An analysis of optimization problems involving ReLU neural networks

Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the number of layers. We survey and propose different approaches to analyze and improve the run time behavior of mixed-integer programming solvers in this context. Among them are clipped variants and regularization techniques applied during training as well as optimization-based bound tightening and a novel scaling for given ReLU networks. We numerically compare these approaches for three benchmark problems from the literature. We use the number of linear regions, the percentage of stable neurons, and overall computational effort as indicators. As a major takeaway we observe and quantify a trade-off between the often desired redundancy of neural network models versus the computational costs for solving related optimization problems.

AudioPairBank: Towards A Large-Scale Tag-Pair-Based Audio Content Analysis

Recently, sound recognition has been used to identify sounds, such as car and river. However, sounds have nuances that may be better described by adjective-noun pairs such as slow car, and verb-noun pairs such as flying insects, which are under explored. Therefore, in this work we investigate the relation between audio content and both adjective-noun pairs and verb-noun pairs. Due to the lack of datasets with these kinds of annotations, we collected and processed the AudioPairBank corpus consisting of a combined total of 1,123 pairs and over 33,000 audio files. One contribution is the previously unavailable documentation of the challenges and implications of collecting audio recordings with these type of labels. A second contribution is to show the degree of correlation between the audio content and the labels through sound recognition experiments, which yielded results of 70% accuracy, hence also providing a performance benchmark. The results and study in this paper encourage further exploration of the nuances in audio and are meant to complement similar research performed on images and text in multimedia analysis.