from the exact conjugacy condition. Computational experiments independently verify the AES rigidity result, the conjugacy and centralizer formulas, and the finite dimensional estimates in small dimensions.

cs.CR↗

arXiv2026

Representation Redundancy and Structural Complexity in Finite-Field Inversion

The representation chosen for a mathematical operation can affect both its algebraic form and its empirical learning difficulty. We study this phenomenon for inversion over $\mathbb F_{2^n}$, with field elements expressed in varying ordered $\mathbb F_2$-bases. We prove that two ordered bases induce the same coordinate inversion map if and only if they belong to the same Galois orbit. Since every orbit has size $n$, the correspondence between ordered bases and distinct inversion maps is exactly $n$-to-one. We then analyze three Boolean formulations of inversion. The reference formulation has algebraic degree $n-1$ and joint ANF leap $1$, the mixed representation formulation has degree $2(n-1)$ and joint ANF leap $2$, and the complete raw formulation has degree at most $3(n-1)$ and joint ANF leap at least $n$. Exhaustive computations agree with the theoretical results and bounds in the cases considered. Controlled experiments with multilayer perceptrons show the same ordering in learning difficulty, while Galois orbit redundancy provides only a limited generalization benefit under the tested conditions. These results show that exact redundancy among representations can coexist with changes in Boolean structure and learning behavior when the representation is exposed as part of the input.

cs.LG↗

arXiv2026

From Symmetry to Invariance: Learning Galois Equivalent Representations in Finite Fields

Neural networks can learn algebraic operations from finite examples, but it remains unclear whether this ability transfers across mathematically equivalent representations of the same operation. We study this question through multiplication in finite fields under changes of basis. The Galois action organizes basis representations into orbits, and bases in the same orbit induce the same coordinate multiplication map. This structure allows us to separate learning multiplication from transferring it to basis representations that are not used for training. We examine several ways of providing or recovering the relevant orbit structure, including invariant labels, basis matrices, orbit recognition, and algebraic decomposition. Our main approach trains a model to predict the Galois action between basis representations. Repeated applications of the learned transformation are then used to construct a canonical representative for each orbit, which supports multiplication on held-out bases through exact canonical matching. This provides a concrete mechanism for converting a learned algebraic symmetry into an invariant representation that can be used for transfer.

cs.LG↗

arXiv2026

An Inexact Riemannian Proximal Momentum Variance-Reduced Method: Complexity Bounds and KL Sequential Convergence

We develop a unified analysis of inexact stochastic Riemannian proximal optimization for finite-sum nonsmooth composite problems over compact embedded submanifolds. The framework accommodates variance-reduced gradient estimators, projected momentum, and inexact tangent-space proximal solves under a single conditional error-dissipation condition, verified for projection-based SVRG, SARAH/SPIDER, SAGA, and SAG. A computable Fenchel-dual residual criterion, with tolerance prescribed before sampling and inner iterations, enables explicit control of the inner work. We establish conditional expected descent, subsequential stationarity, and an $O(ε^{-2})$ outer complexity. With SARAH/SPIDER and accumulative regularization, iRPMVR attains $O(n+\sqrt n\,ε^{-2})$ component-gradient and $O(ε^{-3})$ proximal-operator complexities. We further develop an abstract KL principle for conditional expected descent with memory and summable tails using only the ordinary pointwise KL property. A counterexample shows that a power-type expected-KL implication used in earlier stochastic analyses can fail. The principle yields almost-sure finite length, whole-sequence convergence, and deterministic KL rates.

math.OC↗

arXiv2026

Electronic phonon-induced magnetism in moiré Mott-Wigner crystals

We show that magnetism in moiré Mott-Wigner crystals can be induced by the collective vibration of electrons around their equilibrium positions (i.e., electronic phonons), even without spin interactions between electrons. Due to a geometric valley-orbit coupling from the Berry phase effect, the zero-point energy of electronic phonons reaches minimum when electrons are fully valley polarized. This leads to a spontaneous magnetization when below a critical temperature. We also propose to engineer the magnetism through the photoexcitation of chiral electronic phonons.

