Extracting formulae in many-valued logic from deep neural networks
We propose a new perspective on deep ReLU networks, namely as circuit counterparts of Lukasiewicz infinite-valued logic–a many-valued (MV) generalization of Boolean logic. An algorithm for extracting formulae in MV logic from deep ReLU networks is presented. As the algorithm applies to networks with general, in particular also real-valued, weights, it can be used to extract logical formulae from deep ReLU networks trained on data.
Deep neural networks learn cellular automaton rules in many-valued logic
We develop a theory characterizing the fundamental capability of deep neural networks to learn, from evolution traces, the logical rules governing the behavior of cellular automata (CA). This is accomplished by first establishing a novel connection between CA and Łukasiewicz propositional logic. While binary CA have been known for decades to essentially perform operations in Boolean logic, no such relationship exists for general CA. We demonstrate that many-valued (MV) logic, specifically Łukasiewicz propositional logic, constitutes a suitable language for characterizing general CA as logical machines. This is done by interpolating CA transition functions to continuous piecewise linear functions, which, by virtue of the McNaughton theorem, yield formulae in MV logic characterizing the CA. Recognizing that deep rectified linear unit (ReLU) networks realize continuous piecewise linear functions, it follows that these formulae are naturally extracted from CA evolution traces by deep ReLU networks. A corresponding algorithm together with a software implementation is provided. Finally, we show that the dynamical behavior of CA can be realized by recurrent neural networks.
Direction-of-arrival estimation for correlated sources and low sample size
We study the problem of recovering the direction-of-arrival in difficult scenarios of highly correlated source signals and only few available snapshots. We propose a method that integrates the l2,1-mixed-norm minimization formulation into the spectral search of the partial relaxation estimators. Simulation results show that the proposed estimator has superior error performance in difficult scenarios and alleviates the disadvantages of both methods.
Distributed robust Bayesian cluster enumeration criterion for unsupervised learning
We propose a robust decentralized diffusionbased cluster enumeration method that enables distributed sensor nodes to estimate the number of clusters in their respective data sets through cooperation with their immediate neighbors. The proposed method is robust to the presence of heavy-tailed noise and outliers, which is useful for sensor networks as outliers can occur due to measurement errors or sensor failure. Through experiments, we show that the proposed method is promising, and achieves the performance of a centralized network using a fusion center.
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Heart rate variability analysis (ECG signals)
We developed advanced robust signal processing and statistical learning algorithms to identify and evaluate novel and established markers of autonomic disfunction in symptomatic and asymptomatic heart failure.
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