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This paper introduces a bounded modulation rule for Self-Modulating Quantum Fast-Weight Programmers (QFWPs), which enhances quantum sequence modeling by stabilizing the memory state during long sequences. The proposed method applies a sign-preserving tanh gate to the recurrent memory branch, effectively preventing divergence while maintaining performance on quantum-dynamics forecasting tasks and telecommunication activity prediction. Results indicate that this bounded approach significantly improves robustness and consistency in performance compared to standard QFWP and its unbounded variants.
Bounded modulation in Self-Modulating QFWPs not only stabilizes memory in long sequences but also enhances predictive performance across diverse quantum forecasting tasks.
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.
