Decoded
Feed

On the stability of learning

arXiv:2610.35856q-bio.NCLG26 oct 20261 min readHN ×5PDF

Learning can blow up when correct-on-average feedback arrives too rarely and too noisily.

2

Ratio s/ρ where learning destabilizes

Above this ratio, errors flip sign and grow every update.

How it works

  1. Feedback is intermittent

    Synapses in the brain may get gradient signals rarely, at random times, with noise, even if correct on average.

  2. Model random arrivals

    Gradients arrive by a Poisson process at rate ρ. Track weight variance in linear, two-layer, and deep linear networks.

  3. Critical arrival rate

    Below a threshold ρc, variance diverges while the average still converges. Regularization, pooling, and averaging lower ρc.

gated byscaled 1/ρvariancesolveTruegradientPoissonarrivalsSparse noisyupdatesCovariancedynamicsStabilitycondition ρ>ρcgated byscaled 1/ρvariancesolveTruegradientPoissonarrivalsSparse noisyupdatesCovariancedynamicsStabilitycondition ρ>ρc
From the paper