Anxin Guo

Jiabin Liu, Zihao Zhou, Jialei Yan et al.

Precise three-dimensional (3D) reconstruction of wave free surfaces and associated velocity fields is essential for developing a comprehensive understanding of ocean physics. To address the high computational cost of dense visual reconstruction in long-term ocean wave observation tasks and the challenges introduced by persistent visual occlusions, we propose an wave free surface visual reconstruction neural network, which is designed as an attention-augmented pyramid architecture tailored to the multi-scale and temporally continuous characteristics of wave motions. Using physics-based constraints, we perform time-resolved reconstruction of nonlinear 3D velocity fields from the evolving free-surface boundary. Experiments under real-sea conditions demonstrate millimetre-level wave elevation prediction in the central region, dominant-frequency errors below 0.01 Hz, precise estimation of high-frequency spectral power laws, and high-fidelity 3D reconstruction of nonlinear velocity fields, while enabling dense reconstruction of two million points in only 1.35 s. Built on a stereo-vision dataset, the model outperforms conventional visual reconstruction approaches and maintains strong generalization in occluded conditions, owing to its global multi-scale attention and its learned encoding of wave propagation dynamics.

Anxin Guo, Jingwei Li

Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns. We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters with the continuous log-loss of LLMs. By analyzing this problem in the regime where facts are sparse in the universe of plausible claims, we establish a rate-distortion theorem: the optimal memory efficiency is characterized by the minimum KL divergence between score distributions on facts and non-facts. This theoretical framework provides a distinctive explanation for hallucination: even with optimal training, perfect data, and a simplified "closed world" setting, the information-theoretically optimal strategy under limited capacity is not to abstain or forget, but to assign high confidence to some non-facts, resulting in hallucination. We validate this theory empirically on synthetic data, showing that hallucinations persist as a natural consequence of lossy compression.

Anxin Guo, Aravindan Vijayaraghavan

We consider the problem of learning an arbitrarily-biased ReLU activation (or neuron) over Gaussian marginals with the squared loss objective. Despite the ReLU neuron being the basic building block of modern neural networks, we still do not understand the basic algorithmic question of whether one arbitrary ReLU neuron is learnable in the non-realizable setting. In particular, all existing polynomial time algorithms only provide approximation guarantees for the better-behaved unbiased setting or restricted bias setting. Our main result is a polynomial time statistical query (SQ) algorithm that gives the first constant factor approximation for arbitrary bias. It outputs a ReLU activation that achieves a loss of $O(\mathrm{OPT}) + \varepsilon$ in time $\mathrm{poly}(d,1/\varepsilon)$, where $\mathrm{OPT}$ is the loss obtained by the optimal ReLU activation. Our algorithm presents an interesting departure from existing algorithms, which are all based on gradient descent and thus fall within the class of correlational statistical query (CSQ) algorithms. We complement our algorithmic result by showing that no polynomial time CSQ algorithm can achieve a constant factor approximation. Together, these results shed light on the intrinsic limitation of gradient descent, while identifying arguably the simplest setting (a single neuron) where there is a separation between SQ and CSQ algorithms.