# Self-Modulating Quantum Fast-Weight Programmers for Efficient Adaptive Sequential Learning

arXiv: https://arxiv.org/abs/2606.24933 · HTML: https://mlsanity.com/paper/2606.24933/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 30 of 39)

- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Going Beyond Linear Transformers with Recurrent Fast Weight Programmers](https://mlsanity.com/paper/2106.06295/) (2021)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [PQLM -- Multilingual Decentralized Portable Quantum Language Model for Privacy Protection](https://mlsanity.com/paper/2210.03221/) (2022)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Applying QNLP to sentiment analysis in finance](https://mlsanity.com/paper/2307.11788/) (2023)
- [Practical Computational Power of Linear Transformers and Their Recurrent and Self-Referential Extensions](https://mlsanity.com/paper/2310.16076/) (2023)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Validating Large-Scale Quantum Machine Learning: Efficient Simulation of Quantum Support Vector Machines Using Tensor Networks](https://mlsanity.com/paper/2405.02630/) (2024)
- [Policy Gradients using Variational Quantum Circuits](https://mlsanity.com/paper/2203.10591/) (2022)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Efficient quantum recurrent reinforcement learning via quantum reservoir computing](https://mlsanity.com/paper/2309.07339/) (2023)
- [Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2412.08845/) (2024)
- [Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computers](https://mlsanity.com/paper/2503.14088/) (2025)
- [Quantum Adaptive Self-Attention for Quantum Transformer Models](https://mlsanity.com/paper/2504.05336/) (2025)
- [Rapid training of quantum recurrent neural networks](https://mlsanity.com/paper/2207.00378/) (2022)
- [Enhancing variational quantum state diagonalization using reinforcement learning techniques](https://mlsanity.com/paper/2306.11086/) (2023)
- [Reinforcement learning-assisted quantum architecture search for variational quantum algorithms](https://mlsanity.com/paper/2402.13754/) (2024)

## Built on by (most cited first, 2 of 2)

- [Stable Self-Modulating Quantum Fast-Weight Programmers with Bounded Memory Gates](https://mlsanity.com/paper/2607.02363/) (2026)
- [Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting](https://mlsanity.com/paper/2607.27945/) (2026)

## Abstract (arXiv)

Recent advances in quantum machine learning have motivated efficient models for sequential data processing. In this paper, we propose Self-Modulating Quantum Fast Weight Programmers, or Self-Modulating QFWP, which extends Quantum Fast Weight Programmers by introducing adaptive modulation over both newly generated fast-weight updates and historical fast-weight memory. Numerical results show that the proposed mechanism improves convergence stability and prediction performance across varying model settings, including different numbers of qubits and input sequence lengths. We further provide theoretical arguments explaining how self-modulation balances new information injection with memory retention, thereby enhancing temporal information propagation. These results suggest that Self-Modulating QFWP is a compact and effective framework for quantum machine learning on time-series data.