CEREBELLAR REGULARIZATION VIA SPARSE VIRTUAL SAMPLES

The cerebellum learns efficiently by expanding mossy-fiber inputs into a huge parallel fiber (PF) space. But high capacity comes with a classic problem: the risk of overfitting. A striking biological clue is that many PF–Purkinje cell synapses are silent, suggesting that the circuit actively keeps unnecessary connections in check. Why, and how, could this be done robustly in the presence of correlated inputs?

We propose a simple mechanism: sparse spontaneous PF events act as “virtual samples.” These events are task-irrelevant and should ideally produce no Purkinje-cell output. When they do, the resulting error signal can drive LTD at the active synapses—equivalent to a continuous regularization pressure on synaptic weights. In our framework, this pressure is determined by the second-moment structure of spontaneous PF patterns.

A key result is that what matters most is sparsity, not strict independence. The shape (isotropy) of the induced regularization can be summarized by the condition number cond(Σ), and in uniform sparse models it scales simply with co-activation: cond(Σ) ≈ s, where s is the average number of PFs co-active per spontaneous event. Simulations further show a collapse of generalization performance onto a single curve versus cond(Σ), across multiple correlation structures. Sparse events also minimize interference with task learning by keeping task-driven and regularization-driven updates nearly orthogonal, and—combined with synaptic non-negativity—naturally produce hard silencing (exact zeros), matching silent-synapse-like pruning.

Together, sparse “virtual samples” offer a robust, testable principle for cerebellar generalization in realistic, correlated circuits.