Data-driven Weight Initialization with Sylvester Solvers

Abstract

In this work, we propose a data-driven scheme to initialize the parameters of a deep neural network. This is in contrast to traditional approaches which randomly initialize parameters by sampling from transformed standard distributions. Such methods do not use the training data to produce a more informed initialization. Our method uses a sequential layer-wise approach where each layer is initialized using its input activations. The initialization is cast as an optimization problem where we minimize a combination of encoding and decoding losses of the input activations, which is further constrained by a user-defined latent code. The optimization problem is then restructured into the well-known Sylvester equation, which has fast and efficient gradient-free solutions. Our data-driven method achieves a boost in performance compared to random initialization methods, both before start of training and after training is over. We show that our proposed method is especially effective in few-shot and fine-tuning settings. We conclude this paper with analyses on time complexity and the effect of different latent codes on the recognition performance.

Parameter Prediction for Unseen Deep Architectures

“…Besides the works discussed in § 6, our work is also loosely related to other parameter prediction methods [113,98,114], analysis of graph structure of neural networks [46], knowledge distillation from multiple teachers [115], compression methods [116] and optimization-based initialization [117][118][119]. Denil et al [113] train a model that can predict a fraction of network parameters given other parameters requiring to retrain the model for each new architecture.…”

“…The HyperGAN [114] allows to generate an ensemble of trained parameters in a computationally efficient way, but as the aforementioned works is constrained to a particular architecture. Finally, MetaInit [117], GradInit [118] and Sylvester-based initialization [119] can initialize arbitrary networks by carefully optimizing their initial parameters, but due to the optimization loop they are generally more computationally expensive compared to predicting parameters using GHNs. Overall, these prior works did not formulate the task nor proposed the methods of predicting performant parameters for diverse and large-scale architectures as ours.…”

Towards Theoretically Inspired Neural Initialization Optimization

“…Previous initialization methods are mostly handcrafted. They focus on finding proper variance patterns of randomly initialized weights [18,16,40,36] or rely on empirical evidence derived from certain architectures [58,23,15,7]. Recently, [60,8] propose learning-based initialization that learns to tune the norms of the initial weights so as to minimize a quantity that is intimately related to favorable training dynamics.…”