arXiv subjects

Tianyu Zhao

Publications and source records attributed to Tianyu Zhao.

At least 37 records · Page 2Linked to original sources

arXiv2026

Upper bounds on gaps between zeros of $L$-functions

We prove two unconditional upper bounds on the gaps between ordinates of consecutive non-trivial zeros of a general $L$-function $L(s)$. This extends previous work of Hall and Hayman (2000) on the Riemann zeta-function and work of Siegel (1945) on Dirichlet $L$-functions. Interestingly, we observe that while Hall and Hayman's method gives a sharper estimate when the degree of $L(s)$ is sufficiently small compared to the analytic conductor, Siegel's method does better in the other regime.

math.NT↗

arXiv2026

Detection of Lensed Gravitational Waves in the Millihertz Band Using Frequency-Domain Lensing Feature Extraction Network

The space-based gravitational wave (GW) detectors are expected to observe lensed GW events, offering new opportunities for cosmology and fundamental physics.Across the millihertz band, lensing effects transition from the wave-optics regime at lower frequencies to the geometric-optics approximation at higher frequencies.Although traditional GW identification methods, such as matched filtering, are well established and effective, the intense computational resources required motivate the search for more efficient alternatives to accelerate candidate event screening. To address this bottleneck, we introduce a Dual-Channel Lensing feature extraction eXtended Long Short-Term Memory Network (DCL-xLSTM). Unlike conventional recurrent architectures, DCL-xLSTM uses a matrix-valued memory structure and a memory-mixing mechanism to effectively capture amplitude patterns that span the entire millihertz frequency band. Trained on data generated by Point Mass (PM) and Singular Isothermal Sphere (SIS) models accounting for the transition from wave-optics to geometric-optics, the proposed method achieves an area under the curve (AUC) exceeding 0.99, maintaining a true positive rate (TPR) above $98\%$ at a false positive rate (FPR) below $1\%$.The network is robust against variations in signal-to-noise ratio, lens type, and lens mass, establishing its viability as a high-efficiency tool for future space-based GW detection.

astro-ph.IM↗

arXiv2026

Source localization realizes single frame super-resolution for fluorescence imaging

Existing super-resolution microscopy is often constrained by inherent trade-offs between resolution, acquisition speed, phototoxicity, and hardware complexity. Computational post-processing approaches offer a promising alternative, but they typically suffer from linearity distortion, high computational cost, reliance on pre-training data, or reconstruction artifacts. Here, we present Source Localization (SoLo), a novel single-frame super-resolution algorithm for fluorescence imaging without these limitations. Built on the principle of inferring fluorescent source positions via sampling-detection strategy, SoLo achieves non-iterative, parallelizable computation, enabling real-time live-cell imaging with high spatiotemporal resolution. The intensity linearity preservation of SoLo makes it compatible with quantitative analysis such as calcium imaging and fluorescence resonance energy transfer. We further extended this framework to 3D-SoLo for volumetric imaging and nonlinear SoLo (NL-SoLo) for high-density fluorescence fluctuation imaging. With its ease of parameter tuning and compatibility with existing imaging systems, SoLo offers an accessible solution for ordinary labs, enabling diverse biomedical imaging applications.

physics.optics↗

arXiv2026

Unconditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros

We make explicit a result of Selberg on the argument of Dirichlet $L$-functions averaged over non-principal characters modulo a prime $q$. As a corollary, we show for all sufficiently large prime $q$ that the height of the lowest non-trivial zero of the corresponding family of $L$-functions is less than $1075\cdot \frac{2π}{\log q}$. Here the scaling factor $\frac{2π}{\log q}$ is the average spacing between consecutive low-lying zeros with height at most 1, say. We also obtain a lower bound on the proportion of $L$-functions whose first zero lies within a given multiple of the average spacing. These appear to be the first explicit unconditional results of their kinds.

math.NT↗

arXiv2026

FluxMC: Rapid and High-Fidelity Inference for Space-Based Gravitational-Wave Observations

Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional parameter spaces expose the universal vulnerability of conventional methods, e.g., Markov Chain Monte Carlo (MCMC), which struggle with the prohibitive costs of likelihood evaluations and the risk of entrapment in local optima. To resolve this impasse, we introduce FluxMC (Flow-guided Unbiased eXploration Monte Carlo), a machine learning-enhanced framework designed to shift the inference paradigm from blind local search to globally guided transport. It integrates Flow Matching with Parallel Tempering MCMC, effectively combining the global foresight of generative AI with the rigorous asymptotic convergence and local robustness of temperature-based sampling. We showcase the efficacy of this framework through the lens of space-based gravitational-wave (GW) astronomy -- a field representing the frontier of challenging parameter inversion. In the analysis of massive black hole binaries using high-fidelity waveforms (IMRPhenomHM), FluxMC achieves robust convergence in under five hours, whereas traditional Parallel Tempering MCMC fails to converge even after hundreds of hours, yielding high Jensen-Shannon divergences (JSD) of $O(10^{-1})$. Our method reduces the distributional error by two to three orders of magnitude. Furthermore, for computationally efficient models (IMRPhenomD), it eliminates systematic biases caused by local-optima entrapment. Ultimately, FluxMC removes the necessity to compromise between model accuracy and analysis speed, establishing a new computational foundation where scientific discovery is limited only by observational data quality, not by algorithmic capacity.

astro-ph.IM↗

arXiv2026

APPA: Adaptive Preference Pluralistic Alignment for Fair Federated RLHF of LLMs

Aligning large language models (LLMs) with diverse human preferences requires pluralistic alignment, where a single model must respect the values of multiple distinct groups simultaneously. In federated reinforcement learning from human feedback (FedRLHF), these groups align a shared policy without centralizing preference data, which makes fair reward aggregation essential. Existing aggregation methods exhibit clear trade offs: average based aggregation systematically under aligns worst performing groups, while min aggregation prioritizes worst group performance at the cost of overall alignment. We propose APPA, an Adaptive Preference Pluralistic Alignment framework that dynamically reweights group level rewards based on historical alignment rewards. Our approach prioritizes under aligned groups without degrading well aligned ones, while requiring no access to raw preference data. Integrated into a proximal policy optimization (PPO) based FedRLHF pipeline and evaluated on GLOBALQA and OQA across three model families (Gemma 2 2B, Llama 3.2 3B, Qwen3 0.6B), APPA achieves strong fairness alignment trade offs, improving worst group alignment by up to 28% over average aggregation while maintaining higher overall alignment than min aggregation across most configurations.

cs.LG↗

arXiv2026

The limits of bio-molecular modeling with large language models : a cross-scale evaluation

The modeling of bio-molecular system across molecular scales remains a central challenge in scientific research. Large language models (LLMs) are increasingly applied to bio-molecular discovery, yet systematic evaluation across multi-scale biological problems and rigorous assessment of their tool-augmented capabilities remain limited. We reveal a systematic gap between LLM performance and mechanistic understanding through the proposed cross-scale bio-molecular benchmark: BioMol-LLM-Bench, a unified framework comprising 26 downstream tasks that covers 4 distinct difficulty levels, and computational tools are integrated for a more comprehensive evaluation. Evaluation on 13 representative models reveals 4 main findings: chain-of-thought data provides limited benefit and may even reduce performance on biological tasks; hybrid mamba-attention architectures are more effective for long bio-molecular sequences; supervised fine-tuning improves specialization at the cost of generalization; and current LLMs perform well on classification tasks but remain weak on challenging regression tasks. Together, these findings provide practical guidance for future LLM-based modeling of molecular systems.

cs.LG↗

arXiv2026

Conditional estimates on the argument of Dirichlet $L$-functions with applications to low-lying zeros

Under the generalized Riemann hypothesis, we use Beurling-Selberg extremal functions to bound the mean and mean square of the argument of Dirichlet $L$-functions to a large prime modulus $q$. As applications, we give alternative proofs of several results on low-lying zeros of $L(s,χ)$ and obtain a new lower bound on the proportion of $L(s,χ)$ modulo $q$ with zeros close to the central point $s=1/2$. In particular, we show conditionally that for any $β>1/4$, there exist a positive proportion of Dirichlet $L$-functions whose first zero has height less than $β$ times the average spacing between consecutive zeros.

