Differentiable Attention Sparsity via Structured $D$-Gating

A core component of modern large language models is the attention mechanism, but its immense parameter count necessitates structured sparsity for resource-efficient optimization and inference. Traditional sparsity penalties, such as the group lasso, are non-smooth and thus incompatible with standard stochastic gradient descent methods. To address this, we propose a deep gating mechanism that reformulates the structured sparsity penalty into a fully differentiable optimization problem, allowing effective and principled norm-based group sparsification without requiring specialized non-smooth optimizers. Our theoretical analysis and empirical results demonstrate that this approach enables structured sparsity with simple stochastic gradient descent or variants while maintaining predictive performance.