Study Reveals Exponential Efficiency Gap Between Weight and Neuron Pruning Methods
A new theoretical analysis shows that neuron pruning requires exponentially larger neural networks than weight pruning to achieve the same approximation accuracy. The research isolates the intrinsic limitations of neuron pruning by studying how a two-layer network can approximate a single ReLU neuron through different pruning strategies. This finding has implications for understanding the practical trade-offs between hardware efficiency and network size in neural network optimization.
Researchers have demonstrated a significant theoretical gap between two common neural network pruning approaches: structured pruning (neuron pruning) and unstructured pruning (weight pruning). Using the framework of the Strong Lottery Ticket Hypothesis, which posits that large randomly initialized networks contain sparse subnetworks capable of function approximation without training, the authors prove that neuron pruning requires network sizes scaling as Ω(1/ε) to achieve ε-approximation accuracy, while weight pruning needs only O(log(1/ε)) hidden units. The analysis focuses on the simplified but revealing case of approximating a single bias-free ReLU neuron in a two-layer network. This exponential separation explains why weight pruning has dominated theoretical analyses despite neuron pruning's practical appeal for direct hardware acceleration, suggesting fundamental computational differences between the two approaches.
What's missing
The study's scope is limited to approximating a single ReLU neuron in a two-layer network; the authors do not address how these theoretical results extend to deeper networks, more complex target functions, or practical pruning scenarios involving training. Additionally, the analysis assumes bias-free neurons and does not explore how results change with different activation functions or network architectures.
What different sources said
- arXiv cs.AICenter
Structured vs. Unstructured Pruning: An Exponential Gap
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