arXiv subjects

Jizhou Guo

Publications and source records attributed to Jizhou Guo.

12 recordsLinked to original sources

arXiv2026

Logarithmic Chowla Correlations Across All Shift Scales

Let $\lambda(n)=(-1)^{\Omega(n)}$ be the Liouville function. We prove a fixed power-logarithmic bound for its logarithmically weighted two-point correlations across the full shift range. There is an absolute $c>0$ such that every sufficiently large $x$ admits a single set $\mathcal E_x\subseteq[1,x]$ with $|\mathcal E_x\cap[1,H]|\ll_A H(\log x)^{-A}$ $(1\le H\le x)$ for every fixed $A>0$, while $\max_{\substack{1\le h\le x\ h\notin\mathcal E_x}}\sup_{1\le y\le x}\left|\sum_{n\le y}\frac{\lambda(n)\lambda(n+h)}{n}\right|\ll(\log x)^{1-c}$. The same exceptional-set formulation extends, without an upper cutoff, to all positive integer shifts. Earlier full-range theorems average over the shift; here a fixed saving holds pointwise outside one set whose density in every initial segment is smaller than every fixed negative power of $\log x$. The new middle-scale argument combines a general-good-modulus Liouville deletion lemma with a linear bad-modulus score, a progression Fourier estimate, and a Mellin-localized dilation that separates divisor-dependent endpoints. Maximal fixed-moment bounds evacuate the low prefix and control the long-shift range. Assuming GRH for primitive Dirichlet $L$-functions, we also prove, uniformly for $h\in\mathbb N$ and $1\le y\le x$, $\left|\sum_{n\le y}\frac{\lambda(n)\lambda(n+h)}{n}\right|\le\log(2\min{h,y})+O((\log x)^{1-c_{\mathrm G}})$ for an absolute $c_{\mathrm G}>0$, with no exceptional shifts.

math.NT↗

arXiv2026

Reinhardt's Maximum-Perimeter Polygon Problem for n=16, 32, and 64

A convex polygon is called small if its diameter is at most one. Reinhardt proved the universal perimeter bound $\operatorname{perim}(P)\le U_n:=2n\sin(\pi/(2n))$, and the bound is attained whenever $n$ has a nontrivial odd divisor. The remaining power-of-two cases have resisted exact solution beyond $n=8$. We give computer-assisted proofs of the first three cases, $n=16,32,64$, and in each case prove uniqueness of the maximizing congruence class. The proof architecture is common to all three cases: pass to the difference body $P-P$; encode its reconstruction by a sign code; prove that every global maximizer is saturated, so all difference-body vertices lie on the unit circle; localize every competitive configuration near the regular angle vector; exhaustively screen the sign codes using exact arithmetic; eliminate all nonwinning dihedral orbits; and prove uniqueness inside the winning code by strong convexity and a quantitative KKT argument. The exact certificates cover $2^{15}$ normalized codes for $n=16$, $2^{31}$ normalized codes for $n=32$, and all $2^{64}$ half-codes for $n=64$, leaving respectively $16$, $96$, and $896$ survivors before orbit elimination. The accompanying source package contains the verifiers, recorded outputs, hashes, and separate computational cross-checks.

cs.CG↗

arXiv2026

HAS-Bench: Evaluating LLM-Based Human-Agent Systems under Configurable Human Participation

Large language models increasingly operate in settings where humans are active collaborators rather than passive task providers. We introduce HAS-Framework, a graph-based framework that represents humans and LLM-powered agents as first-class participants with explicit roles, permissions, communication paths, and action authority. Building on this framework, HAS-Bench evaluates Human-Agent Systems under configurable human participation across agency levels, interaction channels, and persona policies. The benchmark measures both task outcomes and process-level collaboration behavior, including clarification quality, feedback utilization, control calibration, safety, initiative, and interaction cost. Experiments across six domains show that human participation can substantially improve task completion and failure recovery, but the gains depend on when, how, and by whom human input is exercised.

