Attractive and Repulsive Pattern Control in Sequence Generation

2026-06-19

AI Summary

This work addresses the tendency of variable-order Markov models to fall into repetitive high-order patterns—such as local periodicity or suffix repetition—during long-sequence generation. To mitigate this issue, the authors propose a signed pattern control mechanism that introduces, for the first time, a positive–negative coupling scheme into sequence generation. Within the BP-Regular sampling framework, the method computes target pattern activation scores using weighted recursive automata and enables precise sampling from a corrected distribution via belief propagation, thereby selectively attracting or repelling specific patterns. Experiments on Bach, Telemann, and jazz solo datasets demonstrate a significant reduction in 8-gram self-reuse rates, an increase in the number of effective 8-grams, and improved coverage of training-supported 4-grams, all while preserving lower-order structural properties. These results confirm the approach’s cross-style generalizability and online adaptive control capability.

Abstract

Variable-order Markov models preserve local symbolic syntax by adapting context length, but long continuations can enter recurring high-order "tunnels": repeated suffixes, locally periodic passages, or copied fragments longer than the formal Markov order. This paper introduces signed pattern control for variable-order Markov generation with BP-Regular sampling. A weighted recurrence automaton computes an activation R for a chosen family of target patterns, and belief propagation samples exactly from P_beta(x) proportional to P_0(x) exp(beta R(x)). Negative coupling makes the target patterns costly during sampling; positive coupling rewards the same patterns and turns them into controlled attractors. The target family may be mined online from overactive generated material, supplied by a score or style vocabulary, or designed as an experimental probe. The main experiments use the online homeostatic case, choosing patterns that become overactive in the sampling history. On six duration-bearing monophonic sources, including Bach and Telemann material, the negative branch reduces generated 8-gram self-reuse, increases the effective number of generated 8-grams, and increases coverage of training-supported 4-gram contexts while preserving substantial lower-order support. A pitch-sequence replication on five Weimar Jazz Database solos gives the same anti-reuse signature outside Baroque material. The same signed mechanism also provides a positive branch for probing attractor basins, phase transitions, and hysteresis in the underlying variable-order model.

Problem

• sequence generation
• variable-order Markov models
• pattern repetition
• attractor control
• redundancy

Innovation

• signed pattern control
• variable-order Markov models
• BP-Regular sampling
• recurrence automaton
• anti-reuse generation