arXiv subjects

Jian Li

Publications and source records attributed to Jian Li.

At least 19 recordsLinked to original sources

arXiv2026

Stabilization of hydroelastic waves in deep water

We consider the stabilization of two-dimensional periodic hydroelastic waves in deep water beneath a massless nonlinear Cosserat sheet by means of a localized pres- sure feedback. For sufficiently regular solutions, under an explicit condition relating gravity, flexural rigidity and the localization profile, we prove a uniform spacetime estimate and a localized dissipation observability inequality. As a consequence, the hydroelastic Hamiltonian decays quantitatively as long as the solution remains in a small geometric regime. The proof combines an energy dissipation identity with a nonlinear multiplier method adapted to the infinite-depth geometry, together with a coercivity analysis of the Cosserat bending energy.

math.AP↗

arXiv2026

Hydroelastic waves near shear flows

In this paper, we prove that symmetric, doubly-periodic, three-dimensional hydroelastic waves of small amplitude, bifurcating from a non-uniform shear flow, are necessarily two-dimensional to leading order. A detailed analysis of the solvability condition at quadratic order reveals that all Fourier coefficients with transverse dependence vanish identically. The dimensional reduction is controlled entirely by the vertical structure of the shear flow and is robust under changes to the dynamic boundary condition.

math.AP↗

arXiv2026

Typical dynamical properties of operators on $\ell_p$

We investigate the typical dynamical properties of hypercyclic operators in $\mathcal{L}_M(X)$, the set of all bounded linear operators on $X$ whose norms are at most $M$, when $X=\ell_p$, $1< p<\infty$. We show that, with respect to SOT$^*$, a typical operator $T\in \mathcal{L}_M(X)$ is weakly mixing, is weakly disjoint from a given hypercyclic operator $S$, is not topologically ergodic, and satisfies $(T,T^2,\dotsc,T^k)$ is disjoint hypercyclic for any $k\geq 2$. We also show that the similar typical dynamical properties for the concrete family $\mathcal{M}=\{I+B_w\in \mathcal{L}(X)\colon w\in c_0(\mathbb{Z})\}$, endowed with the norm topology, where $B_w$ is a bilateral weighted backward shift.

math.FA↗

arXiv2026

Feature-Adaptive Fusion in Hybrid Quantum-Classical Neural Networks for Robust Biomedical Image Classification

Hybrid quantum-classical neural networks provide a promising approach for incorporating quantum circuits into machine learning in the noisy intermediate-scale quantum regime. However, existing hybrid models often rely on fixed or globally shared fusion strategies, which may limit their ability to exploit complementary information carried by quantum branches, especially under distribution shifts. In this work, we propose a Feature-Adaptive Fusion Hybrid Quantum-Classical Neural Network (FAF-HQNN) for biomedical image classification. The model combines a classical deep feature encoder with a variational quantum circuit (VQC) and introduces a feature-adaptive fusion mechanism to dynamically weight classical and quantum predictions. We evaluate FAF-HQNN on two MedMNIST benchmarks, PathMNIST and BloodMNIST, under clean and corrupted test conditions. FAF-HQNN achieves the strongest overall performance on clean data among the compared methods and shows improved robustness under Gaussian, salt-and-pepper, and Poisson corruptions. Further analysis of circuit layout, measurement basis, and depth shows that even shallow variational quantum circuits can provide useful complementary information. These results demonstrate that feature-adaptive fusion is an effective strategy for improving accuracy and robustness in hybrid quantum-classical models for biomedical image classification.

quant-ph↗

arXiv2026

When Bias Pretends to Be Truth: How Spurious Correlations Undermine Hallucination Detection in LLMs

Despite substantial advances, large language models (LLMs) continue to exhibit hallucinations, generating plausible yet incorrect responses. In this paper, we highlight a critical yet previously underexplored class of hallucinations driven by spurious correlations -- superficial but statistically prominent associations between features (e.g., surnames) and attributes (e.g., nationality) present in the training data. We demonstrate that these spurious correlations induce hallucinations that are confidently generated, immune to model scaling, evade current detection methods, and persist even after refusal fine-tuning. Through systematically controlled synthetic experiments and empirical evaluations on state-of-the-art open-source and proprietary LLMs (including GPT-5), we show that existing hallucination detection methods, such as confidence-based filtering and inner-state probing, fundamentally fail in the presence of spurious correlations. Our theoretical analysis further elucidates why these statistical biases intrinsically undermine confidence-based detection techniques. Our findings thus emphasize the urgent need for new approaches explicitly designed to address hallucinations caused by spurious correlations.

