用FPGA加速神经网络分层训练，省电又快。

The rising computational and energy demands of deep learning, particularly in large-scale architectures such as foundation models and large language models (LLMs), pose significant challenges to sustainability. Traditional gradient-based training methods are inefficient, requiring numerous iterative updates and high power consumption. To address these limitations, we propose a hybrid framework that combines hierarchical decomposition with FPGA-based direct equation solving and incremental learning. Our method divides the neural network into two functional tiers: lower layers are optimized via single-step equation solving on FPGAs for efficient and parallelizable feature extraction, while higher layers employ adaptive incremental learning to support continual updates without full retraining. Building upon this foundation, we introduce the Compound LLM framework, which explicitly deploys LLM modules across both hierarchy levels. The lower-level LLM handles reusable representation learning with minimal energy overhead, while the upper-level LLM performs adaptive decision-making through energy-aware updates. This integrated design enhances scalability, reduces redundant computation, and aligns with the principles of sustainable AI. Theoretical analysis and architectural insights demonstrate that our method reduces computational costs significantly while preserving high model performance, making it well-suited for edge deployment and real-time adaptation in energy-constrained environments.