cond-mat.mes-hall↗

arXiv2026

Evaluating the Generation Capabilities of Large Chinese Language Models

This paper unveils CG-Eval, the first-ever comprehensive and automated evaluation framework designed for assessing the generative capabilities of large Chinese language models across a spectrum of academic disciplines. CG-Eval stands out for its automated process, which critically assesses models based on their proficiency in generating precise and contextually relevant responses to a diverse array of questions within six key domains: Science and Engineering, Humanities and Social Sciences, Mathematical Calculations, Medical Practitioner Qualification Examination, Judicial Examination, and Certified Public Accountant Examination. Alongside this, we introduce Gscore, an innovative composite index developed from a weighted sum of multiple metrics. Gscore uniquely automates the quality measurement of a model's text generation against reference standards, providing a detailed and nuanced assessment of model performance. This automation not only enhances the efficiency and scalability of the evaluation process but also ensures objective and consistent assessment across various models. The detailed test data and results, highlighting the robust capabilities and comparative performance of the evaluated models, are accessible at http://cgeval.besteasy.com/.

cs.CL↗

arXiv2026

HorizonBench: Long-Horizon Personalization with Evolving Preferences

User preferences evolve across months of interaction, and tracking them requires inferring when a stated preference has been changed by a subsequent life event. We define this problem as long-horizon personalization and observe that progress on it is limited by data availability and measurement, with no existing resource providing both naturalistic long-horizon interactions and the ground-truth provenance needed to diagnose why models fail. We introduce a data generator that produces conversations from a structured mental state graph, yielding ground-truth provenance for every preference change across 6-month timelines, and from it construct HorizonBench, a benchmark of 4,245 items from 360 simulated users with 6-month conversation histories averaging ~4,300 turns and ~163K tokens. HorizonBench provides a testbed for long-context modeling, memory-augmented architectures, theory-of-mind reasoning, and user modeling. Across 25 frontier models, the best model reaches 52.8% and most score at or below the 20% chance baseline. When these models err on evolved preferences, over a third of the time they select the user's originally stated value without tracking the updated user state. This belief-update failure persists across context lengths and expression explicitness levels, identifying state-tracking capability as the primary bottleneck for long-horizon personalization.

cs.CL↗

arXiv2026

Long-Horizon Plan Execution in Large Tool Spaces through Entropy-Guided Branching

Large Language Models (LLMs) have significantly advanced tool-augmented agents, enabling autonomous reasoning via API interactions. However, executing multi-step tasks within massive tool libraries remains challenging due to two critical bottlenecks: (1) the absence of rigorous, plan-level evaluation frameworks and (2) the computational demand of exploring vast decision spaces stemming from large toolsets and long-horizon planning. To bridge these gaps, we first introduce SLATE (Synthetic Large-scale API Toolkit for E-commerce), a large-scale context-aware benchmark designed for the automated assessment of tool-integrated agents. Unlike static metrics, SLATE accommodates diverse yet functionally valid execution trajectories, revealing that current agents struggle with self-correction and search efficiency. Motivated by these findings, we next propose Entropy-Guided Branching (EGB), an uncertainty-aware search algorithm that dynamically expands decision branches where predictive entropy is high. EGB optimizes the exploration-exploitation trade-off, significantly enhancing both task success rates and computational efficiency. Extensive experiments on SLATE demonstrate that our dual contribution provides a robust foundation for developing reliable and scalable LLM agents in tool-rich environments.

cs.AI↗

arXiv2026

CharacterFlywheel: Scaling Iterative Improvement of Engaging and Steerable LLMs in Production

