用费曼积分技巧让神经网络持续学习更稳定
Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs): A Feynman-Based Architecture for Continuous Learning Over Streaming Data
- 用积分形式替代传统反向传播，更新依赖历史数据整体
- 在流式数据上实现更平滑的稳定学习，无梯度爆炸问题
- 适合需要长期连续学习的场景，如在线推荐、传感器监控
实时连续学习在流式数据中仍是深度学习的核心挑战。传统基于梯度的模型（如通过时间反向传播，BPTT）在处理无界时间数据时面临计算与稳定性瓶颈。本文提出一种新架构——量子启发可微分积分神经网络（QIDINNs），利用费曼的积分号下微分技巧，将神经网络更新表示为对历史数据的积分。该重构使学习动态更平滑、更稳定，兼具物理可解释性与计算可行性。受费曼路径积分形式启发，且兼容量子梯度估计框架，QIDINNs为经典-量子混合神经计算开辟了新路径。我们在合成及真实流式任务上验证了模型有效性，并提出量子扩展与可扩展实现的方向。
原文摘要 · Abstract (English)
Real-time continuous learning over streaming data remains a central challenge in deep learning and AI systems. Traditional gradient-based models such as backpropagation through time (BPTT) face computational and stability limitations when dealing with temporally unbounded data. In this paper, we introduce a novel architecture, Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs), which leverages the Feynman technique of differentiation under the integral sign to formulate neural updates as integrals over historical data. This reformulation allows for smoother, more stable learning dynamics that are both physically interpretable and computationally tractable. Inspired by Feynman's path integral formalism and compatible with quantum gradient estimation frameworks, QIDINNs open a path toward hybrid classical-quantum neural computation. We demonstrate our model's effectiveness on synthetic and real-world streaming tasks, and we propose directions for quantum extensions and scalable implementations.
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