arXiv subjects

Li Li

Publications and source records attributed to Li Li.

At least 19 recordsLinked to original sources

arXiv2026

Graded Betti numbers of general curves of large degree

Let $C$ be a smooth projective complex curve of genus $g$ and gonality $k$, and $L$ be a very ample line bundle on $C$. When $L$ has sufficiently large degree, the vanishing and nonvanishing of the Koszul cohomology groups $K_{p,q}(C,L)$ have been determined previously, but the exact values of the graded Betti numbers $\kappa_{p,q}(C, L)$ remain largely unknown. In this paper, we give explicit closed formulas for all graded Betti numbers $\kappa_{p,q}(C, L)$ when the Brill--Noether locus $W_k^1(C)$ has the expected dimension and $H^1(C, L \otimes \omega_C^{-1})=0$. Consequently, we determine the complete Betti table for a general curve when $\deg L \geq 4g-3$ or when $\deg L \geq 3g-3$ and $L$ is general. We also explicitly compute the Boij--S\"{o}derberg coefficient of the section ring $R(C, L)$ governing asymptotic purity, and show eventual monotonicity of the remaining coefficients: they decrease for hyperelliptic curves and increase under a natural generic reducedness assumption on the relevant Brill--Noether loci.

math.AG↗

arXiv2026

Self-powered InAs nanowire detector arrays for extended-SWIR spectrometry at room temperature

Spectral sensing in the extended shortwave infrared (e-SWIR) is important for molecular analysis, infrared imaging, and machine vision, motivating the development of compact spectrometers for broader applications. However, conventional commercial off-the-shelf spectrometers in this wavelength region are expensive and bulky due to their reliance on external dispersive optics/filters and/or cryogenic accessories. Other emerging computational spectrometers are based on Si and InGaAs photodetectors that remain focused on the visible and near-infrared, with few detector platforms operating in the e-SWIR regime that simultaneously provide broadband sensitivity, low-noise room-temperature operation, and diverse spectral signatures for accurate identification and reconstruction. Here, we report a room-temperature e-SWIR computational spectrometer based on InAs/InP core-shell nanowire photodetector arrays with geometry-encoded spectral responses. The detectors exhibit self-powered broadband photoresponse across the 1--3 $\mu$m range, with responsivity up to 0.215 A W$^{-1}$, detectivity up to $1.6 \times 10^{9}$ cm Hz$^{1/2}$ W$^{-1}$, and microsecond response times. The excellent detector performance is leveraged to demonstrate filter-free spectral reconstruction using a compact multipixel photodetector array device. This enables high-accuracy molecular absorption spectrum reconstruction and hyperspectral imaging. Our results indicate that InAs nanowire arrays are a promising platform for compact computational spectrometry and imaging in the e-SWIR at room temperature.

physics.optics↗

arXiv2026

Understanding Deep Learning via Entropy Space Theory

Deep learning is often criticized for its theoretical research lagging behind practice. To make deep learning easier to understand, the entropy space theory is first introduced here. The entropy space can cover all the possibilities of any deep learning model by topological structure. It is independent of network parameters. Through the designed fundamental operations and norm, entropy space is proven to be a normed space within the formal axiomatic framework. Based on the theory, a unified coordinate system is proposed. It can coordinatize every state of a model and rank them by compression of the maximal value of information entropy. The theory offers a novel priori framework for mathematical fundamentals of deep learning.

cs.AI↗

arXiv2026

Signless Laplacian spectral conditions for rainbow matchings in a collection of bipartite graphs

