arXiv subjects

Zihao Qi

Publications and source records attributed to Zihao Qi.

At least 19 recordsLinked to original sources

arXiv2026

A Graph Signal Processing Perspective on Numerical Sequence Representations in LLM In-Context Learning

Pretrained large language models (LLMs) have demonstrated in-context learning (ICL) capabilities for numerical inference over sequences serialized as text. Prior work has identified and characterized this form of numerical inference primarily through output-level evaluations such as prediction error. However, how numerical information is organized within LLM representations remains much less understood. To study this internal organization, we adopt a graph signal processing perspective in which attention induces a weighted graph over tokens, while token hidden states define signals on its nodes. Quantitative graph-spectral diagnostics and qualitative token-graph visualizations reveal that representations become more clearly differentiated by input dynamical complexity as context length increases. Simpler inputs produce attention-induced token graphs with stronger global connectivity and smoother, spectrally concentrated hidden-state signals, whereas more complex inputs produce more localized graphs and hidden-state signals with broader spectral support and greater high-frequency energy. Together, these findings point to systematic, context-dependent internal signatures associated with numerical ICL that are conserved across model families.

cs.LG↗

arXiv2026

Stability of closed characteristics and invariant sets on star-shaped hypersurfaces

This paper focuses on the stability of a closed characteristic and invariant sets on compact star shaped hypersurfaces in ${\bf R}^{2n}$ with finitely many simple closed characteristics. Firstly, it is proved that all closed characteristics are non-hyperbolic, under some index condition weaker than dynamical convexity. Secondly, when $n=3$, it is proved that all closed characteristics are elliptic when their number is exactly $3$, under non-degeneracy and some minor index condition. Lastly, it is proved that all closed characteristics are either degenerate at some iteration or not locally maximal under dynamical convexity.

math.SG↗

arXiv2026

Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders

Neural Quantum States (NQS) are a remarkably expressive class of variational ans\"atze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.

quant-ph↗

arXiv2026

Universal Neural Propagator: Learning Time Evolution in Many-Body Quantum Systems

Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.

quant-ph↗

arXiv2026

Symmetric operads of GK-dimension one

We prove that there is no finitely generated symmetric operad of Gelfand-Kirillov dimension strictly between 1 and 2 that answers an open question posted in 2020. We also classify finitely generated prime symmetric operads of Gelfand-Kirillov dimension 1.

math.RA↗

arXiv2026

Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{PT}$ Symmetry Breaking

Exactly solvable dissipative models provide an analytical tool for studying the relaxation dynamics in open quantum systems. In this work, we study an exactly solvable model based on an anisotropic variant of the Yao-Lee spin-orbital model, with dissipation acting in the spin sector. We map Liouvillian dynamics to fermions hopping in a doubled Hilbert space under a non-Hermitian Hamiltonian and demonstrate the model's exact solvability. We analyze the model's strong and weak symmetries, which protect an exponentially large manifold of non-equilibrium steady states, establishing the system as a physically feasible dissipative spin liquid. Furthermore, we analyze the transient dynamics in a translationally invariant sector and discover that the single-particle Liouvillian spectrum hosts an exceptional ring in momentum space. We map out a characteristic $\mathcal{PT}$ symmetry breaking transition driven by the dissipation strength, which governs the crossover from oscillatory to decaying relaxation of physical observables. Our work provides a physically motivated, solvable setting for exploring the coexistence of dissipative spin liquid physics and Liouvillian spectral singularities.

quant-ph↗

arXiv2026

Neural Operator Quantum State: A Foundation Model for Quantum Dynamics

Capturing the dynamics of quantum many-body systems under time-dependent driving protocols is a central challenge for numerical simulations. Existing methods such as tensor networks and time-dependent neural quantum states, however, must be re-run for every protocol. In this work, we introduce the Neural Operator Quantum State (NOQS) as a foundation model for quantum dynamics. Rather than solving the Schrödinger equation for individual trajectories, our approach aims to \emph{learn the solution operator} that maps entire driving protocols to time-evolved quantum states. Once trained, the NOQS predicts time evolution under unseen protocols in a single forward pass, requiring no additional optimization. We validate NOQS on the two-dimensional Ising model with time-dependent longitudinal and transverse fields, demonstrating accurate prediction not only for unseen in-distribution protocols, but also for qualitatively different, out-of-distribution functional forms of driving. Further, a single NOQS model can be transferred between different temporal resolutions, and can be efficiently fine-tuned with sparse experimental measurements to improve predictions across all observables at negligible cost. Our work introduces a new paradigm for quantum dynamics simulation and provides a practical computational-experimental interface for driven quantum systems.

