arXiv subjects

Zhiyuan Li

Publications and source records attributed to Zhiyuan Li.

At least 109 records · Page 6Linked to original sources

arXiv2026

A data-driven model reduction approach for backward fractional diffusion-wave equations

In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure in the finite dimensional space. Theoretical results show model reduction approaches constructed for the observation system also work well for the forward problem, which significantly improve the efficiency of solving the inverse problem. Several numerical examples are presented to support our finding.

math.NA↗

arXiv2026

Chip-based f-2f interferometry in periodically tapered lithium niobate nanophotonic waveguides

Nanophotonic supercontinuum generation offers a practical route to chip-based f-2f interferometry by leveraging coexisting chi(2) and chi(3) nonlinearities. In conventional uniform waveguides, the phase-matching bandwidth for second-harmonic generation (SHG) is intrinsically narrow, restricting the spectral overlap factor for heterodyne beating. To address this limitation, we introduce a periodically-tapered nanophotonic waveguide made from MgO-doped, z-cut thin-film lithium niobate for energy-efficient and fabrication-robust f-2f operation. By adiabatically varying the waveguide width within a dual phase-matching window that supports concurrent dispersive wave (DW) emission and SHG, we routinely achieved a broad spectral overlap between the SHG and DW components. This capability enables robust detection of the carrier-envelope offset frequency (fceo) at substantially lower pulse energies than that in uniform-waveguide approaches. We further developed a compact waveguide module that operates reliably under temperature fluctuations and is capable of interfacing with high-repetition-rate (500 MHz) mode-locked lasers, enabling detection and phase locking of fceo with a signal-to-noise ratio of 48 dB. These results highlight the potential of nanophotonic chips for developing compact, field-deployable frequency comb systems.

physics.optics↗

arXiv2026

How VLAs (Really) Work In Open-World Environments

Vision-language-action models (VLAs) have been extensively used in robotics applications, achieving great success in various manipulation problems. More recently, VLAs have been used in long-horizon tasks and evaluated on benchmarks, such as BEHAVIOR1K (B1K), for solving complex household chores. The common metric for measuring progress in such benchmarks is success rate or partial score based on satisfaction of progress-agnostic criteria, meaning only the final states of the objects are considered, regardless of the events that lead to such states. In this paper, we argue that using such evaluation protocols say little about safety aspects of operation and can potentially exaggerate reported performance, undermining core challenges for future real-world deployment. To this end, we conduct a thorough analysis of state-of-the-art models on the B1K Challenge and evaluate policies in terms of robustness via reproducibility and consistency of performance, safety aspects of policies operations, task awareness, and key elements leading to the incompletion of tasks. We then propose evaluation protocols to capture safety violations to better measure the true performance of the policies in more complex and interactive scenarios. At the end, we discuss the limitations of the existing VLAs and motivate future research.

cs.RO↗

arXiv2026

Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture

We investigate in this paper the so-called pointed Shafarevich problem for families of primitive symplectic varieties. More precisely, for any fixed pointed curve $(B, 0)$ and any fixed primitive symplectic variety $X$, among all locally trivial families of $\mathbb{Q}$-factorial and terminal primitive symplectic varieties over $B$ whose fiber over $0$ is isomorphic to $X$, we show that there are only finitely many isomorphism classes of generic fibers. Moreover, assuming semi-ampleness of isotropic nef divisors, which holds true for all hyper-Kähler manifolds of known deformation types, we show that there are only finitely many such projective families up to isomorphism. These results are optimal since we can construct infinitely many pairwise non-isomorphic (not necessarily projective) families of smooth hyper-Kähler varieties over some pointed curve $(B, 0)$ such that they are all isomorphic over the punctured curve $B\backslash \{0\}$ and have isomorphic fibers over the base point $0$.

math.AG↗

arXiv2026

Unpolarized Shafarevich conjectures for hyper-Kähler varieties

The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was proved by Y. She. For hyper-Kähler varieties, which are higher-dimensional analogs of K3 surfaces, Y. André proved the Shafarevich conjecture for hyper-Kähler varieties of a given dimension and admitting a very ample polarization of bounded degree. In this paper, we provide a unification of both results by proving the (unpolarized) Shafarevich conjecture for hyper-Kähler varieties in a given deformation type. We also discuss the cohomological generalization of the Shafarevich conjecture by replacing the good reduction condition by the unramifiedness of the cohomology, where our results are subject to a certain necessary assumption on the faithfulness of the action of the automorphism group on cohomology. In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-Kähler varieties of CM type in a given deformation type defined over a number field with bounded degree. A key to our approach to these results is a uniform Kuga--Satake map, inspired by She's work, and we study its arithmetic properties, which are of independent interest.

