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Jing Liu

Jing Liu contributes to research discovery and scholarly infrastructure.

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Published work

5 published item(s)

preprint2026arXiv

FlexProofs: A Vector Commitment with Flexible Linear Time for Computing All Proofs

In this paper, we introduce FlexProofs, a new vector commitment (VC) scheme that achieves two key properties: (1) the prover can generate all individual opening proofs for a vector of size $N$ in optimal time ${\cal O}(N)$, and there is a flexible batch size parameter $b$ that can be increased to further reduce the time to generate all proofs; and (2) the scheme is directly compatible with a family of zkSNARKs that encode their input as a multi-linear polynomial. As a critical building block, we propose the first functional commitment (FC) scheme for multi-exponentiations with batch opening. Compared with HydraProofs, the only existing VC scheme that computes all proofs in optimal time ${\cal O}(N)$ and is directly compatible with zkSNARKs, FlexProofs may speed up the process of generating all proofs, if the parameter $b$ is properly chosen. Our experiments show that for $N=2^{16}$ and $b=\log^2 N$, FlexProofs can be $6\times$ faster than HydraProofs. Moreover, when combined with suitable zkSNARKs, FlexProofs enable practical applications such as verifiable secret sharing and verifiable robust aggregation.

preprint2026arXiv

MinGLE: A Minimalist, Configurable, and Pedagogical Geant4 Application Template

The Geant4 toolkit is the leading software for the simulation of particle transport through matter, widely used in nuclear physics, high-energy physics, and medical physics. However, the initial learning curve for new developers can be steep, often due to the complexity and experiment-specific nature of many introductory examples. This paper introduces MinGLE (Mini Geant4 Learning Example), a dedicated application template designed to be a universal, flexible, and educational starting point for Geant4 projects. MinGLE achieves a complete, functional simulation kernel using fewer than 70 lines of core C++ code. This minimalism is realized by leveraging contemporary Geant4 features, including factory classes for run management and physics, and the Text Geometry format for detector definition. Furthermore, MinGLE employs a unique pedagogical structure, using Git tags to document the incremental development of eleven core Geant4 components, with each tagged version being fully compilable, executable, and testable, providing a clear, step-by-step learning resource.

preprint2026arXiv

Proof of a Conjecture on Young Tableaux with Walls

Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by Chang, Fuchs, Liu, Wallner, and Yu leads to the verification of a conjecture on tree-child networks proposed by Pons and Batle. This conjecture was regarded as a specific and challenging problem in the Phylogenetics community until it was finally resolved by the present work.

preprint2026arXiv

Semantic-Enriched Latent Visual Reasoning

Multimodal latent-space reasoning aims to replace explicit thinking with images by performing visual reasoning directly in a compact latent space. However, existing approaches largely rely on visual supervision and produce latent representations that lack sufficient semantic richness, limiting their ability to support diverse region-level reasoning tasks. In this work, we introduce Semantic-Enriched Latent Visual Reasoning (SLVR), a two-stage learning framework that enriches latent representations with attribute-level visual semantics and aligns them with diverse reasoning objectives. In the first stage, SLVR learns semantically enriched region-centric latents under fine-grained attribute supervision. In the second stage, we design Multi-query Group Relative Policy Optimization (M-GRPO) to align latent representations across multiple queries grounded in the same region. To support this framework, we construct SLV-Set, comprising approximately 400K region-level attribute annotations and 800K multi-query question answering samples, and introduce SV-QA, a benchmark that evaluates latent reasoning under semantic variation. Experiments demonstrate that SLVR improves the robustness and semantic consistency of latent visual reasoning compared to existing baselines.

preprint2026arXiv

UrbanNav: Learning Language-Guided Urban Navigation from Web-Scale Human Trajectories

Navigating complex urban environments using natural language instructions poses significant challenges for embodied agents, including noisy language instructions, ambiguous spatial references, diverse landmarks, and dynamic street scenes. Current visual navigation methods are typically limited to simulated or off-street environments, and often rely on precise goal formats, such as specific coordinates or images. This limits their effectiveness for autonomous agents like last-mile delivery robots navigating unfamiliar cities. To address these limitations, we introduce UrbanNav, a scalable framework that trains embodied agents to follow free-form language instructions in diverse urban settings. Leveraging web-scale city walking videos, we develop an scalable annotation pipeline that aligns human navigation trajectories with language instructions grounded in real-world landmarks. UrbanNav encompasses over 1,500 hours of navigation data and 3 million instruction-trajectory-landmark triplets, capturing a wide range of urban scenarios. Our model learns robust navigation policies to tackle complex urban scenarios, demonstrating superior spatial reasoning, robustness to noisy instructions, and generalization to unseen urban settings. Experimental results show that UrbanNav significantly outperforms existing methods, highlighting the potential of large-scale web video data to enable language-guided, real-world urban navigation for embodied agents.