Beyond Size: How Gradients Shape Pruning Decisions in Large Language Models

arXiv:2311.04902 · cs.CL, cs.AI, cs.LG · Submitted 2023-11-08 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: Today's paper: "Beyond Size: How Gradients Shape Pruning Decisions in Large Language Models".

Jane: The gist Large Language Models (LLMs) can be pruned effectively using Gradientbased Language Model Pruner (GBLM-Pruner), a novel,

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So we're looking at this paper called "Beyond Size: How Gradients Shape Pruning Decisions in Large Language Models." The authors are Rocktim Jyoti Das and colleagues from institutions like Carnegie Mellon and Mohamed bin Zayed University of AI. They're tackling the problem of pruning huge models by removing weights without hurting performance.

Jane: Right, so the main idea here is that past methods, like magnitude pruning or SparseGPT, only looked at the weights or maybe mixed them with activation information. But they missed something important: the gradients derived from pre-trained LLMs themselves.

Lu: Exactly. This paper proposes a new method called Gradient-based Language Model Pruner, or GBLM-Pruner. They claim this method uses the first-order term of the Taylor expansion to figure out what weights are important without needing any training for pruning itself.

Meng: Training free is good for us because retraining takes time and resources. So how does it work? Does it just look at the weight magnitude, or is there something more sophisticated here?

Tom: It leverages properly normalized gradients from just a few calibration samples to determine the pruning metric. The core idea is to use these gradients as a proxy for importance. They state that this method substantially outperforms competitors like SparseGPT and Wanda across multiple benchmarks.

Jane: And it's not just about the weights anymore, because they incorporate feature activations into the final metric for better performance. They define a weight importance score, W m

i, j: , using both the gradient norm and the input feature norm squared.

Lalam: Lalam here is very confident in this approach. The theoretical analysis revisits the Optimal Brain Surgeon framework by incorporating gradients through that first-order Taylor approximation of the Hessian matrix. They find that the pruning metric using W m times X squared + W m times g yields the most favorable results for pruning decisions, according to Equation twenty <ref:2311.04902#pg3>.

Meng: So, it's using gradients to get a more nuanced importance score than just looking at raw weight values or even just input feature norms as Wanda does. What does that actually mean in practice for someone trying to deploy a model?

Tom: It means the method is designed to be simple enough to explain, but effective because it uses information from the LLM's internal structure—the gradients—to make decisions about which weights to cut.

Conclusion: Jane: So, wrapping up this discussion on "Beyond Size: How Gradients Shape Pruning Decisions in Large Language Models," what's the big picture here? The authors are showing that you don't have to rely solely on weight magnitude or simple activation checks when pruning these massive models.

Tom: They present GBLM-Pruner as a training-free way to prune, using gradients to identify structural patterns in the parameter space. This approach seems particularly interesting because it shows that unstructured pruning can reveal geometric interdependence within the LLM's structure.

Lu: What this implies is that we might be able to find more meaningful sparsity patterns than just picking the smallest weights. If this works, it could lead to much better model compression while maintaining high predictive accuracy on things like LLaMA-series and Vision Transformers.

Meng: From a deployment standpoint, if it’s training free and doesn't require intensive weight updates like SparseGPT does, that simplifies the entire pipeline for production environments. It sounds like it minimizes disruption during the pruning process.

Lalam: I agree with Meng on the deployment aspect. The paper shows GBLM-Pruner surpasses magnitude pruning and Wanda by significant margins in evaluations on LLaMA-one and LLaMA-two and it’s robust to variations in how many calibration samples you use compared to methods like SparseGPT <ref:2311.04902#pg1>.

Jane: It sounds like a solid piece of work because they're not just claiming better results, they are linking the pruning metric directly back to the Taylor expansion of the Hessian matrix, giving it a solid theoretical foundation. It moves beyond just empirical tricks.

Tom: So, in short, this paper suggests that incorporating gradients into pruning metrics is a way to capture more of the LLM's internal structure and lead to better compression without needing retraining. It’s an important step for making these models more efficient on real hardware.

