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Jiahong Yu

Publications and source records attributed to Jiahong Yu.

13 recordsLinked to original sources

A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map

We construct a smooth connected rigid analytic curve over $\mathbb C_p$ with an affinoid perfectoid profinite \'etale $\mathbb Z_p^2$-torsor whose geometric Sen morphism is not surjective, thereby disproving Rodr\'\i guez Camargo's conjectured implication from perfectoidness to surjectivity. The construction relies on a pullback theorem showing that perfectoid profinite \'etale towers are preserved under universally injective morphisms of rigid analytic spaces.

math.AG

Lift-independence problem in the $P$-adic Simpson correspondence for curves

Let $X$ be a proper smooth rigid analytic variety over a complete algebraically closed field $p$-adic field $\mathbf C$. Fix an continuation $\mathrm{Exp}$ of $\exp$. Faltings (in the curve case) and Heuer showed that any lifting $\widetilde X$ of $X$ over $\mathbf{B}_{\rm dR}^+/t^2$ induces an equivalence bewteen the category of Higgs bundles on $X_{\mathrm{\acute{e}t}}$ and the category of $v$-bundles on $X_v$. In this paper, we aim to study how the equivalence depends on the choice of such a lifting $\widetilde X$ when $X$ is a curve of genus $g\geqslant 2$. More precisely, we call a Higgs bundle lift-independent if it always corresponds to the same $v$-bundle under $p$-adic Simpson correspondence with respect to any lifting $\widetilde X$ and then we will show that (1) There exists some $r(g)\geqslant \sqrt{g-1}$ such that any semistable lift-independent Hitchin-small Higgs bundle of rank $r\leqslant r(g)$ has zero Higgs field. (2) There always exists a semistable Higgs bundle of degree $0$ with non-zero Higgs field that is lift-independent.

math.AG

On some open problems in commutative algebra resolved by Rethlas

We report on a collection of open problems in commutative algebra and related areas that have been resolved (proved or disproved) using the Rethlas natural-language automated reasoning system. The problems are drawn from several published lists, including Open Problems in Commutative Ring Theory (Cahen-Fontana-Frisch-Glaz), Erman-Sam's survey of Boij-S\"oderberg theory. For each problem we record the precise statement and a self-contained proof produced (with no human intervention) by Rethlas and subsequently verified by human experts.

math.AC

Almost Vector Bundles over Perfectoid Spaces

In this paper, we define vector bundles within the framework of almost mathematics (referred to as almost vector bundles) and establish the $v$-descent theorem together with a structure theorem for these bundles over perfectoid spaces. The proof yields several interesting intermediate results.

math.AG

TrackTeller: Temporal Multimodal 3D Grounding for Behavior-Dependent Object References

Understanding natural-language references to objects in dynamic 3D driving scenes is essential for interactive autonomous systems. In practice, many referring expressions describe targets through recent motion or short-term interactions, which cannot be resolved from static appearance or geometry alone. We study temporal language-based 3D grounding, where the objective is to identify the referred object in the current frame by leveraging multi-frame observations. We propose TrackTeller, a temporal multimodal grounding framework that integrates LiDAR-image fusion, language-conditioned decoding, and temporal reasoning in a unified architecture. TrackTeller constructs a shared UniScene representation aligned with textual semantics, generates language-aware 3D proposals, and refines grounding decisions using motion history and short-term dynamics. Experiments on the NuPrompt benchmark demonstrate that TrackTeller consistently improves language-grounded tracking performance, outperforming strong baselines with a 70% relative improvement in Average Multi-Object Tracking Accuracy and a 3.15-3.4 times reduction in False Alarm Frequency.

cs.CV

Fields of Fractions in Rigid Geometry

Let $A$ be an affinoid integral domain over a non-Archimedean field $K$, and let $L$ be its field of fractions. We prove that the normalization of $A$ can be reconstructed from $L$ by taking the intersection of all maximal discrete valuation subrings. As a corollary, taking the field of fractions induces a fully faithful functor from the category of normal affinoid integral domains over $K$ to the category of field extensions of $K$. This provides another $p$-adic analogue of the Riemann Hebbarkeitssatz.

