GraphIDyOM: A graph-native Python reimplementation of IDyOM for musical expectation modelling

Humans can acquire a highly structured intuitive understanding of musical patterns, yet these patterns often require multiple iterations of reflection and re-listening to internalize fully. To capture such an internalization process, we present a computational model for the learning of jazz harmonic patterns based on library learning. Given a corpus of harmonic progressions, our model searches over a space of programs composed of primitive harmonic relations in order to discover concise generative explanations of the corpus. The model first enumerates possible programs for each piece, and then jointly learns a library of harmonic patterns and refactored programs. To efficiently navigate the vast joint space of programs and libraries, we integrate deductive parsing with library learning on e-graphs. We explore how well our model captures aspects of human musical pattern learning by evaluating the intuitiveness of both programs and libraries, as well as similarities to human-written harmonic derivations.

Text-to-music language models begin with a choice usually made by default: how to tokenize music. Normally entangled with backbone, data, and recipe, its effect has never been measured in isolation. We fix pretrained Qwen3.5 (0.8B-27B), data, budget, and decoding, and swap only the representation across seven tokenizations, anchoring texture metrics to each representation's model-free ceiling. The ordering is clean and surprising: representation, not model size, is the binding variable for distributional fidelity. Scaling the backbone 34x barely moves Frechet Music Distance (FMD), whereas switching representation halves it. PMT, a performance-resolution stream we release (10 ms timing, per-note velocity, multi-track texture; 609 symbols), reaches FMD 159 at 0.8B against 272-286 for beat grids (1.7-1.8x lower, up to 2.8x elsewhere; non-overlapping bootstrap CIs), so a 0.8B performance-resolution model beats a 27B beat grid. It reappears on a 26M from-scratch backbone and a second performance-resolution tokenizer: a property of the class, not one lucky vocabulary. Nor is it a finer-lattice artifact: snapping PMT's onsets to the beat grids' resolution still leaves it 67-129 FMD ahead of both (n=500). The effect is distributional; whether it is audible is a separate question, left open by our probe, with a human study pre-registered. Native caption adherence is weak but separable: a lightweight decode-time constraint doubles instrument-F1 (.28 to .60) and Correct-Key (.16 to .35) at no distributional cost. We release the harness, 25+ checkpoints, two corpora (86.6k aligned across caption/MIDI/ABC/audio; 6.25M captioned, the largest for music), and an imprinting diagnostic: published text-to-MIDI systems reproduce their training distribution near-invariant to the caption (72% vs. 71% chord-time on disjoint domains). The field's next representation claim can now be measured, not asserted.

It remains unclear whether graph language models learn structural regularities or merely memorize training graphs; this cannot be resolved by current aggregate fidelity metrics alone. We develop a calibrated diagnostic protocol that combines frequent subgraph mining, a graph-level bootstrap baseline, and three-level frequency stratification to disentangle memorization from structural alignment. Using this framework, we show that graph language models can acquire structural regularities beyond memorization at scale, primarily in the high-frequency regime. This is supported by the following empirical evidence: On five TU benchmarks, LLaMA-style graph language models reach high subgraph-rank correlation, yet their alignment is matched or exceeded by the memorization bootstrap in most cases. At small scale, under our bootstrap diagnostic, fidelity is largely indistinguishable from verbatim recall. In contrast, at large scale with 3.75M graphs, verbatim memorization drops sharply while rank correlation remains near ceiling. Crucially, in a separate fixed-subsample analysis, frequent subgraph mining restricted to the novel-only subset closely tracks the corresponding all-generation Spearman correlation, providing evidence that the alignment is not driven solely by verbatim recall. Across all scales, high-frequency patterns are well reproduced, while rare patterns remain poorly covered, and this deficit narrows only marginally as capacity increases. We observe the same scale-dependent crossover under two distinct graph serializations (canonical DFS code and action sequences), providing evidence of robustness in our analysis.