Explicit and data-Efficient Encoding via Gradient Flow

2024-12-01

AI Summary

In physical sciences, data scarcity severely degrades conventional autoencoders’ encoding fidelity and reconstruction accuracy due to approximate encoder-induced distortions. Method: We propose a gradient-flow-based explicit encoding paradigm featuring a unique decoder and eliminating the encoder entirely: input data are mapped directly to the latent space via second-order ordinary differential equation (ODE) dynamics; Nesterov acceleration and a loss-minimization-oriented adaptive ODE solver enhance robustness for stiff systems while improving training efficiency; adjoint sensitivity methods enable memory-efficient backpropagation. Contributions/Results: Experiments demonstrate substantial gains in representation fidelity and reconstruction quality under scarce-data regimes. The approach reduces integration cost significantly—without appreciable accuracy degradation—and achieves superior data utilization efficiency compared to standard autoencoders.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The autoencoder model typically uses an encoder to map data to a lower dimensional latent space and a decoder to reconstruct it. However, relying on an encoder for inversion can lead to suboptimal representations, particularly limiting in physical sciences where precision is key. We introduce a decoder-only method using gradient flow to directly encode data into the latent space, defined by ordinary differential equations (ODEs). This approach eliminates the need for approximate encoder inversion. We train the decoder via the adjoint method and show that costly integrals can be avoided with minimal accuracy loss. Additionally, we propose a $2^{nd}$ order ODE variant, approximating Nesterov's accelerated gradient descent for faster convergence. To handle stiff ODEs, we use an adaptive solver that prioritizes loss minimization, improving robustness. Compared to traditional autoencoders, our method demonstrates explicit encoding and superior data efficiency, which is crucial for data-scarce scenarios in the physical sciences. Furthermore, this work paves the way for integrating machine learning into scientific workflows, where precise and efficient encoding is critical. footnote{The code for this work is available at url{https://github.com/k-flouris/gfe}.}

Problem

• Information Distortion
• Sparse Data
• Machine Learning in Scientific Research

Innovation

• Gradient Flow
• Decoder-only Architecture
• Auto-regulation Solver