This report presents CharacterFlywheel, an iterative flywheel process for improving large language models (LLMs) in production social chat applications across Instagram, WhatsApp, and Messenger. Starting from LLaMA 3.1, we refined models across 15 generations using data from both internal and external real-user traffic. Through continuous deployments from July 2024 to April 2025, we conducted controlled 7-day A/B tests showing consistent engagement improvements: 7 of 8 newly deployed models demonstrated positive lift over the baseline, with the strongest performers achieving up to 8.8% improvement in engagement breadth and 19.4% in engagement depth. We also observed substantial gains in steerability, with instruction following increasing from 59.2% to 84.8% and instruction violations decreasing from 26.6% to 5.8%. We detail the CharacterFlywheel process which integrates data curation, reward modeling to estimate and interpolate the landscape of engagement metrics, supervised fine-tuning (SFT), reinforcement learning (RL), and both offline and online evaluation to ensure reliable progress at each optimization step. We also discuss our methods for overfitting prevention and navigating production dynamics at scale. These contributions advance the scientific rigor and understanding of LLMs in social applications serving millions of users.

cs.CL↗

arXiv2026

Paying Less Generalization Tax: A Cross-Domain Generalization Study of RL Training for LLM Agents

Generalist LLM agents are often post-trained on a narrow set of environments but deployed across far broader, unseen domains. In this work, we investigate the challenge of agentic post-training when the eventual test domains are unknown. Specifically, we analyze which properties of reinforcement learning (RL) environments and modeling choices have the greatest influence on out-of-domain performance. First, we identify two environment axes that strongly correlate with cross-domain generalization: (i) state information richness, i.e., the amount of information for the agent to process from the state, and (ii) planning complexity, estimated via goal reachability and trajectory length under a base policy. Notably, domain realism and text-level similarity are not the primary factors; for instance, the simple grid-world domain Sokoban leads to even stronger generalization in SciWorld than the more realistic ALFWorld. Motivated by these findings, we further show that increasing state information richness alone can already effectively improve cross-domain robustness. We propose a randomization technique, which is low-overhead and broadly applicable: add small amounts of distractive goal-irrelevant features to the state to make it richer without altering the task. Beyond environment-side properties, we also examine several modeling choices: (a) SFT warmup or mid-training helps prevent catastrophic forgetting during RL but undermines generalization to domains that are not included in the mid-training datamix; and (b) turning on step-by-step thinking during RL, while not always improving in-domain performance, plays a crucial role in preserving generalization.

cs.AI↗

arXiv2026

Rotate Your Character: Revisiting Video Diffusion Models for High-Quality 3D Character Generation

Generating high-quality 3D characters from single images remains a significant challenge in digital content creation, particularly due to complex body poses and self-occlusion. In this paper, we present RCM (Rotate your Character Model), an advanced image-to-video diffusion framework tailored for high-quality novel view synthesis (NVS) and 3D character generation. Compared to existing diffusion-based approaches, RCM offers several key advantages: (1) transferring characters with any complex poses into a canonical pose, enabling consistent novel view synthesis across the entire viewing orbit, (2) high-resolution orbital video generation at 1024x1024 resolution, (3) controllable observation positions given different initial camera poses, and (4) multi-view conditioning supporting up to 4 input images, accommodating diverse user scenarios. Extensive experiments demonstrate that RCM outperforms state-of-the-art methods in both novel view synthesis and 3D generation quality.

cs.CV↗

arXiv2025

A min-max reformulation and proximal algorithms for a class of structured nonsmooth fractional optimization problems

