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Jiakai Li

Publications and source records attributed to Jiakai Li.

13 recordsLinked to original sources
arXiv2026

Existential Opacity for Discrete-Event Systems with State Observations

Opacity is a fundamental system property for confidentiality in discrete-event systems (DES). Classical opacity is typically defined under event-based observations, requiring that any secret system behavior remains indistinguishable from some non-secret behavior to an external intruder. However, in many applications such as path planning or opacity-preserving tasks, the intruder observes system states rather than events. Moreover, it often suffices that the system exhibits secret behaviors that can be exploited for opacity-preserving task execution, but such a system property cannot be fully captured by existing notions of state-observation-based opacity. Motivated by this limitation, we propose a relaxed notion of existing state-observation-based opacity, called existential opacity (EO), which only requires the existence of secret behaviors (instead of all secret behaviors) that are indistinguishable from a non-secret behavior under the state observations of the intruder. We show that the notion of EO is more expressive than existing state-observation-based opacity notions. In addition, a class of EO properties together with their corresponding verification approaches are developed, enabling the analysis of existential opacity in discrete-event systems and providing a new criterion for determining the feasibility of opacity-preserving problems.

eess.SY↗
arXiv2026

Multi-framed real monopole Floer theory

This paper constructs a framed real monopole Floer homology for three-manifolds with involutions, marked with multiple basepoints. The relative gradings of these Floer homologies depend on the framing information and the paper gives a sufficient condition for the existence of relative mod two gradings. Assuming orientability and choices of orientations, this paper also proposes a definition of $\mathbf{Z}$-valued framed real Seiberg--Witten invariants for 4-manifolds with involutions, marked with circles.

math.GT↗
arXiv2026

Stop When Further Reasoning Won't Help: Attention-State Adaptive Generation in Reasoning Models

By incorporating test-time compute scaling, large reasoning models (LRMs) can solve complex problems through explicit chain-of-thought (CoT) reasoning processes. However, they often suffer from overthinking, resulting in redundant token outputs and degraded accuracy. Current methods to mitigate this issue remain limited: training-based approaches require substantial computational resources, while training-free methods rely on well-crafted prompts or unreliable confidence signals. In this work, we investigate early stopping from the perspective of attention distributions and propose a simple method, ASAG, which infers the model's reasoning state and adaptively adjusts the generation strategy. The proposed framework is training-free and plug-and-play, enabling seamless integration into existing LRMs. Extensive experiments on nine benchmarks demonstrate consistent improvements across mainstream LRMs with varying parameter scales, including the DeepSeek-R1-Distill and Qwen3 series. Specifically, ASAG improves average accuracy by 3.2% while reducing the number of generated tokens by nearly 40% across all reasoning tasks on Qwen3-8B.

cs.CL↗
arXiv2026

Toward Robust GraphRAG: Mitigating Retrieval Drift and Hallucination from Imperfect Knowledge Graphs

Graph Retrieval-Augmented Generation (GraphRAG) has become a common approach for multi-hop reasoning by using knowledge graphs (KGs) as structured retrieval indexes. However, most existing GraphRAG methods implicitly assume that LLM-constructed KGs provide structural support for evidence chaining. In this paper, we show that this assumption does not always hold in practice through an empirical analysis, and identify two recurring KG issue modes often overlooked by current retrievers: spurious noise and incomplete information. Spurious noise induces retrieval drift toward plausible but unsupported triples, whereas incomplete information leads to retrieval hallucination by forcing continuation through under-supported graph structure. To address these challenges, we propose CS-RAG, a robust GraphRAG framework that mitigates the impact of imperfect KGs during retrieval rather than relying on KG repair. CS-RAG first plans each query as an ordered sequence of executable atomic constraints and performs fine-grained anchor- and relation-aware retrieval to constrain evidence acquisition around the intended hop semantics. It then applies a sufficiency check to decide whether the retrieved evidence can safely induce variable bindings for subsequent propagation and activates textual recovery when structural support is insufficient, thereby reducing hallucinated structural continuation. Experiments on three multi-hop QA benchmarks show that CS-RAG is less sensitive to builder choice and remains stable under controlled KG issue injection. Code is available at: https://github.com/myz12138/CS-RAG/

cs.IR↗
arXiv2026

Rethinking LLM-Driven Heuristic Design: Generating Efficient and Specialized Solvers via Dynamics-Aware Optimization

