Research on Representation Stability of Deep Neural Networks: A New Perspective for Predicting Model Performance

This master's thesis study explores predicting the final performance of models by monitoring the stability of internal representations in deep neural networks, providing new ideas for training early stopping strategies and model performance evaluation. The core hypothesis is that representation stability is correlated with the performance of shallow surrogate models. Experiments use ResNet-18 on the CIFAR-10 dataset for validation, combining CKA (geometric similarity) and DRS (decision consistency) metrics to detect representation stability.

In deep learning training, the internal processes of networks are often regarded as black boxes. The core insight of this study: internal representations of neural networks change significantly during training, and when they tend to stabilize, it means effective features have been learned. Core hypothesis: Representation stability is correlated with the performance of shallow surrogate models—if representations are stable at a certain moment, training a simple classifier using frozen representations will yield performance close to the final performance of the complete network, providing a basis for early stopping and performance prediction.

The research framework uses ResNet-18 for experiments on the CIFAR-10 dataset, employing two complementary metrics:

1. CKA (Centered Kernel Alignment): Measures the geometric similarity of representations between adjacent epochs; low CKA values across consecutive checkpoints indicate stable geometric structure.
2. DRS (Decision Robustness Score): Evaluates the consistency of classification decisions of linear probes between adjacent epochs, focusing on functional stability. Only when both meet the stability conditions simultaneously is the representation considered truly stable.

Technical details of the experiment:

• Training: ResNet-18 uses the SGD optimizer (to avoid CKA noise from Adam), saving checkpoints and representations every 5 epochs.
• Feature extraction: Focuses on the penultimate layer (the representation layer before the classifier).
• Stability determination: When both CKA and DRS are below 0.02 for 5 consecutive checkpoints, it is recorded as the stable moment t*.

The core findings support the hypothesis: The accuracy of surrogate classifiers (such as logistic regression, LightGBM, etc.) trained using frozen representations at moment t* is close to the final performance of the complete network. This means that the marginal gain of continuing training after representation stabilization is limited, providing a theoretical basis for early stopping strategies. It also proposes a new model selection method—monitoring representation stability early to predict potential. Additionally, CKA (geometric) and DRS (functional) are complementary, avoiding biases from a single metric.

Limitations: Experiments were only conducted on ResNet-18 and CIFAR-10; conclusions need to be validated on larger models/complex datasets. The stability thresholds (τ=0.02, K=5) are empirical values and may vary depending on tasks/architectures. Future directions: Explore adaptive threshold strategies; apply to scenarios such as transfer learning, continuous learning, and neural architecture search.

Implications for practitioners: Monitoring representation changes (not just loss/accuracy) provides deeper insights; simple surrogate models can predict the performance of complex networks (useful in resource-constrained scenarios). For researchers: Provides methodological references (combination of CKA+DRS, strict determination criteria). This study provides a new direction for deep learning interpretability and efficient training methods. Although it is a starting point, it inspires follow-up research and promotes the healthy development of the field.