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Title: The Generalization-Stability Tradeoff in Neural Network Pruning

Paper content:
Pruning neural network parameters is often viewed as a means to compress models, but pruning has also been motivated by the desire to prevent overfitting.
This motivation is particularly relevant given the perhaps surprising observation that a wide variety of pruning approaches increase test accuracy despite sometimes massive reductions in parameter counts.
To better understand this phenomenon, we analyze the behavior of pruning over the course of training, finding that pruning's effect on generalization relies more on the instability it generates (defined as the drops in test accuracy immediately following pruning) than on the final size of the pruned model.
We demonstrate that even the pruning of unimportant parameters can lead to such instability, and show similarities between pruning and regularizing by injecting noise, suggesting a mechanism for pruning-based generalization improvements that is compatible with the strong generalization recently observed in over-parameterized networks.
Pruning weights and/or convolutional filters from deep neural networks (DNNs) can substantially shrink parameter counts with minimal loss in accuracy (LeCun et al., 1990; Hassibi & Stork, 1993; Han et al., 2015a; Li et al., 2016; Molchanov et al., 2017; Louizos et al., 2017; Liu et al., 2017; Ye et al., 2018) , enabling broader application of DNNs via reductions in memory-footprint and inference-FLOPs requirements.
Moreover, many pruning methods have been found to actually improve generalization (measured by model accuracy on previously unobserved inputs) (Narang et al., 2017; Frankle & Carbin, 2018; You et al., 2019) .
Consistent with this, pruning was originally motivated as a means to prevent over-parameterized networks from overfitting to comparatively small datasets (LeCun et al., 1990) .
Concern about over-parameterizing models has weakened, however, as many recent studies have found that adding parameters can actually reduce a DNN's generalization-gap (the drop in performance when moving from previously seen to previously unseen inputs), even though it has been shown that the same networks have enough parameters to fit large datasets of randomized data (Neyshabur et al., 2014; Zhang et al., 2016) .
Potential explanations for this unintuitive phenomenon have come via experiments (Keskar et al., 2016; Morcos et al., 2018; Yao et al., 2018; Belkin et al., 2018; Nagarajan & Kolter, 2019) , and the derivation of bounds on DNN generalization-gaps that suggest less overfitting might occur as parameter counts increase (Neyshabur et al., 2018) .
This research has implications for neural network pruning, where a puzzling question has arisen: if larger parameter counts don't increase overfitting, how does pruning parameters throughout training improve generalization?
To address this question we first introduce the notion of pruning instability, which we define to be the size of the drop in network accuracy caused by a pruning iteration (Section 3).
We then empirically analyze the instability and generalization associated with various magnitude-pruning (Han et al., 2015b) algorithms in different settings, making the following contributions:
1. We find a tradeoff between the stability and potential generalization benefits of pruning, and show iterative pruning's similarity to regularizing with noise-suggesting a mechanism unrelated to parameter counts through which pruning appears to affect generalization.
2. We characterize the properties of pruning algorithms which lead to instability and correspondingly higher generalization.
In this study, we defined the notion of pruning algorithm instability, and applied several pruning approaches 5 to multiple neural networks, assessing the approaches' effects on instability and generalization.
Throughout these experiments, we observed that pruning algorithms that generated more instability led to better generalization (as measured by test accuracy).
For a given pruning target and total pruning percentage, instability and generalization could be fueled by raising iterative pruning rates (Figure 4, Section 4.3) .
Additionally, targeting more important weights, again holding total parameters pruned constant, led to more instability and generalization than targeting less important weights (Figure 1, Section 4.1) .
These results support the idea that the generalization benefits of pruning cannot be explained solely by pruning's effect on parameter counts-the properties of the pruning algorithm must be taken into account.
Our analysis also suggests that the capacity effects of weight-removal may not even be necessary to explain how pruning improves generalization.
Indeed, we provide an interpretation of iterative pruning as noise injection, a popular approach to regularizing DNNs, and find that making pruning noise impermanent provides pruning-like generalization benefits while not removing as much capacity as permanent pruning ( Figure 5 , Section 4.4).

assistant: text: We demonstrate that pruning methods which introduce greater instability into the loss also confer improved generalization, and explore the mechanisms underlying this effect.