Title: Adaptive Convolutional Neural Networks. Abstract: The quest for increased visual recognition performance has led to the development of highly complex neural networks with very deep topologies. To avoid high computing resource requirements of such complex networks and to enable operation on devices with limited resources, this paper introduces adaptive kernels for convolutional layers. Motivated by the non-linear perception response in human visual cells, the input image is used to define the weights of a dynamic kernel called Adaptive kernel. This new adaptive kernel is used to perform a second convolution of the input image generating the output pixel. Adaptive kernels enable accurate recognition with lower memory requirements; This is accomplished through reducing the number of kernels and the number of layers needed in the typical CNN configuration, in addition to reducing the memory used, increasing 2X the training speed and the number of activation function evaluations. Our experiments show a reduction of 70X in the memory used for MNIST, maintaining 99% accuracy and 16X memory reduction for CIFAR10 with 92.5% accuracy.