Let ${\cal G}=\{G_1,\ldots,G_k\}$ be a collection of (not necessarily distinct) bipartite graphs on the same vertex bipartition $(X,Y)$, where $|X|=a$, $|Y|=b$ and $2\le k\le a\le b$. A \emph{rainbow matching} of ${\cal G}$ is a set of pairwise disjoint edges that can be chosen from distinct members of ${\cal G}$. Denote by $q(G)$ the signless Laplacian spectral radius of a graph $G$. In this paper, we prove that if $q(G_i)\ge b+k-1$ for each $i\in\{1,2,\ldots,k\}$, then ${\cal G}$ admits a rainbow matching of size $k$ unless $G_1=\cdots=G_k\cong K_{k-1,b}\cup\overline{K_{a-k+1}}$, and show that the threshold is sharp and attained by the exceptional collection. The condition is also extended to larger collections for a prescribed level $t$. In addition, we obtain a lower bound for the rainbow matching number in terms of the ordered signless Laplacian spectral radii of the members, and provide a stability version of the extremal characterization. In the proofs, we use the shifting technique and a quotient matrix arising from an equitable partition of a signless Laplacian matrix.

math.CO↗

arXiv2026

FLM: Frequency-Aware Language Models for Generative Image Compression

Generative models have significantly improved the performance ceiling of image lossy compression at low bitrates by exploiting learned priors. However, the generated textures and semantic details may deviate from the source content, thereby affecting the fidelity of image reconstruction. To solve these challenges, we propose FLM, a frequency-aware language model that improves compression efficiency through frequency-domain probabilistic modeling while retaining deterministic reconstruction. At the encoder, the input image is transformed into quantized DCT coefficients, which are organized into discrete sequences using macroblock-based coefficient tokenization. FLM then performs next-coefficient prediction to autoregressively estimate token-wise conditional probability distributions for arithmetic coding, thereby generating a compact bitstream. At the decoder, the LLM and arithmetic decoder jointly recover the frequency-domain data, followed by inverse transformations for image reconstruction. A task-specific frequency-domain dataset and a two-stage fine-tuning strategy are further developed to enable the model to operate across multiple bitrate settings. FLM is a versatile compressor that is compatible with both lossy compression and lossless JPEG recompression frameworks. Experiments show that FLM exceeds conventional and generative lossy compression methods in rate-distortion performance. FLM achieves BD-PSNR gains of 3.30 dB, 3.83 dB, and 3.80 dB than JPEG baseline on Kodak, Tecnick, and CLIC2020, respectively. Better qualitative quality of FLM can be achieved in improving semantically high fidelity and suppressing blocking artifacts. FLM is also validated to be applicable to the lossless recompression task with competitive performance.

cs.CV↗

arXiv2026

Frequency-Aware Continual Learning for Smart Contract Vulnerability Detection with Large Language Models

Smart contract vulnerability detection with Large Language Models (LLMs) faces three causally linked challenges. First, new vulnerability categories demand parameter-efficient adaptation, since full retraining is prohibitive for sequentially arriving tasks. Second, training per-task adapters on a shared backbone causes catastrophic forgetting of previously learned vulnerabilities. Third, the resulting multiplicity of adapters must be consolidated into a single model, since task identity is unknown at inference time. Each challenge arises directly from the solution to its predecessor, making an integrated framework essential. We propose a three-stage pipeline in which each stage addresses one challenge and feeds into the next. The adaptation stage uses Frequency-Aware Low-Rank Adaptation (FA-LoRA), which performs adaptation in the Fourier domain with per-frequency importance gates, requiring only 0.4% trainable parameters while outperforming standard LoRA and QLoRA. The continual learning stage applies Forget-Aware Replay (FAR), which uses these frequency gates to estimate per-sample forgetting risk via loss dynamics and prioritizes vulnerable knowledge for rehearsal, achieving an average Micro-F1 of 0.8022 across sequential tasks. The deployment stage employs Anchor-Protected Progressive Merging (APPM), which exploits the asymmetric generalization produced by FAR training to identify the strongest-generalizing adapter as an anchor and consolidates all adapters into a single model via anchor-protected weighted merging with frequency-domain gate competition. APPM achieves a Micro-F1 of 0.8085, within 2.7% of the independent per-task upper bound, at a merge cost of 156 ms and no additional runtime memory. Experiments on DIVE confirm the framework effectively addresses all three challenges for evolving blockchain ecosystems.

cs.AI↗

arXiv2026

OpenHarmony Bench: Evaluating LLMs and Coding Agents on OpenHarmony App Development

