Solbakken Research Initiative · April 2026 · Preprint

The Conversion Floor

Tokens, Modal Tokens, and the Two-Source Noise Condition for Photonic AI Acceleration

Thesis

The discrete token is a hardware artifact of electronic accelerators, not a principled unit of meaning. Architectural pressure is already relocating discreteness from the computational core to the system boundary. Photonic matrix-vector multiplication is a candidate substrate for the hybrid primitive this trajectory requires — the modal token — but its viability is gated by a two-dimensional noise condition defined by weight memory stability (δₘ) and modulation noise (σ_mod) as physically distinct axes.

The core argument

Two Noise Sources, One Floor

Under the simplest separable noise model, the ADC precision requirement b for a photonic MVM system satisfies a two-axis constraint — not one. Weight memory drift and modulation noise are physically distinct and independently variable, and the Goldilocks window where photonic MVM delivers net efficiency gain is bounded on both axes simultaneously.

b ≥ max( f(δₘ), g(σ_mod) )

Appendix A of the paper derives this as the worst-case approximation of a full SNR constraint under separability. The γ cross-term in the variance decomposition captures the grain-boundary coupling between the two axes in the ferroelectric-graphene stack — a structural consequence of the shared interface, absent in TFLN and silicon-photonic architectures.

A secondary consequence is the phase-fragile similarity regime: for interference-based similarity, σ_mod does not merely set a floor for numerical precision. It sets a floor for semantic fidelity. Near a destructive-interference condition, small phase errors produce step-function flips in similarity value, not gradual degradation.

§3.4 — Back-of-envelope

Placements on the Two-Axis Map

The new contribution in v11 is a first back-of-envelope placement of two deployed commercial systems on the (δₘ, σ_mod) map, using only public specifications and published noise literature. Error bars are a factor of 3–10; the purpose is structure, not precision.

Lightmatter Envise

δₘ: high
σ_mod: low

Silicon photonics, thermo-optic MZI weights. Tax paid through run-time analog gain control — an ongoing operational cost.

Q.ANT NPS

δₘ: low
σ_mod: moderate

TFLN eliminates thermal crosstalk; binding constraint shifts to TCCR noise. Tax paid through post-fabrication annealing — a one-time investment.

Neither system appears, from public data, to be operating natively inside the Goldilocks window without compensation. Both are paying a conversion floor tax; the tax takes different structural forms depending on substrate choice. This is precisely what Unknown Seven asks about, and it is now testably approximate rather than merely conceptually located.

Scope

What the Framework Does and Does Not Claim

Claims: a two-dimensional noise envelope, derivable from SNR, with published-data anchors on both axes.

Does not claim: the modal token is formally specified, implemented, or demonstrated.

Does not claim: either placement in §3.4 is inside or outside the Goldilocks window with certainty. The placements are structural, not numerical.

Does not claim: Unknown One-A (interference-based similarity complexity advantage) is resolved.

The eight named unknowns collected in §8 of the paper are themselves a contribution: precision about where the framework ends and speculation begins. The most important empirical question is whether any deployed photonic MVM system operates inside the Goldilocks window without compensation. The most important theoretical question is whether a softmax-equivalent normalization exists for interference-based similarity without reintroducing O(n²) cost.

Current state

Status

Modal token formalized Minimal (Appendix A)

Modal token implemented No

Conversion floor derivation SNR worst-case bound

f(δₘ), g(σ_mod) forms Unknown Two

§3.4 placements Order-of-magnitude

Goldilocks occupancy Unknown Seven

Open questions

Named Unknowns

One

Formal specification of the modal token Appendix A provides a minimal instantiation sufficient to derive the conversion floor and expose phase-sensitive failure modes. State space geometry, operator algebra, observable structure, and full complexity properties remain unspecified. Theoretical

One-A

Computational advantage of interference-based similarity The most important theoretical open question. Whether the interference integral offers asymptotic or constant-factor advantage over O(n²) attention is undemonstrated. The hard sub-problem is softmax-equivalent normalization without reintroducing quadratic cost. Speculative candidate: optical gain saturation. Theoretical · hardest

Two

Functional forms of f and g Physically motivated and order-of-magnitude anchored by §3.4 placements, but not formally derived. Until derived, the conversion floor is approximately located but not numerically bounded with engineering precision. Open

Three

Binding constraint for Route I Whether δₘ or σ_mod binds first under operating conditions determines engineering priority. Given phase-fragile similarity, if σ_mod binds the failure mode is semantic collapse rather than precision loss. Open

Four

Magnitude of noise-source correlation The γ cross-term captures grain-boundary coupling between axes. Whether this correlation changes effective ADC precision by a small correction or a substantial factor is unknown — no analogue exists in TFLN or silicon photonic systems. Open

Five

Sufficiency of Raman spectroscopy Whether Raman at grain boundary sites fully characterizes σ_mod, or whether waveguide surface roughness, thermal phonon-photon coupling, and shot noise contribute at comparable magnitude. Open

Six

Comparative floor across substrates A full comparative analysis across silicon photonics, TFLN, graphene-ferroelectric, PCM, and RRAM architectures has not been performed. Whether photonic MVM offers a superior two-dimensional floor profile relative to electronic analog alternatives is not established. Open

Seven

Does any existing system operate inside the Goldilocks window? The most important empirical open question. §3.4 suggests the answer is no, not natively: Lightmatter manages δₘ through run-time gain control; Q.ANT manages σ_mod through substrate optimization and annealing. Device-level characterization would resolve the question. Empirical · hardest

Eight

Training dynamics under coupled noise Gradient behavior under coupled δₘ and σ_mod with phase-SNR constraint, noise accumulation during learning, and convergence before inference becomes useful. Harder than in standard analog compute proposals. Open

Downstream

Extensions

The Conversion Floor is the foundational document in an expanding framework. The following extensions introduce further named unknowns and refine specific aspects of the two-axis floor.

→ The Mortal Token A Coherence-Gated Persistence Filter · Introduces Unknowns Nine–Eleven · April 2026

Mortal Token proposes temporal self-limitation as a fifth required property of the modal token and extends the conversion floor to a third axis h(m, τ) — the governance tax for operating near the mortality boundary.

Related work

Quantitative Anchor

§6 of the paper references the graphene integration route framework (Routes I, F, J) that provides the Bayesian Monte Carlo joint-probability mapping of the stability envelope for the ferroelectric-graphene architecture.

→ Graphene Integration Route Selection Bayesian Monte Carlo · 10 routes · 64×64 MVM tile · Solbakken Research Initiative

Attribution

Citation

Haaland, N. The Conversion Floor: Tokens, Modal Tokens, and the Two-Source Noise Condition for Photonic AI Acceleration. Solbakken Research Initiative, April 2026. github.com/bluebflatminor/conversion-floor