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Jiaping Wang

Publications and source records attributed to Jiaping Wang.

At least 19 recordsLinked to original sources
arXiv2026

Cross-View Sequential Visual Localization with Spatio-Temporal Context Modeling for Autonomous Driving

Continuous and reliable localization is essential for autonomous driving. Cross-view visual localization matches ground images with satellite maps, providing complementary localization cues for pipelines that depend on Global Navigation Satellite System (GNSS) signals and high-definition (HD) maps. Most existing cross-view visual localization methods process each frame independently, leaving temporal information underused and limiting accuracy under dynamic occlusion, illumination variation, and repetitive textures. This study proposes a temporal-context-enhanced framework for cross-view sequence visual localization. The proposed recurrent cross-frame module aggregates historical context from the previous state to enhance the coarse ground feature of each current frame. These enhanced features facilitate satellite candidate-region classification, while hierarchical fine-grained features enable precise local offset estimation. On the CVIS dataset, the proposed method reduces mean localization error from 3.80 m to 1.57 m and increases R@1 m from 8.14% to 40.22%. Direct transfer to KITTI-CVL achieves a mean error of 2.61 m, with target-domain fine-tuning further reducing the mean error to 2.27 m. Zero-shot field experiments on a real-world vehicle achieve a mean error of 2.84 m and R@5 m of 96.86%. These results demonstrate that temporal context enhancement significantly improves cross-view localization accuracy and supports robust deployment on public benchmarks and real-world roads.

cs.CV↗
arXiv2026

Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound

Under a necessary topological assumption, two global results are established for complete three dimensional manifolds. The first one provides a sharp upper bound for the bottom spectrum in terms of the scalar curvature lower bound. The second one shows that such manifolds do not admit any positive Green's function if the scalar curvature is bounded from below by a positive constant.

math.DG↗
arXiv2025

Consultant Decoding: Yet Another Synergistic Mechanism

The synergistic mechanism based on Speculative Decoding (SD) has garnered considerable attention as a simple yet effective approach for accelerating the inference of large language models (LLMs). Nonetheless, the high rejection rates require repeated LLMs calls to validate draft tokens, undermining the overall efficiency gain of SD. In this work, we revisit existing verification mechanisms and propose a novel synergetic mechanism Consultant Decoding (CD). Unlike SD, which relies on a metric derived from importance sampling for verification, CD verifies candidate drafts using token-level likelihoods computed solely by the LLM. CD achieves up to a 2.5-fold increase in inference speed compared to the target model, while maintaining comparable generation quality (around 100% of the target model's performance). Interestingly, this is achieved by combining models whose parameter sizes differ by two orders of magnitude. In addition, CD reduces the call frequency of the large target model to below 10%, particularly in more demanding tasks. CD's performance was even found to surpass that of the large target model, which theoretically represents the upper bound for speculative decoding.

cs.CL↗
arXiv2025

Sharp integral bound of scalar curvature on $3$-manifolds

It is shown that the integral of the scalar curvature on a geodesic ball of radius $R$ in a three-dimensional complete manifold with nonnegative Ricci curvature is bounded above by $8\pi R$ asymptotically for large $R$ provided that the scalar curvature is bounded between two positive constants.

math.DG↗
arXiv2025

LeetDecoding: A PyTorch Library for Exponentially Decaying Causal Linear Attention with CUDA Implementations

The machine learning and data science community has made significant while dispersive progress in accelerating transformer-based large language models (LLMs), and one promising approach is to replace the original causal attention in a generative pre-trained transformer (GPT) with \emph{exponentially decaying causal linear attention}. In this paper, we present LeetDecoding, which is the first Python package that provides a large set of computation routines for this fundamental operator. The launch of LeetDecoding was motivated by the current lack of (1) clear understanding of the complexity regarding this operator, (2) a comprehensive collection of existing computation methods (usually spread in seemingly unrelated fields), and (3) CUDA implementations for fast inference on GPU. LeetDecoding's design is easy to integrate with existing linear-attention LLMs, and allows for researchers to benchmark and evaluate new computation methods for exponentially decaying causal linear attention. The usage of LeetDecoding does not require any knowledge of GPU programming and the underlying complexity analysis, intentionally making LeetDecoding accessible to LLM practitioners. The source code of LeetDecoding is provided at \href{https://github.com/Computational-Machine-Intelligence/LeetDecoding}{this GitHub repository}, and users can simply install LeetDecoding by the command \texttt{pip install leet-decoding}.

cs.LG↗
arXiv2024

Bottom spectrum of three-dimensional manifolds with scalar curvature lower bound

A classical result of Cheng states that the bottom spectrum of complete manifolds of fixed dimension and Ricci curvature lower bound achieves its maximal value on the corresponding hyperbolic space. The paper establishes an analogous result for three-dimensional complete manifolds with scalar curvature lower bound subject to some necessary topological assumptions. The rigidity issue is also addressed and a splitting theorem is obtained for such manifolds with the maximal bottom spectrum.

math.DG↗
arXiv2024

Experimenting a New Programming Practice with LLMs

The recent development on large language models makes automatically constructing small programs possible. It thus has the potential to free software engineers from low-level coding and allow us to focus on the perhaps more interesting parts of software development, such as requirement engineering and system testing. In this project, we develop a prototype named AISD (AI-aided Software Development), which is capable of taking high-level (potentially vague) user requirements as inputs, generates detailed use cases, prototype system designs, and subsequently system implementation. Different from existing attempts, AISD is designed to keep the user in the loop, i.e., by repeatedly taking user feedback on use cases, high-level system designs, and prototype implementations through system testing. AISD has been evaluated with a novel benchmark of non-trivial software projects. The experimental results suggest that it might be possible to imagine a future where software engineering is reduced to requirement engineering and system testing only.

