[Paper Review] Overfitting Mechanism and Avoidance in Deep Neural Networks

Shaeke Salman, Xiuwen Liu|arXiv (Cornell University)|Jan 19, 2019

Neural Networks and ApplicationsComputer Science19 references107 citations

TL;DR

The paper analyzes overfitting in deep neural networks as driven by continuous gradient updates and softmax input scaling, and proposes a consensus-based classification algorithm using multiple models to identify and reject ambiguously classified samples, improving accuracy with small training sets.

ABSTRACT

Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and natural language processing. As they are being used in critical applications, understanding underlying mechanisms for their successes and limitations is imperative. In this paper, we show that overfitting, one of the fundamental issues in deep neural networks, is due to continuous gradient updating and scale sensitiveness of cross entropy loss. By separating samples into correctly and incorrectly classified ones, we show that they behave very differently, where the loss decreases in the correct ones and increases in the incorrect ones. Furthermore, by analyzing dynamics during training, we propose a consensus-based classification algorithm that enables us to avoid overfitting and significantly improve the classification accuracy especially when the number of training samples is limited. As each trained neural network depends on extrinsic factors such as initial values as well as training data, requiring consensus among multiple models reduces extrinsic factors substantially; for statistically independent models, the reduction is exponential. Compared to ensemble algorithms, the proposed algorithm avoids overgeneralization by not classifying ambiguous inputs. Systematic experimental results demonstrate the effectiveness of the proposed algorithm. For example, using only 1000 training samples from MNIST dataset, the proposed algorithm achieves 95% accuracy, significantly higher than any of the individual models, with 90% of the test samples classified.

Motivation & Objective

• Explain how overfitting arises in deep neural networks beyond data quantity.
• Demonstrate that continuous gradient updating and scaling of softmax inputs drive validation loss increases.
• Propose a consensus-based classification algorithm to avoid overfitting by rejecting ambiguous samples.
• Show that consensus across multiple models reduces extrinsic factors and improves intrinsic accuracy especially with small training sets.

Proposed method

• Empirical analysis of good solution abundance via interpolation between trained network solutions on MNIST.
• Observation and analysis of training dynamics show training loss decreases while validation loss increases due to scaling effects on softmax inputs.
• Development of a consensus-based classification algorithm (Algorithm 1) using probabilities from multiple models to decide classifications or reject ambiguous samples.
• Experimentation with multiple architectures and datasets to assess intrinsic (consistently classified) versus extrinsic (random factors) classifications.
• Evaluation of the effect of different thresholds p_t on intrinsic accuracy and CCS sample proportion.
• Comparison with single-model performance and exploration of dropout effects on CCS outcomes.

Experimental results

Research questions

• RQ1 Why does overfitting occur in deep neural networks despite overparameterization and abundance of good solutions?
• RQ2 Can a consensus-based approach across multiple models identify and reject overgeneralized or ambiguous samples to improve generalization with limited data?
• RQ3 How do training dynamics of correctly versus incorrectly classified samples relate to softmax input scaling and cross-entropy losses?
• RQ4 What is the impact of model diversity (different architectures) and regularization (dropout) on intrinsic classification accuracy?

Key findings

• Overfitting can manifest as decreasing training loss and increasing validation loss due to continuous gradient updates increasing magnitudes of softmax inputs.
• Incorrectly classified samples drive the rise in validation loss, while correctly classified samples’ losses decrease.
• A consensus-based classification approach using multiple models can classify consistently classified samples and reject ambiguous ones, improving intrinsic accuracy especially with small training sets.
• Using a threshold parameter p_t, the method increases intrinsic accuracy and the proportion of consistently classified samples (CCS) compared to individual models.
• The approach yields substantial accuracy gains when training with limited data (e.g., MNIST with 1000 training samples) and shows robustness across architectures.
• Dropout and ensemble-like dynamics influence CCS, but the consensus method can outperform single models even with varying regularization.