An analog memristive-crossbar Winner-Take-All classifier. Inputs “fall” toward the stored pattern that pulls hardest — a one-step vector–matrix multiply by Ohm’s and Kirchhoff’s laws.
The Crossbar
Rows are input lines held at voltages Vi. Columns are output neurons. At each junction sits a memristor of conductance Gij (brightness = conductance). Each column sums its junction currents in one physical step; the winner-take-all lights the column drawing the most current — the stored pattern nearest your input.
column current Ij = Σi Vi · Gij (Ohm + Kirchhoff) · winner = argmaxj Ij
or click the input grid (top-left) to scribble
0% bit-flip / analog jitter
Honest two-layer
real physics A memristive crossbar computes an analog vector–matrix multiply in a single step. Driving rows at voltages Vi and reading column currents gives Ij = Σi Vi Gij directly from Ohm’s law (I=VG) at each junction and Kirchhoff’s current law (currents sum on the shared column). This is exactly the dot-product / matched-filter classifier computed on this page — the numbers in the bars and the winner are the true Σ ViGij, not an animation cheat.
real physicsMemristive analog weights and hardware winner-take-all are established: analog VMM in metal-oxide crossbars (Hu et al., Adv. Mater. 2018), TiO₂ memristor training (Prezioso et al., Nature 2015), Ag₂S/Ag atomic-switch synapses, and current-mode WTA circuits (Lazzaro et al., 1988).
design / disclosure The “Gravity Processor” name and the falling-toward-the-well framing are a ROOT0 conceptual disclosure — a way to picture argmax as a potential well. This specific packaged device is not a fabricated chip and not a granted patent.
symbolic toy The word “gravity” here is a metaphor, not a force in the circuit. Nothing gravitational happens; the pull is the dot-product V·G. Junction conductances are shown on a clean linear scale (0→Gmax); real devices have I–V nonlinearity, wire (IR) drop, and write stochasticity not modeled here.
To disclose a design is real work; it is not a granted patent or a fabricated device.
References
Hu, M. et al. “Memristor-Based Analog Computation and Neural Network Classification with a Dot-Product Engine.” Advanced Materials 30, 1705914 (2018).
Prezioso, M. et al. “Training and operation of an integrated neuromorphic network based on metal-oxide memristors.” Nature 521, 61–64 (2015).
Lazzaro, J. et al. “Winner-Take-All Networks of O(N) Complexity.” NIPS (1988).
Chua, L. “Memristor — The Missing Circuit Element.” IEEE Trans. Circuit Theory 18, 507–519 (1971).