Rocktim Jyoti Das, Mingjie Sun, Liqun Ma, Zhiqiang Shen

Mohamed bin Zayed University of AI · Carnegie Mellon University

cs.CL, cs.AI, cs.LG

Submitted: 2023-11-08

Updated: 2026-10-14

Comments: Code and models at https://github.com/VILA-Lab/GBLM-Pruner

Code: https://github.com/VILA-Lab/GBLM-Pruner

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 88/100

The gist: The gist Large Language Models (LLMs) can be pruned effectively using Gradientbased Language Model Pruner (GBLM-Pruner), a novel, training-free method that leverages first-order Taylor expansion

Key concepts

Gradient-based Pruning
This technique uses the first derivative (gradient) information from a few calibration samples to estimate how important each model weight is. It operates without retraining or weight updates, making it efficient for pruning large models.
Taylor Expansion
The paper uses the first-order term of the Taylor expansion to analyze the optimization problem. This mathematical tool helps derive a pruning metric that effectively captures the structural importance of weights based on their relationship with gradients.
Pruning Metric
The final metric used by GBLM-Pruner combines two factors: the weight's absolute value multiplied by its gradient norm, and its absolute value multiplied by feature activations. This combined score is optimized to select the most structurally important weights for removal.

Terminology

Summary

The gist Large Language Models (LLMs) can be pruned effectively using Gradientbased Language Model Pruner (GBLM-Pruner), a novel, training-free method that leverages first-order Taylor expansion terms to determine pruning metrics from properly normalized gradients, substantially outperforming prior approaches like SparseGPT and Wanda on LLaMA models and Vision Transformers.

Prior Solutions

Previous methods for pruning LLMs primarily rely on weight magnitude or combinations of magnitude and activation information because they are either too complex or lack theoretical justification for advanced LLMs While existing solutions for pruning LLMs primarily employ either weight magnitude (Han et al., 2015a; 2016) or a combination of magnitude and activation (Frantar & Alistarh, 2023), they are, to a degree, either too complex to use like SparseGPT by computing matrix inverses and updating weights, or heuristic and lack profound theoretical justification like Wanda

GBLM-Pruner Approach

The GBLM-Pruner method operates in a training-free manner by harnessing properly normalized gradients from a few calibration samples to determine the pruning metric Specifically, the importance score attributed to a specific weight, W[i, j], is determined as follows: Wm[i, j] = W[i, j] · ∥G[:, i, j]∥p (Equation 4) Furthermore, the final pruning metric incorporates feature activations to get better performance: Wm[i, j] = α · W[i, j] · ∥G[:, i, j]∥p + W[i, j] · ∥X[:, j]∥2 (Equation 5) The scaling factor α is chosen using a held-out validation set

Theoretical Analysis and Metric Refinement

The theoretical analysis revisits the Optimal Brain Surgeon (OBS) framework by incorporating considerations of the gradient, i.e., the first-order term in Taylor approximation The final solution for the optimization problem in Equation 6 can be expressed as: δEm = w 2 m / H-1 mm − wm g T · H-1 Im / H-1 mm + I T m · H-1 g 2/2H-1 mm − 1/2 g T · H-1 g (Equation 20) The investigation reveals that the pruning metric (wm · ∥xm∥ squared + wm · gm) yields the most favorable results

Experimental Results and Robustness

Extensive evaluations on LLaMA-1 and LLaMA-2 across various benchmarks show that GBLM-Pruner surpasses magnitude pruning, Wanda and SparseGPT by significant margins For instance, in the WikiText perplexity evaluation, GBLM-Pruner with l1 norm outperforms both Wanda and reconstruction-based SparseGPT significantly across both LLaMA-1 and LLaMA-2 models The method also demonstrates robustness to variations in the number of calibration samples, exhibiting a relatively lower sensitivity to variations in the number of calibration samples in contrast to SparseGPT

Visualization and Conclusion

The visualization of learned pruning pattern illustrates that after the integration of gradients, the method of unstructured pruning tends to unveil certain structural patterns following the pruning process, which reflects the inherent geometric interdependence found in the parameter structure of the LLMs In conclusion, GBLM-Pruner performs in a training-free manner and applies gradient-based statistical magnitude to discern and selectively prune the model’s parameters, enabling substantial reductions in model size while preserving the model’s predictive accuracy The proposed approach has surpassed all previous LLM pruning methods in terms of perplexity, zero-shot performance and interpretability, marking a pivotal advancement in the field

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The gist Large Language Models (LLMs) can be pruned effectively using Gradientbased Language Model Pruner (GBLM-Pruner), a novel, training-free method that leverages first-order Taylor expansion terms to determine pruning metrics from properly normalized gradients, substantially outperforming prior approaches like SparseGPT and Wanda on LLaMA models and Vision Transformers.