We present OPENHARMONY BENCH, an app-level coding benchmark for evaluating LLM-based coding agents on OpenHarmony ArkTS applications. Unlike function-level benchmarks, it evaluates complete app-level changes: each task requires an agent to modify a buildable ArkTS project so that a requested behavior works end to end, involving UI state, data persistence, build configuration, and platform APIs. The benchmark installs and drives the delivered application on a device to check whether the behavior is observable. It covers three input sources: natural-language feature requests (new-feature), structured scenario specifications (spec-driven), and bug descriptions (bug-fix). The benchmark contains 153 top-level tasks and 242 Feature points (F-points), where an F-point is one executable behavior check. The snapshot includes 32 new-feature tasks, 50 spec-driven tasks with 139 F-points, and 71 bug-fix tasks. The main leaderboard is scored over top-level tasks rather than independently weighted F-points. We describe the benchmark construction, statistics, and build-and-test evaluation pipeline, and evaluate DevEco Code with eight LLMs across three independent full-suite runs per configuration. Three findings emerge. First, newer generations complete more tasks than their predecessors within evaluated model-family pairs. Second, buildability is close to saturated while behavioral correctness is not: mean Final Build Success Rate is 94.77% to 100.00%, whereas mean Task Completion is 48.36% to 58.39%. Third, spec-driven tasks have the lowest Task Completion under all-checks task scoring, with no configuration exceeding 35%. The code, data, tasks, reference solutions, tests, evaluation scripts, and leaderboard are released through the official OPENHARMONY BENCH website at https://bench.matrix.openharmony.cn/.

cs.SE↗

arXiv2026

Statistically Steady Holographic Quantum Turbulence: Hyperuniform Vortex Matter and Crossover

A long-standing obstacle in quantum turbulence has been the difficulty of sustaining robust statistical steady states, preventing unambiguous identification of universal vortex organization and kinetic scaling. We construct such a steady state in two-dimensional holographic superfluid turbulence by continuous Landau-instability driving, sustaining ${\sim}2500$ vortices free from transient artifacts. The topological charge structure factor $S_c(k)$ reveals Class I disordered hyperuniformity with $S_c(k)\propto k^{\alpha>1}$ as $k\to0$, where $k$ is the wavenumber. This constitutes the strongest long-range order of its kind and its first observation in a strongly driven, far-from-equilibrium quantum fluid with topological defects as the organizing principle, establishing a novel non-equilibrium vortex phase. Exploiting this platform, we resolve the scaling controversy: the apparent $k^{-5/3}$ signature in the kinetic energy spectrum is a narrow crossover between the $k^{-1}$ single-vortex and $k^{-3}$ core regimes, not a genuine Kolmogorov inertial range. The real-space second-order structure function provides decisive evidence via $S_2(r)\propto \ln r$ where $r$ is the spatial separation, with no $r^{2/3}$ Kolmogorov scaling, ruling out a true inertial cascade. These findings reveal that strongly coupled quantum turbulence lacks an inverse cascade due to the absence of macroscopic Onsager clusters, demonstrating energy transport fundamentally distinct from weakly coupled superfluids.

hep-th↗

arXiv2026

SheetCompass: Hierarchical Relation Graphs for Agentic Spreadsheet Reasoning

Spreadsheets are widely used to organize, analyze, and manipulate semi-structured data, yet automated spreadsheet reasoning remains challenging for large language models (LLMs). Real-world workbooks often contain implicit cross-table associations, fine-grained column dependencies, and complex spatial layouts. Existing methods typically flatten these multidimensional structures into sequential strings, losing important intra-sheet boundaries and inter-sheet semantics. Consequently, LLMs cannot exploit the global spatial context that human experts naturally use when inspecting spreadsheets. We propose SheetCompass, a graph-guided and memory-driven agentic framework for spreadsheet reasoning and automation. SheetCompass explicitly models structural relationships within and across worksheets while maintaining task-relevant information in memory, enabling agents to reason more effectively over complex workbooks.

