Order-Sensitivity Margin Regularizer

Add the regularizer at each recurrent layer and timestep immediately before threshold/reset. During the forward pass, separate incoming pulses into positive and negative masses over the current coarse timestep: a=sum_j max(Delta_j,0), b=sum_j max(-Delta_j,0), and let x be the membrane potential after leak but before these pulses. Compute d_net, d_E, and m using the displayed equations. For the robust-simulation variant, construct two counterfactual states from the same events: E-first applies all positive pulses, thresholds and resets, then applies negative pulses; I-first applies all negative pulses, then positive pulses. Run the remaining recurrent computation for both branches to obtain y_E and y_I, then add mu times their squared difference to the task loss. For the margin variant, use a straight-through or detached indicator for m>0 and clip m to a fixed range. Start with lambda and mu between 0.001 and 0.1 times the task loss, then sweep them. First test on a synthetic temporal classification task whose labels are invariant to within-bin event order, followed by SHD or N-MNIST with deliberately coarse bins. Compare baseline BPTT, margin-only training, and counterfactual consistency training at equal compute; compute counterfactuals on a random 25 percent of timesteps if needed. Success is lower E-first/I-first output disagreement and equal or better test accuracy under random delay perturbations, plus fewer threshold oscillations and lower seed variance. For order-sensitive tasks, omit the consistency term and test margin-only training.