Modulation Gray-Box Modeling

Reference

Alistair Carson, Alec Wright, and Stefan Bilbao, "Gradient-based Optimisation of Modulation Effects", arXiv:2601.04867, submitted 8 January 2026.

Why It Matters

This paper is directly relevant to Greybound's modulation models because it targets the same live-guitar problem space:

• phaser, flanger, and chorus effects,
• analog reference units,
• gray-box / DDSP-style structure instead of pure black-box neural inference,
• training in the time-frequency domain,
• time-domain inference with zero added latency,
• low computational cost compared with heavier neural approaches.

The strongest architectural point for Greybound is that the runtime model should remain explicit and controllable. Neural or gradient-based optimization should identify internal parameters, not replace the rig graph with an opaque network.

Implementation Takeaways

For Greybound, this suggests a staged path:

• Keep the existing device descriptors, rig format, bypass state, and runtime controls.
• Promote modulation models to structured gray-box blocks whose parameters can be fitted.
• Start with the existing Tron, Jetstream, and Celeste models because they map directly to phaser, flanger, and chorus.
• Treat training/optimization as an offline toolchain that emits runtime coefficients.
• Keep live inference sample-by-sample and zero-latency.
• Prefer interpretable parameters: fractional delay, feedback, LFO shape, all-pass/JFET resistance law, BBD bandwidth, mix, and output gain.

Candidate Mapping

Tron:

• Current role: optical-style phaser.
• Research direction: move from heuristic all-pass sweep to fitted time-varying phase network.
• Candidate fitted parameters: sweep range, stage spread, feedback, lamp/LDR smoothing, nonlinear resistance law.

Jetstream:

• Current role: BBD-style flanger.
• Research direction: fitted fractional-delay path with feedback and bandwidth limits.
• Candidate fitted parameters: manual delay, sweep depth, feedback gain/sign, pre/post delay low-pass filters, wet/dry balance.

Celeste:

• Current role: BBD-style chorus.
• Research direction: fitted short-delay modulation with analog bandwidth and mix behavior.
• Candidate fitted parameters: delay offsets, LFO phase spread, wet-path tone, BBD filtering, level compensation.

Validation Requirements

Before replacing the current hand-tuned models, each fitted gray-box model should pass:

• impulse and chirp sanity checks,
• no added latency at inference,
• bounded feedback under all exposed controls,
• parameter smoothing without zipper noise,
• CPU budget under live period-size values,
• WAV render comparison against current model and target captures,
• monitor-log validation with no xruns and no unexpected clipping.

Open Questions

• Should the optimizer live inside this Rust workspace or in a separate Python training tool?
• What capture protocol should produce dry/wet training pairs for real pedals?
• Do we fit one model per reference unit, or one conditional model across knob settings?
• Should fitted coefficient files become part of the rig, the model descriptor, or a separate asset registry?