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Zhiyuan Yang

Publications and source records attributed to Zhiyuan Yang.

At least 19 recordsLinked to original sources
arXiv2026

On the largest prime factors less than $y$ of consecutive shifted primes

For an integer $n > 1$, let $P^+(n)$ be the largest prime factor of $n$, and let $P_y^+(n)$ denote the largest prime factor of $n$ not exceeding $y$. One of Erdős and Turán's conjectures asserts that the asymptotic density of integers $n$ satisfying $P^+(n) 0$ such that \begin{align*} \#\{p\leq x:P_y^+(p-1)<P_y^+(p+1)\}\geq(h(α)+o(1))π(x). \end{align*} In particular, the function $h$ satisfies $\lim_{α\rightarrow 0^+}h(α)=1/2$. Similar result also holds for $\#\{n\leq x:P_y^+(n)<P_y^+(n+1)\}$, which improves a previous result $\lim_{α\rightarrow 0^+} h(α)=1/4$ due to Wang (2019).

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arXiv2026

AWLS: Advantage-Weighted Latent Steering for One-Step Generative Robotic Manipulation Policies

Human-collected real-world robotic manipulation demonstrations often contain mixed-quality trajectories, including hesitant, indirect, or inefficient action segments. While diffusion- and flow-based policies can model such multimodal data, standard behavior cloning (BC) assigns equal likelihood to all demonstrated actions and may therefore reproduce suboptimal modes. Offline RL value estimates offer a natural signal for biasing policies toward higher-value behavioral modes, but directly fine-tuning the generative policy or using critic gradients for policy steering can amplify critic errors and induce prior drift. We propose Advantage-Weighted Latent Steering (AWLS), an offline post-training method for improving frozen one-step generative manipulation policies without updating their decoders. AWLS learns a residual noise shaper, an observation-conditioned residual correction to the policy's latent noise, and trains it with an advantage-weighted action reconstruction objective. The advantages are detached, scale-normalized, and used only as supervised weights on demonstrated actions, avoiding critic-gradient policy updates while preserving fast single-step inference. We further introduce a rollout-free decoder-sensitivity criterion for selecting pretrained checkpoints that remain responsive to latent-noise perturbations. Experiments on simulated and real-world robotic manipulation tasks with clean and mixed-quality demonstrations show that AWLS improves over the frozen base policy while limiting drift from the pretrained behavior prior. Project page: https://awls-corl2026.github.io/

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arXiv2026

On Relative Biexactness of Amalgamated Free Product von Neumann Algebras

Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective von Neumann subalgebra $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. When $M_1$ and $M_2$ are injective but not necessarily tracial, we further show that $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to the amalgam $B$, and if $B$ is mixing in each of $M_1$ and $M_2$, $M_{1}\overline{*}_{B}M_{2}$ itself is biexact. We also develop a new criterion for upgrading relative biexactness and obtain structural decomposition and subalgebra absorption results for amalgamated free product von Neumann algebras that generalize the group case.

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arXiv2026

FR-VLA: Implicit Force Reasoning VLA for Contact-Rich Manipulation

Integrating force awareness into Vision-Language-Action (VLA) models involves not merely encoding wrench measurements as an additional modality, but determining when and how strongly physical interaction should influence robot action generation. Existing VLAs that use force typically inject it through a fixed pathway, without explicitly determining when it is relevant to the current action. This calls for an intermediate force relevance mechanism inside the VLA, in which visual-language context estimates the relevance of physical feedback to the current task before force enters the action pathway. FR-VLA addresses this gap with a Vision-Language Force-Reasoning Model that uses learnable force query tokens to derive a force admission signal grounded in visual-language context, and uses this signal to modulate an external tokenized force pathway for action generation. In real-world experiments on five contact-rich tasks across two robotic platforms, FR-VLA achieves the highest mean success rate over six evaluated stages, and trajectory visualizations show that its force admission varies with the interaction phase.

