Scalar Invariant Networks with Zero Bias

Just like weights, bias terms are the learnable parameters of many popular machine learning models, including neural networks. Biases are believed to effectively increase the representational power of neural networks to solve a wide range of tasks in computer vision. However, we argue that if we consider the intrinsic distribution of images in the input space as well as some desired properties a model should have from the first principles, biases can be completely ignored in addressing many image-related tasks, such as image classification. Our observation indicates that zero-bias neural networks could perform comparably to neural networks with bias at least on practical image classification tasks. In addition, we prove that zero-bias neural networks possess a nice property called scalar (multiplication) invariance, which allows the prediction of neural networks remains the same when altering the contrast of the input image. We then extend scalar invariance to more general cases that allow us to formally verify certain convex regions of the input space. Besides that, we show the fairness of zero-bias neural networks in predicting the zero image. In contrast to the state-of-art models which lean towards certain labels, zero-bias neural networks have a uniform belief in all labels. Based on those merits, we believe dropping bias terms can be considered as a prior in designing neural network architecture for some CV tasks, which shares the spirit of adapting convolutions as the transnational invariance prior.