Structured vs. Unstructured Pruning: An Exponential Gap
arXiv:2603.02234v1 Announce Type: new Abstract: The Strong Lottery Ticket Hypothesis (SLTH) posits that large, randomly initialized neural networks contain sparse subnetworks capable of approximating a target function at initialization without training, suggesting that pruning alone is sufficient. Pruning methods are typically classified as unstructured, where individual weights can be removed from the network, and structured, where parameters are removed according to specific patterns, as in neuron pruning. Existing theoretical results supporting the SLTH rely almost exclusively on unstructured pruning, showing that logarithmic overparameterization suffices to approximate simple target networks. In contrast, neuron pruning has received limited theoretical attention. In this work, we consider the problem of approximating a single bias-free ReLU neuron using a randomly initialized bias-free two-layer ReLU network, thereby isolating the intrinsic limitations of neuron pruning. We show t
arXiv:2603.02234v1 Announce Type: new Abstract: The Strong Lottery Ticket Hypothesis (SLTH) posits that large, randomly initialized neural networks contain sparse subnetworks capable of approximating a target function at initialization without training, suggesting that pruning alone is sufficient. Pruning methods are typically classified as unstructured, where individual weights can be removed from the network, and structured, where parameters are removed according to specific patterns, as in neuron pruning. Existing theoretical results supporting the SLTH rely almost exclusively on unstructured pruning, showing that logarithmic overparameterization suffices to approximate simple target networks. In contrast, neuron pruning has received limited theoretical attention. In this work, we consider the problem of approximating a single bias-free ReLU neuron using a randomly initialized bias-free two-layer ReLU network, thereby isolating the intrinsic limitations of neuron pruning. We show that neuron pruning requires a starting network with $\Omega(d/\varepsilon)$ hidden neurons to $\varepsilon$-approximate a target ReLU neuron. In contrast, weight pruning achieves $\varepsilon$-approximation with only $O(d\log(1/\varepsilon))$ neurons, establishing an exponential separation between the two pruning paradigms.
Executive Summary
This article examines the theoretical limitations of structured pruning, specifically neuron pruning, in approximating a target function. In contrast to unstructured pruning, which has received significant attention, neuron pruning has been relatively under-explored. The authors provide a formal analysis of neuron pruning's ability to approximate a single bias-free ReLU neuron using a randomly initialized bias-free two-layer ReLU network. The results show a significant gap between the two pruning paradigms, with weight pruning requiring exponentially fewer neurons to achieve a similar level of approximation. This study sheds new light on the intrinsic limitations of neuron pruning and highlights the importance of understanding the theoretical underpinnings of pruning methods.
Key Points
- ▸ The article provides a theoretical analysis of neuron pruning's ability to approximate a target function.
- ▸ The results show an exponential gap between neuron pruning and unstructured pruning.
- ▸ The study highlights the importance of understanding the theoretical underpinnings of pruning methods.
Merits
Strength of theoretical analysis
The article provides a rigorous and comprehensive theoretical analysis of neuron pruning, shedding new light on its intrinsic limitations.
Demerits
Limited scope
The study focuses on a specific case, approximating a single bias-free ReLU neuron, which may limit its generalizability to more complex scenarios.
Expert Commentary
The article's findings have significant implications for the field of deep learning. The exponential gap between neuron pruning and unstructured pruning suggests that the latter may be a more effective approach for approximating complex target functions. However, the study's limitations, such as its focus on a specific case, must be taken into account when interpreting its results. Nevertheless, the article's rigorous analysis and comprehensive theoretical framework provide a valuable contribution to the field of deep learning and pruning methods. Future research should build on this study's findings to explore the applicability of these results to more complex scenarios.
Recommendations
- ✓ Future research should investigate the applicability of these results to more complex scenarios, such as approximating multiple target functions or incorporating additional regularization techniques.
- ✓ The development of efficient pruning methods for deep learning models should prioritize understanding the theoretical underpinnings of pruning methods, as highlighted by this study.