math.AG↗

arXiv2026

Precise $^{136}$Xe Double Beta Decay Measurement in PandaX-4T with Implications on the Nuclear Matrix Elements and Majorons

The continuous spectrum of double beta decay ($ββ$) provides a sensitive probe to test the predictions of the standard model and to search for signatures of new physics beyond it. We present a comprehensive analysis of the $^{136}$Xe $ββ$ spectrum utilizing $39.1 \pm 0.7~\textrm{kg}\cdot\textrm{yr}$ of $^{136}$Xe exposure from the PandaX-4T experiment. The analysis yields the most precise measurement to date of the $^{136}$Xe two-neutrino double beta decay ($2νββ$) half-life, $(2.14 \pm 0.05) \times 10^{21}$ years, the uncertainty of which is reduced by a factor of 2 compared to our previous result. We measure the parameter $ξ_{31}^{2ν}$, defined as the ratio between the subleading and leading components of the $^{136}$Xe $2νββ$ nuclear matrix element, to be $0.59^{+0.41}_{-0.38}$, which is consistent with theoretical predictions. We also search for Majoron-emitting modes of $^{136}$Xe $ββ$, establishing the most stringent limit for the spectral index $n=7$.

nucl-ex↗

arXiv2026

Survival or Destruction: Effects of Spheroidal Satellite Collisions on Bars in Milky Way-Like Galaxies

Although stellar bars are prevalent in local galaxies, unbarred galaxies constitute a significant fraction, particularly at high redshifts. While some galaxies are unbarred by nature due to stability against the bar instability, several mechanisms capable of transforming barred galaxies into unbarred systems have also been proposed, such as central mass concentration, specific dark matter halo morphologies and tidal interactions. Regarding galactic interactions, mergers can undoubtedly disrupt bars while potentially destroying the entire disk. However, the effects of pure collisions (non-merging scenarios) on bars remain unclear, with limited existing studies yielding contradictory conclusions. Here we aim to systematically investigate the disruptive effects of collisions on bars hosted by Milky Way-like galaxies using N-body/SPH simulations. We model collisions between the barred galaxy and a spherical intruder, conducting multiple simulations by varying interaction parameters, with mass ratios set at 1:3, 1:5, and 1:15. We find that bars are remarkably robust, with most interactions failing to significantly reduce their strength or pattern speed. Only off-center high-inclination retrograde collisions can effectively destroy bars, while central high-inclination collisions can substantially decrease the pattern speed. Such destruction and deceleration primarily arise from gravitational forces rather than gas-related processes. Notably, compared to collisions occurring along the bar's major axis, those along the minor axis cause greater weakening but can slow the bar's natural deceleration. Furthermore, changes in mass resolution do not significantly affect the results when the resolution is better than ~10^5 Solar mass.

astro-ph.GA↗

arXiv2026

Hyena Operator for Fast Sequential Recommendation

Sequential recommendation models, particularly those based on attention, achieve strong accuracy but incur quadratic complexity, making long user histories prohibitively expensive. Sub-quadratic operators such as Hyena provide efficient alternatives in language modeling, but their potential in recommendation remains underexplored. We argue that Hyena faces challenges in recommendation due to limited representation capacity on sparse, long user sequences. To address these challenges, we propose HyenaRec, a novel sequential recommender that integrates polynomial-based kernel parameterization with gated convolutions. Specifically, we design convolutional kernels using Legendre orthogonal polynomials, which provides a smooth and compact basis for modeling long-term temporal dependencies. A complementary gating mechanism captures fine-grained short-term behavioral bursts, yielding a hybrid architecture that balances global temporal evolution with localized user interests under sparse feedback. This construction enhances expressiveness while scaling linearly with sequence length. Extensive experiments on multiple real-world datasets demonstrate that HyenaRec consistently outperforms Attention-, Recurrent-, and other baselines in ranking accuracy. Moreover, it trains significantly faster (up to 6x speedup), with particularly pronounced advantages on long-sequence scenarios where efficiency is maintained without sacrificing accuracy. These results highlight polynomial-based kernel parameterization as a principled and scalable alternative to attention for sequential recommendation.

