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Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions EngageTriBoost: Predictive Modeling of User Engagement in Digital Mental Health Intervention Using Explainable Machine Learning Reservoir observer enhanced with residual calibration and attention mechanism Efficient RL Training for LLMs with Experience Replay Wireless Communication Enhanced Value Decomposition for Multi-Agent Reinforcement Learning Adversarial Sensor Errors for Safe and Robust Wind Turbine Fleet Control IKKA: Inversion Classification via Critical Anomalies for Robust Visual Servoing Adaptive Simulation Experiment for LLM Policy Optimization EvoLen: Evolution-Guided Tokenization for DNA Language Model Smartwatch-Based Sitting Time Estimation in Real-World Office Settings Structural Evaluation Metrics for SVG Generation via Leave-One-Out Analysis Loom: A Scalable Analytical Neural Computer Architecture Spectral Geometry of LoRA Adapters Encodes Training Objective and Predicts Harmful Compliance Finite-Sample Analysis of Nonlinear Independent Component Analysis:Sample Complexity and Identifiability Bounds How does Chain of Thought decompose complex tasks? 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Understanding the Expressivity and Trainability of Fourier Neural Operator: A Mean-Field Perspective
Takeshi Koshizuka, Masahiro Fujisawa, Yusuke Tanaka, Issei Sato · 2023-10-10 · via cs.LG updates on arXiv.org

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation into the expressivity of a random FNO involves examining the ordered-chaos phase transition of the network based on the weight distribution. This phase transition demonstrates characteristics unique to the FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Furthermore, we identify a connection between expressivity and trainability: the ordered and chaotic phases correspond to regions of vanishing and exploding gradients, respectively. This finding provides a practical prerequisite for the stable training of the FNO. Our experimental results corroborate our theoretical findings.

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