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arXiv2026

Noise-Invariant Spatial Encoding for 3D Manipulation Policies under Depth Corruption

3D manipulation policies derive actions from explicit scene geometry rather than color images alone, enabling them to reason over metric distances, object relations, and robot-scene reachability. This geometric interface is also a vulnerability: commodity RGB-D sensors return missing measurements, boundary artifacts, and plausible but wrong surfaces around transparent, reflective, thin, or textureless objects. We study this failure under realistic depth corruption and observe a sharp depth-noise cliff across modern 3D policies, even when they are trained with matched noisy depth. This residual gap motivates a spatial-encoding approach: corrupted depth becomes entangled with the token coordinates and geometry features consumed by the action expert. We propose Noise-Invariant Spatial Encoding (NISE), a 3D policy architecture that learns trustworthy geometry features even facing imperfect depth. NISE uses Geometric Cross-View Self-Supervision to shape shared policy features with calibrated multi-view depth, and Gaussian Marginalized 3D Attention to carry position uncertainty into deployed attention rather than treating every lifted token as exact. Across simulated benchmarks with sensor-realistic corruption and real-robot tasks involving transparent and reflective materials, NISE improves depth-noise robustness while preserving clean-depth performance, supporting 3D policies designed for commodity RGB-D deployment rather than clean-depth benchmarks alone.

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arXiv2026

Note on the largest prime factors of consecutive integers

In this paper, we give an alternative proof of Tao-Teräväinen's results by showing \begin{align*} &\#\{n\leq x:P^+(n-1) \max_iP^+(n+a_i)\}\gg x,\\&\#\{n\leq x:P^+(n-1)>P^+(n) \max_iP^+(n+a_i)\}\gg x, \end{align*} where the $a_i$ are at most finite in number, with $|a_i| = O(1)$. We also obtain some comparison results for five numbers under the Elliott-Halberstam conjecture for friable integers. For any $\varepsilon>0$, we also show \begin{align*} &\#\left\{n\leq x:1\leq \frac{P^+(n+1)}{P^+(n)}<1+\varepsilon\right\}\gg_\varepsilon \frac{x}{\log x}, \end{align*} which improves a previous result $\gg x(\log x)^{-50}$ due to S. Kim (2020).

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arXiv2026

UA-Bench: Benchmarking Large Audio-Language Models on Underwater Acoustic Recognition

Large audio-language models (LALMs) are fast becoming a general interface to sound, yet how far their broad pretraining carries into specialized domains remains largely open. Vessel monitoring, maritime safety, and ocean sensing all depend on recognizing underwater signals, but to our knowledge LALMs have not been systematically evaluated on them. Annotated recordings are costly to collect, and a faithful synthetic alternative has to bring together many interacting factors: the structure of detection pulses, communication waveforms, and ship-radiated noise, and the sound-speed profile, geometry, and multipath propagation through which each reaches the receiver. We address this by proposing \textbf{UA-Bench}, to our knowledge the first large-scale benchmark for evaluating LALMs on underwater acoustic signal recognition. It comprises 375,051 audio records that couple parameterized sources with modeled propagation, so that every record can be traced to the conditions that produced it. The records span these three signal families, and each carries a three-level label hierarchy (13 leaf classes), a templated multi-turn dialogue, and source and channel metadata. We evaluate on a balanced 2,600-record subset with a gated coarse-to-fine protocol that locates each error at source routing, fine-grained classification, or output format, and add a paired silent-audio control to test whether the waveform is actually used. Nine open LALMs, evaluated without task-specific adaptation, reach only 2.0\%--13.1\% leaf accuracy, against a random reference of 7.7\%. The waveform helps source routing far more than leaf recognition (for one model, +29.5 versus +2.3 points over silence), and just four models gain reliably at the leaf level, by at most 4.7 points. UA-Bench thus gives a reference point for these models, and its released training partition supports follow-up adaptation work.

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arXiv2026

Note on fractional sum of the divisor function

Let $d(n)$ be the divisor function and denote by $[t]$ the integral part of the real number $t$. We prove that \begin{align*} \sum_{n\leq x^{1/c}}d\left(\left[\frac{x}{n^c}\right]\right)=d_cx^{1/c}+O_{\varepsilon,c}(x^{θ_c+\varepsilon}), \end{align*} where $d_c$ is a suitable constant, $θ_c<2/(3c+2)$ for $0<c<2/11$. This result constitutes an improvement upon that of Y. Feng (2024).

