We design an interpretable network model by introducing explainable components into a Deep Neural Network (DNN). We substituted the first kernels of a Convolutional Neural Network (CNN) and a ResNet-50 with the well-known edge detecting filters such as Sobel, Prewitt, and other filters. Each filters' relative importance scores are measured with a variant of Layer-wise Relevance Propagation (LRP) method proposed by [1]. Since the effects of the edge detecting filters are well understood, our model provides three different scores to explain individual predictions: the scores with respect to (1) colors, (2) edge filters, and (3) pixels of the image. Our method provides more tools to analyze the predictions by highlighting the location of important edges and colors in the images. Furthermore, the general features of a category can be shown in our scores as well as individual predictions. At the same time, the model does not degrade performances on MNIST, Fruit360 and ImageNet datasets.

An input space is a set of all the possible inputs for a neural network. An element or a group of elements in the input space can easily be understood by projecting them on their original forms. Even though Piece-wise Linear Neural Networks (PLNNs) are a nonlinear system in general, a PLNN can also be expressed in terms of linear constraints because the Rectified Linear Units (ReLU) function is a piece-wise linear function. A PLNN divides the input space into disjoint linear regions. We proved that all components of the outputs are continuous at the boundary between two different adjacent regions. This continuity implies that the boundary corresponding to a unit itself should be continuous regardless of the regions. Furthermore, we also obtained the boundaries of a single-class region, which has the same predicted classes in the interior of the region. Finally, we suggested that the point-wise robustness of a neural network can be calculated by investigating the boundaries of linear regions and the single-class regions. We obtained adversarial examples in which Euclidean distances from original inputs are less than 0.01 pixels.

We applied pre-defined kernels also known as filters or masks developed for image processing to convolution neural network. Instead of letting neural networks find its own kernels, we used 41 different general-purpose kernels of blurring, edge detecting, sharpening, discrete cosine transformation, etc. for the first layer of the convolution neural networks. This architecture, thus named as general filter convolutional neural network (GFNN), can reduce training time by 30% with a better accuracy compared to the regular convolutional neural network (CNN). GFNN also can be trained to achieve 90% accuracy with only 500 samples. Furthermore, even though these kernels are not specialized for the MNIST dataset, we achieved 99.56% accuracy without ensemble nor any other special algorithms.

Modeling and evaluating the performance of large-scale wireless sensor networks (WSNs) is a challenging problem. The traditional method for representing the global state of a system as a cross product of the states of individual nodes in the system results in a state space whose size is exponential in the number of nodes. We propose an alternative way of representing the global state of a system: namely, as a probability mass function (pmf) which represents the fraction of nodes in different states. A pmf corresponds to a point in a Euclidean space of possible pmf values, and the evolution of the state of a system is represented by trajectories in this Euclidean space. We propose a novel performance evaluation method that examines all pmf trajectories in a dense Euclidean space by exploring only finite relevant portions of the space. We call our method Euclidean model checking . Euclidean model checking is useful both in the design phase—where it can help determine system parameters based on a specification—and in the evaluation phase—where it can help verify performance properties of a system. We illustrate the utility of Euclidean model checking by using it to design a time difference of arrival (TDoA) distance measurement protocol and to evaluate the protocol's implementation on a 90-node WSN. To facilitate such performance evaluations, we provide a Markov model estimation method based on applying a standard statistical estimation technique to samples resulting from the execution of a system.

We propose a new probabilistic temporal logic, iLTL, which captures properties of systems whose state can be represented by probability mass functions (pmfs). Using iLTL, we can specify reachability to a state (i.e., a pmf), as well as properties representing the aggregate (expected) behavior of a system. We then consider a class of systems whose transitions are governed by a Markov Chain-in this case, the set of states a system may be in is specified by the transitions of pmfs from all potential initial states to the final state. We then provide a model checking algorithm to check iLTL properties of such systems. Unlike existing model checking techniques, which either compute the portions of the computational paths that satisfy a specification or evaluate properties along a single path of pmf transitions, our model checking technique enables us to do a complete analysis on the expected behaviors of large-scale systems. Desirable system parameters may also be found as a counterexample of a negated goal. Finally, we illustrate the usefulness of iLTL model checking by means of two examples: assessing software reliability and ensuring the results of administering a drug.