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the second part is the difference of a smooth nonconvex function and a nonsmooth convex function. This model problem has many important applications, for example, the scale-invariant sparse signal recovery in signal processing. However, the existing methods for fractional programs are not suitable for solving this problem due to its special structure. We first present a novel nonfractional min-max reformulation for the original fractional program and show the connections between their global (local) optimal solutions and stationary points. Based on the reformulation, we propose an alternating maximization proximal descent algorithm and show its subsequential convergence towards a critical point of the original fractional program under a mild assumption. Moreover, we prove that the proposed algorithm can find an $ε$-critical point of the considered problem within $\mathcal{O}(ε^{-2})$ iterations. By further assuming the Kurdyka-Łojasiewicz (KL) property of an auxiliary function, we also establish the convergence of the entire solution sequence generated by the proposed algorithm. Finally, some numerical experiments on the $L_1/L_2$ least squares problem and scale-invariant sparse signal recovery are conducted to demonstrate the efficiency of the proposed method.

math.OC↗

arXiv2025

An efficient proximal algorithm for squared L1 over L2 regularized sparse recovery

In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal method for solving a general fractional optimization problem which has the squared $L_1/L_2$ regularized model as a special case. We prove that any accumulation point of the solution sequence generated by the proposed method is a critical point of the fractional optimization problem. Under additional KL assumptions on some potential function, we establish the sequential convergence of the proposed method. When this method is specialized to the squared $L_1/L_2$ regularized model, the proximal operator involved in each iteration admits a simple closed form solution that can be computed with very low computational cost. Furthermore, for each of the three concrete models, the solution sequence generated by this specialized algorithm converges to a critical point. Numerical experiments demonstrate the superiority of the proposed algorithm for sparse recovery based on squared $L_1/L_2$ regularization.

math.OC↗

arXiv2025

Proximal methods for structured nonsmooth optimization over Riemannian submanifolds

In this paper, we consider a class of structured nonsmooth optimization problems over an embedded submanifold of a Euclidean space, where the first part of the objective is the sum of a difference-of-convex (DC) function and a smooth function, while the remaining part is a weakly convex function over a smooth function. This model problem has many important applications in machine learning and scientific computing, for example, the sparse Fisher discriminant analysis. We propose a manifold proximal-gradient-subgradient algorithm (MPGSA) and show that under mild conditions any accumulation point of the solution sequence generated by it is a critical point of the underlying problem. By assuming the Kurdyka-Łojasiewicz property of an auxiliary function, we further establish the convergence of the full sequence generated by MPGSA under some suitable conditions. When the second component of the DC function involved is the maximum of finite continuously differentiable convex functions, we also propose an enhanced MPGSA with guaranteed subsequential convergence to a lifted B-stationary points of the optimization problem. Finally, some preliminary numerical experiments are conducted to illustrate the efficiency of the proposed algorithms.

math.OC↗

arXiv2025

Machine Learning Integrated Near-Infrared Surface-Enhanced Raman Spectroscopy for Accurate Strain-Level Virus Identification

Strain-level identification of viruses is critical for effective public health responses to potential outbreaks, yet current diagnostic methods often lack the necessary speed or sensitivity. Surface-enhanced Raman spectroscopy (SERS) offers great potential for fast and precise virus clarification through unique vibrational fingerprints of biological components. However, existing protocols typically operate outside of the tissue's transparent near-infrared (NIR) window, and are further limited by the intrinsic complexity of clinical viral samples, which complicates spectral analysis and recognition. Here, we report an artificial intelligence (AI)-empowered NIR-SERS platform that integrates machine learning with a rationally designed hybrid substrate: gold nanostars (AuNSt) coupled with gold-coated carbon nanotube arrays (AuCNT). This architecture generates highly localized plasmonic hot spots resonant tuned to NIR excitation, as confirmed by electron energy-loss spectroscopy (EELS), enabling effective signal amplification from viral components. Our system and protocols provide accurate classification of respiratory viruses, including influenza viruses and coronaviruses, not only at the type and subtype levels, but also the more challenging strain level. This approach overcomes the plasmonic mismatch in conventional SERS and the lack of generalizability in AI-driven diagnostics. It shows promise for enhancing rapid virus detection and identification of novel strains and outbreak response capabilities, thus potentially addressing critical challenges in global public health preparedness.

physics.chem-ph↗