cs.AI↗

arXiv2026

OpenLoopEvolve: A Verifiable Self-Evolution Framework for Loop Policies in Long-Horizon Complex Tasks

Long-horizon complex tasks require agents to repeatedly observe states, formulate plans, invoke tools, verify results, and recover from failures in continuously changing environments. However, such control experience often remains confined to a single context or a fixed prompt, and is difficult to accumulate and reuse across historical traces. This paper presents OpenLoopEvolve (OLE), a self-evolution framework centered on the Loop Policy. OLE represents an agent's observation, planning, memory, action, verification, recovery, stopping, and budget control as portable policy assets with versions and lineages, and provides online and offline evolution modes that can be selected according to practical needs: the online mode triggers candidate generation based on feedback from continuous operation, whereas the offline mode searches for candidate policies from archived traces and failure evidence. Both modes share an evolution mechanism consisting of autonomous proposals by a large language model, Champion--Challenger paired evaluation, and robust release. Policies released online are activated at a subsequent task boundary, monitored using subsequent feedback, and rolled back to their parent versions when degradation conditions are met. On the simulated business benchmark YC-Bench, both modes improve aggregate task performance, task success rate, and risk metrics relative to a fixed initial Loop Policy. The results indicate that treating the Loop Policy as a governable asset can support the accumulation, comparison, release, and reuse of control experience and improve agent performance on long-horizon complex tasks.

cs.AI↗

arXiv2026

Point-gap topology in amorphous non-Hermitian quantum systems

Recent studies have revealed that not only does the correspondence between spectral winding numbers and skin modes break down in non-Hermitian systems, but the energy spectrum itself is highly sensitive to generic perturbations, system size, and boundary conditions. In amorphous non-Hermitian systems, where the positions of lattice sites are uncertain, the spectral instability becomes even more severe, making it difficult to identify stable topological edge states from the eigenvalue spectrum alone. To overcome this challenge, we introduce a correspondence between stable zero-mode singular states and mid-gap states of the energy spectrum in the thermodynamic limit. Because the singular value spectrum is highly robust against small perturbations and variation in size, topological edge states can be reliably probed via singular values even in finite-sized systems. Based on the singular-value decomposition of the Hamiltonian, we construct a topological invariant in real space to characterize the associated topologically protected edge states. Our approach provides a general strategy for exploring point-gap topology in real space and redefine the non-Hermitian skin effect from a new perspective.

quant-ph↗

arXiv2026

From Compressing Complexity to Accommodating Complexity: How AI Transforms Standardization and Individualization

Why do societies composed of individuals pursuing individuality repeatedly generate highly standardized systems? This paper argues that the answer lies in the evolution of information processing capacity. Artificial intelligence represents a historical transition in this capacity, enabling social systems to accommodate forms of complexity that previously had to be compressed. Industrial standardization was not merely a consequence of capital preference or power relations, but an institutional arrangement for maintaining the manageability of large-scale systems under limited information-processing capacity by reducing the variety of the controlled system. The fundamental change in the AI era lies in the expansion of information processing capacity across three dimensions: perception, computation, and execution. This expansion shifts personalized production from physical adaptation toward information-based adaptation and enables a transition from discrete to continuous objectification of difference. This paper proposes "cognitive fixed cost" as an analytical concept to describe how the upfront concentration of cognitive labor transforms the cost structure of personalized production. It further argues that standardization has not disappeared but has moved from explicit constraints at the product level to implicit generation rules embedded in infrastructures, shifting the central contradiction from "whether to have commonality" to "who controls commonality." The evolution of civilizational production logic is not a movement from commonality to individuality, but from compressing complexity to accommodating complexity.