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arXiv2026

What Makes High-Magnification Knowledge Transferable? A Study of Cross-Resolution Distillation in Whole-Slide Imaging

Cross-resolution knowledge distillation aims to improve low-magnification whole- slide analysis by transferring high-magnification representations, yet the conditions for useful transfer remain unclear. We develop a decomposition-based analysis of teacher access, representation loss, and model excess, motivating three questions: whether (a) teacher targets help the task, (b) low-magnification students can predict them, and (c) slide models benefit from those predictions. We investigate them through controlled experiments across ten pathology cohorts spanning classifi- cation, grading, and survival prediction. In the main comparison, providing teacher regional means alongside native low-magnification features improves downstream performance in all ten cohorts. Direct prediction achieves lower reconstruction error than residual prediction, yet the predicted features underrepresent variation in the teacher targets. Moreover, better reconstruction does not consistently improve downstream scores, and retaining native features changes performance even when the predicted teacher features are held fixed. Together, these findings expose a gap between reconstructing teacher representations and realizing their downstream value. They challenge the sufficiency of reconstruction error as a measure of cross-resolution transfer and provide a diagnostic framework for examining where that transfer breaks down. Future distillation designs must account for both what students can predict and how slide models use those predictions.

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arXiv2026

Gated Spatial Redundancy Projection for Pathology Transformer Attentions

Transformer models are increasingly used for whole-slide image analysis in computational pathology. Yet, WSIs differ fundamentally from natural images: neighbouring patches often contain highly similar tissue type, stain, texture, and cellular composition. We identify this local spatial redundancy as a pathology-specific failure mode of self-attention, where dominant neighbourhood features can be repeatedly mixed into patch-tokens and weaken subtle diagnostic or prognostic deviations. We propose Gated Spatial Redundancy Projection (Gated SRP), a lightweight drop-in correction module for self-attention layers. For each patch token and attention head, Gated SRP estimates a local redundancy axis from neighbouring value vectors, projects the attention output onto this axis, and applies a learned signed gate to correct the redundancy-aligned component geometrically. Across five TCGA survival cohorts, Gated SRP obtains the highest mean C-index among the compared attention variants in all cohorts, with an average improvement over the base attention, while adding only +0.02% parameters. Across five slide-level classification datasets, it improves the base attention on 12 of 16 reported metrics and achieves the best AUC on three datasets. Code is publicly available at https://github.com/AtlasAnalyticsLab/GatedSRP.

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arXiv2026

The lower bound of shifted primes with large prime factors

In this paper, we consider the asymptotic density of $T_c(x):=\#\{p\leq x:P^+(p-1)\geq p^c\}$, where $P^+(n)$ denote the largest prime factor of $n$. We show that for $x\rightarrow\infty$, for any $0 0$ for $11/32 0.0436$. This improves a previous result by Liu-Wu-Xi (2020), who showed \begin{align*} \mathop{\lim\inf}_{x\rightarrow\infty}\frac{T_c(x)}{π(x)}&\geq\max\left(1-4ρ\left(\frac{1}{c}\right),1-c\right), \end{align*} for $0<c\leq 1/2$.

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arXiv2026

Bi-exact Wreath-like Product Groups

In this short paper, we prove the bi-exactness of all wreath-like product groups $G\in\mathcal{WR}(A,B\curvearrowright I)$, whenever $A$ is amenable, $B$ is bi-exact, and the action $B\curvearrowright I$ has amenable stabilizers. As applications, we obtain solidity for the associated group von Neumann algebras and, by combining our result with existing rigidity theorems, new examples exhibiting the McDuff superrigidity.

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arXiv2026

SG-WAM: Self-Guided World Modeling in Geometry-Aware Policy Space

World Action Models (WAMs) couple action generation with prediction of future states. Their effectiveness depends on whether future dynamics are modeled in a space that is both aligned with action generation and sufficiently geometry-aware to capture where and how actions change the scene. Existing WAMs typically satisfy only part of this requirement, relying on either perceptually heavy observation-space targets or auxiliary latent spaces that are not jointly structured for action relevance and geometry. We propose SG-WAM, a self-guided framework that learns geometry-aware action-conditioned dynamics directly in the policy-derived representation space. SG-WAM introduces learnable dynamics tokens and a Self-Guided World Predictor that forecasts their future latent states conditioned on intervening robot actions. Prediction targets are generated by an exponential moving average copy of the same policy backbone, providing stable supervision within the representation family used by the action expert. Geometric supervision further structures the policy image-token representations, providing spatially grounded context for the dynamics tokens and yielding a future-alignment space that is both action-relevant and geometry-aware. Latent future prediction, geometric grounding, and flow-matching action generation are jointly optimized end-to-end in a unified framework. Built on a 0.9B model without large-scale embodied pretraining, SG-WAM achieves 98.5% average success on LIBERO and 73% on LIBERO-Plus, while outperforming strong baselines in both in-distribution and out-of-distribution real-world evaluations.

