I’ve been trying to reduce the parameter count of transformer models without a drop in performance—think of it as a pruning algorithm that stays near the theoretical lower bound for model size. Got a moment to dissect the math and see if we can squeeze more out of the architecture?

Let’s formalize the Hessian‑based pruning first, then sketch the head re‑weighting. The Hessian, \(H=\nabla^2 L(\theta)\), gives a second‑order importance measure; we’ll approximate its diagonal or use a block‑diagonal structure to keep it tractable. For each parameter \( \theta_i \), we compute \(g_i^2/H_{ii}\) and prune where that ratio is below a threshold—this keeps the parameters with the largest curvature impact. Once we prune, we’ll replace the dropped entries with zero, then recompute the loss and retrain for a few epochs with a very small learning rate to let the remaining parameters adapt. After that, we’ll move to the attention heads: compute mutual information between each head’s output and the final logits, scale each head’s weights by \( \alpha_i = \frac{I_i}{\sum_j I_j}\), then fine‑tune with L2 regularization to keep the weights from blowing up. Finally, we’ll apply a low‑rank factorization—\(W \approx U V^T\) with rank chosen to satisfy \(\text{rank} \leq \log_2(\text{dim})\) so we stay near the information‑theoretic bound. We’ll test each step’s impact on perplexity and FLOPs before moving on. Does that workflow line up with what you had in mind?