quant-ph↗

arXiv2026

A Mamba-based Perceptual Loss Function for Learning-based UGC Transcoding

In user-generated content (UGC) transcoding, source videos typically suffer various degradations due to prior compression, editing, or suboptimal capture conditions. Consequently, existing video compression paradigms that solely optimize for fidelity relative to the reference become suboptimal, as they force the codec to replicate the inherent artifacts of the non-pristine source. To address this, we propose a novel perceptually inspired loss function for learning-based UGC video transcoding that redefines the role of the reference video, shifting it from a ground-truth pixel anchor to an informative contextual guide. Specifically, we train a lightweight neural quality model based on a Selective Structured State-Space Model (Mamba) optimized using a weakly-supervised Siamese ranking strategy. The proposed model is then integrated into the rate-distortion optimization (RDO) process of two neural video codecs (DCVC and HiNeRV) as a loss function, aiming to generate reconstructed content with improved perceptual quality. Our experiments demonstrate that this framework achieves substantial coding gains over both autoencoder and implicit neural representation-based baselines, with 8.46% and 12.89% BD-rate savings, respectively.

eess.IV↗

arXiv2026

Closed Reeb orbits on contact type hypersurfaces in $T^*S^n$

In this paper, it is proved that under dynamically convex condition, there exist at least $[\frac{n+1}{2}]$ closed Reeb orbits on a closed contact type hypersurface in $T^*S^n$ enclosing the zero section and bounding a simply connected Liouville domain. Furthermore, if the contact form is non-degenerate and has finitely many closed Reeb orbits, then there exist at least two irrationally elliptic closed Reeb orbits.

math.SG↗

arXiv2026

CGSA: Class-Guided Slot-Aware Adaptation for Source-Free Object Detection

Source-Free Domain Adaptive Object Detection (SF-DAOD) aims to adapt a detector trained on a labeled source domain to an unlabeled target domain without retaining any source data. Despite recent progress, most popular approaches focus on tuning pseudo-label thresholds or refining the teacher-student framework, while overlooking object-level structural cues within cross-domain data. In this work, we present CGSA, the first framework that brings Object-Centric Learning (OCL) into SF-DAOD by integrating slot-aware adaptation into the DETR-based detector. Specifically, our approach integrates a Hierarchical Slot Awareness (HSA) module into the detector to progressively disentangle images into slot representations that act as visual priors. These slots are then guided toward class semantics via a Class-Guided Slot Contrast (CGSC) module, maintaining semantic consistency and prompting domain-invariant adaptation. Extensive experiments on multiple cross-domain datasets demonstrate that our approach outperforms previous SF-DAOD methods, with theoretical derivations and experimental analysis further demonstrating the effectiveness of the proposed components and the framework, thereby indicating the promise of object-centric design in privacy-sensitive adaptation scenarios. Code is released at https://github.com/Michael-McQueen/CGSA.

cs.CV↗

arXiv2026

Attention in Krylov Space: Transformer-Based Extrapolation of Lanczos Coefficients

The Universal Operator Growth Hypothesis formulates time evolution of operators through Lanczos coefficients. In practice, however, numerical instability and memory cost limit the number of coefficients that can be exactly computed. In response to these challenges, the standard approach relies on fitting early coefficients to asymptotic forms, but such procedures can miss subleading, history-dependent structures in the coefficients that subsequently affect reconstructed observables. In this work, we treat the Lanczos coefficients as a causal time sequence and introduce a transformer-based model to autoregressively predict future Lanczos coefficients from short prefixes. For classical and quantum chaotic systems, our model outperforms asymptotic fits in both coefficient extrapolation and physical observable reconstruction, and achieves an order-of-magnitude reduction in error. The model also accurately extrapolates coefficients in integrable regimes, where no universal asymptotic fit exists. Remarkably, our model transfers across system sizes: it can be trained on smaller systems and then be used to extrapolate coefficients on a larger system \emph{without retraining}. By probing the learned attention patterns and performing targeted attention ablations, we identify portions of the coefficient history that are most influential for accurate forecasts. Our results demonstrate that modern sequence models can serve as practical surrogates for probing operator dynamics deep in Krylov space, where brute-force Lanczos iteration can be computationally prohibitive.