math.AC

$\delta$-lifting and $1$-dimensional analytic fields

Let $k$ be an algebraically closed complete non-Archimedean field, and let $K$ be a finitely generated field extension over $k$ with transcendence degree $1$. Equip $K$ a non-Archimedean norm extending the one on $k$, and let $\mathcal{K}$ denote the completion of $K$. We will prove that the valuation ring $\mathcal{K}^+$ admits a flat $\delta$-lifting over $\mathbb{A}_{\mathrm{inf}}(k^+)$ if and only if $\mathcal{K}$ is not of type 4.

math.AC

Rational Hodge--Tate prismatic crystals of quasi-l.c.i algebras and non-abelian $p$-adic Hodge theory

Consider a bounded prism $(A,I)$ and a bounded quasi-l.c.i algebra $R$ over $\overline{A}$. In this paper, for any prism $S/A$ with a surjection $S\to R$ such that $\widehat{\mathbb L}_{\overline{S}/\overline{A}}$ is a $p$-completely flat module over $\overline{S}$, we establish an equivalence of categories between rational Hodge-Tate crystals on $(R/A)_{\Delta}$ and topologically nilpotent integrable connections on the Hodge--Tate cohomology ring $\overline{\Delta}_{R/S}$. As an application, for a non-zero divisor $a\in \overline{A}$, we introduce the concept of $a$-smallness for a rational Hodge-Tate prismatic crystal on $(R/A)_{\Delta}$. Finally, we focus on some special algebras $R$ over $\mathcal O_{\mathbb C_p}$ (or generally, the ring of integers of an algebraic closed and complete non-archimedean field) including all $p$-completely smooth algebras, $p$-complete algebras with semi-stable reductions and geometric valuation rings. By using our equivalence, we analyze the restriction functor from the category of $a$-small rational Hodge-Tate prismatic crystals to the category of $v$-vector bundles. This yields some new results in $p$-adic non-abelian Hodge Theory.

math.NT

Toward Robust and Efficient ML-Based GPU Caching for Modern Inference

In modern GPU inference, cache efficiency remains a major bottleneck, and heuristic policies such as \textsc{LRU} can perform far worse than the offline optimum. Existing learning-based caching systems improve hit rates mainly through predictor design, but often follow learned predictions blindly, making performance unreliable when predictions are inaccurate. In contrast, emerging learning-augmented caching algorithms~\cite{pmlr-v80-lykouris18a,mitzenmacher2022algorithms} provide performance guarantees by carefully integrating predictions into caching policies, achieving both \emph{consistency} (near-optimality under perfect predictions) and \emph{robustness} (bounded worst-case performance under prediction errors). However, deployment remains challenging. A practical algorithm should satisfy strict time and space efficiency constraints, which some theoretical work overlooks, while also incurring low deployment overhead. We propose learning-augmented LRU, a deployment-oriented learning-augmented caching algorithm that guarantees \emph{1-consistency} and \emph{$O(k)$-robustness}, incurs low time and space overhead, and maintains strong compatibility. We further build a GPU cache, called \textsc{LCR}, on top of learning-augmented LRU to benefit from its theoretical guarantees and translate them into practical performance. In experiments, \textsc{LCR} reduces P99 time-to-first-token (TTFT) by up to 28.3\% on LLM workloads and increases throughput by up to 24.2\% on deep learning recommendation (DLRM) workloads. Even with poor predictions, performance degrades gracefully and remains close to \textsc{LRU}, demonstrating robustness with practical value.

cs.LG

A Conjecture of Bhatt--Lurie and weakly $p$-nilpotent Hodge--Tate stacks

Let $k$ be a perfect field of characteristic $p$, and let $X/k$ be a smooth variety. It is known that given a Frobenius lifting of $X$, we can identify prismatic crystals and nilpotent Higgs bundles, known as a positive characteristic version of the Simpson correspondence of $X$. However, Ogus--Vologodsky point out in their original paper of non-abelian Hodge theory in characteristic $p$ that, if we are just given a smooth lifting over $\W_2(k)$, there is a non-abelian Hodge theory on $p$-nilpotent Higgs bundles. Hence, it is natural to ask that whether there exists a subcategory of Hodge--Tate crystals on $X$, which can be described as $p$-nilpotent Higgs bundles. In this paper, we construct an analogue of the Hodge--Tate stack, so called the weakly $p$-nilpotent Hodge--Tate stack, on which the vector bundles are identified with certain Hodge--Tate crystals on $X$ that can be locally described by weakly $p$-nilpotent Higgs bundles. Furthermore, we prove that the weakly $p$-nilpotent Hodge--Tate stack is indeed a gerbe banded by $T_{X/k}\otimes{\alpha_p}$, and the obstruction class coincides with the obstruction of the existence of a Frobenius lifting of $X$, which is a conjecture of Bhatt and Lurie.

