OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case

2025-09-09

AI Summary

Existing methods for few-shot image denoising and deblurring suffer from model redundancy, excessive memory consumption, and heavy reliance on manually designed architectures. Method: This paper proposes an autoencoder framework grounded in optimal control theory and low-rank tensor manifold approximation. The encoder-decoder is formulated as an optimal control problem subject to ordinary differential equation (ODE) constraints; its continuous-time dynamics are derived via Lagrangian variational calculus, and an adaptive explicit integration scheme is designed on a low-rank tensor manifold to approximate the solution trajectory. Contribution/Results: To our knowledge, this is the first work to unify optimal control principles with tensor-structured priors for neural architecture learning. It achieves memory-efficient training—significantly reducing GPU memory footprint—and fully automatic architecture discovery without human intervention. Experiments demonstrate that the resulting compact models exhibit strong robustness and high reconstruction fidelity under diverse noise and blur degradations.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Combining optimal control and tensor methods for autoencoder training
• Formulating learning as constrained optimization with differential equations
• Enabling memory-efficient training and automated architecture discovery

Innovation

• Combines optimal control and tensor methods
• Uses adaptive explicit integration scheme
• Enables memory-efficient automated architecture discovery