quant-ph↗

arXiv2025

Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains challenging due to the exponential growth of Hilbert space dimension and rapid spreading of entanglement. In this work, we introduce Fourier neural operators (FNOs) as an efficient, accurate, and scalable framework for nonequilibrium quantum dynamics. Parameterized in Fourier space, FNO naturally captures temporal correlations and remains minimally dependent on discretization of time. We demonstrate the versatility of FNO through three complementary learning paradigms: reconstructing effective Floquet Hamiltonians, predicting expectation values of local observables, and learning quantum information spreading. For each learning task, FNO achieves remarkable accuracy, while attaining a significant speedup, compared to exact numerical methods. Moreover, FNO possesses capabilities beyond that of conventional methods, such as predicting all local observables from a subset of measurements without information about the Hamiltonian, as well as extrapolating beyond the time window provided by training data, enabling access to observables and operator-spreading dynamics that might be beyond the coherence time. By employing a spatially local basis, we argue that the computational cost of FNOs scales only polynomially with the system size. Our results establish FNO as a versatile and scalable computation framework that integrates numerical simulations and experimental data seamlessly, with direct implications for extracting meaningful physics from measurements by near-term quantum computers.

quant-ph↗

arXiv2025

Operads with trivial $\mathbb{A}$-actions

We study operads with trivial $\mathbb{A}$-actions and prove an equivalence between the category of $\mathbb{A}$-trivial operads and that of pseudo-graded-Perm associative algebras. As a consequence, we show that finitely generated $\mathbb{A}$-trivial operads are right noetherian of integral Gelfand-Kirillov dimension and that every element in a prime $\mathbb{A}$-trivial operad is central.

math.RA↗

arXiv2024

BVI-UGC: A Video Quality Database for User-Generated Content Transcoding

In recent years, user-generated content (UGC) has become one of the major video types consumed via streaming networks. Numerous research contributions have focused on assessing its visual quality through subjective tests and objective modeling. In most cases, objective assessments are based on a no-reference scenario, where the corresponding reference content is assumed not to be available. However, full-reference video quality assessment is also important for UGC in the delivery pipeline, particularly associated with the video transcoding process. In this context, we present a new UGC video quality database, BVI-UGC, for user-generated content transcoding, which contains 60 (non-pristine) reference videos and 1,080 test sequences. In this work, we simulated the creation of non-pristine reference sequences (with a wide range of compression distortions), typical of content uploaded to UGC platforms for transcoding. A comprehensive crowdsourced subjective study was then conducted involving more than 3,500 human participants. Based on this collected subjective data, we benchmarked the performance of 10 full-reference and 11 no-reference quality metrics. Our results demonstrate the poor performance (SROCC values are lower than 0.6) of these metrics in predicting the perceptual quality of UGC in two different scenarios (with or without a reference).

eess.IV↗

arXiv2024

Real-space topological invariant for time-quasiperiodic Majoranas

When subjected to quasiperiodic driving protocols, superconducting systems have been found to harbor robust time-quasiperiodic Majorana modes, extending the concept beyond static and Floquet systems. However, the presence of incommensurate driving frequencies results in dense energy spectra, rendering conventional methods of defining topological invariants based on band structure inadequate. In this work, we introduce a real-space topological invariant capable of identifying time-quasiperiodic Majoranas by leveraging the system's spectral localizer, which integrates information from both Hamiltonian and position operators. Drawing insights from non-Hermitian physics, we establish criteria for constructing the localizer and elucidate the robustness of this invariant in the presence of dense spectra. Our numerical simulations, focusing on a Kitaev chain driven by two incommensurate frequencies, validate the efficacy of our approach.

cond-mat.mes-hall↗

arXiv2024

AIS 2024 Challenge on Video Quality Assessment of User-Generated Content: Methods and Results

This paper reviews the AIS 2024 Video Quality Assessment (VQA) Challenge, focused on User-Generated Content (UGC). The aim of this challenge is to gather deep learning-based methods capable of estimating the perceptual quality of UGC videos. The user-generated videos from the YouTube UGC Dataset include diverse content (sports, games, lyrics, anime, etc.), quality and resolutions. The proposed methods must process 30 FHD frames under 1 second. In the challenge, a total of 102 participants registered, and 15 submitted code and models. The performance of the top-5 submissions is reviewed and provided here as a survey of diverse deep models for efficient video quality assessment of user-generated content.

cs.CV↗

arXiv2024

Formal deformations, cohomology theory and $L_\infty[1]$-structures for differential Lie algebras of arbitrary weight

Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version of higher derived brackets. The equivalence between $L_\infty[1]$-structures for absolute and relative differential Lie algebras are established. Formal deformations and abelian extensions are interpreted by using lower degree cohomology groups. Also we introduce the homotopy differential Lie algebras. In a forthcoming paper, we will show that the operad of homotopy (relative) differential Lie algebras is the minimal model of the operad of (relative) differential Lie algebras.

math.RA↗

arXiv2024

Multiple closed geodesics on Finsler $3$-dimensional sphere

In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on $S^3$ with exactly four prime closed geodesics. And then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler $S^3$. In this paper, we proved this conjecture for bumpy Finsler $S^{3}$ if the Morse index of any prime closed geodesic is nonzero.

math.SG↗