The process of determining the physical locations of nodes in a wireless sensor network is known as localization . Self-localization is critical for large-scale sensor networks, because manual or assisted localization is often impractical due to time requirements, economic constraints, or inherent limitations of the deployment scenarios. We propose scalable solutions for reliably localizing wireless sensor networks in environments conducive to several types of ranging errors. We follow a hybrid hardware-software approach for acoustic ranging or radio interferometry to acquire internode distance measurements, and a resilient self-localization algorithm to compute the node location estimates. The acoustic ranging method improves on previous work, extending the practical measurement range up to 35 m in grassy outdoor environments, achieving a distance-invariant median measurement error of about 1% (33 cm). The localization algorithm is based on least-squares scaling with soft constraints. Empirical evaluation using ranging results obtained from sensor network field experiments and simulations confirms that our approach is more resilient than multidimensional scaling (MDS) algorithms against large-magnitude ranging errors and sparse range measurements: conditions that are common in large-scale outdoor sensor network deployments.

We develop a localization algorithm based on global environmental events observed by a sensor network. Examples of such events include the sound of thunder, the shades of moving clouds, or the vibrations in seismic data. Because our localization method does not generate signals for distance measurements, it saves energy. In fact, the algorithm may use existing sensor recordings to determine the locations of nodes at which the recordings were taken. Moreover, the method does not accumulate errors, making it also effective for large and sparse sensor networks. The localization uses time synchronization; we provide an algorithm to compensate for clock synchronization errors. Versions for both two dimensional and three dimensional localization of the algorithm are presented. Simulation results suggest that the algorithm can provide a high degree of accuracy when many events are recorded.

A compositional method for estimating software reliability of many threaded programs is developed. The method uses estimates of the reliability of individual modules and the probability of transitions between the modules to estimate the reliability of a program in terms of its current state. The reliability of a program is expressed using iLTL, a probabilistic linear temporal logic whose atomic propositions are linear inequalities about transitions of the probability mass function of a discrete time Markov chain. We then use a Markov reward model to estimate software reliability. The technique is illustrated in terms of an example.

The process of computing the physical locations of nodes in a wireless sensor network is known as localization. Self-localization is critical for large-scale sensor networks because manual or assisted localization is often impractical due to time requirements, economic constraints or inherent limitations of deployment scenarios. We have developed a service for reliably localizing wireless sensor networks in environments conducive to ranging errors by using a custom hardware-software solution for acoustic ranging and a family of self-localization algorithms. The ranging solution improves on previous work, extending the practical measurement range threefold (20-30m) while maintaining a distance-invariant median measurement error of about 1% of maximum range (33cm). The localization scheme is based on least squares scaling with soft constraints. Evaluation using ranging results obtained from sensor network field experiments shows that the localization scheme is resilient against large-magnitude ranging errors and sparse range measurements, both of which are common in large-scale outdoor sensor network deployments.

We present a novel method for tracking the movement of people or vehicles in open outdoor environments using sensor networks. Unlike other sensor network-based methods, which depend on determining distance to the target or the angle of arrival of the signal, our cooperative tracking approach requires only that a sensor be able to determine if an object is somewhere within the maximum detection range of the sensor. We propose cooperative tracking as a method for tracking moving objects and extrapolating their paths in the short term. By combining data from neighboring sensors, this approach enables tracking with a resolution higher than that of the individual sensors being used. We employ statistical estimation and approximation techniques to further increase the tracking precision, and to enable the system to exploit the tradeoff between accuracy and timeliness of the results. We analyze the behavior of the cooperative tracking algorithm through simulation, focusing on the effects of approximation techniques on the quality of estimates achieved. This work focuses on acoustic tracking, however the presented methodology is applicable to any sensing modality where the sensing range is relatively uniform.