How Biological Synapses Self-Assemble Gradient Learning
Qianli Liao, Liu Ziyin, Yulu Gan, Brian Cheung, Mark T. Harnett, Tomaso Poggio
cs.NE
2024-12-28
MIT's SAM circuit grows its own feedback pathway from random wiring under one local plasticity rule, matching SGD on seven image datasets and beating it on six.
Biologically plausible alternatives to backprop are well established: Feedback Alignment (fixed random matrices carry the error), Weight Mirroring, and Kolen–Pollack (backward weights learn to become the transpose of forward ones). They explain how a given circuit can learn. They do not explain where the circuit comes from, because the one-to-one wiring between forward and backward pathways is simply assumed. The authors call this architectural circularity.
Their reframing treats biological plausibility as a graded axis: how much of a learning system's structure is stipulated versus grown from local interactions. Backprop and its variants self-organize only the weights. This paper pushes one level further down and asks the learning circuit itself to assemble from random connectivity.
The building block is the Self-Assembling Motif (SAM): two information streams and four synaptic matrices.
Every update is the same outer product of a postsynaptic and a presynaptic signal, plus weight decay. The postsynaptic signal comes from the other stream's feedback rather than the neuron's own forward activity, which is what makes the rule heterosynaptic. The four matrices differ only in learning rate; V̄ typically needs about four times the rate of W.
The key theoretical step is Lemma 1. When V and V̄ share a learning rate, the interface mismatch Ev = V − V̄ᵀ shrinks by a factor (1−γ) each step, so V̄ converges to the transpose of V without anyone wiring it. Given that, Theorem 1 shows the update to W approximates H times the SGD update, where H = V̄V̄ᵀ is positive semidefinite. In effect the optimizer carries a learned matrix-valued learning rate. The residual is controlled by two alignment errors: the interface error Ev, and the pathway error Ep, the gap between the forward operator and the feedback operator.
What is still stipulated is the two-stream scaffold with only modulatory cross-talk, which the authors argue is close to a stability requirement for perception.
Baselines are SGD, FA, WM and KP, all on fully connected networks, five runs each. Accuracy (%):
| Dataset | SGD | FA | WM | KP | SAM |
| CIFAR10 | 50.36 | 47.85 | 49.35 | 48.16 | 51.91 |
| MNIST | 98.44 | 97.80 | 98.40 | 98.45 | 98.85 |
| Fashion MNIST | 88.63 | 85.41 | 88.34 | 88.52 | 88.86 |
| ChestMNIST | 73.26 | - | - | - | 73.21 |
| SVHN | 78.20 | 78.03 | 78.08 | 78.20 | 78.50 |
| STL10 | 41.00 | 39.29 | 39.48 | 40.32 | 41.50 |
The baseline columns for ChestMNIST and PathMNIST are scrambled in the extracted text, so only verifiable numbers are shown. SAM beats SGD on six of seven datasets and trails by 0.05 points on ChestMNIST. Most margins are a fraction of a point up to 1.5 points, which reads as parity.
In the CIFAR-10 ablation, updating only W matches a linear model; adding plasticity to V̄ alone lifts accuracy from about 40% to about 46%; making all four plastic reaches SGD level. A wider feedback pathway also helps: with the upstream width fixed at 200, the best downstream size is roughly 5 to 8 times larger in parameters, peaking near 8x on CIFAR10.
This is not a drop-in replacement for backprop; it carries an extra feedback pathway and gives no compute advantage on GPUs. The value is on the neuroscience side, where it yields testable predictions: four plastic synapse types per motif, heterosynaptic dependence, and more feedback than feedforward connections (the paper cites V1-to-LGN feedback at roughly 10 times the retinal input synapses). For ML, a preconditioner that learns itself is a curious by-product, but nothing here is tested at LLM scale.