Similarity of Neural Networks with Gradients
arXiv:2003.11498
Abstract
A suitable similarity index for comparing learnt neural networks plays an important role in understanding the behaviour of the highly-nonlinear functions, and can provide insights on further theoretical analysis and empirical studies. We define two key steps when comparing models: firstly, the representation abstracted from the learnt model, where we propose to leverage both feature vectors and gradient ones (which are largely ignored in prior work) into designing the representation of a neural network. Secondly, we define the employed similarity index which gives desired invariance properties, and we facilitate the chosen ones with sketching techniques for comparing various datasets efficiently. Empirically, we show that the proposed approach provides a state-of-the-art method for computing similarity of neural networks that are trained independently on different datasets and the tasks defined by the datasets.
References in corpus (6)
- Neural Tangent Kernel: Convergence and Generalization in Neural Networks
- Similarity of Neural Network Representations Revisited
- Algorithms for Learning Kernels Based on Centered Alignment
- SVCCA: Singular Vector Canonical Correlation Analysis for Deep Learning Dynamics and Interpretability
- Fisher-Rao Metric, Geometry, and Complexity of Neural Networks
- Generalizing Point Embeddings using the Wasserstein Space of Elliptical Distributions