[Paper Review] Inconsistency, Instability, and Generalization Gap of Deep Neural Network Training

Rie Johnson, Tong Zhang|arXiv (Cornell University)|May 31, 2023

Neural Networks and Applications4 citations

TL;DR

This paper proposes inconsistency and instability of model outputs as key predictors of deep neural network generalization gap, showing through theory and experiments that inconsistency—measurable on unlabeled data—outperforms loss landscape sharpness in predicting generalization. Reducing inconsistency via algorithmic regularization improves test performance, offering a theoretical basis for methods like co-distillation and ensembling.

ABSTRACT

As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we first present a theoretical analysis in which the bound of generalization gap depends on what we call inconsistency and instability of model outputs, which can be estimated on unlabeled data. Our empirical study based on this analysis shows that instability and inconsistency are strongly predictive of generalization gap in various settings. In particular, our finding indicates that inconsistency is a more reliable indicator of generalization gap than the sharpness of the loss landscape. Furthermore, we show that algorithmic reduction of inconsistency leads to superior performance. The results also provide a theoretical basis for existing methods such as co-distillation and ensemble.

Motivation & Objective

• To identify fundamental properties of deep neural networks that correlate with generalization gap, particularly focusing on stochastic training dynamics.
• To develop a theoretical framework linking generalization gap to inconsistency and instability of model outputs, estimable on unlabeled data.
• To empirically validate that inconsistency is a stronger predictor of generalization gap than loss landscape sharpness.
• To demonstrate that algorithmic reduction of inconsistency improves model generalization and performance.
• To provide a theoretical foundation for existing techniques such as co-distillation and ensemble learning.

Proposed method

• Proposes a theoretical bound on generalization gap using three components: inconsistency of model outputs, instability of model outputs, and information-theoretic instability of model parameter distributions.
• Defines inconsistency as the expected 1-norm discrepancy between model outputs on the same training data, estimated via multiple forward passes with same data.
• Defines instability as the expected discrepancy in model outputs due to different training data samples, estimated across multiple training sets.
• Uses KL-divergence-based inconsistency for training regularization, enabling smooth optimization and compatibility with standard cross-entropy objectives.
• Employs unlabeled data to estimate inconsistency and instability, avoiding reliance on labels or full test set access.
• Applies consistency regularization during training by minimizing KL-divergence between predictions of two forward passes on the same input.

Experimental results

Research questions

• RQ1 How do inconsistency and instability of model outputs relate to the generalization gap in deep neural networks?
• RQ2 Can inconsistency and instability be reliably estimated on unlabeled data, and how predictive are they of generalization performance?
• RQ3 Is inconsistency a more reliable indicator of generalization gap than loss landscape sharpness?
• RQ4 Can algorithmic reduction of inconsistency lead to improved generalization and state-of-the-art performance?
• RQ5 What is the theoretical and empirical connection between inconsistency and existing methods like co-distillation and ensemble learning?

Key findings

• Inconsistency and instability of model outputs are strongly predictive of generalization gap across diverse deep learning settings.
• Inconsistency is a more reliable predictor of generalization gap than loss landscape sharpness, especially in cases where sharpness remains high despite low generalization error.
• When training randomness is low, inconsistency alone is almost as predictive as the combined effect of inconsistency and instability.
• Algorithmic reduction of inconsistency leads to improved test performance, demonstrating its practical utility in model training.
• Theoretical analysis shows that generalization gap is bounded by inconsistency, instability, and parameter distribution instability, with inconsistency playing a central role.
• The results provide a theoretical foundation for co-distillation and ensemble methods, which implicitly reduce inconsistency through model averaging.