arXiv subjects

Jianru Shen

Publications and source records attributed to Jianru Shen.

8 recordsLinked to original sources

arXiv2026

TopoBudget: Persistent-Connectivity-Preserving Web Graph Sparsification for Reusable Community Analytics

Web and social graphs are analyzed repeatedly for community structure, yet many of their edges are redundant for this purpose, which motivates sparsification. Existing sparsifiers preserve spectral quantities, cuts, local similarity, or a single clustering, but none preserves the thresholded connectivity structure of an edge-relevance filtration, the multiscale pattern by which groups form at high relevance and merge through weaker bridges. We study persistent-connectivity-preserving sparsification: given a graph, an edge-relevance filtration, and a proxy partition computed once during preprocessing, select a budgeted subgraph that preserves the labeled component partition at every threshold, and hence the zero-dimensional persistence diagram, while retaining community evidence for later analyses. Our method, TopoBudget, first extracts a tie-aware persistence backbone that enforces this constraint, then allocates the residual edge budget by greedily maximizing a backbone-conditioned submodular objective that rewards balanced recovery of proxy-internal degree. We prove exact preservation of the component partition at every threshold, and that the conditioned objective is monotone and submodular, so greedy attains a (1-1/e) guarantee for the fixed-backbone residual problem. On held-out synthetic benchmarks and six real Web and social graphs at equal budget, TopoBudget gives the strongest community preservation among topology-preserving methods under Louvain, remains competitive under Infomap, incurs zero topology mismatch, and runs substantially faster than an effective-resistance baseline. A no-backbone ablation shows that, on the real graphs, the mandatory backbone improves average quality while providing the exact guarantee. TopoBudget thus couples exact multiscale connectivity with budgeted, reusable community preservation.

cs.SI↗

arXiv2026

Provable Limits and Certified Deferral for Verbalized Uncertainty in Small Language Models

Small open-weight language models increasingly run in private, offline, and cost-sensitive settings, where the key deployment question is not only what a model answers but when it should defer to a human. We study whether verbalized confidence can support risk-controlled deferral, evaluating eleven instruction-tuned models from three families, 0.5B to 14B parameters, on ARC-Challenge and TruthfulQA with 25,168 local predictions. Three theoretical results delimit what calibration can provide: strictly monotone calibration preserves the risk-coverage frontier and error-detection AUROC; temperature scaling cannot calibrate models whose confidence stays above one half while accuracy falls below it; and a Clopper-Pearson procedure converts a 200-question calibration set into a finite-sample risk certificate under an i.i.d. deployment assumption. Empirically, eight of 22 model-task pairs hit the temperature-scaling infeasibility floor within one percentage point of the predicted bound. Platt scaling reduces ECE to as low as 0.02, yet certified autonomy at a 20% risk budget is granted to only three model-task pairs and to none at 10%. We also identify and repair an answer-ordering artifact in the multiple-choice form of TruthfulQA. Calibration gives confidence semantics; certified deferral determines when small models are safe to use.

cs.CL↗

arXiv2026

Closed-Loop Validation-Repair for Healthcare Interoperability: A Multi-Model Study of Schema Compliance in Clinical LLMs

Healthcare interoperability requires AI systems to produce structured outputs conforming to standardized schemas including ICD-10 for diagnostic coding, CPT for procedure billing, and HL7 FHIR for data exchange. While large language models demonstrate clinical reasoning capabilities, their integration into electronic health record systems faces a critical barrier: schema noncompliance. We evaluate three open-source models, Qwen2.5 7B, Llama 3.1 8B, and Gemma2 9B, via local deployment across 320 clinical scenarios spanning ten medical specialties, yielding 960 model-scenario pairs assessed under paired baseline and validation-repair conditions. First, schema noncompliance is consistent across the three model families, with baseline compliance rates ranging from 85.9 to 91.6 percent despite varying architectures and training data, suggesting shared gaps in medical training corpora rather than model-specific limitations. Second, 96 percent of validator-detected failures are representation-level format violations such as alternative medical abbreviations and code prefixes, indicating models follow clinical writing conventions but lack awareness of healthcare IT standards. Third, the validation-repair framework achieves 99.0 percent overall compliance, ranging from 98.4 to 99.4 percent across models, with most errors resolving within one or two iterations. Exact McNemar p-values below 0.001 and absolute improvements of 7.8 to 12.5 percentage points across model sizes confirm statistical significance. These results support closed-loop validation-repair as an effective system-level safeguard for healthcare interoperability, improving schema-level readiness for downstream clinical system integration.

cs.CL↗

arXiv2026

Discrete Ricci Curvature on Protein Contact Graphs for Lightweight Fold Classification

