Hayoung Choi

Hyunwoo Lee, Yunho Kim, Seung Yeop Yang et al.

Appropriate weight initialization settings, along with the ReLU activation function, have become cornerstones of modern deep learning, enabling the training and deployment of highly effective and efficient neural network models across diverse areas of artificial intelligence. The problem of \textquotedblleft dying ReLU," where ReLU neurons become inactive and yield zero output, presents a significant challenge in the training of deep neural networks with ReLU activation function. Theoretical research and various methods have been introduced to address the problem. However, even with these methods and research, training remains challenging for extremely deep and narrow feedforward networks with ReLU activation function. In this paper, we propose a novel weight initialization method to address this issue. We establish several properties of our initial weight matrix and demonstrate how these properties enable the effective propagation of signal vectors. Through a series of experiments and comparisons with existing methods, we demonstrate the effectiveness of the novel initialization method.

Manolis C. Tsakiris, Liangzu Peng, Aldo Conca et al.

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in diverse domains such as computer vision, data mining, communications and biology. In its simplest form, it is tantamount to solving a linear system of equations, for which the entries of the right hand side vector have been permuted. This type of data corruption renders the linear regression task considerably harder, even in the absence of other corruptions, such as noise, outliers or missing entries. Existing methods are either applicable only to noiseless data or they are very sensitive to initialization or they work only for partially shuffled data. In this paper we address these issues via an algebraic geometric approach, which uses symmetric polynomials to extract permutation-invariant constraints that the parameters $ξ^* \in \Re^n$ of the linear regression model must satisfy. This naturally leads to a polynomial system of $n$ equations in $n$ unknowns, which contains $ξ^*$ in its root locus. Using the machinery of algebraic geometry we prove that as long as the independent samples are generic, this polynomial system is always consistent with at most $n!$ complex roots, regardless of any type of corruption inflicted on the observations. The algorithmic implication of this fact is that one can always solve this polynomial system and use its most suitable root as initialization to the Expectation Maximization algorithm. To the best of our knowledge, the resulting method is the first working solution for small values of $n$ able to handle thousands of fully shuffled noisy observations in milliseconds.