cs.CL↗

arXiv2026

On the Residual Scaling of Looped Transformers: Stability and Transferability

Looped (weight-tied) Transformers apply a shared residual block $N$ times ($h \leftarrow h + \varepsilon\,f(h)$, same $f$ at each step), increasing effective depth without adding parameters. Prior depth-scaling analyses prescribe $\varepsilon = 1/\!\sqrt{L}$ for depth-$L$ residual networks. We show that this is insufficient for looped architectures: weight sharing makes residual updates correlated across iterations, requiring the stronger scaling $\varepsilon = 1/N$. For multi-layer blocks ($L$ unique layers looped $N$ times), we derive a factored parameterization $\varepsilon = λ/(N\!\sqrt{L})$ that separates the two sources of growth: $1/N$ controls the within-layer loop correlation, and $1/\!\sqrt{L}$ controls the across-layer variance. A key consequence is that the optimal learning rate depends only on the number of unique layers $L$, not on the loop count $N$, enabling direct hyperparameter transfer from small to large $N$ without retuning. Experiments on looped Transformers confirm that $1/N$ scaling improves trainability and yields better loss than $1/\!\sqrt{N}$ scaling across loop counts.

cs.LG↗

arXiv2026

AdaRoPE: Not All Attention Heads Should Rotate and Scale Equally

Rotary Position Embedding (RoPE) is widely adopted in Transformers to encode positional information, yet standard implementations enforce a uniform frequency schedule and scaling across all attention heads. Using simplified retrieval tasks and length generalization scenarios, we show -- both empirically and theoretically -- that heads with different functional roles require distinct frequency ranges and attention scaling factors to operate effectively. Ignoring this structure leads to suboptimal utilization of embedding dimensions and degraded performance, particularly under long-context settings. To address these limitations, we propose AdaRoPE, which equips each attention head with learnable rotation frequencies and attention scaling factors. Pretrained LLMs with AdaRoPE consistently outperform existing RoPE variants, including partial RoPE and NoPE baselines. For context extension, we further show that uniform frequency and attention scaling, used in methods such as YaRN, are suboptimal. By applying head-specific scaling, AdaRoPE enables better context extension while better preserving short-context performance in both the extrapolation setting and the long-context continued pretraining setting. These results highlight the importance of optimizing rotary position embedding at the level of individual attention heads.

cs.AI↗

arXiv2026

SMELT: Scaling Laws for Compute-Matched MoE Looped Transformers

Looped Transformers increase effective depth by iterating a shared block of layers, but most evaluations compare at fixed model size, conflating architectural advantage with extra FLOPs. We study looping on Mixture-of-Experts Transformers while closely matching per-token FLOPs, total non-embedding parameters, and KV cache. Through a series of ablations, we arrive at a recipe we call SMELT (Sparse MoE Transformer, middle layers Loop Twice), which loops the middle half of layers twice while matching the unlooped Baseline on all three budgets. We scale SMELT across four sizes up to 54B non-embedding parameters and fit a separate Chinchilla-style scaling law for each architecture. SMELT's loss drops faster with compute, saving 6.8--18.0\% of training FLOPs on the compute-optimal frontier. The advantage transfers to downstream benchmarks beyond what validation loss predicts, is largest on Code, and grows with sample length and the number of in-context examples. Mechanistic analysis shows that the second visit reduces the attention sink and redirects mass toward content-relevant tokens, an inductive bias that may underlie the observed performance gains. These results show that looping can improve Transformers even under budget matching, offering a practical recipe that turns depth reuse into measurable gains.

cs.LG↗

arXiv2026

Quantum convolutional neural network for predicting nuclear charge radii

Quantum machine learning has the potential to become a new tool for understanding complex nuclear structures. In this work, we apply a hybrid quantum convolutional neural network (QCNN) to nuclear charge-radius prediction for the first time, aiming to explore the feasibility of quantum machine learning in nuclear-physics data analysis. Based on a classical convolutional neural network (CNN) framework, a small variational quantum convolutional filter is introduced as a quantum feature map to extract local correlations on the nuclear chart. The QCNN shows promising predictive accuracy and training stability, and provides a reliable description of the charge-radius evolution along several representative isotopic chains. These results support further investigation of quantum convolutional architectures for nuclear-structure data analysis.

nucl-th↗

arXiv2026

Gaussian Belief Propagation Network for Depth Completion

Depth completion aims to predict a dense depth map from a color image with sparse depth measurements. Although deep learning methods have achieved state-of-the-art (SOTA), effectively handling the sparse and irregular nature of input depth data in deep networks remains a significant challenge, often limiting performance, especially under high sparsity. To overcome this limitation, we introduce the Gaussian Belief Propagation Network (GBPN), a novel hybrid framework synergistically integrating deep learning with probabilistic graphical models for end-to-end depth completion. Specifically, a scene-specific Markov Random Field (MRF) is dynamically constructed by the Graphical Model Construction Network (GMCN), and then inferred via Gaussian Belief Propagation (GBP) to yield the dense depth distribution. Crucially, the GMCN learns to construct not only the data-dependent potentials of MRF but also its structure by predicting adaptive non-local edges, enabling the capture of complex, long-range spatial dependencies. Furthermore, we enhance GBP with a serial \& parallel message passing scheme, designed for effective information propagation, particularly from sparse measurements. Extensive experiments demonstrate that GBPN achieves SOTA performance on the NYUv2 and KITTI benchmarks. Evaluations across varying sparsity levels, sparsity patterns, and datasets highlight GBPN's superior performance, notable robustness, and generalizable capability.