Prior Solutions

Previous methods for pruning LLMs primarily rely on weight magnitude or combinations of magnitude and activation information because they are either too complex or lack theoretical justification for advanced LLMs

Visualization and Conclusion

The visualization of learned pruning pattern illustrates that after the integration of gradients, the method of unstructured pruning tends to unveil certain structural patterns following the pruning process, which reflects the inherent geometric interdependence found in the parameter structure of the LLMs In conclusion, GBLM-Pruner performs in a training-free manner and applies gradient-based statistical magnitude to discern and selectively prune the model’s parameters, enabling substantial reductions in model size while preserving the model’s predictive accuracy

--- Page 6 ---

The gist Large Language Models (LLMs) can be pruned effectively using Gradientbased Language Model Pruner (GBLM-Pruner), a novel, training-free method that leverages first-order Taylor expansion terms to determine pruning metrics from properly normalized gradients, substantially outperforming prior approaches like SparseGPT and Wanda on LLaMA models and Vision Transformers.

Improvements for AI systems

  1. A novel sparsity-centric pruning method, GBLM-Pruner, can be implemented in a training-free manner by harnessing properly normalized gradients from a few calibration samples to determine the pruning metric. This allows for significant model compression without subsequent retraining or weight updates.

  2. The system can achieve substantial performance gains over existing methods; for instance, GBLM-Pruner substantially outperforms magnitude pruning, Wanda and SparseGPT by significant margins on LLaMA-1 and LLaMA-2 models across various benchmarks.

  3. The pruned model can be evaluated using both Perplexity and Zero-shot Evaluation on the Harness Benchmark, providing a more readily interpretable assessment of model performance. This allows researchers to assess the compressed model's accuracy in common-sense reasoning tasks like RTE and WinoGrande.

  4. The system can reveal structural patterns in unstructured pruning by incorporating gradients, which mirrors the geometric interdependence inherent in the LLMs’ parameter structure. This provides a deeper understanding of how weights are important based on their sensitivity to loss changes.

  5. The pruning metric can be optimized for best results by using the formulation W ·∥X∥2 + α · W · Gp, where α is calibrated, leading to the best result for unstructured pruning across all models. This specific metric balances weight magnitude, activation norms, and gradient information.

Abstract

Large Language Models (LLMs) with billions of parameters are prime targets for network pruning, which removes some model weights without hurting performance. Prior approaches such as magnitude pruning, SparseGPT, and Wanda either concentrated solely on weights or integrated weights with activations for sparsity. However, they overlooked the informative gradients derived from pretrained LLMs. In this paper, we present a novel sparsity-centric pruning method for pretrained LLMs, termed Gradient-based Language Model Pruner (GBLM-Pruner). GBLM-Pruner leverages the first-order term of the Taylor expansion, operating in a training-free manner by harnessing properly normalized gradients from a few calibration samples to determine the pruning metric, and substantially outperforms competitive counterparts like SparseGPT and Wanda in multiple benchmarks. Intriguingly, by incorporating gradients, unstructured pruning with our method tends to reveal some structural patterns, which mirrors the geometric interdependence inherent in the LLMs' parameter structure. Additionally, GBLM-Pruner functions without any subsequent retraining or weight updates to maintain its simplicity as other counterparts. Extensive evaluations on LLaMA-series, Qwen-Series and Deepseek models across zero-shot, STEM-Reasoning and Coding benchmarks show that GBLM-Pruner surpasses magnitude pruning and Wanda by significant margins and performs competitively against SparseGPT which involves intensive weight updates. We further extend our approach on Vision Transformer and Vision Language Models. Our code and models are available at https://github.com/VILA-Lab/GBLM-Pruner.

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