Volumetric Recurrent Computing

Core conjecture

Reuse matter as an operator; preserve the field as state

A fixed configurable nonlinear 3D physical operator can be reused recurrently on persistent physical state, providing additional computational depth without recurrence-indexed parameters or increasing state size.

If the configured medium implements Fθ and the transient field is xₜ, the proposed computation is xₜ₊₁ = Fθ(xₜ, uₜ). Additional recurrence should produce genuinely useful transformations—not merely repeated filtering, decay, or controller-side work.

Decisive distinction

What would make it more than an optical neural-network layer?

• The same physical operator is reused at every recurrent step.
• The evolving physical field carries computational state between steps.
• Increasing recurrence adds effective computation at fixed operator and fixed state size.
• Encoding, control, and readout costs are counted rather than hidden outside the substrate.

What has been learned

A failed regime is criticism, not erasure

The first recursive-MNIST experiment reused one simulated local volumetric operator. Recurrence changed state and confidence but did not reliably improve correctness. That result falsified the selected substrate-and-training regime; it did not establish that every recurrent physical substrate must fail.

The effort therefore shifted toward measuring effective controllable dimension, dynamical capacity, observation boundaries, and explicit material–mechanism–interface combinations before interpreting task performance.

Falsification posture

What evidence would weaken the architecture?

The central motivation is weakened if additional recurrence, under fixed operator and fixed state size, repeatedly fails to increase effective computation on increasingly compositional tasks—or if any apparent gain is explained by external control, extra parameters, readout, or encoding.