[Paper Review] Paradox in Deep Neural Networks: Similar yet Different while Different yet Similar

Arash Akbarinia, Karl R. Gegenfurtner|arXiv (Cornell University)|Mar 12, 2019

Cell Image Analysis TechniquesBiochemistry, Genetics and Molecular Biology31 references3 citations

TL;DR

This paper investigates the paradoxical relationship between kernel weight similarity and performance generalization in deep neural networks, finding that highly correlated kernels can yield vastly different performance under distortions, while uncorrelated kernels can perform similarly. The key contribution is demonstrating that intrinsic weight similarity does not predict functional robustness, challenging assumptions in transfer learning and interpretability of DNNs.

ABSTRACT

Machine learning is advancing towards a data-science approach, implying a necessity to a line of investigation to divulge the knowledge learnt by deep neuronal networks. Limiting the comparison among networks merely to a predefined intelligent ability, according to ground truth, does not suffice, it should be associated with innate similarity of these artificial entities. Here, we analysed multiple instances of an identical architecture trained to classify objects in static images (CIFAR and ImageNet data sets). We evaluated the performance of the networks under various distortions and compared it to the intrinsic similarity between their constituent kernels. While we expected a close correspondence between these two measures, we observed a puzzling phenomenon. Pairs of networks whose kernels' weights are over 99.9% correlated can exhibit significantly different performances, yet other pairs with no correlation can reach quite compatible levels of performance. We show implications of this for transfer learning, and argue its importance in our general understanding of what intelligence is, whether natural or artificial.

Motivation & Objective

• To investigate whether intrinsic similarity in kernel weights correlates with functional performance across deep neural networks.
• To evaluate how robustness to image distortions correlates with weight similarity in identical architectures trained under different conditions.
• To challenge the assumption that weight similarity predicts functional similarity in deep networks.
• To explore implications for transfer learning and understanding artificial and biological intelligence.

Proposed method

• Trained multiple instances of ResNet50 on CIFAR-10 and ImageNet with different random seeds and hyperparameters.
• Evaluated each network’s performance on eight image distortion types (e.g., noise, contrast reduction) to measure visual intelligence.
• Computed Pearson correlation coefficients between kernel weight matrices across all convolutional layers to quantify intrinsic similarity.
• Performed direct weight transfer from a fine-tuned child network to its parent to test performance improvement.
• Analyzed layer-wise weight correlations to identify which layers deviate most after fine-tuning.
• Used Riemannian geometry-inspired reasoning to interpret how low-level feature representations evolve across layers.

Experimental results

Research questions

• RQ1 To what extent does intrinsic weight similarity between deep neural networks predict their functional robustness under image distortions?
• RQ2 Why do networks with highly correlated kernels exhibit divergent performance on the same set of distortions?
• RQ3 Can performance be significantly improved by transferring only a small subset of kernel weights, even when the rest remain unchanged?
• RQ4 Do middle-level convolutional layers encode integrated representations of multiple low-level visual features?
• RQ5 How does the intrinsic similarity of kernels relate to the hierarchical feature representation in deep networks?

Key findings

• Networks with over 99.9% correlated kernel weights exhibited significantly different performance levels under image distortions, demonstrating a strong paradox in functional behavior.
• Conversely, pairs of networks with nearly uncorrelated kernel weights achieved highly compatible performance across all distortion types, challenging the assumption of weight-similarity-functionality correspondence.
• Transferring only the weights of a single convolutional layer (res3c_branch2c) from a fine-tuned child network to its parent improved the parent’s visual intelligence score by 2%, from 0.53 to 0.55.
• The same layer, res3c_branch2c, showed consistent correlation patterns across all offspring networks, indicating it encodes a composite representation of low-level visual features such as contrast and noise.
• Transferring all convolutional layer weights from a child to parent network achieved performance identical to the child, despite the fully connected layer remaining unchanged.
• The layer-wise correlation analysis revealed that middle-level layers (e.g., res3c_branch2c) are most sensitive to distortions, suggesting they serve as hubs for integrating low-level visual variations.