cs.CV↗

arXiv2026

Weak disjointness of hypercyclic operators

We study the weak disjointness of hypercyclic operators to refine the classifications of hypercyclic operators. We establish an analogue of the Weiss-Akin-Glasner Theorem from topological dynamics within the framework of linear dynamics, which gives a characterization of the weak disjointness of each class of mixing operators with respect to a given Furstenberg family. The key ingredient is an analogue of the Weiss-Akin-Glasner Lemma from topological dynamics, which gives a characterization of subsets of non-negative integers which can be realized by the return time sets of mixing operators with respect to a given Furstenberg family. We also provide several examples to distinguish some classes of hypercyclic operators and end with the characterization of the mixing property with respect to Furstenberg families of direct sums of backward shifts on Fréchet sequence spaces.

math.DS↗

arXiv2026

Non-Hermitian Topology and Boundary Jordan Chains with Generalized Chiral Symmetry

We study a generalization of chiral symmetry applicable to non-Hermitian systems and its topological consequences on one-dimensional chains. We find a rich family of topological phases characterized not by a single winding number, but a vector of them. More importantly, we uncover a novel type of bulk-boundary correspondence, where the vector of winding numbers in the bulk corresponds to the set of Jordan chains of various length at the boundary. This in turn leads to highly unconventional chiral-charge distributions on both edges. Our work extends the topological classification of the non-Hermitian AIII class along a new axis.

cond-mat.mes-hall↗

arXiv2026

A semi-analytical Ring-Arc model for Plutino perturbations

Neptune's 2:3 mean motion resonance induces an asymmetric spatial distribution of Plutinos. We previously proposed a 9000-point-mass arc model that successfully captures the resulting influence on planetary ephemerides. However, integrating thousands of point masses involves significant computational cost. In this paper, to more efficiently simulate the total perturbation of Plutinos, we develop a semi-analytical Ring-Arc model described by gravitational potentials. This model consists of an outer ring and two inner arcs, representing the resonant spatial distribution of Plutinos. The model parameters are derived from observed Plutinos and theoretical sampling, yielding consistent structures. Numerical simulations show that the perturbations on the Sun-Neptune and Sun-Saturn distances from the semi-analytical Ring-Arc model agree with those from the 9000-point-mass arc model within 4\% over 50 years, while outperforming a simple ring model in comparison with the bias-corrected Plutino population. Our semi-analytical approach preserves the dynamical characteristics while significantly enhancing computational efficiency, offering a state-of-the-art tool for ephemeris modelling.

astro-ph.EP↗

arXiv2026

ArtSociety: Multi-Agent Multimodal Collaboration for Art Emotion Understanding

The AffectiveArt Multidimensional Art Emotion Understanding task asks to jointly predict an artwork's fine-grained emotion (12 classes, 1549:1 head-to-tail ratio), binary valence/arousal, and five attribute-grounded descriptions -- sub-tasks that exhibit strong empirical trade-offs, so the single-model solutions we tried do not jointly optimize all of them well. We present ArtSociety, a multi-agent framework that assembles heterogeneous multimodal experts -- a DINOv2-Giant vision agent (A1), a scene-grounded CoT fine-tuned MLLM (A2), and three closed-source reasoning agents (A3-A5) -- and coordinates them with two training-free controllers: (i) a rare-class-aware voting arbiter that lowers the agreement threshold for tail emotions, exploiting decorrelated error patterns across agent families; and (ii) a description-first reasoning agent whose DESCRIBE-then-CLASSIFY chain of thought forces visual evidence before label commitment, yielding near-perfect grounded descriptions. A task-routing policy directs the hard emotion task to the full five-agent ensemble while assigning the near-saturated valence/arousal and generative description tasks to the single strongest reasoning agent. On the official test set (1,000 artworks), ArtSociety achieves an Overall Score of 0.8870 (Classification 0.7789, Description 0.9952). An eleven-variant ablation study reveals that, once method and scale saturate at around 0.76, the decisive gains come from agent collaboration and data-side supervision -- a 30B MoE model trained on older data does not outperform an 8B model trained on better data. Code is available at https://github.com/swordlidev/ArtSociety

cs.CV↗

arXiv2026

Automatic Item Generation for Personality Situational Judgment Tests with Large Language Models

