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新论文 · v1arXiv:2611.04157

Nonparametric GARCH: An Iterated Neural Estimator

Ruizhi Deng, Guohao Shen, Ngai Hang Chan

原文摘要

We study nonparametric estimation and forecasting for GARCH-type processes and propose an iterated neural estimator that alternates between estimating the recursion map and updating the unobserved conditional variances. Under mild conditions, we establish finite-sample bounds for the time-averaged in-sample variance-path error and show that the estimator is minimax rate-optimal up to logarithmic factors. Under stationarity and mixing conditions, we establish the same rate for recursion-map estimation and derive finite-sample bounds for out-of-sample variance forecasts and expected excess Gaussian quasi-likelihood (QLIKE) loss. The convergence rates depend on the true lag orders and remain unchanged when the fitted orders are overspecified. Simulation studies illustrate the effectiveness of our estimators under nonlinear and time-varying volatility dynamics. Real-data applications suggest that our neural methods perform competitively and can incorporate option-price and high-frequency information.

stat.ML · cs.LG · math.ST · stat.ME

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.36801

API-TAIL: Detecting Model Substitution in LLM APIs through Temperature-Aligned Likelihood Tails

Haocheng Mei, Yuchuan Tian, Ye Yuan, Chao Xu, Allen Chen, Kai Han, Yunhe Wang

原文摘要

Commercial language model APIs return only text, allowing a provider to cut costs by quietly routing a fraction of user requests to a cheaper substitute model while billing for the advertised one. Detecting such partial substitution is challenging because honest providers also alter the output distribution through undocumented decoding and serving choices, such as temperature scaling, sampling truncation, repetition and presence penalties, and default system prompts, forcing an audit to test against a composite null of legitimate configurations rather than a single reference. Our key insight is that these legitimate variations primarily shift response typicality across the entire batch, whereas partial substitution injects individual responses that remain anomalous under the claimed model. Building on this, we introduce API-TAIL, a typicality audit that first absorbs batch-level shifts by aligning a single effective temperature to center standardized surprisal scores across the audited batch, and then flags the endpoint if the number of remaining tail responses exceeds a threshold calibrated across legitimate configurations. Evaluated on real-world API responses and constructed substitution mixtures, API-TAIL controls false alarms across diverse honest providers and detects low-rate partial substitution with a small query budget. Under a common composite calibration, it outperforms the adapted rank- and MMD-based audit baselines.

cs.LG · cs.CL

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.34949

Correlation-Aware Exploration for Long-Trace Reasoning

Junxing Hu, Zicheng Zhang, Zhiqian Zhang, Ai Han, Yifeng Zhang, Pengzhang Liu, Ling Li

原文摘要

Reasoning models trained with Group Relative Policy Optimization (GRPO) now produce chains of thought thousands of tokens long, and recent studies reveal that such training is prone to policy collapse. Entropy regularization is the standard remedy, but it works by pushing probability mass away from the few tokens that carry it and toward the vast low-probability tail of the vocabulary, and it applies this force once for every token of the reasoning trace. This puts the bonus in direct conflict with the entropy decay that convergence requires, and makes its coefficient difficult to set in the long-trace regime. To resolve this tension, we propose Info-GRPO, an information-theoretic framework that cultivates correlation between the policy and a latent prior. Rather than raising entropy everywhere, Info-GRPO builds on the mutual information between a latent variable and the trajectory it induces: augmenting prompts with latent seeds during training lets the model explore diverse policies correlated with the prior, while the seed-conditioned entropy is guided toward convergence. Diversity is therefore carried across whole reasoning traces rather than by per-token randomness, and exploration no longer fights entropy reduction. Experiments show that Info-GRPO outperforms vanilla GRPO and entropy-regularized GRPO across diverse reasoning benchmarks. On AIME24, it improves $Avg@8$ over GRPO by 3.75%, 1.66%, 4.16%, and 4.17% on four backbones, and it reaches the same majority-vote accuracy with $8\times$ fewer samples. Code and models will be publicly released.

cs.LG · cs.AI · cs.CL

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arXiv ↗PDF ↗