First testable efficiency model — 20 Watts Was Enough

lusoris contributors

Purpose

This model compares a conditional architecture with a dense baseline on the same task using directly measured system quantities.

Per-event cost

For event $x$ , let the dense baseline execute modules $1\ldots n$ . Its measured energy is

E_D(x)=E_{D,\text{compute}}+E_{D,\text{memory}} +E_{D,\text{network}}+E_{D,\text{host}}.

Every $E_D$ component is joules per event at the same declared physical boundary. For conditional gates $g_i(x)\in\{0,1\}$ , the candidate uses

E_C(x)=E_{\text{gate}}(x) +\sum_{i=1}^{n} g_i(x)E_i(x) +E_{C,\text{memory}}(x) +E_{C,\text{network}}(x) +E_{C,\text{host}}(x).

$E_i(x)$ and every other $E_C$ component are joules per event at that same boundary; $g_i(x)$ is dimensionless. The net event saving is

S_E(x)=1-\frac{E_C(x)}{E_D(x)}.

$S_E$ is dimensionless, and $S_E>0$ indicates lower measured energy. It is reported only for event strata whose quality and risk remain inside the declared equivalence envelope.

Lifecycle cost

Let $E_{\text{train}}$ , $E_{\text{consolidate}}$ , and $E_{\text{mature}}$ be measured one-time lifecycle energies in joules at the same boundary. For a dimensionless count $N$ of qualified deployment events,

E_{\text{life/event}} =\frac{E_{\text{train}}+E_{\text{consolidate}}+E_{\text{mature}}}{N} +\frac{1}{N}\sum_{j=1}^{N}E_C(x_j).

$E_{\text{life/event}}$ is joules per qualified event; $x_j$ is qualified event $j$ , and $E_C(x_j)$ is its measured energy in joules. Pruning or hardening is beneficial over the measured lifetime only when its one-time cost is smaller than the accumulated deployment saving.

Quality equivalence

Candidate $C$ is comparable to baseline $D$ only if

Q_C \ge Q_D-\epsilon_Q, \qquad R_C \le R_D+\epsilon_R, \qquad L_{C,p95}\le L_{\max}.

$Q_C$ and $Q_D$ use one declared task-quality unit, so $\epsilon_Q$ has that same unit. $R_C$ and $R_D$ use one declared risk unit, so $\epsilon_R$ has that same unit. $L_{C,p95}$ and the ceiling $L_{\max}$ are seconds at the 95th percentile. All tolerances are fixed before the experiment. Reporting only average quality is insufficient when conditional compute can fail selectively on rare events. The full comparison record is defined in the energy-model chapter.

Brain counterfactual: unresolved

The dimensional form

P_{\text{counterfactual}} =P_{\text{brain}} \frac{\eta_{\text{brain}}}{\eta_{\text{machine}}}

$P_{\text{brain}}$ and $P_{\text{counterfactual}}$ are power in watts. $\eta_{\text{brain}}$ and $\eta_{\text{machine}}$ must both be measured in the same qualified functional-output units per joule, making their ratio dimensionless. This requires the same task, quality, risk, time, and accounting boundary. Current “brain FLOP” estimates and accelerator arithmetic do not meet that condition. Consequently claim C-016 remains disputed and no numerical range is derived here.

Initial hypotheses

H-E1: conditional routing reduces device energy at matched quality only above a workload-dependent module granularity.
H-E2: memory and interconnect savings, not arithmetic savings alone, determine whether sparse capacity wins end to end.
H-E3: consolidation increases short-term energy but reduces amortized energy when it replaces frequent full-model updates.
H-E4: structural pruning yields more portable energy savings than unstructured weight sparsity.

These hypotheses become claims only after experiments and ledger review.