cs.IR↗

arXiv2026

Ruling out conventional photoionization models in the closest LINER M31 with CFHT/SITELLE observations

The ionization mechanisms of low-ionization nuclear emission-line regions (LINERs), which are common in the local Universe, have been debated for decades. Our nearest large neighbor, M31, is classified as a LINER based on its optical emission line properties within the central kpc. In this work, we present a detailed photoionization modeling of the circumnuclear ionized gas in M31, explicitly tailored to its well-constrained physical conditions, including the absence of ongoing star formation and a currently inactive active galactic nucleus (AGN). Using spatially resolved CFHT/SITELLE observations, we find that photoionization by hot, evolved low-mass stars distributed throughout the bulge can roughly reproduce the observed radial intensity profiles of Hα, H\b{eta}, and [NII]. However, these models fail to match the observed [OIII] emission, producing radial profiles and [O III]/H\b{eta} ratios that are significantly steeper than observed. This discrepancy indicates a deficit of high-energy ionizing photons in standard stellar photoionization models, even with extended ionizing sources. We explore whether this tension can be alleviated by invoking either a bulge-filling, low-density ionized medium surrounding a denser Hα-emitting disk, or enhanced AGN activity in the recent past. While both scenarios can partially increase the [O III] emission, neither provides a fully satisfactory explanation under physically plausible conditions. Together with our earlier results for M81, these findings underscore persistent challenges in explaining LINER-like emission solely through conventional photoionization mechanisms.

astro-ph.GA↗

arXiv2026

Counting Balanced Triangles on Social Networks With Uncertain Edge Signs

On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs, however in the real-world graphs with ground-truth signs are near non-existent, particularly on a large-scale. In reality, edge signs are inferred via various techniques with differing levels of confidence, meaning the edge signs on these graphs should be modelled with a probability value. In this work, we adapt balanced and unbalanced triangles to a setting with uncertain edge signs and explore the problems of triangle counting and enumeration. We provide a baseline and improved method (leveraging the inherent information provided by the edge probabilities in order to reduce the search space) for fast exact counting and enumeration. We also explore approximate solutions for counting via different sampling approaches, including leveraging insights from our improved exact solution to significantly reduce the runtime of each sample resulting in upwards of two magnitudes more queries executed per second. We evaluate the efficiency of all our solutions as well as examine the effectiveness of our sampling approaches on real-world topological networks with a variety of probability distributions.

cs.DS↗

arXiv2026

On Learning Verifiers and Implications to Chain-of-Thought Reasoning

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which can be checked with a formal verifier, is one approach to addressing this issue. However, currently LLMs are simply not good enough to solve complex problems in a formal way, and even just formalizing an informal problem statement can be challenging. Motivated by this fact, in this work we consider the problem of learning reliable verifiers for natural language Chain-of-Thought reasoning. That is, given a problem statement and step-by-step solution in natural language, the aim of the verifier is to output [Yes] if the reasoning steps in the solution are all valid, and [No] otherwise. In this work we give a formal PAC-learning framework for studying this problem. We propose and analyze several natural verification goals, at different levels of strength, in this framework. We provide sample complexity upper-bounds for learning verifiers satisfying these goals, as well as lower-bound and impossibility results for learning other natural verification objectives without additional assumptions.

cs.LG↗

arXiv2026

SAIL: Self-Amplified Iterative Learning for Diffusion Model Alignment with Minimal Human Feedback

