# Stable Self-Modulating Quantum Fast-Weight Programmers with Bounded Memory Gates

arXiv: https://arxiv.org/abs/2607.02363 · HTML: https://mlsanity.com/paper/2607.02363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [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)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Quantum Long Short-Term Memory (QLSTM) vs Classical LSTM in Time Series Forecasting: A Comparative Study in Solar Power Forecasting](https://mlsanity.com/paper/2310.17032/) (2023)
- [Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computers](https://mlsanity.com/paper/2503.14088/) (2025)
- [Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.14026/) (2025)
- [QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory](https://mlsanity.com/paper/2512.05049/) (2025)
- [Benchmarking Quantum and Classical Sequential Models for Urban Telecommunication Forecasting](https://mlsanity.com/paper/2508.04488/) (2025)
- [Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning](https://mlsanity.com/paper/2605.06734/) (2026)
- [Quantum Long Short-Term Memory for Drug Discovery](https://mlsanity.com/paper/2407.19852/) (2024)
- [Generative Quantum-inspired Kolmogorov-Arnold Eigensolver](https://mlsanity.com/paper/2605.04604/) (2026)
- [Parameter-Efficient Quantum-Inspired Fast Weight Programmers for Traffic-Matrix Forecasting](https://mlsanity.com/paper/2606.27821/) (2026)
- [Recursive QLSTM with Dynamic Variational Quantum Circuit Adaptation](https://mlsanity.com/paper/2606.24932/) (2026)
- [Self-Modulating Quantum Fast-Weight Programmers for Efficient Adaptive Sequential Learning](https://mlsanity.com/paper/2606.24933/) (2026)

## Built on by (most cited first, 1 of 1)

- [Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting](https://mlsanity.com/paper/2607.27945/) (2026)

## Abstract (arXiv)

Quantum Fast-Weight Programmers (QFWPs) store temporal information in dynamically programmed variational-circuit parameters rather than in nonlinear recurrent hidden states, offering a practical route to quantum sequence modeling. Self-Modulating QFWP improves this framework by using input-dependent gates for both new fast-weight updates and the accumulated fast-weight state, but its unbounded old-state multiplier can diverge in long-sequence regimes. We propose a bounded old-state modulation rule that applies a sign-preserving tanh gate only to the recurrent memory branch while leaving the additive update and new-update modulation unchanged. We evaluate standard QFWP, full Self-Modulating QFWP, Only-New, and Only-Old variants on two CUDA-Q quantum-dynamics forecasting tasks and on Milan SMS telecommunication activity prediction. The quantum-dynamics results show that old-state modulation is the most consistent source of improvement over Standard QFWP, and that bounding the old-state gate removes long-sequence divergence while improving aggregate robustness. On Milan SMS forecasting, the original unbounded Self-Modulating QFWP converges across the tested grid and shows its clearest gains at longer input windows, with behavior close to the Only-Old ablation. These findings identify accumulated-memory modulation as the key mechanism of Self-Modulating QFWP and bounded old-state gating as a targeted stabilization strategy.