arXiv subjects

Yukai Song

Publications and source records attributed to Yukai Song.

3 recordsLinked to original sources

arXiv2026

Sparse coloring for isosceles-free grids: an AI-assisted proof case study

We study the largest size $C(n)$ of a subset of the $n\times n$ integer grid containing no isosceles triple, including equally spaced collinear triples. We prove $C(n)=Ω\left(n\sqrt{\log\log n/\log n}\right)$ by applying the sparse hypergraph coloring theorem of Cooper and Mubayi. Elementary geometry and primitive-direction counts give maximum degree $O(n^2\log n)$ and pair-codegree at most $5n$ for the forbidden-triple hypergraph. The resulting bound improves the explicit guarantee in PatternBoost by a factor of order $\sqrt{\log\log n}$. Recovered interaction records document how a Codex literature proposal, human route selection, finite verification, and author-relayed review informed proof synthesis and repair. We connect these actions to successive proof artifacts and extract two case-derived checking practices: tracking objects, parameters and conclusions in theorem applications, and seeding a definitional omission to test a finite verifier. Separately implemented enumerators agree on complete edge sets for every $2\le n\le12$; suppressing the degenerate-case branch loses exactly the equally spaced collinear triples. These records document assistance under human direction, and finite checks support implementation consistency rather than the asymptotic theorem itself.

math.CO↗

arXiv2026

COVER: Learning to Accept More in Selective Sleep Staging

Traditional sleep-staging methods apply the same model to every EEG epoch. Such uniform deployment expends computation on epochs that a smaller model could handle reliably, motivating cascades in which a primary classifier accepts its reliable predictions and defers the remainder to a more capable model. In this paper, we study the first stage of such a cascade: maximizing the coverage of fixed primary predictions subject to a prescribed accepted-risk target. We propose COVER (COVerage-oriented Error Ranking), which integrates two key innovations: (i) auxiliary-informed primary-error learning, which replaces maximum softmax probability (MSP) with a learned error score while preserving the primary labels, and (ii) fixed-scale scorer refinement, which builds on this score to directly maximize coverage under an empirical accepted-risk constraint rather than error-prediction accuracy over all epochs. We evaluate COVER on Sleep-EDF-20 at a 5% accepted-risk target, with subjects held out from all fitting and selection. Auxiliary-informed error learning raises mean subject coverage from 31.5% for MSP to 48.8% at similar subject-equal risk. At equal acceptance volume, with MSP accepting the same number of epochs as the learned scorer in each subject (20,639 in total), errors fall from 1,467 to 867. Fixed-scale refinement then adds 1.7 percentage points of coverage over its initialization in nested development, and COVER attains the highest mean coverage among eight evaluated scorers, 50.4% at 4.5% subject-equal risk, above the selective-ranking baseline SELE (49.3%) and the probability-fusion comparator DuoF (43.6%). To the best of our knowledge, this is the first work to combine auxiliary-informed primary-error learning with fixed-scale coverage refinement for selective sleep staging, offering a basis for reliability-aware allocation of computation in cascaded sleep staging.

cs.LG↗

arXiv2025

Two-Stage Voting for Robust and Efficient Suicide Risk Detection on Social Media

Suicide rates have risen worldwide in recent years, underscoring the urgent need for proactive prevention strategies. Social media provides valuable signals, as many at-risk individuals - who often avoid formal help due to stigma - choose instead to share their distress online. Yet detecting implicit suicidal ideation, conveyed indirectly through metaphor, sarcasm, or subtle emotional cues, remains highly challenging. Lightweight models like BERT handle explicit signals but fail on subtle implicit ones, while large language models (LLMs) capture nuance at prohibitive computational cost. To address this gap, we propose a two-stage voting architecture that balances efficiency and robustness. In Stage 1, a lightweight BERT classifier rapidly resolves high-confidence explicit cases. In Stage 2, ambiguous inputs are escalated to either (i) a multi-perspective LLM voting framework to maximize recall on implicit ideation, or (ii) a feature-based ML ensemble guided by psychologically grounded indicators extracted via prompt-engineered LLMs for efficiency and interpretability. To the best of our knowledge, this is among the first works to operationalize LLM-extracted psychological features as structured vectors for suicide risk detection. On two complementary datasets - explicit-dominant Reddit and implicit-only DeepSuiMind - our framework outperforms single-model baselines, achieving 98.0% F1 on explicit cases, 99.7% on implicit ones, and reducing the cross-domain gap below 2%, while significantly lowering LLM cost.

cs.CL↗