Aligning diffusion models with human preferences remains challenging, particularly when reward models are unavailable or impractical to obtain, and collecting large-scale preference datasets is prohibitively expensive. \textit{This raises a fundamental question: can we achieve effective alignment using only minimal human feedback, without auxiliary reward models, by unlocking the latent capabilities within diffusion models themselves?} In this paper, we propose \textbf{SAIL} (\textbf{S}elf-\textbf{A}mplified \textbf{I}terative \textbf{L}earning), a novel framework that enables diffusion models to act as their own teachers through iterative self-improvement. Starting from a minimal seed set of human-annotated preference pairs, SAIL operates in a closed-loop manner where the model progressively generates diverse samples, self-annotates preferences based on its evolving understanding, and refines itself using this self-augmented dataset. To ensure robust learning and prevent catastrophic forgetting, we introduce a ranked preference mixup strategy that carefully balances exploration with adherence to initial human priors. Extensive experiments demonstrate that SAIL consistently outperforms state-of-the-art methods across multiple benchmarks while using merely 6\% of the preference data required by existing approaches, revealing that diffusion models possess remarkable self-improvement capabilities that, when properly harnessed, can effectively replace both large-scale human annotation and external reward models.

cs.CV↗

arXiv2026

Information-Theoretic Multi-Model Fusion for Target-Oriented Adaptive Sampling in Materials Design

Target-oriented discovery under limited evaluation budgets requires making reliable progress in high-dimensional, heterogeneous design spaces where each new measurement is costly, whether experimental or high-fidelity simulation. We present an information-theoretic framework for target-oriented adaptive sampling that reframes optimization as trajectory discovery: instead of approximating the full response surface, the method maintains and refines a low-entropy information state that concentrates search on target-relevant directions. The approach couples data, model beliefs, and physics/structure priors through dimension-aware information budgeting, adaptive bootstrapped distillation over a heterogeneous surrogate reservoir, and structure-aware candidate manifold analysis with Kalman-inspired multi-model fusion to balance consensus-driven exploitation and disagreement-driven exploration. Evaluated under a single unified protocol without dataset-specific tuning, the framework improves sample efficiency and reliability across 14 single- and multi-objective materials design tasks spanning candidate pools from $600$ to $4 \times 10^6$ and feature dimensions from $10$ to $10^3$, typically reaching top-performing regions within 100 evaluations. Complementary 20-dimensional synthetic benchmarks (Ackley, Rastrigin, Schwefel) further demonstrate robustness to rugged and multimodal landscapes.

cs.LG↗

arXiv2026

Sparsely Supervised Diffusion

Diffusion models have shown remarkable success across a wide range of generative tasks. However, they often suffer from spatially inconsistent generation, arguably due to the inherent locality of their denoising mechanisms. This can yield samples that are locally plausible but globally inconsistent. To mitigate this issue, we propose sparsely supervised learning for diffusion models, a simple yet effective masking strategy that can be implemented with only a few lines of code. Interestingly, the experiments show that it is safe to mask up to 98\% of pixels during diffusion model training. Our method delivers competitive FID scores across experiments and, most importantly, avoids training instability on small datasets. Moreover, the masking strategy reduces memorization and promotes the use of essential contextual information during generation.

cs.LG↗

arXiv2026

Study of Switched Step-size Based Filtered-x NLMS Algorithm for Active Noise Cancellation

While the filtered-x normalized least mean square (FxNLMS) algorithm is widely applied due to its simple structure and easy implementation for active noise control system, it faces two critical limitations: the fixed step-size causes a trade-off between convergence rate and steady-state residual error, and its performance deteriorates significantly in impulsive noise environments. To address the step-size constraint issue, we propose the switched \mbox{step-size} FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the \mbox{mean-square} deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different \mbox{step-sizes}, the optimal step-size for each iteration is selected. Furthermore, to enhance the algorithm's robustness in impulsive noise scenarios, we integrate a robust strategy into the SSS-FxNLMS algorithm, resulting in a robust variant of it. The effectiveness and superiority of the proposed algorithms has been confirmed through computer simulations in different noise scenarios.

