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

2026-07-02

AI Summary

This work addresses the divergence issue in self-modulating quantum fast weight programmers during long-sequence modeling, which arises from unbounded multiplicative factors applied to old memory states. To mitigate this, the authors propose a sign-preserving tanh gating mechanism applied exclusively to the recurrent memory branch, imposing bounded modulation on the old state while preserving additive updates and modulation of the new state. The study explicitly identifies cumulative memory modulation as central to performance gains and introduces targeted stabilization accordingly. Leveraging variational quantum circuits and CUDA-Q-based quantum dynamics simulation, experiments on quantum dynamical systems and Milan SMS traffic forecasting demonstrate that the proposed bounded modulation significantly enhances model stability and robustness over long sequences, thereby validating the critical role of controlled old-state modulation.

Abstract

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.

Problem

• Quantum Fast-Weight Programmers
• Self-Modulating
• bounded memory gates
• long-sequence divergence
• recurrent memory

Innovation

• Quantum Fast-Weight Programmers
• Self-Modulating
• Bounded Memory Gates
• Old-State Modulation
• Sequence Modeling