Manifold-constrained plasticity enables stable learning in recurrent neural circuits

The activity of large neuronal populations is often confined to low-dimensional manifolds that can drift over time, posing a challenge for learning rules that assume stable, full-rank representations. Here, we introduce SPLiT (Synaptic Projection Learning with intrinsic Tracking), a synaptic plasticity rule for recurrent neural networks that combines unsupervised manifold tracking with supervised learning. SPLiT uses an online Oja rule to continuously estimate the intrinsic low-dimensional activity subspace and performs normalized least-mean-squares learning in manifold coordinates. In this way, SPLiT keeps synaptic weights aligned with evolving population dynamics. Using a rate-based recurrent network, we show that SPLiT reliably learns time-varying target signals under both constrained dynamics, where activity is restricted to a fixed low-dimensional manifold, and unconstrained dynamics exhibiting changes in the dominant activity subspace. We show that manifold-constrained learning with SPLiT yields faster convergence, less sensitivity to recurrent gain, smaller weight updates, and is more robust to noisy teaching signals. Analytical results show that SPLiT learns the optimal decoder projected onto the instantaneous principal subspace and maintains bounded error under drift. Together, these findings provide a mechanistic account of how synaptic plasticity can leverage the structure of neural manifolds to enable stable and efficient supervised learning despite representational drift.