cs.CY↗

arXiv2026

SpecBox: Speculative Sandbox Scheduling for Efficient LLM Agent Serving

As LLM agents increasingly rely on the Model Context Protocol (MCP) to invoke isolated external sandboxes, disaggregated sandbox deployment introduces a fundamental tension between resource utilization and interactive tail latency. Persistent long-lived sandbox reservations incur excessive memory overhead at scale, while lazy on-demand instantiation generates severe cold-start penalties that degrade response performance under multi-tenant, multi-turn agent workloads. To resolve this dilemma, we present SpecBox, a runtime built around speculative sandbox preallocation tailored for dynamic LLM agent execution pipelines. At its core, SpecBox implements keyword matching and streaming semantic embedding to enable intent-driven sandbox prewarming, which identifies pending tool execution demands mid-LLM token generation and fully overlaps sandbox bootstrapping with model inference. To extend prewarming windows across sequential agent steps, the framework leverages context-aware stochastic prefetching atop a sandbox dependency graph to probabilistically forecast future sandbox switches ahead of execution. We complement these speculative mechanisms with two orthogonal optimizations: a semantic result cache that prunes redundant repeated sandbox invocations, and a dedicated out-of-band shared-memory transport plane that bypasses conventional network serialization to deliver zero-copy artifact transfers. Evaluated on high-concurrency multi-turn agent traces, our prototype demonstrates that SpecBox cuts P99 end-to-end latency by up to $2.9\times$ relative to the on-demand sandbox baseline, while slashing peak memory consumption by $45.9\%$ compared to permanently reserved sandbox deployments.

cs.DC↗

arXiv2026

Citation Pathways in the AI Era: Interpretive Knowledge Nodes, Citation Compression Layers, and the Measurement Boundary of Scholarly Impact

This article identifies "citation pathway" as a long-neglected analytical dimension in scientometrics. Traditional evaluation metrics focus on measuring citation counts while paying insufficient attention to the intermediate nodes through which knowledge flows from its original source to the citing author. Building on an analysis of the normative structure of current reference systems, this article introduces two new concepts: Interpretive Knowledge Nodes (IKN) - academic papers that provide structured reorganizations of classic works - and Citation Compression Layers (CCL) - the intermediate layers that emerge when such knowledge products acquire stable publication identities and enter formal citation networks at scale. The central proposition is that AI has not changed citation rules themselves but has transformed the cost structure of producing citable knowledge intermediaries. Under conditions of full compliance, the network position effects of citation pathways may become a salient variable affecting the validity of impact measurement. Through a thought experiment involving a hypothetical journal R and a parsimonious "Citation Gravity conceptual model," this article substantiates this proposition and discusses the measurement boundaries of scholarly impact indicators, as well as the institutional risk of incentive misalignment under extreme scenarios.

physics.soc-ph↗

arXiv2026

An Empirical Study for Android-to-OpenHarmony GUI Test Migration

To reduce the substantial engineering effort required to test the corresponding applications from Android to OpenHarmony, migrating existing GUI test cases has become a critical problem. However, current research neither proposes solutions tailored for OpenHarmony nor provides a systematic evaluation of migration approaches on this system, leaving developers with limited empirical guidance in practice. In this paper, we present the first systematic empirical study of test migration from Android to OpenHarmony. Specifically, we first construct a dataset referred to as the ATH Benchmark, comprising 36 commercial applications with an average of over 9 billion downloads, along with 108 manually designed test cases. Second, we select two state-of-the-art test migration approaches (i.e., ReSPlay and ITeM) and adapt these two approaches to enable their execution on OpenHarmony. Third, we use the preceding infrastructure to evaluate these two approaches from three perspectives, including testing performance, root causes of failures, and the impact of OpenHarmony characteristics. Our results reveal that existing test migration approaches are less effective (15% success-rate on ReSPlay and 26% success-rate on ITeM) in Android-to-OpenHarmony scenarios. Through an in-depth analysis of failed cases, we identify that test performance is primarily hindered by OpenHarmony-specific characteristics, including technical architecture differences and unique ecosystem traits. Utilizing these findings, we propose an enhanced approach based on ITeM, referred as ITeM-HM, which incorporates specific OpenHarmony system features. As a result, ITeM-HM successfully achieves a 214% success-rate relative improvement over the original ITeM (from 26% to 81%).