Protein fold classification can be approached via sequence-based representations or structural descriptors, but direct comparisons between lightweight handcrafted descriptors and pretrained protein language model embeddings remain limited. We investigate discrete Ricci curvature on Calpha contact graphs as a lightweight structural descriptor for fold classification. Each protein domain is represented by a 22-dimensional fixed-length feature derived from summary statistics and quantiles of Ollivier-Ricci and Forman-Ricci edge curvature distributions. We evaluate on CATH top-10 Topology classification and on the ASTRAL 40%-identity SCOPe top-10 Fold benchmark, comparing against geometry, contact-graph statistics, persistent homology, and mean-pooled ESM-2 (150M) baselines. On both datasets, lightweight structural descriptors substantially outperform mean-pooled ESM-2 embeddings, with a larger performance gap on the ASTRAL 40% SCOPe benchmark. Ricci alone uses 22 dimensions, or 3.4% of the ESM-2 baseline dimensionality, and already outperforms mean-pooled ESM-2 on both datasets. Combining Ricci with persistent homology yields the strongest performance, achieving macro-F1 of 0.71 on CATH and 0.68 on SCOPe with a 112-dimensional feature vector. These results identify a regime where lightweight interpretable graph descriptors offer a practical alternative to pretrained protein language model embeddings.

cs.LG↗

arXiv2026

Evidence Graph Consistency in Retrieval-Augmented Generation: A Model-Dependent Analysis of Hallucination Detection

Retrieval-Augmented Generation (RAG) reduces but does not eliminate hallucination in large language models. Existing detection methods rely on flat similarity between generated answers and retrieved passages, ignoring structural relationships among evidence pieces and answer claims. We propose Evidence Graph Consistency (EGC), a framework that constructs a local evidence graph per response and computes five structural consistency measures as hallucination indicators. Evaluated on the full question answering split of RAGTruth across six LLMs (5,767 responses), EGC reveals a consistent model-family split: graph consistency features show the expected diagnostic direction for hallucinations in Llama-2 models but exhibit systematic reversal in GPT-4, GPT-3.5, and Mistral-7B. This reversal suggests qualitatively different hallucination patterns across model families and indicates that embedding-based graph consistency cannot serve as a model-independent hallucination detection signal.

cs.CL↗

arXiv2026

Frequency-Scale Saliency for Spectral Descriptor Analysis in 3D Shape Retrieval

Classical spectral descriptors such as the Heat Kernel Signature and Wave Kernel Signature are widely used for non-rigid 3D shape retrieval, yet their failure modes remain poorly understood. We present a frequency-scale saliency framework that audits these descriptors by quantifying the retrieval-level contribution of each descriptor scale interval through ablation. We introduce class spectral fingerprints to characterize category-level scale dependence, and show that descriptor similarity between class pairs is substantially correlated with retrieval failure, with a Spearman correlation of 0.479. Experiments on SHREC'11 demonstrate that short scales dominate retrieval performance while long scales are harmful, that HKS and WKS exhibit distinct scale dependence patterns, and that saliency-weighted retrieval improves mAP on hard categories by 0.156, with cross-fold and random-weight controls confirming that the gain is stable and not due to arbitrary reweighting.

cs.GR↗

arXiv2026

On the Gap Structure of Generalized Stirling Numbers

Katugampola's 2015 study of generalized fractional differential operators produced triangular arrays of integer coefficients indexed by a fractional order r and by dimensions n and k, but no combinatorial interpretation has been established for any fractional order. We give the first such interpretation, with two main results: (i) a complete combinatorial interpretation for r = 1/2 and n = 1,2,3, and (ii) a rigorous proof that this interpretation cannot extend to n >= 4 within the same framework. For n = 1,2,3, we show that the coefficients for r = 1/2 count binary sequences satisfying two conditions: they contain at least one symbol B, and they have gap <= 1, where the gap is the distance between the first and last occurrence of B. Each sequence is assigned a type k by a parity-dependent rule involving the gap value, and exhaustive enumeration matches Katugampola's coefficients exactly. We then prove an obstruction theorem showing that the gap <= 1 condition forces any such model to produce at most two distinct types per row, whereas Katugampola's array requires at least three types for every n >= 4. Thus the gap <= 1 binary-sequence interpretation works if and only if n = 1,2,3. Our results turn a computational observation into a rigorous impossibility theorem and provide guidance for future attempts to obtain complete combinatorial interpretations of fractional-calculus coefficients.

math.CO↗

arXiv2026

Failure-Aware Enhancements for Large Language Model (LLM) Code Generation: An Empirical Study on Decision Framework

Large language models (LLMs) show promise for automating software development by translating requirements into code. However, even advanced prompting workflows like progressive prompting often leave some requirements unmet. Although methods such as self-critique, multi-model collaboration, and retrieval-augmented generation (RAG) have been proposed to address these gaps, developers lack clear guidance on when to use each. In an empirical study of 25 GitHub projects, we found that progressive prompting achieves 96.9% average task completion, significantly outperforming direct prompting (80.5%, Cohen's d=1.63, p<0.001) but still leaving 8 projects incomplete. For 6 of the most representative projects, we evaluated each enhancement strategy across 4 failure types. Our results reveal that method effectiveness depends critically on failure characteristics: Self-Critique succeeds on code-reviewable logic errors but fails completely on external service integration (0% improvement), while RAG achieves highest completion across all failure types with superior efficiency. Based on these findings, we propose a decision framework that maps each failure pattern to the most suitable enhancement method, giving practitioners practical, data-driven guidance instead of trial-and-error.

cs.SE↗