Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs): A Feynman-Based Architecture for Continuous Learning Over Streaming Data

TL;DR

QIDINNs introduce a quantum-inspired neural architecture that uses integral-based updates for stable, interpretable continuous learning over streaming data, bridging classical and quantum computation.

Contribution

The paper presents a novel neural network architecture inspired by Feynman's integral calculus, enabling stable and interpretable continuous learning in streaming data scenarios.

Findings

Effective on synthetic streaming tasks

Demonstrates stability over traditional methods

Lays groundwork for quantum neural extensions

Abstract

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.