Perceptron theory · the substrate jump · the sixth body
The perceptron in a spin
Every body so far had to bolt on its threshold. This one grows it. Store the weight as a magnetization — a magnetic tunnel junction is low-resistance when its layers align, high when they oppose — and the multiply rides on that conductance, just like the crossbar. But shrink the magnet until thermal jitter can flip it, and something lovely happens: bias it with a current and its time-averaged state is a clean tanh. The sigmoid the others fought for, the spin gives away for free — out of pure noise.
weight = magnetization (MTJ resistance) · spin ↑/spin ↓ · multiply+sum = magnetic crossbar · nonlinearity = a stochastic magnet (p-bit) = tanh for free
✓ STRONG
The magnetic weight. MTJ / tunnel-magnetoresistance is the basis of STT-MRAM — a shipping commercial memory (Everspin, Samsung, embedded TSMC). The weight-as-magnetization, read by resistance, is bedrock.
◐ MIDDLING
The p-bit. Stochastic-MTJ probabilistic computing (Camsari & Datta) builds Ising machines and invertible logic from the free sigmoid — demonstrated at small scale, promising, young.
◔ FRONTIER
The skyrmion neuron. Topologically-protected spin textures (Q=±1) as robust carriers, and all-spin deep nets — open research, the magnetic Möbius.
I · The weight is a magnetization
A magnetic tunnel junction is two ferromagnets with a paper-thin insulator between. The bottom layer is pinned; the top is free. When the two point the same way electrons tunnel easily — low resistance, high conductance. When they oppose, resistance jumps (tunnel magnetoresistance). That conductance is the weight, and it's non-volatile — set by a write current and held with the power off, in the orientation of an electron's spin.
spin-transfer torque switches the state — that's how you program the synapse
free layer (top, flips) · tunnel barrier · pinned layer (bottom) · aligned = low R / high G · opposed = high R / low G
No charge leaks away, no refresh — the bit is which way a magnet points. That's why MRAM survives power-off, and why a magnetic weight holds its value for years.
II · The gift — a magnet that sigmoids out of noise
Now shrink the free layer until its energy barrier is near kT. It can no longer hold still — thermal kicks flip it up and down at random, a p-bit. Left alone it's a fair coin. But push a small input current and you tilt the odds, and the time-average of its flips is exactly ⟨m⟩ = tanh(I) A perfect sigmoid neuron, built from a magnet and heat. Light needed interference, the dot needed blockade — the spin just needs to be small and warm.
left: the magnet flipping (thermal) · middle: the ±1 spike train · right: the tanh response — the measured running average (●) converges onto tanh(I) (curve)
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instantaneous spin
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⟨m⟩ measured (running)
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tanh(I) target
The randomness isn't a defect to be filtered out — it's the compute. A network of p-bits naturally samples probability distributions, which is why stochastic magnets are being built into Ising machines and Bayesian hardware. The thing that ruins a memory makes a neuron.
III · It learns — one cut, depth, and a topological twist
Magnetic-conductance weights, p-bit threshold: the spintronic neuron trains by the same rule and lands the same way — AND and OR in a few sweeps, XOR stuck at 3/4 (verified), freed by a second layer. And the topology you asked about lives here: a skyrmion is a whorl of spins with a protected winding number Q=±1 — you can't smoothly comb it flat, so it carries a bit that noise can't erase. The crossbar was a flat grid; this is the magnetic Möbius.
target:
input plane · violet = the neuron fires · corners ring green when correct
a skyrmion — spins wind from ↑ (centre) to ↓ (rim) · topological charge Q = ±1, protected