math.NT↗

arXiv2026

Density results for $r$-gaps between zeros of the Riemann zeta-function

Let $0<γ_1\leq γ_2\leq \ldots$ denote the positive ordinates of the non-trivial zeros of the Riemann zeta-function. A result first announced by Selberg states that there exist absolute constants $Θ, \vartheta>0$ such that for each $r\in \mathbb{N}$, \[ \limsup_{n\to \infty}\frac{γ_{n+r}-γ_n}{2πr/\log γ_n}\geq 1+\fracΘ{r^α} \qquad \text{and}\qquad \liminf_{n\to \infty}\frac{γ_{n+r}-γ_n}{2πr/\log γ_n}\leq 1-\frac{\vartheta}{r^α} \] where $α$ may be taken as $2/3$, or as $1/2$ if one assumes the Riemann hypothesis. This was recently proved by Conrey and Turnage-Butterbaugh under RH and by Inoue unconditionally. We prove that in fact a positive proportion of $r$-gaps are large (and small) to the above extent, and we provide explicit estimates for the sizes and proportions of these gaps. In the case $r=1$, this quantitatively improves an unconditional result of Simonič, Trudgian and Turnage-Butterbaugh.

math.NT↗

arXiv2026

Train Short, Inference Long: Training-free Horizon Extension for Autoregressive Video Generation

Autoregressive video diffusion models have emerged as a scalable paradigm for long video generation. However, they often suffer from severe extrapolation failure, where rapid error accumulation leads to significant temporal degradation when extending beyond training horizons. We identify that this failure primarily stems from the spectral bias of 3D positional embeddings and the lack of dynamic priors in noise sampling. To address these issues, we propose FLEX (Frequency-aware Length EXtension), a training-free inference-time framework that bridges the gap between short-term training and long-term inference. FLEX introduces Frequency-aware RoPE Modulation to adaptively interpolate under-trained low-frequency components while extrapolating high-frequency ones to preserve multi-scale temporal discriminability. This is integrated with Antiphase Noise Sampling (ANS) to inject high-frequency dynamic priors and Inference-only Attention Sink to anchor global structure. Extensive evaluations on VBench demonstrate that FLEX significantly outperforms state-of-the-art models at 6x extrapolation (30s duration) and matches the performance of long-video fine-tuned baselines at 12x scale (60s duration). As a plug-and-play augmentation, FLEX seamlessly integrates into existing inference pipelines for horizon extension. It effectively pushes the generation limits of models such as LongLive, supporting consistent and dynamic video synthesis at a 4-minute scale. Project page is available at https://ga-lee.github.io/FLEX_demo.

cs.CV↗

arXiv2026

TAP: A Token-Adaptive Predictor Framework for Training-Free Diffusion Acceleration

Diffusion models achieve strong generative performance but remain slow at inference due to the need for repeated full-model denoising passes. We present Token-Adaptive Predictor (TAP), a training-free, probe-driven framework that adaptively selects a predictor for each token at every sampling step. TAP uses a single full evaluation of the model's first layer as a low-cost probe to compute proxy losses for a compact family of candidate predictors (instantiated primarily with Taylor expansions of varying order and horizon), then assigns each token the predictor with the smallest proxy error. This per-token "probe-then-select" strategy exploits heterogeneous temporal dynamics, requires no additional training, and is compatible with various predictor designs. TAP incurs negligible overhead while enabling large speedups with little or no perceptual quality loss. Extensive experiments across multiple diffusion architectures and generation tasks show that TAP substantially improves the accuracy-efficiency frontier compared to fixed global predictors and caching-only baselines.

cs.CV↗

arXiv2026

Towards Realistic Detection Pipelines of Taiji: New Challenges in Data Analysis and High-Fidelity Simulations of Space-Based Gravitational Wave Antenna

