模擬式記憶體內運算與數碼 NPU：每次 MAC 能耗的比較論證

The dominant cost in any digital accelerator is not arithmetic. It is moving numbers to the place where the arithmetic happens. A multiply-accumulate on a modern process node costs a fraction of a picojoule; fetching the operands from memory costs one to two orders of magnitude more. This is the von Neumann bottleneck, and it has been the real design constraint in computing for thirty years.

Analog in-memory computing attacks it directly. Instead of moving weights to an arithmetic unit, the weights are stored as conductances in a crossbar array, and a voltage applied across a row produces a current that is the sum of the products. Kirchhoff's laws do the multiply and the accumulate in one physical step, at the location where the data already lives. No fetch, no register file, no clock.

The energy per operation, measured in the array, is measured in femtojoules. That number is roughly a thousand times better than a digital MAC. It is also, on its own, almost meaningless, and understanding why is the whole story of where this technology ships and where it does not.

The part the datasheet leaves out

An analog crossbar produces an analog current. To use it in a digital system, that current has to be converted to a number, and conversion is where the advantage evaporates.

A data converter that can resolve enough levels to be useful consumes power that scales with its resolution and its speed. If your array computes a thousand products in one shot and then hands the result to a converter that costs more than a thousand digital MACs, you have gained nothing. The efficiency claim only holds when the array is large, the conversion is amortised, and the required precision is low.

Precision is the second constraint. Digital arithmetic is exact. Analog arithmetic is subject to device variation, thermal drift, IR drop across the array, and shot noise. You can average repeated reads to improve the signal, but each repetition costs time and energy, and the returns diminish.

Analog in-memory computing wins on energy per operation only when the array is large and the required precision is low, and those two conditions define its entire market.

Where the conditions are met

The first place both conditions hold is always-on sensing. A microphone, an accelerometer or an image sensor produces a continuous stream of low-precision data, and the job is to detect a pattern rather than to compute an exact answer. Keyword spotting, gesture recognition, anomaly detection: these are small models, tolerant of noise, and dominated by the energy cost of staying awake.

The second is inference on very small models where the weights fit in the array and never move. A three-layer network doing vibration analysis on a motor does not need sixteen bits of precision. It needs to run for a year on a coin cell.

The third, and the one that gets the headlines, is the attempt to run large language models. This is where the physics becomes unkind. A transformer layer needs consistent precision across a large dynamic range, and the output of each layer feeds the next, so errors compound. The arrays required are enormous, the conversion overhead grows with the number of tiles, and the calibration burden grows with temperature variation across the die.

The calibration problem deserves its own paragraph, because it is the reason several well-funded analog programmes quietly became digital ones. A crossbar's conductances drift with temperature and with the history of the voltages applied to them, so the mapping from a weight to a physical conductance is not constant. A device that has to be recalibrated when the die warms by ten degrees is a device that needs a calibration engine, a reference array, and a software stack that knows when to run it.

That engine costs area and power, and it competes directly with the arithmetic savings. The programmes that have shipped have generally solved it by keeping the model small enough that the drift stays inside the error budget, which is another way of saying they stayed inside the niche.

The comparison that matters

Set a digital NPU and an analog array against the same task and the result is not a winner and a loser, it is a boundary.

Below roughly a million operations per inference, with eight bits or fewer of required precision, the analog array is dramatically more efficient, because the conversion cost is small relative to the arithmetic saved and the model fits in one array. Above that, the conversion cost and the calibration overhead dominate, and the digital design wins on both energy and predictability.

The digital NPU also wins on the thing that decides most purchases: software. A digital accelerator has an instruction set, a compiler, and a debugging story. An analog array has a calibration procedure and a set of weights that may need retuning when the die warms up. That asymmetry is why analog designs have repeatedly been announced and rarely shipped in high volume.

What this does to the market

The realistic forecast is not that analog replaces digital. It is that analog captures the always-on tier, where the alternative is not a better NPU but a battery that dies.

Stated with its reasoning: the always-on sensing market is currently a few billion dollars of silicon annually and is growing as more devices add continuous perception. If analog arrays take a meaningful share of that tier by 2030, the incremental revenue lands between one and four billion dollars a year, with the low end assuming incumbents solve the same problem with aggressively duty-cycled digital designs and the high end assuming a calibration-free device arrives.

The decisive question is not whether analog can be more efficient, but whether it can be made predictable enough that a product team will bet a shipping schedule on it.

What is actually transferable

The lesson generalises well beyond crossbars. Every architecture that moves computation into the structure where data lives, whether analog or digital, buys efficiency by giving up generality. That trade is worth making exactly when the workload is fixed and the precision requirement is low.

The same reasoning explains why fixed-function video decoders beat general-purpose cores on phones, why cryptographic accelerators exist, and why in-memory digital compute is gaining traction for recommendation models where the weights are large and the arithmetic is simple.

The transferable habit is to ask what the conversion cost is. Every time a specialised engine hands its result back to a general system, there is a tax, and the tax is usually what determines whether the specialisation pays. Analog computing is not a story about physics beating electronics. It is a story about a thousand-fold arithmetic advantage being spent on the interface.

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