# Attractive and Repulsive Pattern Control in Sequence Generation

arXiv: https://arxiv.org/abs/2606.24911 · HTML: https://mlsanity.com/paper/2606.24911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 12 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [Maximum entropy models capture melodic styles](https://mlsanity.com/paper/1610.03414/) (2016)
- [Exact Regular-Constrained Variable-Order Markov Generation via Sparse Context-State Belief Propagation](https://mlsanity.com/paper/2605.07839/) (2026)

## Abstract (arXiv)

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.