$$\eta(t)$$

Equation 2 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

That structural fact can be written compactly. If $P_{\text{budget}}$ is the (roughly fixed, application-set) power envelope in watts and $\eta(t)$ is the achieved energy efficiency of the best available accelerator at time t , measured in tera-operations per second per watt, then the usable on-device compute throughput is approximately

Meanings in this article

• $\eta$: the achieved energy efficiency of the best available accelerator at time t , measured in tera-operations per second per watt.
• $t$: the time or time index used in this relationship.

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Equation 6 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

This is not a scaling law in the sense of a fitted curve; it is closer to an accounting identity, and its value is in what it rules out. Because $P_{\text{budget}}$ is nearly constant for a given device class, essentially all of the growth in on-device model capability that anyone can expect by 2035 has to come from growth in $\eta(t)$ — from architecture, from process, from numerical precision, and, in the discontinuity scenario below, from a different physical mechanism entirely. Reuther and colleagues’ survey of commercial AI accelerators, which compiles peak-performance and power figures across dozens of parts and computes efficiency relative to that peak, documents exactly this pattern:…

Meanings in this article

• $\eta$: the achieved energy efficiency of the best available accelerator at time t , measured in tera-operations per second per watt.
• $t$: the time or time index used in this relationship.

Equation guide → · Article →

Equation 7 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

$\eta(t)$ itself is not free to grow indefinitely inside conventional CMOS. Horowitz, Alon, and Patil’s widely cited analysis of chip power scaling made the mechanism explicit: as feature size shrank across recent nodes, supply voltage and threshold voltage stopped scaling down at the historical rate, because pushing them lower drives subthreshold leakage up sharply, and power — not transistor count — became the binding limiter on how fast or how densely a chip could usefully run [ 11 ] . That single fact is the quiet premise behind most edge-AI marketing that promises “10x more efficient” silicon every generation: within one switching technology, each further gain in $\eta(t)$ gets structurally…

Meanings in this article

• $\eta$: the achieved energy efficiency of the best available accelerator at time t , measured in tera-operations per second per watt.
• $t$: the time or time index used in this relationship.

Equation guide → · Article →

Equation 8 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

$\eta(t)$ itself is not free to grow indefinitely inside conventional CMOS. Horowitz, Alon, and Patil’s widely cited analysis of chip power scaling made the mechanism explicit: as feature size shrank across recent nodes, supply voltage and threshold voltage stopped scaling down at the historical rate, because pushing them lower drives subthreshold leakage up sharply, and power — not transistor count — became the binding limiter on how fast or how densely a chip could usefully run [ 11 ] . That single fact is the quiet premise behind most edge-AI marketing that promises “10x more efficient” silicon every generation: within one switching technology, each further gain in $\eta(t)$ gets structurally…

Meanings in this article

• $\eta$: the achieved energy efficiency of the best available accelerator at time t , measured in tera-operations per second per watt.
• $t$: the time or time index used in this relationship.

Equation guide → · Article →

Equation 11 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

The compute-per-watt equation above has an implicit assumption baked into it: that $\eta(t)$ 's growth comes from refining one underlying switching technology, conventional digital CMOS. The clearest documented case for how that assumption could break is analog, compute-in-memory silicon, which does not perform a multiply-accumulate as a sequence of digital switching events at all, but as a physical operation — current summation on a resistive or phase-change element — colocated with storage.

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Equation 12 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Scenario A — incremental compounding. $\eta(t)$ continues to improve mainly through architecture, quantization, and process refinements within digital CMOS, compounding at a slowing but still positive rate as the Horowitz-style voltage floor is approached more closely each generation. Event cameras and neuromorphic processors remain concentrated in the applications where their narrow strengths already fit — industrial sensing, some automotive perception, always-on wake tasks — without breaking into general-purpose vision. On-device privacy architecture spreads because it is commercially and operationally convenient under AI Act-style obligations, not because any law explicitly mandates it.…

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Equation 13 · Edge AI & Electronics

Edge AI Electronics and Sensor Systems in 2035: Scenarios, Signals, and Falsifiable Predictions

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Scenario B — an in-memory or neuromorphic discontinuity. Compute-in-memory silicon, or a comparably disruptive alternative to digital CMOS switching, clears the manufacturability and yield bar that has so far kept it in research and niche deployments, and $\eta(t)$ takes a step change rather than a compounding curve for at least one significant device class. This scenario assumes that a design house or foundry solves device-to-device variability and endurance at commercial volumes — the specific engineering problem that has kept every in-memory demonstration to date at the scale of tens of megabytes of weights rather than production-scale models.

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