Hanyu Hu

Nathanael Tepakbong, Hanyu Hu, Chengyu Liu et al.

Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary losses. We show that this supervision term acts as an operator-level preconditioner: for suitable weights, our comparison bounds guarantee a substantially smaller condition number than under the standard PINN loss, independently of how the pointwise labels are obtained. For a broad class of PDEs admitting a Feynman-Kac (FK) representation, we generate such labels by Monte Carlo averages of the FK functional, resulting in what we call ``FK-PINNs", and using the excess risk decomposition approach, we derive non-asymptotic $L^2(Ω)$-error bounds for FK-PINNs with $\tanh$ activation trained by finitely many steps of gradient descent. Along the way, we establish pseudo-dimension bounds for first- and second-order derivatives of $\tanh$ neural networks, which are of independent interest and, to the best of our knowledge, new. Numerical experiments on Poisson, Schrödinger, mean exit time, and committor problems corroborate the theory, and show that FK-PINNs can successfully solve PDEs for which standard PINNs exhibit severe failure modes.

Pengxiang Zhao, Hanyu Hu, Ping Li et al.

Pruning is a critical strategy for compressing trained large language models (LLMs), aiming at substantial memory conservation and computational acceleration without compromising performance. However, existing pruning methods often necessitate inefficient retraining for billion-scale LLMs or rely on heuristic methods such as the optimal brain surgeon framework, which degrade performance. In this paper, we introduce FISTAPruner, the first post-training pruner based on convex optimization models and algorithms. Specifically, we propose a convex optimization model incorporating $\ell_1$ norm to induce sparsity and utilize the FISTA solver for optimization. FISTAPruner incorporates an intra-layer cumulative error correction mechanism and supports parallel pruning. We comprehensively evaluate FISTAPruner on models such as OPT, LLaMA, LLaMA-2, and LLaMA-3 with 125M to 70B parameters under unstructured and 2:4 semi-structured sparsity, demonstrating superior performance over existing state-of-the-art methods across various language benchmarks.

Hanyu Hu, Pengxiang Zhao, Ping Li et al.

The rapid increase in the size of large language models (LLMs) has significantly escalated their computational and memory demands, posing challenges for efficient deployment, especially on resource-constrained devices. Structured pruning has emerged as an effective model compression method that can reduce these demands while preserving performance. In this paper, we introduce FASP (Fast and Accurate Structured Pruning), a novel structured pruning framework for LLMs that emphasizes both speed and accuracy. FASP employs a distinctive pruning structure that interlinks sequential layers, allowing for the removal of columns in one layer while simultaneously eliminating corresponding rows in the preceding layer without incurring additional performance loss. The pruning metric, inspired by Wanda, is computationally efficient and effectively selects components to prune. Additionally, we propose a restoration mechanism that enhances model fidelity by adjusting the remaining weights post-pruning. We evaluate FASP on the OPT and LLaMA model families, demonstrating superior performance in terms of perplexity and accuracy on downstream tasks compared to state-of-the-art methods. Our approach achieves significant speed-ups, pruning models such as OPT-125M in 17 seconds and LLaMA-30B in 15 minutes on a single NVIDIA RTX 4090 GPU, making it a highly practical solution for optimizing LLMs.

Hanyu Hu, Xiaoming Yuan

The deployment of large language models (LLMs) is often constrained by their substantial computational and memory demands. While structured pruning presents a viable approach by eliminating entire network components, existing methods suffer from performance degradation, reliance on heuristic metrics, or expensive finetuning. To address these challenges, we propose SPAP (Structured Pruning via Alternating Optimization and Penalty Methods), a novel and efficient structured pruning framework for LLMs grounded in optimization theory. SPAP formulates the pruning problem through a mixed-integer optimization model, employs a penalty method that effectively makes pruning decisions to minimize pruning errors, and introduces an alternating minimization algorithm tailored to the splittable problem structure for efficient weight updates and performance recovery. Extensive experiments on OPT, LLaMA-3/3.1/3.2, and Qwen2.5 models demonstrate SPAP's superiority over state-of-the-art methods, delivering linear inference speedups (1.29$\times$ at 30% sparsity) and proportional memory reductions. Our work offers a practical, optimization-driven solution for pruning LLMs while preserving model performance.