Jiayang Gao

Jiayang Zou, Luyao Fan, Jiayang Gao et al.

We construct a smooth, strictly positive, Gaussian-decaying density on $\R^2$ for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--Geng log-convexity conjecture in dimension two and, by tensorization, in every dimension $d\ge2$. Consequently, the multidimensional forms of the Gaussian completely monotone conjecture, McKean's conjecture, and Toscani's entropy power conjecture also fail. This complements the recent one-dimensional counterexample of Gu and Sellke. The counterexample is a small hexagonal perturbation on the triangular torus, transferred to $\R^2$ by a Gaussian envelope, and supported by explicit two-dimensional numerics. Finally, we initiate the study of the sharp constants $θ_d^*$ by proving $θ_1^*=1$, establishing monotonicity in the dimension, and recording an intrinsic simplex resonance family in every fixed dimension. The explicit two-dimensional counterexample was found by GPT-5.5 Pro.

Jiayang Zou, Luyao Fan, Jiayang Gao et al.

In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical attainability results typically rely on compactness of the reproduction alphabet together with continuity of the distortion function, which may fail in many noncompact settings. We identify two complementary existence mechanisms under lower semi-continuity on locally compact Polish alphabets. For bounded distortions, we prove that the rate-distortion infimum is attained via the one-point compactification argument. For unbounded coercive distortions, we establish existence via concentration-compactness. We also give several counterexamples showing that our attainability results are close to sharp. Our results provide a unified and transparent existence theorem for rate-distortion problems with lower semi-continuous distortions.

Chaodong Tong, Qi Zhang, Jiayang Gao et al.

Large Language Models (LLMs) excel at question answering (QA) but often generate hallucinations, including factual errors or fabricated content. Detecting hallucinations from internal uncertainty signals is attractive due to its scalability and independence from external resources. Existing methods often aim to accurately capture a single type of uncertainty while overlooking the complementarity among different sources, particularly between token-level probability uncertainty and the uncertainty conveyed by internal semantic representations, which provide complementary views on model reliability. We present \textbf{HaluNet}, a lightweight and trainable neural framework that integrates multi granular token level uncertainties by combining semantic embeddings with probabilistic confidence and distributional uncertainty. Its multi branch architecture adaptively fuses what the model knows with the uncertainty expressed in its outputs, enabling efficient one pass hallucination detection. Experiments on SQuAD, TriviaQA, and Natural Questions show that HaluNet delivers strong detection performance and favorable computational efficiency, with or without access to context, highlighting its potential for real time hallucination detection in LLM based QA systems.

Jiayang Gao, Tianyi Zheng, Jiayang Zou et al.

Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance. Motivated by this insight, we introduce \textbf{Control Classifier-Free Guidance (C$^2$FG)}, a novel, training-free, and plug-in method that aligns the guidance strength with the diffusion dynamics via an exponential decay control function. Extensive experiments demonstrate that C$^2$FG is effective and broadly applicable across diverse generative tasks, while also exhibiting orthogonality to existing strategies.

Qihan Ren, Jiayang Gao, Wen Shen et al.

This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.

Hannah K. Wayment-Steele, Wipapat Kladwang, Andrew M. Watkins et al.

Messenger RNA-based medicines hold immense potential, as evidenced by their rapid deployment as COVID-19 vaccines. However, worldwide distribution of mRNA molecules has been limited by their thermostability, which is fundamentally limited by the intrinsic instability of RNA molecules to a chemical degradation reaction called in-line hydrolysis. Predicting the degradation of an RNA molecule is a key task in designing more stable RNA-based therapeutics. Here, we describe a crowdsourced machine learning competition ("Stanford OpenVaccine") on Kaggle, involving single-nucleotide resolution measurements on 6043 102-130-nucleotide diverse RNA constructs that were themselves solicited through crowdsourcing on the RNA design platform Eterna. The entire experiment was completed in less than 6 months, and 41% of nucleotide-level predictions from the winning model were within experimental error of the ground truth measurement. Furthermore, these models generalized to blindly predicting orthogonal degradation data on much longer mRNA molecules (504-1588 nucleotides) with improved accuracy compared to previously published models. Top teams integrated natural language processing architectures and data augmentation techniques with predictions from previous dynamic programming models for RNA secondary structure. These results indicate that such models are capable of representing in-line hydrolysis with excellent accuracy, supporting their use for designing stabilized messenger RNAs. The integration of two crowdsourcing platforms, one for data set creation and another for machine learning, may be fruitful for other urgent problems that demand scientific discovery on rapid timescales.