Quantifying the similarity between artificial neural networks (ANNs) and their biological counterparts is an important step toward building more brain-like artificial intelligence systems. Recent efforts in this direction use neural predictivity, or the ability to predict the responses of a biological brain given the information in an ANN (such as its internal activations), when both are presented with the same stimulus. We propose a new approach to quantifying neural predictivity by explicitly mapping the activations of an ANN to brain responses with a non-linear function, and measuring the error between the predicted and actual brain responses. Further, we propose to use a neural network to approximate this mapping function by training it on a set of neural recordings. The proposed method was implemented within the TensorFlow framework and evaluated on a suite of 8 state-of-the-art image recognition ANNs. Our experiments suggest that the use of a non-linear mapping function leads to higher neural predictivity. Our findings also reaffirm the observation that the latest advances in classification performance of image recognition ANNs are not matched by improvements in their neural predictivity. Finally, we examine the impact of pruning, a widely used ANN optimization, on neural predictivity, and demonstrate that network sparsity leads to higher neural predictivity.