cs.AI↗

arXiv2025

Deep Research with Open-Domain Evaluation and Multi-Stage Guardrails for Safety

Deep research frameworks have shown promising capabilities in synthesizing comprehensive reports from web sources. While deep research possesses significant potential to address complex issues through planning and research cycles, existing frameworks are deficient in sufficient evaluation procedures and stage-specific protections. They typically treat evaluation as exact match accuracy of question-answering, but overlook crucial aspects of report quality such as credibility, coherence, breadth, depth, and safety. This oversight may result in hazardous or malicious sources being integrated into the final report. To address this, we introduce DeepResearchGuard, a framework featuring four-stage safeguards with open-domain evaluation, and DRSafeBench, a novel stage-wise safety benchmark. Evaluating across GPT-4o, o4-mini, Gemini-2.5-flash, DeepSeek-v3, GPT-5, DeepResearchGuard improves defense success rates by 16.53% while reducing over-refusal to 6%. Through extensive experiments, we show that DRSafeBench enables comprehensive open-domain evaluation and stage-aware defenses that effectively block harmful content propagation, while systematically improving report quality without excessive over-refusal rates.

cs.CL↗

arXiv2025

RECODE-H: A Benchmark for Research Code Development with Interactive Human Feedback

Large language models (LLMs) show the promise in supporting scientific research implementation, yet their ability to generate correct and executable code remains limited. Existing works largely adopt one-shot settings, ignoring the iterative and feedback-driven nature of realistic workflows of scientific research development. To address this gap, we present RECODE-H, a benchmark of 102 tasks from research papers and repositories that evaluates LLM agents through multi-turn interactions with LLM-simulated human feedback. It includes structured instructions,unit tests, and a five-level feedback hierarchy to reflect realistic researcher-agent collaboration. We further present ReCodeAgent, a framework that integrates feedback into iterative code generation. Experiments with leading LLMs, including GPT-5, Claude-Sonnet-4, DeepSeek-V3.1, and Gemini 2.5, show substantial performance gains with richer feedback, while also highlighting ongoing challenges in the generation of complex research code. RECODE-H establishes a foundation for developing adaptive, feedback-driven LLM agents in scientific research implementation

cs.CL↗

arXiv2025

LLM DNA: Tracing Model Evolution via Functional Representations

The explosive growth of large language models (LLMs) has created a vast but opaque landscape: millions of models exist, yet their evolutionary relationships through fine-tuning, distillation, or adaptation are often undocumented or unclear, complicating LLM management. Existing methods are limited by task specificity, fixed model sets, or strict assumptions about tokenizers or architectures. Inspired by biological DNA, we address these limitations by mathematically defining LLM DNA as a low-dimensional, bi-Lipschitz representation of functional behavior. We prove that LLM DNA satisfies inheritance and genetic determinism properties and establish the existence of DNA. Building on this theory, we derive a general, scalable, training-free pipeline for DNA extraction. In experiments across 305 LLMs, DNA aligns with prior studies on limited subsets and achieves superior or competitive performance on specific tasks. Beyond these tasks, DNA comparisons uncover previously undocumented relationships among LLMs. We further construct the evolutionary tree of LLMs using phylogenetic algorithms, which align with shifts from encoder-decoder to decoder-only architectures, reflect temporal progression, and reveal distinct evolutionary speeds across LLM families.

cs.LG↗

arXiv2025

PSG-Agent: Personality-Aware Safety Guardrail for LLM-based Agents

Effective guardrails are essential for safely deploying LLM-based agents in critical applications. Despite recent advances, existing guardrails suffer from two fundamental limitations: (i) they apply uniform guardrail policies to all users, ignoring that the same agent behavior can harm some users while being safe for others; (ii) they check each response in isolation, missing how risks evolve and accumulate across multiple interactions. To solve these issues, we propose PSG-Agent, a personalized and dynamic system for LLM-based agents. First, PSG-Agent creates personalized guardrails by mining the interaction history for stable traits and capturing real-time states from current queries, generating user-specific risk thresholds and protection strategies. Second, PSG-Agent implements continuous monitoring across the agent pipeline with specialized guards, including Plan Monitor, Tool Firewall, Response Guard, Memory Guardian, that track cross-turn risk accumulation and issue verifiable verdicts. Finally, we validate PSG-Agent in multiple scenarios including healthcare, finance, and daily life automation scenarios with diverse user profiles. It significantly outperform existing agent guardrails including LlamaGuard3 and AGrail, providing an executable and auditable path toward personalized safety for LLM-based agents.

cs.AI↗

arXiv2025

LENS: Learning Ensemble Confidence from Neural States for Multi-LLM Answer Integration