Large Language Models (LLMs) have advanced the field of Combinatorial Optimization through automated heuristic generation. Instead of relying on manual design, this LLM-Driven Heuristic Design (LHD) process leverages LLMs to iteratively generate and refine solvers to achieve high performance. However, existing LHD frameworks face two critical limitations: (1) Endpoint-only evaluation, which ranks solvers solely by final gap to a reference solution, ignoring the convergence process and runtime efficiency; (2) High adaptation costs, where distribution shifts necessitate re-adaptation to generate specialized solvers for heterogeneous instance groups. To address these issues, we propose Dynamics-Aware Solver Heuristics (DASH), a framework that co-optimizes solver search mechanisms and runtime schedules guided by a convergence-aware metric, thereby identifying efficient and high-performance solvers. Furthermore, to mitigate expensive re-adaptation, DASH incorporates Profiled Library Retrieval (PLR), which maintains group-specialized solvers for profile-aware warm starts. These solvers are archived concurrently during evolution, allowing DASH to reuse matched specialists across heterogeneous distributions without restarting adaptation. Experiments on four combinatorial optimization problems demonstrate that DASH improves runtime efficiency by over 4 times while outperforming prior LHD baselines in the overall balance between gap and runtime across diverse problem scales. Furthermore, by enabling profile-aware warm starts, DASH maintains lower gap under distribution shift while reducing LLM adaptation costs by about 90%.

cs.LG↗
arXiv2025

DSAS: A Universal Plug-and-Play Framework for Attention Optimization in Multi-Document Question Answering

While large language models (LLMs) show considerable promise across various fields, they have notable limitations in handling multi-document question answering (Multi-doc QA) tasks. The first challenge is long-range dependency modeling, where LLMs struggle to focus on key information in long texts, which weakens important semantic connections. Second, most LLMs suffer from the ''lost-in-the-middle'' issue, where they have difficulty processing information in the middle of long inputs. Current solutions either truncate global dependencies or demand costly finetuning, ultimately lacking a universal and simple solution for these challenges. To resolve these limitations, we propose Dual-Stage Adaptive Sharpening (DSAS) containing two modules. (i) The Contextual Gate Weighting (CGW) module alleviates ''lost-in-the-middle'' by assessing paragraph relevance through layer-wise attention tracking and position-aware weighting. (ii) The Reciprocal Attention Suppression (RAS) module enhances focus on critical paragraphs by suppressing information exchange between key and irrelevant texts, thus mitigating the limitations in long-range dependency modeling. Notably, DSAS functions as a plug-and-play solution requiring no architectural modifications or extra training parameters. Extensive experiments on four benchmarks demonstrate DSAS's efficacy across mainstream LLMs (Llama, Qwen, Mistral, and Deepseek), with an average F1-score improvement of 4.2% in Multi-doc QA tasks on Llama-3.1-8B-Instruct and Qwen2.5-14B-Instruct. Ablation studies confirm the essential contributions of both the CGW and RAS modules. In addition, detailed discussions in the Appendix further validate the robustness and scalability of DSAS.

cs.CL↗
arXiv2025

Quantum Mechanical Approach for Modeling of Ternary Based Strained-Layer Superlattice