Personality assessment through situational judgment tests (SJTs) offers unique advantages over traditional Likert-type self-report scales, yet their development remains labor-intensive, time-consuming, and heavily dependent on subject matter experts. Recent advances in large language models (LLMs) have shown promise for automatic item generation (AIG). Building on these developments, the present study focuses on developing and evaluating a structured and generalizable framework for automatically generating personality SJTs, using GPT-4 and ChatGPT-5 as empirical examples. Three studies were conducted. Study 1 systematically compared the effects of prompt design and temperature settings on the content validity of LLM-generated items to develop an effective and stable LLM-based AIG approach for personality SJT. Results showed that optimized prompts and a temperature of 1.0 achieved the best balance of creativity and accuracy on GPT-4. Study 2 examined the cross-model generalizability and reproducibility of this automated SJT generation approach through multiple rounds. The results showed that the approach consistently produced reproducible and high-quality items on ChatGPT-5. Study 3 evaluated the psychometric properties of LLM-generated SJTs covering five facets of the Big Five personality traits. Results demonstrated satisfactory reliability and validity across most facets, though limitations were observed in the convergent validity of the compliance facet and certain aspects of criterion-related validity. These findings provide robust evidence that the proposed LLM-based AIG approach can produce culturally appropriate and psychometrically sound SJTs with efficiency comparable to or exceeding traditional methods.

cs.CL↗

arXiv2026

Summarization is Not Dead Yet

The progress of large language models (LLMs) has fueled claims that model-generated summaries rival or even surpass human-written references, raising questions about whether summarization remains an open research problem. We re-examine this narrative through a multi-track evaluation covering diverse datasets and state-of-the-art LLMs, combining controlled human assessment, bias-mitigated LLM-as-Judge protocols, factuality verification against external knowledge, and corpus-level linguistic analysis. Our findings reveal a more nuanced landscape in which human references continue to demonstrate advantages in informativeness and faithfulness, whereas LLM outputs are preferred mainly for surface-level coherence and fluency. Factuality verification indicates that human references remain more reliable, particularly for claims involving reasoning or synthesis, and linguistic analysis uncovers a pattern of stylistic homogeneity across different models. These observations suggest that current LLMs have raised the floor of summarization quality, but the ceiling of their performance remains below human capabilities.

cs.CL↗

arXiv2026

Fast radio bursts, magnetars and earthquakes: their "family feud"?

Fast radio bursts (FRBs) are millisecond-duration cosmic transients whose origin remains elusive. Competing models invoke either earthquake-like processes or flare-like mechanisms. To discriminate between these scenarios, we develop a novel diagnostic, the Pincus-Lyapunov diagram (PLD), to characterize the energetic transients in the stochasticity-chaos phase space. We compile burst sequences from five representative FRBs (FRB 20121102A, FRB 20190520B, FRB 20201124A, FRB 20220912A, and FRB 20240114A), together with those from magnetar flares (SGR J1550$-$5418, SGR J0501+4516, SGR 1806$-$20, SGR 1900+14, and SGR J1935+2154), pulsar glitches, solar flares, and earthquakes, and map them onto the PLD for comparative analysis. The resulting diagram shows that FRBs occupy a distinct region of the phase space. Specifically, a permutation test reveals a statistically significant difference in the distributions of magnetar flares and pulsar glitches compared to those of repeating FRBs ($p$-value $\simeq 0.05$). To examine whether temporal variations in source activity can shift a repeater's position in this phase space, we analyze the time evolution of the most prolific repeater, FRB~20240114A. For this repeating FRB, both Pincus Index and Lyapunov Exponent demonstrate statistically stable behaviour over the eight-month observation session, with Augmented Dickey--Fuller tests yielding $p \simeq 1.78\times10^{-3}$ and $9.91\times10^{-3}$, respectively. By assembling the most comprehensive dataset to date, our work indicates that the trigger mechanisms of repeating FRBs are likely to be distinct from those driving magnetar flares, pulsar glitches, solar flares, and earthquakes.

astro-ph.HE↗

arXiv2026

Density properties of orbits for a hypercyclic operator on a Banach space

We study density properties of orbits for a hypercyclic operator $T$ on a separable Banach space $X$, and show that exactly one of the following four cases holds: (1) every vector in $X$ is asymptotic to zero with density one; (2) generic vectors in $X$ are distributionally irregular of type $1$; (3) generic vectors in $X$ are distributionally irregular of type $2\frac{1}{2}$ and no hypercyclic vector is distributionally irregular of type $1$; (4) every hypercyclic vector in $X$ is divergent to infinity with density one. We also present some examples concerned with weighted backward shifts on $\ell^p$ to show that all the above four cases can occur. Furthermore, we show that similar results hold for $C_0$-semigroups.

math.FA↗