The perceptron in light

Photonics is built for this, with one catch. The multiply falls out of interference — two laser fields beat at a beamsplitter and a balanced detector reads their product, exactly, at the speed of light, no transistor. The sum is free: photocurrents from many channels just add on one wire. What light won't do is the threshold — photons ignore each other — so the nonlinearity is the part that fights back. Two-thirds of a perceptron for free; the last third is the whole research field.

weights & inputs = field amplitudes · multiply = interference at a 50:50 beamsplitter · sum = photocurrents add on a bus · threshold = square-law detect + electronics

✓ STRONG

The optical MAC. Matrix multiply by light — MZI meshes (MIT, Shen 2017) and microring weight-banks (broadcast-and-weight, Tait) are fabricated and commercial (Lightmatter). The multiply-and-sum is real and fast.

◐ MIDDLING

A full photonic neural net. End-to-end inference is demonstrated, but weight-loading, data conversion (O/E/O) and I/O overheads often eat the speed win — advantage is regime-specific.

◔ FRONTIER

All-optical nonlinearity & in-situ training. A threshold without leaving the optical domain (saturable absorbers, cavity effects) and training the phases optically are genuinely open.

I · Multiplication by interference

Two laser diodes launch a signal field x and a weight field w into a 50:50 beamsplitter. The outputs are (x+w)/√2 and (x−w)/√2; two photodiodes square them, and the balanced difference is |x+w|²/2 − |x−w|²/2 = 2·x·w A real multiplication, done by two beams crossing. Sign rides on phase (a π flip = a minus sign). Slide the amplitudes — the balanced reading is the product.

signal x weight w

signal x + weight w → 50:50 beamsplitter → two photodiodes (D⁺, D⁻) → balanced output D⁺−D⁻ = 2xw · scope shows the interference fringe

+0.00

balanced output D⁺ − D⁻ = 2·x·w

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vs arithmetic 2·x·w

multiply= the interference cross-termthe sign= a π phase flipspeed= time-of-flight, no clock

Flip either field negative (phase π) and the product flips — interference handles signed weights natively. Hit sweep to watch the photodiode power trace a cosine fringe on the scope: that fringe is the analog multiply.

II · The neuron — many multiplies, one wire, one threshold

Stack the multipliers. Each input channel xᵢ beats against its weight field wᵢ; every channel's photocurrent drops onto a shared bus and they simply add — the accumulate is just Kirchhoff's law. The summed current hits a comparator: above the line, the neuron fires. The optical part ends at the detector; the threshold is where electrons quietly take over.

x₁ x₂ w₁ w₂ bias

two homodyne multipliers on the bench · photocurrents sum on the bus · comparator = the threshold (electronic)

0.00

Σ photocurrent = b + Σ xᵢwᵢ

DARK

fires when Σ > 0

The sum costs nothing — currents add by themselves. That's the structural reason photonics is fast: an N-wide dot product is one pass of light, not N multiply-adds. The bottleneck isn't the math; it's data in and the threshold out.

III · It learns — one cut, then depth

Train the weight fields with the perceptron rule and the photonic neuron learns a linearly-separable rule outright. As ever, it draws one straight cut — AND and OR fall; XOR stalls at 3/4 (verified). The fix repeats across every body: a second layer — a nonlinear node feeding a second photonic stage — folds the space. Coupled dots, dendrites, hidden layers, stacked crossbars, a second optical stage: one idea, many costumes.

target:

input plane · the beam color marks where the neuron fires · corners ringed green when correct

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cases correct

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verdict

Pick a target and hit train — for AND/OR the weight fields settle and all four corners ring green in a few sweeps. Switch to XOR and one corner stays crossed: one cut can't split the diagonals. Add a 2nd optical layer and the boundary bends — XOR snaps to 4/4. Depth is the universal escape from the line.