Recent progress on many imaging and vision tasks has been driven by the use of deep feed-forward neural networks, which are trained by propagating gradients of a loss defined on the final output, back through the network up to the first layer that operates directly on the image. We propose back-propagating one step further---to learn camera sensor designs jointly with networks that carry out inference on the images they capture. In this paper, we specifically consider the design and inference problems in a typical color camera---where the sensor is able to measure only one color channel at each pixel location, and computational inference is required to reconstruct a full color image. We learn the camera sensor's color multiplexing pattern by encoding it as layer whose learnable weights determine which color channel, from among a fixed set, will be measured at each location. These weights are jointly trained with those of a reconstruction network that operates on the corresponding sensor measurements to produce a full color image. Our network achieves significant improvements in accuracy over the traditional Bayer pattern used in most color cameras. It automatically learns to employ a sparse color measurement approach similar to that of a recent design, and moreover, improves upon that design by learning an optimal layout for these measurements.

Paper is nicely written, methodology is easy to follow, and validation shows the benefit of the proposed approach. Comments below: One main question that could arise in learning automatically a color filter pattern, is the dependence on the dataset. Would the use of a different heterogeneous dataset produce a completely different sensor pattern? If the pattern changes significantly between training sets, would it be relevant to question the robustness of a chosen pattern? On the same note, how could this impact camera designs, ie., could a universal pattern exist, or would there be multiple patterns, each designed for particular situations (could patterns designed for outdoor, indoor, urban or nature settings, produce a much better image quality than using a universal pattern?)

They propose that backpropagation with respect to a loss function is equivalent to a single step of a "back-matching propagation" procedure in which, after a forward evaluation, we alternately optimize the weights and input activations for each block to minimize a loss for the block's output. The authors propose that architectures and training procedures which improve the condition number of the Hessian of this back-matching loss are more efficient and support this by analytically studying the effects of orthonormal initialization, skip connections, and batch-norm. They offer further evidence for this characterization by designing a blockwise learning-rate scaling method based on an approximation of the backmatching loss and demonstrating an improved learning curve for VGG13 on CIFAR10 and CIFAR100.

This paper provides a comprehensive and detailed derivation of the backpropagation algorithm for graph convolutional neural networks using matrix calculus. The derivation is extended to include arbitrary element-wise activation functions and an arbitrary number of layers. The study addresses two fundamental problems, namely node classification and link prediction. To validate our method, we compare it with reverse-mode automatic differentiation. The experimental results demonstrate that the median sum of squared errors of the updated weight matrices, when comparing our method to the approach using reverse-mode automatic differentiation, falls within the range of $10^{-18}$ to $10^{-14}$. These outcomes are obtained from conducting experiments on a five-layer graph convolutional network, applied to a node classification problem on Zachary's karate club social network and a link prediction problem on a drug-drug interaction network. Finally, we show how the derived closed-form solution can facilitate the development of explainable AI and sensitivity analysis.

This approach can be used to (a) dynamically select the number of hidden units. The method Rumelhart suggests involves adding penalty terms to the usual error function. In this paper we introduce Rumelhart·s minimal networks idea and compare two possible biases on the weight search space. These biases are compared in both simple counting problems and a speech recognition problem.

In my previous blog I discussed a type of network with Human Brain Analogy, how it functions and how it is similar to the Human Brain and also covered various features of Neural Networks- Weights, Sum and Non-Linearity and ended it by classifying some important types of networks. Now lets know the complete working of a Neural Network. These are the main root behind the working of a neural network. Now, lets see all one by one. As you all know, there are some particular inputs on left side which passes through some nodes in the network and gets on the output side, so this movement of information from left side towards the output on right side is called Forward Propagation.

The previous article was all about forward propagation in neural networks, how it works and why it works. One of the important entities in forward propagation is weights. We saw how tuning the weights can take advantage of the non-linearity introduced in each layer to leverage the resultant output. As we said we are going to randomly initialize the weights and biases and let the network learn these weights over time. Now comes the most important question.

Back propagation based visualizations have been proposed to interpret deep neural networks (DNNs), some of which produce interpretations with good visual quality. However, there exist doubts about whether these intuitive visualizations are related to the network decisions. Recent studies have confirmed this suspicion by verifying that almost all these modified back-propagation visualizations are not faithful to the model's decision-making process. Besides, these visualizations produce vague "relative importance scores", among which low values can't guarantee to be independent of the final prediction. Hence, it's highly desirable to develop a novel back-propagation framework that guarantees theoretical faithfulness and produces a quantitative attribution score with a clear understanding. To achieve the goal, we resort to mutual information theory to generate the interpretations, studying how much information of output is encoded in each input neuron. The basic idea is to learn a source signal by back-propagation such that the mutual information between input and output should be as much as possible preserved in the mutual information between input and the source signal. In addition, we propose a Mutual Information Preserving Inverse Network, termed MIP-IN, in which the parameters of each layer are recursively trained to learn how to invert. During the inversion, forward Relu operation is adopted to adapt the general interpretations to the specific input. We then empirically demonstrate that the inverted source signal satisfies completeness and minimality property, which are crucial for a faithful interpretation. Furthermore, the empirical study validates the effectiveness of interpretations generated by MIP-IN.

Recent progress on many imaging and vision tasks has been driven by the use of deep feed-forward neural networks, which are trained by propagating gradients of a loss defined on the final output, back through the network up to the first layer that operates directly on the image. We propose back-propagating one step further---to learn camera sensor designs jointly with networks that carry out inference on the images they capture. In this paper, we specifically consider the design and inference problems in a typical color camera---where the sensor is able to measure only one color channel at each pixel location, and computational inference is required to reconstruct a full color image. We learn the camera sensor's color multiplexing pattern by encoding it as layer whose learnable weights determine which color channel, from among a fixed set, will be measured at each location. These weights are jointly trained with those of a reconstruction network that operates on the corresponding sensor measurements to produce a full color image.