Traditional convolutional neural networks (CNN) are stationary and feedforward.

In this paper, we present an optimization-based framework for generating estimation-aware trajectories in scenarios where measurement (output) uncertainties are state-dependent and set-valued. The framework leverages the concept of regularity for set-valued output maps. Specifically, we demonstrate that, for output-regular maps, one can utilize a set-valued observability measure that is concave with respect to finite-horizon state trajectories. By maximizing this measure, optimized estimation-aware trajectories can be designed for a broad class of systems, including those with locally linearized dynamics. To illustrate the effectiveness of the proposed approach, we provide a representative example in the context of trajectory planning for vision-based estimation. We present an estimation-aware trajectory for an uncooperative target-tracking problem that uses a machine learning (ML)-based estimation module on an ego-satellite.

Traditional convolutional neural networks (CNN) are stationary and feedforward.

This work demonstrates that, for a simple case of 10 randomly positioned atoms, a neural network can be trained to infer atomic coordinates from Patterson maps. The network was trained entirely on synthetic data. For the training set, the network outputs were 3D maps of randomly positioned atoms. From each output map, a Patterson map was generated and used as input to the network. The network generalized to cases not in the test set, inferring atom positions from Patterson maps. A key finding in this work is that the Patterson maps presented to the network input during training must uniquely describe the atomic coordinates they are paired with on the network output or the network will not train and it will not generalize. The network cannot train on conflicting data. Avoiding conflicts is handled in 3 ways: 1. Patterson maps are invariant to translation. To remove this degree of freedom, output maps are centered on the average of their atom positions. 2. Patterson maps are invariant to centrosymmetric inversion. This conflict is removed by presenting the network output with both the atoms used to make the Patterson Map and their centrosymmetry-related counterparts simultaneously. 3. The Patterson map does not uniquely describe a set of coordinates because the origin for each vector in the Patterson map is ambiguous. By adding empty space around the atoms in the output map, this ambiguity is removed. Forcing output atoms to be closer than half the output box edge dimension means the origin of each peak in the Patterson map must be the origin to which it is closest.

Traditional convolutional neural networks (CNN) are stationary and feedforward. They neither change their parameters during evaluation nor use feedback from higher to lower layers. Real brains, however, do. So does our Deep Attention Selective Network (dasNet) architecture. DasNet's feedback structure can dynamically alter its convolutional filter sensitivities during classification. It harnesses the power of sequential processing to improve classification performance, by allowing the network to iteratively focus its internal attention on some of its convolutional filters. Feedback is trained through direct policy search in a huge million-dimensional parameter space, through scalable natural evolution strategies (SNES). On the CIFAR-10 and CIFAR-100 datasets, dasNet outperforms the previous state-of-the-art model on unaugmented datasets.

We study feed-forward nets with arbitrarily many layers, using the standard sigmoid, tanh x. Aside from technicalities, our theorems are: 1. Complete knowledge of the output of a neural net for arbitrary inputs uniquely specifies the architecture, weights and thresholds; and 2. There are only finitely many critical points on the error surface for a generic training problem. Neural nets were originally introduced as highly simplified models of the nervous system. Today they are widely used in technology and studied theoretically by scientists from several disciplines. However, they remain little understood.

We study feed-forward nets with arbitrarily many layers, using the standard sigmoid, tanh x. Aside from technicalities, our theorems are: 1. Complete knowledge of the output of a neural net for arbitrary inputs uniquely specifies the architecture, weights and thresholds; and 2. There are only finitely many critical points on the error surface for a generic training problem. Neural nets were originally introduced as highly simplified models of the nervous system. Today they are widely used in technology and studied theoretically by scientists from several disciplines. However, they remain little understood.

We study feed-forward nets with arbitrarily many layers, using the standard sigmoid,tanh x. Aside from technicalities, our theorems are: 1. Complete knowledge of the output of a neural net for arbitrary inputs uniquely specifies the architecture, weights and thresholds; and 2. There are only finitely many critical points on the error surface for a generic training problem. Neural nets were originally introduced as highly simplified models of the nervous system. Today they are widely used in technology and studied theoretically by scientists from several disciplines. However, they remain little understood.