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

arXiv: https://arxiv.org/abs/2506.12111 · HTML: https://mlsanity.com/paper/2506.12111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)

## Abstract (arXiv)

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.