用最优控制与张量方法，让自编码器自动瘦身并高效训练。
OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case
- 基于微分方程和变分法设计网络结构，实现端到端优化。
- 在图像去噪与去模糊任务中，内存占用显著降低，性能稳定。
- 适合资源受限场景下的模型压缩与自动化架构设计。
本文提出一种基于最优控制与低秩张量方法的新型自编码器深度神经网络框架，通过将学习任务建模为受微分方程约束的优化问题，并利用拉格朗日方法推导出最优性条件。采用自适应显式积分方案在低秩张量流形上近似求解微分方程，实现高效内存压缩。该框架整合为OCTANE（Optimal Control for Tensor-based Autoencoder Network Emergence），可生成紧凑架构、大幅降低内存消耗，并在数据有限时仍保持良好学习能力。实验验证其在图像去噪与去模糊任务中的有效性，同时提供关键超参数设置建议。
原文摘要 · Abstract (English)
This paper presents a novel, mathematically rigorous framework for autoencoder-type deep neural networks that combines optimal control theory and low-rank tensor methods to yield memory-efficient training and automated architecture discovery. The learning task is formulated as an optimization problem constrained by differential equations representing the encoder and decoder components of the network and the corresponding optimality conditions are derived via a Lagrangian approach. Efficient memory compression is enabled by approximating differential equation solutions on low-rank tensor manifolds using an adaptive explicit integration scheme. These concepts are combined to form OCTANE (Optimal Control for Tensor-based Autoencoder Network Emergence) -- a unified training framework that yields compact autoencoder architectures, reduces memory usage, and enables effective learning, even with limited training data. The framework's utility is illustrated with application to image denoising and deblurring tasks and recommendations regarding governing hyperparameters are provided.
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