Hyperplane Arrangements of Trained ConvNets Are Biased

We investigate the geometric properties of the functions learned by trained ConvNets in the preactivation space of their convolutional layers, by performing an empirical study of hyperplane arrangements induced by a convolutional layer. We introduce statistics over the weights of a trained network to study local arrangements and relate them to the training dynamics. We observe that trained ConvNets show a significant statistical bias towards regular hyperplane configurations. Furthermore, we find that layers showing biased configurations are critical to validation performance for the architectures considered, trained on CIFAR10, CIFAR100 and ImageNet

Self-powered Time-Keeping and Time-of-Occurrence Sensing

Self-powered and passive Internet-of-Things (IoT) devices (e.g. RFID tags, financial assets, wireless sensors and surface-mount devices) have been widely deployed in our everyday and industrial applications. While diverse functionalities have been implemented in passive systems, the lack of a reference clock limits the design space of such devices used for applications such as time-stamping sensing, recording and dynamic authentication. Self-powered time-keeping in passive systems has been challenging because they do not have access to continuous power sources. While energy transducers can harvest power from ambient environment, the intermittent power cannot support continuous operation for reference clocks. The thesis of this dissertation is to implement self-powered time-keeping devices on standard CMOS processes. In this dissertation, a novel device that combines the physics of quantum tunneling and floating-gate (FG) structures is proposed for self-powered time-keeping in CMOS process. The proposed device is based on thermally assisted Fowler-Nordheim (FN) tunneling process across high-quality oxide layer to discharge the floating-gate node, therefore resulting in a time-dependent FG potential. The device was fully characterized in this dissertation, and it does not require external powering during runtime, making it feasible for passive devices and systems. Dynamic signature based on the synchronization and desynchronization behavior of the FN timer is proposed for authentication of IoT devices. The self-compensating physics ensure that when distributed timers are subjected to identical environment variances that are common-mode noise, they can maintain synchronization with respect to each other. On the contrary, different environment conditions will desynchronize the timers creating unique signatures. The signatures could be used to differentiate between products that belong to different supply-chains or products that were subjected to malicious tampering. SecureID type dynamic authentication protocols based on the signature generated by the FN timers are proposed and they are proven to be robust to most attacks. The protocols are further analyzed to be lightweight enough for passive devices whose computational sources are limited. The device could also be applied for self-powered sensing of time-of-occurrence. The prototype was verified by integrating the device with a self-powered mechanical sensor to sense and record time-of-occurrence of mechanical events. The system-on-chip design uses the timer output to modulate a linear injector to stamp the time information into the sensing results. Time-of-occurrence can be reconstructed by training the mathematical model and then applying that to the test data. The design was verified to have a high reconstruction accuracy

Systems of difference equations as a model for the Lorenz system

We consider systems of difference equations as a model for the Lorenz system of differential equations. Using the power series whose coefficients are the solutions of these systems, we define three real functions, that are approximation for the solutions of the Lorenz system

Прикладна фізика : українсько-російсько-англійський тлумачний словник. У 4 т. Т. 1. А – Ж

Словник охоплює близько 30 тис. термінів з прикладної фізики і дотичних до неї галузей знань та їх тлумачення трьома мовами (українською, російською та англійською). Багато термінів і визначень, наведених у словнику, якими послуговуються у відповідній галузі знань, досі не входили до жодного зі спеціалізованих словників. Словник призначений для викладачів, науковців, інженерів, аспірантів, студентів вищих навчальних закладів, перекладачів з природничих і технічних дисциплін

The Preimage of Rectifier Network Activities

The preimage of the activity at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, ie all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms.QC 20190916</p

The Preimage of Rectifier Network Activities

The preimage of the activity at a certain level of a deep network is the set of inputs that result in the same node activity. For fully connected multi layer rectifier networks we demonstrate how to compute the preimages of activities at arbitrary levels from knowledge of the parameters in a deep rectifying network. If the preimage set of a certain activity in the network contains elements from more than one class it means that these classes are irreversibly mixed. This implies that preimage sets which are piecewise linear manifolds are building blocks for describing the input manifolds specific classes, ie all preimages should ideally be from the same class. We believe that the knowledge of how to compute preimages will be valuable in understanding the efficiency displayed by deep learning networks and could potentially be used in designing more efficient training algorithms.QC 20190916</p