Random feedback weights support learning indeepneural networks.arXivpreprint

The Interval-valued intuitionistic fuzzy sets (IVIFSs) based on the intuitionistic fuzzy sets combines the classical decision method is in its research and application is attracting attention. After comparative analysis, there are multiple classical methods with IVIFSs information have been applied into many practical issues. In this paper, we extended the classical EDAS method based on cumulative prospect theory (CPT) considering the decision makers (DMs) psychological factor under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, the original EDAS method based on the CPT under IVIFSs (IVIF-CPT-MABAC) method is built for MAGDM issues. Meanwhile, information entropy method is used to evaluate the attribute weight. Finally, a numerical example for project selection of green technology venture capital has been given and some comparisons is used to illustrate advantages of IVIF-CPT-MABAC method and some comparison analysis and sensitivity analysis are applied to prove this new methods effectiveness and stability.

In this study we explore the spontaneous apparition of visible intelligible reasoning in simple artificial networks, and we connect this experimental observation with a notion of semantic information. We start with the reproduction of a DNN model of natural neurons in monkeys, studied by Neromyliotis and Moschovakis in 2017 and 2018, to explain how "motor equivalent neurons", coding only for the action of pointing, are supplemented by other neurons for specifying the actor of the action, the eye E, the hand H, or the eye and the hand together EH. There appear inner neurons performing a logical work, making intermediary proposition, for instance E V EH. Then, we remarked that adding a second hidden layer and choosing a symmetric metric for learning, the activities of the neurons become almost quantized and more informative. Using the work of Carnap and Bar-Hillel 1952, we define a measure of the logical value for collections of such cells. The logical score growths with the depth of the layer, i.e. the information on the output decision increases, which confirms a kind of bottleneck principle. Then we study a bit more complex tasks, a priori involving predicate logic. We compare the logic and the measured weights. This shows, for groups of neurons, a neat correlation between the logical score and the size of the weights. It exhibits a form of sparsity between the layers. The most spectacular result concerns the triples which can conclude for all conditions: when applying their weight matrices to their logical matrix, we recover the classification. This shows that weights precisely perform the proofs.

We show that the disagreement coefficient of certain smooth hypothesis classes is $O(m)$, where $m$ is the dimension of the hypothesis space, thereby answering a question posed in \cite{friedman09}.