Taiji, a Chinese space-based gravitational wave (GW) detection project, aims to explore the millihertz GW universe with unprecedented sensitivity. By observing astrophysical and cosmological sources, including Galactic binaries, massive black hole binaries, extreme mass-ratio inspirals, and stochastic gravitational wave backgrounds, etc., Taiji is expected to deliver transformative insights into astrophysics, cosmology, and fundamental physics. However, Taiji's data analysis faces unique challenges compared to ground-based detectors like LIGO-Virgo-KAGRA, such as the overlap of numerous signals, extended data durations, more rigorous accuracy requirements for the waveform templates, incompletely characterized noise spectra, non-stationary noises, and various data anomalies. Taking Taiji as a representative example, this paper reviews the data characteristics and data analysis challenges of space-based GW detection, and introduces the second round of Taiji Data Challenge, a collection of simulation datasets designed as a shared platform for resolving these critical issues. This platform distinguishes itself from previous works by the systematic integration of orbital dynamics based on a full drag-free and attitude control simulation, extended noise sources, more complicated and overlapping GW signals, second-generation time-delay interferometry, and the coupling effect of time-varying arm-lengths, etc. Concurrently released is the open-source toolkit Triangle, which offers the capabilities for customized simulation of signals, noises, and other instrumental effects. By taking a step further towards realistic detection, Taiji Data Challenge II and Triangle altogether serve as a new testbed, supporting the development of Taiji's global analysis and end-to-end pipelines, and ultimately bridging the gaps between observation and scientific objectives.

gr-qc↗

arXiv2026

Fast-weight Product Key Memory

Sequence modeling layers in modern language models typically face a trade-off between storage capacity and computational efficiency. While softmax attention offers unbounded storage at prohibitive quadratic cost, linear variants are more efficient but suffer from limited, fixed-size storage. We introduce Fast-weight Product Key Memory (FwPKM), a sparse fast-weight memory layer that resolves this tension. FwPKM updates sparsely activated parameters at both training and inference time using chunk-level gradient descent on a local memory-rewrite objective. This performs Test-Time Training (TTT)-style gradient updates on activated slots in a sparse memory, enabling rapid memorization and retrieval of many new key-value associations while keeping per-token compute low and fixed. Experiments show that FwPKM functions as an effective episodic memory that complements the semantic memory of standard modules, yielding significant perplexity reductions on long-context datasets. Notably, in Needle-in-a-Haystack evaluations, FwPKM generalizes to 128K-token contexts despite being trained on only 4K-token sequences.

cs.CL↗

arXiv2025

DrVoice: Parallel Speech-Text Voice Conversation Model via Dual-Resolution Speech Representations

Recent studies on end-to-end (E2E) speech generation with large language models (LLMs) have attracted significant community attention, with multiple works extending text-based LLMs to generate discrete speech tokens. Existing E2E approaches primarily fall into two categories: (1) Methods that generate discrete speech tokens independently without incorporating them into the LLM's autoregressive process, resulting in text generation being unaware of concurrent speech synthesis. (2) Models that generate interleaved or parallel speech-text tokens through joint autoregressive modeling, enabling mutual modality awareness during generation. This paper presents DrVoice, a parallel speech-text voice conversation model based on joint autoregressive modeling, featuring dual-resolution speech representations. Notably, while current methods utilize mainly 12.5Hz input audio representation, our proposed dual-resolution mechanism reduces the input frequency for the LLM to 5Hz, significantly reducing computational cost and alleviating the frequency discrepancy between speech and text tokens and in turn better exploiting LLMs' capabilities. Experimental results demonstrate that DrVoice-7B establishes new state-of-the-art (SOTA) on prominent speech benchmarks including OpenAudioBench, VoiceBench, UltraEval-Audio and Big Bench Audio, making it a leading open-source speech foundation model in ~7B models.

cs.CL↗

arXiv2025

A Systematic Evaluation of Preference Aggregation in Federated RLHF for Pluralistic Alignment of LLMs

