A.2.5 Loss Function and Optimizer For all the experiments except N-MNIST in this work, we use cross entropy and stochastic gradient

This paper addresses modeling and simulating pedestrian trajectories when interacting with an autonomous vehicle in a shared space. Most pedestrian–vehicle interaction models are not suitable for predicting individual trajectories. Data-driven models yield accurate predictions but lack generalizability to new scenarios, usually do not run in real time and produce results that are poorly explainable. Current expert models do not deal with the diversity of possible pedestrian interactions with the vehicle in a shared space and lack microscopic validation. We propose an expert pedestrian model that combines the social force model and a new decision model for anticipating pedestrian–vehicle interactions. The proposed model integrates different observed pedestrian behaviors, as well as the behaviors of the social groups of pedestrians, in diverse interaction scenarios with a car. We calibrate the model by fitting the parameters values on a training set. We validate the model and evaluate its predictive potential through qualitative and quantitative comparisons with ground truth trajectories. The proposed model reproduces observed behaviors that have not been replicated by the social force model and outperforms the social force model at predicting pedestrian behavior around the vehicle on the used dataset. The model generates explainable and real-time trajectory predictions. Additional evaluation on a new dataset shows that the model generalizes well to new scenarios and can be applied to an autonomous vehicle embedded prediction.

We describe an efficient learning procedure for multilayer generative models that combine the best aspects of Markov random fields and deep, directed belief nets. The generative models can be learned one layer at a time and when learning is complete they have a very fast inference procedure for computing a good approximation to the posterior distribution in all of the hidden layers. Each hidden layer has its own MRF whose energy function is modulated by the top-down directed connections from the layer above. To generate from the model, each layer in turn must settle to equilibrium given its top-down input. We show that this type of model is good at capturing the statistics of patches of natural images.

We present a new approach to the supervised learning of lateral interactions for the competitive layer model (CLM) dynamic feature binding architecture. The method is based on consistency conditions, which were recently shown to characterize the attractor states of this linear threshold recurrent network. For a given set of training examples the learning problem is formulated as a convex quadratic optimization problem in the lateral interaction weights. An efficient dimension reduction of the learning problem can be achieved by using a linear superposition of basis interactions. We show the successful application of the method to a medical image segmentation problem of fluorescence microscope cell images.

We present a new approach to the supervised learning of lateral interactions for the competitive layer model (CLM) dynamic feature binding architecture. The method is based on consistency conditions, which were recently shown to characterize the attractor states of this linear threshold recurrent network. For a given set of training examples the learning problem is formulated as a convex quadratic optimization problem in the lateral interaction weights. An efficient dimension reduction of the learning problem can be achieved by using a linear superposition of basis interactions. We show the successful application of the method to a medical image segmentation problem of fluorescence microscope cell images.

We present a new approach to the supervised learning of lateral interactions forthe competitive layer model (CLM) dynamic feature binding architecture. The method is based on consistency conditions, which were recently shown to characterize the attractor states of this linear threshold recurrent network. For a given set of training examples the learning problem isformulated as a convex quadratic optimization problem in the lateral interaction weights. An efficient dimension reduction of the learning problem can be achieved by using a linear superposition of basis interactions.

We first describe a hierarchical, generative model that can be viewed as a nonlinear generalisation of factor analysis and can be implemented in a neural network. The model performs perceptual inference in a probabilistically consistent manner by using top-down, bottom-up and lateral connections. These connections can be learned using simple rules that require only locally available information. We then show how to incorporate lateral connections into the generative model. The model extracts a sparse, distributed, hierarchical representation of depth from simplified random-dot stereograms and the localised disparity detectors in the first hidden layer form a topographic map. When presented with image patches from natural scenes, the model develops topographically organised local feature detectors.

We first describe a hierarchical, generative model that can be viewed as a nonlinear generalisation of factor analysis and can be implemented in a neural network. The model performs perceptual inferencein a probabilistically consistent manner by using top-down, bottom-up and lateral connections. These connections can be learned using simple rules that require only locally available information.We then show how to incorporate lateral connections intothe generative model. The model extracts a sparse, distributed, hierarchical representation of depth from simplified random-dot stereograms and the localised disparity detectors in the first hidden layer form a topographic map. When presented with image patches from natural scenes, the model develops topographically organisedlocal feature detectors.

For example, in the normal visual cortex, long-range lateral connections link areas with similar orientation preference (Gilbert and Wiesel 1989). Like cortical response properties, the connectivity pattern is highly plastic in early development and can be altered by experience (Katz and Callaway 1992). In a cat that is brought up squint-eyed from birth, the lateral connections link areas with the same ocular dominance instead of orientation (Lowel and Singer 1992). Such patterned lateral connections develop at the same time as the orientation selectivity and ocular dominance itself (Burkhalter et al.1993;

For example, in the normal visual cortex, long-range lateral connections link areas with similar orientation preference (Gilbert and Wiesel 1989). Like cortical response properties, the connectivity pattern is highly plastic in early development and can be altered by experience (Katz and Callaway 1992). In a cat that is brought up squint-eyed from birth, the lateral connections link areas with the same ocular dominance instead of orientation (Lowel and Singer 1992). Such patterned lateral connections develop at the same time as the orientation selectivity and ocular dominance itself (Burkhalter et al.1993;