Large Language Models (LLMs) have demonstrated impressive performance across various tasks, with different models excelling in distinct domains and specific abilities. Effectively combining the predictions of multiple LLMs is crucial for enhancing system robustness and performance. However, existing ensemble methods often rely on simple techniques like voting or logits ensembling, which overlook the varying confidence and reliability of models in different contexts. In this work, we propose LENS (Learning ENsemble confidence from Neural States), a novel approach that learns to estimate model confidence by analyzing internal representations. For each LLM, we train a lightweight linear confidence predictor that leverages layer-wise hidden states and normalized probabilities as inputs. This allows for more nuanced weighting of model predictions based on their context-dependent reliability. Our method does not require modifying the model parameters and requires negligible additional computation. Experimental results on multiple-choice and boolean question-answering tasks demonstrate that LENS outperforms traditional ensemble methods by a substantial margin. Our findings suggest that internal representations provide valuable signals for determining model confidence and can be effectively leveraged for ensemble learning.

cs.CL↗

arXiv2025

Mining Intrinsic Rewards from LLM Hidden States for Efficient Best-of-N Sampling

Best-of-N sampling is a powerful method for improving Large Language Model (LLM) performance, but it is often limited by its dependence on massive, text-based reward models. These models are not only computationally expensive but also data-hungry, requiring extensive labeled datasets for training. This creates a significant data challenge, as they overlook a rich, readily available data source: the LLM's own internal hidden states. To address this data and efficiency gap, we introduce SWIFT (Simple Weighted Intrinsic Feedback Technique), a novel and lightweight method that learns a reward function directly from the rich information embedded in LLM hidden states. Operating at the token embedding level, SWIFT employs simple linear layers to effectively distinguish between preferred and dispreferred generations, eliminating the need for computationally intensive text-based modeling. Extensive experiments on standard benchmarks show that SWIFT outperforms existing baselines (12.7% higher accuracy than EurusRM-7B on MATH dataset) while using less than 0.005% of their parameters. Its robust scalability, compatibility with certain closed-source models via logit access, and ability to combine with traditional reward models for additional performance highlight SWIFT's practical value and contribution to more efficient data-driven LLM post-training. Our code is available at https://github.com/aster2024/SWIFT .

cs.LG↗

arXiv2025

LLM-Based Human-Agent Collaboration and Interaction Systems: A Survey

Recent advances in large language models (LLMs) have sparked growing interest in building fully autonomous agents. However, fully autonomous LLM-based agents still face significant challenges, including limited reliability due to hallucinations, difficulty in handling complex tasks, and substantial safety and ethical risks, all of which limit their feasibility and trustworthiness in real-world applications. To overcome these limitations, LLM-based human-agent systems (LLM-HAS) incorporate human-provided information, feedback, or control into the agent system to enhance system performance, reliability, and safety. These human-agent collaboration systems enable humans and LLM-based agents to collaborate effectively by leveraging their complementary strengths. This paper provides the first comprehensive and structured survey of LLM-HAS. It clarifies fundamental concepts, systematically presents core components shaping these systems, including environment and profiling, human feedback, interaction types, orchestration, and communication, explores emerging applications, and discusses unique challenges and opportunities arising from human-AI collaboration. By consolidating current knowledge and offering a structured overview, we aim to foster further research and innovation in this rapidly evolving interdisciplinary field. Paper lists and resources are available at https://github.com/HenryPengZou/Awesome-Human-Agent-Collaboration-Interaction-Systems.

cs.CL↗

arXiv2024

Model-based Large Language Model Customization as Service

Prominent Large Language Model (LLM) services from providers like OpenAI and Google excel at general tasks but often underperform on domain-specific applications. Current customization services for these LLMs typically require users to upload data for fine-tuning, posing significant privacy risks. While differentially private (DP) data synthesis presents a potential alternative, its application commonly results in low effectiveness due to the introduction of excessive noise on data for DP. To overcome this, we introduce Llamdex, a novel framework that facilitates LLM customization as a service, where the client uploads pre-trained domain-specific models rather than data. This client-uploaded model, optionally protected by DP with much lower noise, is inserted into the base LLM via connection modules. Significantly, these connecting modules are trained without requiring sensitive domain data, enabling clients to customize LLM services while preserving data privacy. Experiments demonstrate that Llamdex improves domain-specific accuracy by up to 26% over state-of-the-art private data synthesis methods under identical privacy constraints and, by obviating the need for users to provide domain context within queries, maintains inference efficiency comparable to the original LLM service.

cs.LG↗

arXiv2024

Calibrating Reasoning in Language Models with Internal Consistency

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs. Our code is available at github.com/zhxieml/internal-consistency.

cs.AI↗