Exploring Low-Dimensional Manifolds of Deep Neural Network Parameters for Improved Model Optimization

Manifold learning techniques have significantly enhanced the comprehension of massive data by exploring the geometric properties of the data manifold in low-dimensional subspaces. However, existing research on manifold learning primarily focuses on understanding the intricate data, overlooking the explosive growth of the scale and complexity of deep neural networks (DNNs), which presents a significant challenge for model optimization. In this work, we propose to explore the intrinsic low-dimensional manifold of network parameters for efficient model optimization. Specifically, we analyze parameter distributions in a deep model and perform sampling to map them onto a low-dimensional parameter manifold using the local tangent space alignment (LTSA). Since our focus is on studying parameter manifolds to guide model optimization, we therefore select dynamic optimal training trajectories for sampling and approximate tangent spaces to obtain low-dimensional representations of DNNs. By applying manifold learning techniques and employing a two-step alternate optimization method, we achieve a fixed subspace that reduces training time and resource costs for commonly used deep networks. The trained low-dimensional network can be mapped back to the original parameter space for further use. We demonstrate the benefits of learning low-dimensional parameterization of DNNs on both noisy label learning and federated learning tasks. Extensive experimental results on various benchmarks show the effectiveness of our method concerning both superior accuracy and reduced resource consumption.