Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach (1804.05862v3)

Abstract: Modern neural networks are highly overparameterized, with capacity to substantially overfit to training data. Nevertheless, these networks often generalize well in practice. It has also been observed that trained networks can often be "compressed" to much smaller representations. The purpose of this paper is to connect these two empirical observations. Our main technical result is a generalization bound for compressed networks based on the compressed size. Combined with off-the-shelf compression algorithms, the bound leads to state of the art generalization guarantees; in particular, we provide the first non-vacuous generalization guarantees for realistic architectures applied to the ImageNet classification problem. As additional evidence connecting compression and generalization, we show that compressibility of models that tend to overfit is limited: We establish an absolute limit on expected compressibility as a function of expected generalization error, where the expectations are over the random choice of training examples. The bounds are complemented by empirical results that show an increase in overfitting implies an increase in the number of bits required to describe a trained network.

• The paper demonstrates that compressible networks using pruning and quantization achieve non-vacuous PAC-Bayesian generalization bounds on ImageNet.
• It validates the theory with extensive experiments linking network compression directly to reduced overfitting and improved performance.
• The study introduces compression-aware complexity measures that outperform traditional metrics, suggesting new protocols for efficient deep learning.

Non-vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach

This paper presents significant advancements in understanding the generalization properties of deep neural networks despite their inherent overparameterization, with a focus on ImageNet-scale challenges. The central finding connects the compression potential of neural networks to their ability to generalize, offering a novel perspective through a PAC-Bayesian framework.

Key Contributions and Findings

The authors provide several important contributions:

1. Generalization Bounds Based on Compression: The paper establishes a theoretical framework linking network compressibility to generalization through PAC-Bayesian bounds. The critical insight is that networks which can be compressed without significant loss in performance are indicative of inherent simplicity leading to better generalization. This is concretely demonstrated by providing the first non-vacuous generalization bounds for modern architectures applied to the ImageNet classification task.
2. Empirical Validation: The authors perform extensive experimentation to validate their theoretical claims. By combining off-the-shelf network compression techniques—such as pruning and quantization—with their PAC-Bayesian bounds, they show that compression directly leads to non-vacuous bounds in practice. For instance, they extend their findings to standard datasets such as MNIST and ImageNet using compressed versions of LeNet-5 and MobileNet architectures.
3. Implications of Overfitting and Compressibility: A novel insight is drawn that increased overfitting limits a model's compressibility. This is validated through randomization tests which show that models trained with higher levels of label noise require more memory to achieve similar performance levels, thereby confirming the theoretical prediction.

Implications for Theory and Practice

The theoretical implications of this work challenge traditional notions of model complexity and generalization in deep learning. By leveraging model compressibility, the authors provide an effective complexity measure that correlates with generalization more accurately than conventional measures such as VC-dimensions or Rademacher complexities.

Practically, this research suggests that network compression is not just a tool for resource efficiency, but also a lens through which we can assess the generalizability of models. As such, it opens pathways for developing compression-aware training protocols that could lead to more generalizable models.

Future Speculations in AI

This work has potential implications for the broader development of AI systems, particularly in resource-constrained environments where models must be both efficient and effective—such as mobile and edge devices. As machine learning models are deployed in more diverse and demanding settings, understanding and improving model generalization through compression could become a key consideration in AI development strategies.

Moreover, the insights from this research could be extended to continually learning systems where models must adapt over time to new data, maintaining simplicity and generalization across varied tasks.

In conclusion, this paper provides both robust theoretical insights and practical methodologies that advance the field’s understanding of deep network generalization at scale. The relationship between model compression and generalization not only enriches theoretical explorations but also holds significant implications for the deployment of efficient and adaptable AI systems.