A Sober Look at Neural Network Initializations (1903.11482v2)

Abstract: Initializing the weights and the biases is a key part of the training process of a neural network. Unlike the subsequent optimization phase, however, the initialization phase has gained only limited attention in the literature. In this paper we discuss some consequences of commonly used initialization strategies for vanilla DNNs with ReLU activations. Based on these insights we then develop an alternative initialization strategy. Finally, we present some large scale experiments assessing the quality of the new initialization strategy.

• The paper critically analyzes and critiques existing neural network initialization methods by highlighting their effects on neuron activation states.
• The paper proposes a novel strategy that initializes biases to small positive values, ensuring a balanced distribution of fully active neurons.
• Experimental results show improved convergence, reduced iterations, and lower test errors in both regression and classification tasks.

Overview of Neural Network Initialization Strategies

The paper "A Sober Look at Neural Network Initializations" by Ingo Steinwart provides a comprehensive analysis of initialization strategies for neural networks, specifically focusing on vanilla Deep Neural Networks (DNNs) with ReLU activation functions. Understanding the significance of initialization in neural network training, the paper critically evaluates existing strategies and proposes a novel initialization method. Unlike the optimization phase of training, where stochastic gradient descent (SGD) plays a critical role in navigating the non-convex landscape of neural networks' weights, initialization is often overlooked, despite its potential impact on network performance.

Key Contributions

1. Critique of Existing Strategies:
   • The paper critiques common initialization strategies, such as those proposed by Glorot and Bengio (Xavier initialization) and He et al. (He initialization), which primarily focus on maintaining the variance of the network's weights to prevent gradient explosion or vanishing.
   • It highlights the often-unexplored effects of these strategies, especially concerning the activation behavior of neurons—whether a neuron becomes fully active, semi-active, or inactive.
2. Proposed Initialization Strategy:
   • Steinwart develops a new initialization strategy based on insights from analyzing neuron behavior related to their initialization. The strategy aims to ensure a more balanced distribution of neuron states, moving beyond just considering the variance.
   • The paper emphasizes initializing biases to small positive values as a way to maximize the proportion of fully active neurons, avoiding the severe impact of dead neurons on SGD's effectiveness.
3. Large Scale Experimental Evaluation:
   • Extensive experiments indicate the proposed method's effectiveness in varied settings. Specifically, the paper shows how this method leads to better convergence and improved performance across several data sets in regression and classification tasks.

Experimental Results and Theoretical Implications

The experimental section of the paper demonstrates that the proposed initialization method achieves superior performance in many scenarios compared to traditional methods. This was demonstrated through lower average test errors, faster convergence (fewer iterations), and less training time on different architectures and datasets.

From a theoretical standpoint, the proposed method appropriately addresses the prescription of biases and the variance scaling factor to enhance the learning process's efficiency. In broader terms, this suggests that carefully considering the network’s initial state can provide significant improvements in neural network training, impacting computational efficiency and result robustness.

Future Directions

The findings open several avenues for future research. The implications of these results can drive further inquiry into more complex architectures or other forms of neural networks, such as convolutional networks or recurrent architectures. Furthermore, the interaction between initialization strategies and other network components, such as learning rate scheduling or batch normalization, presents an intriguing area for future exploration.

The paper also suggests potential modifications in initialization tailored for practical constraints or specific application domains, such as networks constrained by hardware limitations or those employed in sparse data environments requiring efficient learning.

In essence, this work re-emphasizes the critical role of initialization in neural network training, providing a balanced critique of existing methods while contributing a novel, effective strategy. The paper underlines the potential gains of employing mathematically grounded, empirically tested initialization techniques that could be pivotal in achieving optimal network configurations.