The effectiveness of convolutional neural networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other sources of invariance, such as rotation invariance, by using group convolutions instead of planar convolutions. However, for reasons of performance and ease of implementation, it has been necessary to limit the group convolution to transformations that can be applied to the filters without interpolation. Thus, for images with square pixels, only integer translations, rotations by multiples of 90 degrees, and reflections are admissible. Whereas the square tiling provides a 4-fold rotational symmetry, a hexagonal tiling of the plane has a 6-fold rotational symmetry. In this paper we show how one can efficiently implement planar convolution and group convolution over hexagonal lattices, by reusing existing highly optimized convolution routines. We find that, due to the reduced anisotropy of hexagonal filters, planar HexaConv provides better accuracy than planar convolution with square filters, given a fixed parameter budget. Furthermore, we find that the increased degree of symmetry of the hexagonal grid increases the effectiveness of group convolutions, by allowing for more parameter sharing. We show that our method significantly outperforms conventional CNNs on the AID aerial scene classification dataset, even outperforming ImageNet pretrained models.

This paper compares the ability of human observers to detect target image curves with that of an ideal observer. The target curves are sampled from a generative model which specifies (probabilistically) the geometry and local intensity properties of the curve. The ideal observer performs Bayesian inference on the generative model using MAP estimation. Varying the probability model for the curve geometry enables us investigate whether human performance is best for target curves that obey specific shape statistics, in particular those observed on natural shapes. Experiments are performed with data on both rectangular and hexagonal lattices. Our results show that human observers' performance approaches that of the ideal observer and are, in general, closest to the ideal for conditions where the target curve tends to be straight or similar to natural statistics on curves. This suggests a bias of human observers towards straight curves and natural statistics.

This paper compares the ability of human observers to detect target image curves with that of an ideal observer. The target curves are sampled from a generative model which specifies (probabilistically) the geometry and local intensity properties of the curve. The ideal observer performs Bayesian inference on the generative model using MAP estimation. Varying the probability model for the curve geometry enables us investigate whether human performance is best for target curves that obey specific shape statistics, in particular those observed on natural shapes. Experiments are performed with data on both rectangular and hexagonal lattices. Our results show that human observers' performance approaches that of the ideal observer and are, in general, closest to the ideal for conditions where the target curve tends to be straight or similar to natural statistics on curves. This suggests a bias of human observers towards straight curves and natural statistics.

This paper compares the ability of human observers to detect target image curveswith that of an ideal observer. The target curves are sampled froma generative model which specifies (probabilistically) the geometry andlocal intensity properties of the curve. The ideal observer performs Bayesian inference on the generative model using MAP estimation. Varyingthe probability model for the curve geometry enables us investigate whether human performance is best for target curves that obey specific shape statistics, in particular those observed on natural shapes. Experiments are performed with data on both rectangular and hexagonal lattices. Our results show that human observers' performance approaches that of the ideal observer and are, in general, closest to the ideal for conditions wherethe target curve tends to be straight or similar to natural statistics on curves. This suggests a bias of human observers towards straight curves and natural statistics.

We describe a self-configuring neuromorphic chip that uses a model of activity-dependent axon remodeling to automatically wire topographic maps based solely on input correlations. Axons are guided by growth cones, which are modeled in analog VLSI for the first time. Growth cones migrate up neurotropin gradients, which are represented by charge diffusing in transistor channels. Virtual axons move by rerouting address-events. We refined an initially gross topographic projection by simulating retinal wave input.

We describe a self-configuring neuromorphic chip that uses a model of activity-dependent axon remodeling to automatically wire topographic maps based solely on input correlations. Axons are guided by growth cones, which are modeled in analog VLSI for the first time. Growth cones migrate up neurotropin gradients, which are represented by charge diffusing in transistor channels. Virtual axons move by rerouting address-events. We refined an initially gross topographic projection by simulating retinal wave input.

We describe a self-configuring neuromorphic chip that uses a model of activity-dependent axon remodeling to automatically wire topographic maps based solely on input correlations. Axons are guided by growth cones, which are modeled in analog VLSI for the first time. Growth cones migrate up neurotropin gradients, which are represented by charge diffusing in transistor channels. Virtual axons move by rerouting address-events. We refined an initially gross topographic projection by simulating retinal wave input. 1 Neuromorphic Systems Neuromorphic engineers are attempting to match the computational efficiency of biological systems by morphing neurocircuitry into silicon circuits [1].