Catalyst: Structured Pruning with Robust Bifurcation Dynamics

Structured pruning reduces the computational cost of neural networks by removing filters, but conventional regularizers such as L1 or Group Lasso exhibit strong magnitude bias and unstable decision boundaries, suggesting suboptimal pruning dynamics. In this work, we revisit pruning through the lens of optimization, geometry and learning dynamics. We first characterize the precise algebraic conditions under which pruning preserves model outputs, then use this insight to design Catalyst, a novel regularizer defined in an extended parameter space with auxiliary variables. Catalyst reshapes the loss landscape to promote emergent bifurcation dynamics between filters to be pruned or preserved, ensuring magnitude-invariant, fair, and robust pruning decisions. Our formulation highlights how high-dimensional learning dynamics can be achieved via a well-founded regularizer for pruning. Empirically, the Catalyst pruning algorithm consistently outperforms standard approaches, demonstrating both its theoretical soundness and practical effectiveness.