Neural Dependencies Emerging from Learning Massive Categories
This work addresses the problem of understanding and leveraging internal correlations in neural networks for researchers and practitioners in machine learning, offering insights into model generalization and robustness, though it is incremental in building on existing theoretical frameworks.
The authors discovered that in large-scale image classification models, the logits for some categories can be linearly predicted from a few others, a phenomenon termed neural dependency, which holds across independently trained models and is explained by redundant logit covariance matrices.
This work presents two astonishing findings on neural networks learned for large-scale image classification. 1) Given a well-trained model, the logits predicted for some category can be directly obtained by linearly combining the predictions of a few other categories, which we call \textbf{neural dependency}. 2) Neural dependencies exist not only within a single model, but even between two independently learned models, regardless of their architectures. Towards a theoretical analysis of such phenomena, we demonstrate that identifying neural dependencies is equivalent to solving the Covariance Lasso (CovLasso) regression problem proposed in this paper. Through investigating the properties of the problem solution, we confirm that neural dependency is guaranteed by a redundant logit covariance matrix, which condition is easily met given massive categories, and that neural dependency is highly sparse, implying that one category correlates to only a few others. We further empirically show the potential of neural dependencies in understanding internal data correlations, generalizing models to unseen categories, and improving model robustness with a dependency-derived regularizer. Code for this work will be made publicly available.