Topological Self-Regulation in Neural Networks

A neural network learns how to use its channels during training, but where those channels sit is decided before the first gradient is taken, by convention rather than by the task. One part of a network can be starved of channels while another carries channels it barely uses. We ask whether training itself can revise this allocation. Topological Self-Regulation (TSR) treats channel width as a budgeted, revisable part of the model: silent candidate channels are attached throughout the network, the ordinary backward pass reveals which of them would be worth introducing and which incumbents contribute least, and capacity is transferred between them through edits that keep every dependent tensor consistent. A coupling calculus makes such edits valid across residual trunks, depthwise stacks, normalization state and optimizer moments, with exact accounting of the parameters they move. Across four image-classification families and four forecasting backbones, the discovered architectures match the dense reference at roughly fifteen percent fewer parameters in vision and at reductions reaching well over half the network in forecasting. Where the reduction is large, the task-directed allocation outperforms a random one of the same size, and pruning the same reference to the same count shows how much of that is reallocation rather than removal.