Online synaptic credit assignment in active dendrites

Credit assignment in neural networks is usually formulated as the computation of an abstract error gradient. Whether such a gradient can take a physical, causal form in biophysically detailed multi-compartment neuron models, and enable online, supervised learning, remains unclear. Here we show that the gradient of a detailed neuron's voltage with respect to a synaptic weight is itself a voltage. Differentiating the discrete backward-Euler update solved by standard simulators yields equations of the same form as the original voltage dynamics, driven by gradient currents. Replaying weight-specific gradient currents forward in time reproduces the exact gradient with high fidelity in an L5 pyramidal neuron across diverse input regimes (R2 > 0.998). Pairing the replayed gradient voltage with a local learning signal yields a causal, online learning rule. A single L5 pyramidal neuron with active dendrites learns to reproduce target voltage trajectories containing calcium plateaus and bursts, and recurrent networks of detailed neurons learn to generate target temporal patterns, far outperforming a readout-only control. These results demonstrate that synaptic credit assignment can be implemented online by the voltage dynamics of detailed neurons, potentially suggesting a physical substrate for gradient-based supervised learning in the brain.