Ternary-based InAs/InAs1-xSbx Strained-Layer Superlattice (SLS)material with type-II band alignment belongs to the 6.1 A family with reasonably small lattice mismatch with GaSb substrate for epitaxial growth. InAs/InAs1-xSbx SLS have been proven to have more advantages such as longer carrier lifetime, better control on growth and manufacturability, and being considered as an alternative material system for infrared photodetectors. In this article a quantum mechanical based modelling on electronic band structure of InAs/InAs1-xSbx is presented. A modified sp3s* empirical tight binding method along with implementing a virtual crystal approximation with a bowing of the s-on-site tight-binding energy, were incorporated. In this approach, a theoretical explanation of atomic segregation in superlattices is suggested and used in calculations. The simulations show good agreement with experimentally measured band gap of InAs/InAs1-xSbx superlattices.

cond-mat.mtrl-sci↗
arXiv2025

Automatic Generation of Safety-compliant Linear Temporal Logic via Large Language Model: A Self-supervised Framework

Converting high-level tasks described by natural language into formal specifications like Linear Temporal Logic (LTL) is a key step towards providing formal safety guarantees over cyber-physical systems (CPS). While the compliance of the formal specifications themselves against the safety restrictions imposed on CPS is crucial for ensuring safety, most existing works only focus on translation consistency between natural languages and formal specifications. In this paper, we introduce AutoSafeLTL, a self-supervised framework that utilizes large language models (LLMs) to automate the generation of LTL specifications complying with a set of safety restrictions while preserving their logical consistency and semantic accuracy. As a key insight, our framework integrates Language Inclusion check with an automated counterexample-guided modification mechanism to ensure the safety-compliance of the resulting LTL specifications. In particular, we develop 1) an LLM-as-an-Aligner, which performs atomic proposition matching between generated LTL specifications and safety restrictions to enforce semantic alignment; and 2) an LLM-as-a-Critic, which automates LTL specification refinement by interpreting counterexamples derived from Language Inclusion checks. Experimental results demonstrate that our architecture effectively guarantees safety-compliance for the generated LTL specifications, achieving a 0% violation rate against imposed safety restrictions. This shows the potential of our work in synergizing AI and formal verification techniques, enhancing safety-aware specification generation and automatic verification for both AI and critical CPS applications.

cs.LO↗
arXiv2024

Real monopoles and a spectral sequence from Khovanov homology

Given a based link $(K,p)$, we define a "tilde"-version $\tilde{HMR}(K,p)$ of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler characteristic of $\tilde{HMR}(K,p)$ is equal to Miyazawa's invariant $|deg(K)|$ arXiv:2312.02041 and examine some examples. Further, we construct a spectral sequence over $\mathbb{F}_2$ abutting to $\tilde{HMR}(K,p)$, whose $E_2$ page is the reduced Khovanov homology $Khr(\overline{K})$ of the mirror link $\overline{K}$.

math.GT↗
arXiv2023

Monopole Invariants for Webs and Foams

We develop a package of monopole Floer-theoretic invariants for webs and foams using real Seiberg-Witten theory with orbifold singularities, based on Kronheimer and Mrowka's framework of monopole Floer homology.

math.GT↗
arXiv2022

Monopole Floer Homology and Real Structures

We define a "real" version of Kronheimer-Mrowka's monopole Floer homology for a 3-manifold equipped with an involution. As a special case, we obtain invariants for links via their double branched covers. The new input is the notion of a real spin-c structure, which consists of a spin-c structure along with a compatible anti-linear involution on the spinor bundle.

math.GT↗
arXiv2021

Short wavelength infrared avalanche photodetector using Sb-based strained layer superlattice

We demonstrate a low noise short wavelength infrared (SWIR) Sb based type II superlattice (T2SL) avalanche photodiodes (APD). The SWIR GaSb/(AlAsSb/GaSb) APD structure was designed based on impact ionization engineering and grown by molecular beam epitaxy on GaSb substrate. At room temperature, the device exhibits a 50 % cut-off wavelength of 1.74 micron. The device revealed to have electron dominated avalanching mechanism with a gain value of 48 at room temperature. The electron and hole impact ionization coefficients were calculated and compared to give better prospect of the performance of the device. Low excess noise, as characterized by the carrier ionization ratio of ~ 0.07, has been achieved.

physics.app-ph↗