Machine layer (epsilon-machines, epsilon-transducers, composed model) and network drawing

[Autoplectic]

Summary

Machine layer (infoflow/machines.py, infer_multiplex(machines=True), infer(..., machines=True))

• Every node gets an ε-machine, reconstructed by CSSR.
• Every discovered edge gets a pairwise ε-transducer, with the source shifted by the edge's delay.
• Every node with parents gets a joint-input ε-transducer over all its parents.
• Measures (shown in the summary table):
  • per node: C_mu, h_mu, E;
  • per transducer: channel complexity, driven entropy rate, and transducer TE with its gap from infoflow's estimate;
  • admitted_by (the estimator that admitted each parent), stability across time halves, and a count of observed symbols each node machine forbids (n_forbidden).
• The layer is off in every infer() preset. With machines=True it runs outside the time budget and is recorded in AutoReport.machines.

Composed model (infoflow/network_model.py)

• Nodes without parents are generated by their ε-machines; nodes with parents by their joint transducers. Feedback loops work because every delay is at least 1.
• simulate and a factorized held-out log_loss, compared with each node's own ε-machine.
• adequacy, a parametric bootstrap check of the factorization.
• to_hmm, guarded by a maximum state count, with exact per-edge flows computed from the explicit model.
• parametric_check: simulate surrogate data, re-infer, and compare networks.

Drawing (infoflow/draw.py)

• Four views:
  • decomposition glyphs: the core is intrinsic, the body is TE, the halo is TDMI;
  • parallel arcs;
  • stacked planes;
  • layer matrices.
• Hyperedge and machine-layer overlays.
• Interactive HoloViews/bokeh, or static matplotlib. Red is intrinsic, blue synergistic, green shared.

Datasets: coupled_tent with tent_ring_coupling, and noisy_eca.

Depends on

dit/sofic cssr-multitrial (multi-trial CSSR). Until it's merged and uv.lock is refreshed, the machine-layer tests skip in CI.

Tests

• tests/test_machines.py: known processes, a delay channel, XOR synergy, exact flows, guards, pickling, and the infer() pass-through.
• tests/test_draw.py: geometry, glyph identities, and both backends.
• Slow tests (-m slow):
  • tests/test_tent_ring.py: coupled Misiurewicz tent maps in five regimes, including documented xfails for infinite Markov order and weak coupling.
  • tests/test_eca_ring.py: rules 90 and 110, where the transducers recover the rule tables.
• Default suite: 184 passed.

Known limitations (documented in docs/machines.rst)

• Coarse symbols (the binary tent partition) make indirect paths look direct.
• transCSSR is expensive for joint histories longer than 2.
• In noisy rule 90, three true edges with about 0.5 bits of TE fail the existing layer significance test. That's in the layer statistics, not investigated here.

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