The Averaging Problem in On-Chip Local Learning for Dense Prediction: Most of the Gap to Backpropagation Is Modulation Granularity

Layer-local three-factor rules train spiking networks within the constraints of on-chip learning. On classification, their gap to backpropagation is attributed to the credit that cannot cross layers. On dense prediction, where none of these rules has been evaluated, we find a larger term in that gap. Every published rule forms its modulatory signal through a class-level readout that averages the per-pixel error into one vector per image. The backbone trained this way ends within one point of a frozen random backbone. Block-averaging the per-pixel error is an orthogonal projection, and a coarse rule discards the residual, which concentrates at the target's boundaries. When only the averaging operator is varied, accuracy rises monotonically with granularity on two datasets and under two local rules. Granularity is the larger term at every depth within the chip's budget. At three layers, it is 78% of the distance from uniform modulation to backpropagation and the larger term on every seed. Letting the gradient cross layers recovers little, and so does a partition aligned to the ground-truth classes. The loss therefore comes from averaging within a region rather than from missing label information. Blocks of $16\times 16$ pixels recover 67–77% of the dense gain at $0.4\%$ of the modulation state. Per-pixel modulation is a per-layer dense readout under the on-chip constraints, and it comes within $2.7$ points of same-architecture backpropagation.