This paper addresses the challenge of aligning large language models (LLMs) with diverse human preferences within federated learning (FL) environments, where standard methods often fail to adequately represent diverse viewpoints. We introduce a comprehensive evaluation framework that systematically assesses the trade-off between alignment quality and fairness when using different aggregation strategies for human preferences. In our federated setting, each group locally evaluates rollouts and produces reward signals, and the server aggregates these group-level rewards without accessing any raw data. Specifically, we evaluate standard reward aggregation techniques (min, max, and average) and introduce a novel adaptive scheme that dynamically adjusts preference weights based on a group's historical alignment performance. Our experiments on question-answering (Q/A) tasks using a PPO-based RLHF pipeline demonstrate that our adaptive approach consistently achieves superior fairness while maintaining competitive alignment scores. This work offers a robust methodology for evaluating LLM behavior across diverse populations and provides a practical solution for developing truly pluralistic and fairly aligned models.

cs.CL↗

arXiv2025

Task-Specific Sparse Feature Masks for Molecular Toxicity Prediction with Chemical Language Models

Reliable in silico molecular toxicity prediction is a cornerstone of modern drug discovery, offering a scalable alternative to experimental screening. However, the black-box nature of state-of-the-art models remains a significant barrier to adoption, as high-stakes safety decisions demand verifiable structural insights alongside predictive performance. To address this, we propose a novel multi-task learning (MTL) framework designed to jointly enhance accuracy and interpretability. Our architecture integrates a shared chemical language model with task-specific attention modules. By imposing an L1 sparsity penalty on these modules, the framework is constrained to focus on a minimal set of salient molecular fragments for each distinct toxicity endpoint. The resulting framework is trained end-to-end and is readily adaptable to various transformer-based backbones. Evaluated on the ClinTox, SIDER, and Tox21 benchmark datasets, our approach consistently outperforms both single-task and standard MTL baselines. Crucially, the sparse attention weights provide chemically intuitive visualizations that reveal the specific fragments influencing predictions, thereby enhancing insight into the model's decision-making process.

cs.CE↗

arXiv2025

Reinforcement Learning Teachers of Test Time Scaling

Training reasoning language models (LMs) with reinforcement learning (RL) for one-hot correctness inherently relies on the LM being able to explore and solve its task with some chance at initialization. Furthermore, a key use case of reasoning LMs is to act as teachers for distilling new students and cold-starting future RL iterations rather than being deployed themselves. From these considerations, we introduce a new framework that avoids RL's exploration challenge by training a new class of Reinforcement-Learned Teachers (RLTs) focused on yielding the most effective downstream distillation. RLTs are prompted with both the question and solution to each problem, and tasked to simply "connect-the-dots" with detailed explanations tailored for their students. We train RLTs with dense rewards obtained by feeding each explanation to the student and testing its understanding of the problem's solution. In practice, the raw outputs of a 7B RLT provide higher final performance on competition and graduate-level tasks than existing distillation and cold-starting pipelines that collect and postprocess the reasoning traces of orders of magnitude larger LMs. Furthermore, RLTs maintain their effectiveness when training larger students and when applied zero-shot to out-of-distribution tasks, unlocking new levels of efficiency and re-usability for the RL reasoning framework. Code available at: https://github.com/SakanaAI/RLT

cs.LG↗

arXiv2025

Reinforcement Learning with Rubric Anchors

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing Large Language Models (LLMs), exemplified by the success of OpenAI's o-series. In RLVR, rewards are derived from verifiable signals-such as passing unit tests in code generation or matching correct answers in mathematical reasoning. While effective, this requirement largely confines RLVR to domains with automatically checkable outcomes. To overcome this, we extend the RLVR paradigm to open-ended tasks by integrating rubric-based rewards, where carefully designed rubrics serve as structured, model-interpretable criteria for automatic scoring of subjective outputs. We construct, to our knowledge, the largest rubric reward system to date, with over 10,000 rubrics from humans, LLMs, or a hybrid human-LLM collaboration. Implementing rubric-based RL is challenging; we tackle these issues with a clear framework and present an open-sourced Qwen-30B-A3B model with notable gains: 1) With only 5K+ samples, our system improves by +5.2% on open-ended benchmarks (especially humanities), outperforming a 671B DeepSeek-V3 model by +2.4%, while preserving general and reasoning abilities. 2) Our method provides fine-grained stylistic control, using rubrics as anchors to mitigate the "AI-like" tone and produce more human-like, expressive responses. We share key lessons in rubric construction, data selection, and training, and discuss limitations and future releases.

cs.AI↗