cs.SE↗
arXiv2023

A Minkowski type inequality for manifolds with positive spectrum

The classical Minkowski inequality implies that the volume of a bounded convex domain is controlled from above by the integral of the mean curvature of its boundary. In this note, we establish an analogous inequality without the convexity assumption for all bounded smooth domains in a complete manifold with its bottom spectrum being suitably large relative to its Ricci curvature lower bound. An immediate implication is the nonexistence of embedded compact minimal hypersurfaces in such manifolds. This nonexistence issue is also considered for steady and expanding Ricci solitons.

math.DG↗
arXiv2022

Area and spectrum estimates for stable minimal surfaces

This note concerns the area growth and bottom spectrum of complete stable minimal surfaces in a three-dimensional manifold with scalar curvature bounded from below. When the ambient manifold is the Euclidean space, by an elementary argument, it is shown directly from the stability inequality that the area of such minimal surfaces grows exactly as the Euclidean plane. Consequently, such minimal surfaces must be at, a well-known result due to Fisher-Colbrie and Schoen as well as do Carmo and Peng. In the case the ambient manifold is the hyperbolic space, explicit area growth estimate is also derived. For the bottom spectrum, upper bound estimates are established in terms of the scalar curvature lower bound of the ambient manifold.

math.DG↗
arXiv2022

Structure at infinity for shrinking Ricci solitons

The paper mainly concerns the structure at infinity for complete gradient shrinking Ricci solitons. It is shown that for such a soliton with bounded curvature, if the round cylinder $\mathbb{R}\times \mathbb{S}^{n-1}/Γ$ occurs as a limit for a sequence of points going to infinity along an end, then the end is asymptotic to the same round cylinder at infinity. The result is then applied to obtain structural results at infinity for four dimensional gradient shrinking Ricci solitons. It is previously known that such solitons with scalar curvature approaching zero at infinity must be smoothly asymptotic to a cone. For the case that the scalar curvature is bounded from below by a positive constant, we conclude that along each end the soliton is asymptotic to a quotient of $\mathbb{R}\times \mathbb{S}^{3}$ or converges to a quotient of $\mathbb{R}^{2}\times \mathbb{S}^{2}$ along each integral curve of the gradient vector field of the potential function.

math.DG↗
arXiv2022

Geometry of three-dimensional manifolds with positive scalar curvature

The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ricci curvature is asymptotically nonnegative.

math.DG↗
arXiv2021

Comparison theorems for three-dimensional manifolds with scalar curvature bound

Two sharp comparison results are derived for three-dimensional complete noncompact manifolds with scalar curvature bounded from below. The first one concerns the Green's function. When the scalar curvature is nonnegative, it states that the rate of decay of an energy quantity over the level set is strictly less than that of the Euclidean space, unless the manifold itself is isometric to the Euclidean space. The result is in turn converted into a sharp area comparison for the level set of the Green's function when in addition the Ricci curvature of the manifold is assumed to be asymptotically nonnegative at infinity. The second result provides a sharp upper bound of the bottom spectrum in terms of the scalar curvature lower bound, in contrast to the classical result of Cheng which involves a Ricci curvature lower bound.

math.DG↗
arXiv2020

Positive solutions to Schrödinger equations and geometric applications

A variant of Li-Tam theory, which associates to each end of a complete Riemannian manifold a positive solution of a given Schrödinger equation on the manifold, is developed. It is demonstrated that such positive solutions must be of polynomial growth of fixed order under a suitable scaling invariant Sobolev inequality. Consequently, a finiteness result for the number of ends follows. In the case when the Sobolev inequality is of particular type, the finiteness result is proven directly. As an application, an estimate on the number of ends for shrinking gradient Ricci solitons and submanifolds of Euclidean space is obtained.

math.DG↗
arXiv2019

Txilm: Lossy Block Compression with Salted Short Hashing

Current blockchains are restricted by the low throughput. Aimed at this problem, we propose Txilm, a protocol that compresses the size of transaction presentation in each block to save the bandwidth of the network. In this protocol, a block carries short hashes of TXIDs instead of complete transactions. Combined with the sorted transactions based on TXIDs, Txilm realizes 80 times of data size reduction compared with the original blockchains. We also evaluate the probability of hash collisions, and provide methods of resolving such collisions. Finally, we design strategies to protect against potential attacks on Txilm.

cs.CR↗
arXiv2019

Weighted Poincare inequality and the Poisson equation

We develop Green's function estimate for manifolds satisfying a weighted Poincare inequality together with a compatible lower bound on the Ricci curvature. The estimate is then applied to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds. As an application, a Liouville property for finite energy holomorphic functions is proven on a class of complete Kähler manifolds. Consequently, such Kähler manifolds must be connected at infinity.

math.DG↗
arXiv2017

Poisson equation on complete manifolds

We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above.

math.DG↗
arXiv2015

A local curvature estimate for the Ricci flow

We show that the norm of the Riemann curvature tensor of any smooth solution to the Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensor, and the elapsed time. This provides a new, direct proof of a result of Sesum, which asserts that the curvature of a solution on a compact manifold cannot blow up while the Ricci curvature remains bounded, and extends its conclusions to the noncompact setting. We also prove that the Ricci curvature must blow up at least linearly along a subsequence at a finite time singularity.

math.DG↗