cs.IT↗

arXiv2026

SimFuzz: Similarity-guided Block-level Mutation for RISC-V Processor Fuzzing

The Instruction Set Architecture (ISA) defines processor operations and serves as the interface between hardware and software. As an open ISA, RISC-V lowers the barriers to processor design and encourages widespread adoption, but also exposes processors to security risks such as functional bugs. Processor fuzzing is a powerful technique for automatically detecting these bugs. However, existing fuzzing methods suffer from two main limitations. First, their emphasis on redundant test case generation causes them to overlook cross-processor corner cases. Second, they rely too heavily on coverage guidance. Current coverage metrics are biased and inefficient, and become ineffective once coverage growth plateaus. To overcome these limitations, we propose SimFuzz, a fuzzing framework that constructs a high-quality seed corpus from historical bug-triggering inputs and employs similarity-guided, block-level mutation to efficiently explore the processor input space. By introducing instruction similarity, SimFuzz expands the input space around seeds while preserving control-flow structure, enabling deeper exploration without relying on coverage feedback. We evaluate SimFuzz on three widely used open-source RISC-V processors: Rocket, BOOM, and XiangShan, and discover 17 bugs in total, including 14 previously unknown issues, 7 of which have been assigned CVE identifiers. These bugs affect the decode and memory units, cause instruction and data errors, and can lead to kernel instability or system crashes. Experimental results show that SimFuzz achieves up to 73.22% multiplexer coverage on the high-quality seed corpus. Our findings highlight critical security bugs in mainstream RISC-V processors and offer actionable insights for improving functional verification.

cs.CR↗

arXiv2026

AGGC: Adaptive Group Gradient Clipping for Stabilizing Large Language Model Training

To stabilize the training of Large Language Models (LLMs), gradient clipping is a nearly ubiquitous heuristic used to alleviate exploding gradients. However, traditional global norm clipping erroneously presupposes gradient homogeneity across different functional modules, leading to an adverse "spill-over" effect where volatile parameters force unnecessary scaling on stable ones. To overcome this, we propose Adaptive Group-wise Gradient Clipping (AGGC). AGGC partitions parameters into groups based on functional types and regulates each according to its historical behavior using an Exponential Moving Average (EMA). Specifically, it constructs an adaptive interval to simultaneously mitigate gradient explosion and vanishing, while employing a time-dependent scheduling mechanism to balance exploration and convergence. Experiments on LLaMA 2-7B, Mistral-7B, and Gemma-7B models show that AGGC consistently outperforms LoRA and frequently surpasses Full Fine-Tuning. On the GSM8K benchmark, Mistral-7B fine-tuned with AGGC achieves an accuracy of 72.93%, exceeding LoRA's 69.5%. AGGC also effectively stabilizes Reinforcement Learning with Verifiable Rewards (RLVR), enhancing the logic deduction of Qwen 2.5 and Llama 3.2 models. Experimental results demonstrate that AGGC effectively addresses the limitations of traditional gradient clipping methods, particularly in overcoming gradient heterogeneity, by utilizing a modular, adaptive clipping strategy to stabilize the training process. Due to its lightweight design, AGGC can be seamlessly integrated into existing post-training pipelines with negligible overhead.

cs.LG↗

arXiv2026

Wind-fed Supermassive Black Hole Accretion in the Ultracompact Dwarf Galaxy M60-UCD1

Ultracompact dwarf galaxies (UCDs) are thought to be remnants of stripped galactic nuclei, among which a handful are known to host a central supermassive black hole (SMBH). As in stripped nuclear star clusters, the SMBHs in UCDs may be fed by stellar winds from old stellar populations, in the absence of substantial gas reservoirs and galactic inflows. In this work, we investigate such a wind-fed accretion scenario for M60-UCD1, which harbors a confirmed $2\times10^7~M_\odot$ SMBH and exhibits X-ray emission suggestive of SMBH accretion signature. Using three-dimensional hydrodynamical simulations, we simulate the SMBH accreting stellar winds from approximately 1500 asymptotic giant branch stars, and explore the role of ram pressure from the ambient interstellar or intracluster medium. After 5 Myr, the majority of the stellar winds form a cold gas disk ($\sim1000~M_\odot$) within $\sim10~\rm pc$ as well as the SMBH's gravitational sphere of influence. Within the inner $10^4~r_{\rm g}$, this disk transitions into a hot ($\sim10^7-10^9~\rm K$), geometrically thick corona that dominates the X-ray emission. The SMBH achieves an accretion rate of $\sim10^{-5}~M_\odot~\rm yr^{-1}$, yielding an X-ray luminosity of $\sim7\times10^{37}~\rm erg~s^{-1}$, well consistent with observations. Including ram pressure stripping reduces both the accretion rate and luminosity by about a factor of two. Our results suggest that the X-ray counterpart of M60-UCD1 originates from a weakly accreting SMBH fed by stellar winds, with broader insights into the feeding mechanisms of central massive black holes and the origins of X-ray sources in other UCDs.

astro-ph.GA↗