ERL-BCP: A balance-controlled plasticity network with energy-regulated liquid timescales

Biologically plausible credit assignment requires local learning signals generated from circuit variables while maintaining stable continuous-time dynamics. However, continuous-time local learning networks often face coupled challenges arising from fixed membrane timescales, load-insensitive current regulation, and potentially unbounded feedback signals. To address these challenges, we introduce a balance-controlled plasticity network with energy-regulated liquid timescales (ERL-BCP), a continuous-time local learning framework that further incorporates bounded inhibitory feedback. In each assembly, the squared magnitudes of excitatory, input-associated inhibitory, and balance-sensitive inhibitory currents define a local current energy. This energy increases membrane decay under high current load and shortens the effective timescale, while a smoothly saturated controller limits task-driven inhibitory feedback. Synaptic updates remain local and are driven by filtered E/I balance deviations. Under the stated assumptions, the energy-dependent dynamics admit a uniform bound on the excitatory membrane state. Across five static, event-based, and sequential benchmarks, ERL-BCP achieves the highest mean best test accuracy among the evaluated local methods in every tested configuration and maintains stable performance across the evaluated network widths and depths. Controlled dynamical probes further show that increasing current load shortens the effective liquid timescale and that shorter timescales accelerate membrane-state establishment and perturbation recovery. Controlled variants show that replacing the balance-derived signal causes the largest deterioration in predictive performance and internal regulation, fixing the timescale reduces accuracy and weakens balance regulation, and removing the feedback bound markedly increases current energy and balance residual with little change in accuracy. At matched parameter states and probe batches, the ERL-BCP update is more closely aligned with supervised descent than a generic local update in all 155 paired evaluations per dataset.