Lapis: Laplacian Spiking Attention via First-Spike Timing and Membrane Leakage

What the math gives to ML

The paper supplies a hardware-oriented replacement for query-key dot products in spiking attention: compare first-spike latency vectors with an l1 metric and convert the distance into a Laplacian affinity. This is more than a generic similarity choice because the exponential kernel has a direct interpretation as the decay of a leaky integrate-and-fire membrane, tying the attention bandwidth to a physical neuron time constant. The resulting score path uses subtraction, absolute value, accumulation, and normalization rather than channelwise multiplication, and power-of-two normalization can make the latter a shift operation. The most promising transfer is a latency-coded attention module for spiking or event-driven transformers, with a second experiment testing whether fixed-point and power-of-two approximations preserve accuracy while materially reducing energy.