math.AG

Prismatic Crystals for schemes in characteristic $p$

Let $(A,\delta_A)$ be a crystalline prism and let $\mathfrak X$ be a finite type $A/p$-scheme admitting a Koszul-regular closed immersion into a smooth formal $A$-scheme $Y$. We construct a sheaf of prismatic envelopes $\Delta_Y(\mathfrak X)$ attached to a Frobenius lift modulo $p^2$ on $Y$, prove that prismatic crystals on $(\mathfrak X/A)_{\Delta}$ are equivalent to integrable topologically quasi-nilpotent $p$-connections on $\Prism_Y(\mathfrak X)$, and identify their prismatic cohomology with the corresponding de Rham complex. When a global Frobenius lift is available, a lifted Ogus--Vologodsky functor gives an equivalence between $p$-connections on the prismatic envelope of the Frobenius twist and connections on the $p$-complete PD-envelope. Gluing this local correspondence yields an equivalence between prismatic crystals on $\mathfrak X^{(1)}$ and crystalline crystals on $\mathfrak X$ for l.c.i. $\mathfrak X$ over $A/p$.

math.AG

On smooth adic spaces over $\mathbb{B}_{\mathrm{dR}}^+$ and sheafified $p$-adic Riemann--Hilbert correspondence

Let $C$ be a completely algebraic closed non-archimedean field over $\mathbb{Q}_p$ and $\alpha,r$ be two positive integers. Denote by $B_\alpha$ the ring $\mathbb{B}_{\mathrm{dR}}^+(C)/(\ker\theta)^\alpha$. This paper first constructs a sheafified $p$-adic Riemann--Hilbert correspondence. Specifically, we construct a canonical sheaf isomorphism on $X_{\mathrm{\acute{e}t}}$, \[ R^1\nu_*\big( \mathrm{GL}_r(\mathbb{B}_{\mathrm{dR}}^+/(\ker\theta)^\alpha) \big) \cong \mathrm{MIC}_{r}(X)\{-1\}, \] where the first term is identified with the sheaf of isomorphism classes of $v$-vector bundles with coefficients in $\mathbb{B}_{\mathrm{dR}}^+/(\ker\theta)^{\alpha}$, and the second term is defined as the sheaf of isomorphism classes of integrable connections of rank $r$. We then define the moduli space of integrable connections on $X$ and the moduli space of $v$-vector bundles on $X$ with coefficients in $\mathbb{B}_{\mathrm{dR}}^+/(\ker\theta)^{\alpha}$, and prove that they are small $v$-stacks in the sense of Scholze. These constructions generalize Heuer's work on $p$-adic Simpson correspondence.

math.AG

Chimera: A Lossless Decoding Method for Accelerating Large Language Models Inference by Fusing all Tokens

Large language models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their widespread application is hindered by the resource-intensive decoding process. To address this challenge, current approaches have incorporated additional decoding heads to enable parallel prediction of multiple subsequent tokens, thereby achieving inference acceleration. Nevertheless, the accuracy of these decoding heads falls short of the auto-regressive decoding approach. In light of these limitations, we propose Chimera, a novel framework specifically designed for speculative sampling. Within this framework, we introduce a lightweight draft model that effectively utilizes previously generated tokens to predict subsequent words. To ensure both accuracy and efficiency, we present two strategies within the lightweight draft model. Firstly, we focus on capturing short-range dependencies at the bottom layer. Secondly, we leverage the readily available representations from the original LLM.Through empirical evaluation on the Vicuna and LlaMA-2 series, Chimera demonstrates impressive results, achieving an average latency speedup ratio of 2.7x compared to the vanilla auto-regressive decoding approach. This highlights the potential of our proposed framework in significantly improving the efficiency of large language models during the decoding process.

cs.CL