cs.SE↗

arXiv2026

An LLM-powered Agentic Recommendation System for Connected TV Content Discovery

Recommendation systems, from traditional multi-stage to recent unified generative architectures, face challenges in incorporating diverse contextual signals, such as trending topics, breaking news, cultural events, and cross-surface user activities, into their ranking pipelines. These systems are designed to consume structured behavioral signals with consistent schemas, and lack the reasoning capability to naturally process unstructured or heterogeneously formatted contextual information. Incorporating such signals typically requires feature engineering, bespoke data pipelines, and carefully tuned heuristics. In this paper, we present an LLM-powered agentic recommendation system designed for Connected TV (CTV) content discovery that addresses these limitations. Our system leverages the reasoning capabilities of large language models to naturally process and synthesize diverse signals across varying schemas and structures, eliminating much of the manual integration inherent in traditional ranking and retrieval systems. Recognizing that current LLM-based solutions still fall short of traditional machine learning models in several recommendation tasks, including retrieval efficiency, personalization precision, and scalability, we adopt an agentic architecture that orchestrates specialized components, allowing each sub-task to be handled by the most suitable method, whether LLM-based or traditional ML. The main contribution of this work is our engineering approach to successfully overcoming the practical limitations of enabling LLM for recommendation, particularly inference latency. We share insights from our work and discuss the trade-offs and lessons learned in building a hybrid system that combines the flexibility of LLMs with the performance of established recommendation techniques.

cs.IR↗

arXiv2026

FBLayout: Optimizing Memory Layout for Efficient LLM Finetuning on Mobile GPUs

Transformer-based models have enabled unprecedented capabilities across language, vision, and multimodal tasks. On-device fine-tuning of transformer models offers a privacy-preserving path to personalized AI, yet remains inefficient on mobile GPUs due to severe memory constraints and frequent layout transformations in attention mechanism during training. Existing mobile training frameworks either use unified layouts for forward and backward passes -- leading to fragmented memory access and poor GPU utilization during backpropagation -- or rely on explicit layout conversions, which introduce significant transformation overhead. To overcome this, we propose FBLayout, a layout-aware framework that co-designs tensor organization with mobile GPU platforms. FBLayout introduces: (1) a unified R-Tile layout for multi-dimensional reductions across forward/backward passes; (2) tile-based index transformation to eliminate physical data movement; and (3) activation-guided layout selection to propagate efficient layouts globally. Evaluations on seven transformer models across different mobile phones (including ARM Mali and Qualcomm Adreno GPUs) show that FBLayout achieves 2.2-5.7x speedup over MNN, TFLite, and TVM, while significantly improving cache efficiency and reducing memory footprint, enabling practical on-device large model fine-tuning.

cs.AI↗

arXiv2026

DRBA: Dynamic Robotic Balance Assistant -- An assist-as-needed gait and balance rehabilitation robot for versatile training

The decline of human balance control due to aging and pathological conditions increases fall risk, a major concern in geriatric care and rehabilitation. Gait training is essential for balance recovery, enhancing walking ability and postural control. However, existing overground robotic gait trainers have limitations: body weight support systems are bulky and impractical for daily use, while end-effector-based systems often compromise transparency, altering natural gait dynamics. This paper presents the Dynamic Robotic Balance Assistant (DRBA), a novel gait trainer providing assist-as-needed body weight and balance support for various training scenarios. DRBA integrates a 3-degree-of-freedom (3-DoF) robotic arm for pelvic support with flexible motion, a compact sit-to-stand assistance module, and user-following and fall detection algorithms to ensure minimal interference and responsive support. Experimental results demonstrated high transparency, with minimal impact on natural gait dynamics. A patient trial with nine elderly patients with varying medical conditions and balance impairments (ranging from severe to mild) further validated DRBA's effectiveness. The results showed that DRBA-assisted training increased step length and walking speed compared to therapist-assisted gait training. Additionally, DRBA enabled users to perform tasks beyond their unaided ability, expanding rehabilitation possibilities. These findings highlight DRBA's potential to enhance rehabilitation outcomes by facilitating higher training intensity and enabling task-oriented exercises.

cs.RO↗