Direct feedback alignment (DFA) trains hidden layers using fixed random projections of output error. With tanh hidden units and independent sigmoid outputs, plain SGD can stall near the loss of a constant predictor of class frequencies. The cause is a common mode in the error, the component shared across inputs. An exact mean-covariance decomposition shows the leading update is rank one and drives tanh units toward saturation.
At initialization, random feedback provides no systematic correction of this shared error on average, so the readout must learn the class prior to weaken the drive. A reduced model initialized from the network predicts the concentration of activation sensitivity across 48 settings. On MNIST, class decodability largely survives collapse, yet readout learning remains slow at a fixed learning rate. Adam learns faster despite deeper collapse.
Calibrating the baseline readout to the class prior suppresses collapse and speeds learning; subtracting the signal's batch mean prevents sustained collapse and improves learning. Replacing errors by their signs sustains collapse. The mechanism generalizes to deeper networks, convolutional networks, and CIFAR-10, with cost depending on readout, optimizer, and input statistics.