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arXiv2026

Closure complexity of longest-edge bisection for triangular meshes

On triangular meshes, we analyze local mesh refinement based on longest-edge bisection equipped with the serial longest-edge propagation-path closure. Ties are resolved by terminal priority: if the incoming shared edge is a longest edge of the neighboring triangle, the pair is declared terminal and that edge is bisected. For every adaptive mesh sequence $\mathcal{T}_0, \mathcal{T}_1, \ldots, \mathcal{T}_L$ with a sequence of marked sets $\mathcal{M}_0, \mathcal{M}_1, \ldots, \mathcal{M}_{L-1}$, we prove the cumulative closure estimate $$\#\mathcal{T}_L-\#\mathcal{T}_0 \lesssim\sum_{\ell=0}^{L-1}\#\mathcal{M}_\ell.$$ The proof derives single-mark locality from the uniform multiplicative gap between possible descendant diameters implied by finite similarity classes, and converts this locality into the cumulative estimate through a Binev--Dahmen--DeVore-type charging argument.

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arXiv2026

Convolution-type Bombieri-Vinogradov theorem with well-factorable weights, and its applications

In this paper, we consider the asymptotic density of $\#\{p\leq x:P^+(p-1)\geq p^c\}$ and $\#\{n\leq x:P^+(n) 0.299x. \end{align*} The first result constitutes an improvement upon that of Ding and Wang (2025), who obatined $\mathop{\lim\sup}_{x\rightarrow\infty} \frac{1}{π(x)}\#\{p\leq x:P^+(p-1)\geq p^c\}\leq \frac{7}{2}\log\frac{1}{c}$. The second result improves a previous result $0.280$ by the author (2026). The key to the proof is that for a special class of convolution forms equipped with well-factorable weights, we may use the level \(x^{5/8-o(1)}\) for Pascadi's prime-distribution result with triple-well-factorable weights. We also use Pascadi's estimation of incomplete Kloosterman sums.

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arXiv2026

Closure complexity of Bänsch-type algorithms for tetrahedral mesh refinement

We prove, to our knowledge, the first unconditional cumulative closure estimates for the Arnold--Mukherjee--Pouly (AMP) refinement algorithm and the original face-marked tetrahedral algorithm of Bänsch on arbitrary conforming initial tetrahedral meshes. Let $T_0,\ldots,T_L$ be an adaptive mesh sequence generated by either algorithm, with $M_\ell\subseteq T_\ell$ denoting the marking set at step $\ell$. Then $$\#T_L-\#T_0\leq C_{\mathrm{clos}}(T_0)\sum_{\ell=0}^{L-1}\#M_\ell.$$ The proof is intrinsic to the physical three-dimensional mesh and requires neither an initial compatibility condition nor a higher-dimensional embedding. It organizes conformity refinements into a causal forest and combines a uniform horizontal-propagation estimate with a weighted packing argument to obtain an explicit closure constant. For the original Bänsch algorithm, every history-dependent resolution of the initial two-edge ambiguity is represented by one of finitely many AMP histories. The estimate therefore holds uniformly for arbitrary deterministic or nondeterministic choices. This resolves a long-standing complexity question for the Bänsch--AMP family.

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arXiv2026

Relative Biexactness for Relative Hyperbolic Groups and Some Applications

In this paper, we confirm a conjecture of Ozawa and others asserting that every finitely generated, relatively hyperbolic, exact group is bi-exact (in the sense of Ozawa) relative to its natural peripheral structure. As a consequence, every such group gives rise to a prime group von Neumann algebra. As an application, we construct a continuum family of property (T), relatively hyperbolic groups $\{G_i\}_{i\in I}$ such that, for every fixed arbitrary free, ergodic, probability measure-preserving action $G_i \curvearrowright Z_i$, the collection of associated group measure space von Neumann algebras $\{L^\infty(Z_i)\rtimes G_i\}_{i\in I}$ are pairwise non-stably $\ast$-isomorphic.

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