The Unseen Frontier: Pushing the Limits of LLM Sparsity with Surrogate-Free ADMM

Neural network pruning is a promising technique to mitigate the excessive computational and memory requirements of large language models (LLMs). Despite its promise, however, progress in this area has diminished, as conventional methods are seemingly unable to surpass moderate sparsity levels (50-60%) without severely degrading model accuracy. This work breaks through the current impasse, presenting a principled and effective method called $\texttt{Elsa}$, which achieves extreme sparsity levels of up to 90% while retaining high model fidelity. This is done by identifying several limitations in current practice, all of which can be traced back to their reliance on a surrogate objective formulation. $\texttt{Elsa}$ tackles this issue directly and effectively via standard and well-established constrained optimization techniques based on ADMM. Our extensive experiments across a wide range of models and scales show that $\texttt{Elsa}$ achieves substantial improvements over existing methods; e.g., it achieves 7.8$\times$ less perplexity than the best existing method on LLaMA-2-7B at 90% sparsity. Furthermore, we present $\texttt{Elsa}_{\text{-L}}$, a quantized variant that scales to extremely large models (27B), and establish its theoretical convergence guarantees. These results highlight meaningful progress in advancing the frontier of LLM sparsity, while promising that significant opportunities for further advancement may remain in directions that have so far attracted limited exploration.

SAFE: Finding Sparse and Flat Minima to Improve Pruning

Sparsifying neural networks often suffers from seemingly inevitable performance degradation, and it remains challenging to restore the original performance despite much recent progress. Motivated by recent studies in robust optimization, we aim to tackle this problem by finding subnetworks that are both sparse and flat at the same time. Specifically, we formulate pruning as a sparsity-constrained optimization problem where flatness is encouraged as an objective. We solve it explicitly via an augmented Lagrange dual approach and extend it further by proposing a generalized projection operation, resulting in novel pruning methods called SAFE and its extension, SAFE$^+$. Extensive evaluations on standard image classification and language modeling tasks reveal that SAFE consistently yields sparse networks with improved generalization performance, which compares competitively to well-established baselines. In addition, SAFE demonstrates resilience to noisy data, making it well-suited for real-world conditions.