Effect of non-polynomial input to a switching circuit

In this paper, the validity of the state-space averaging method is analyzed. We assume that the state-space piecewise method is an exact model for a fast switching circuit. Based on this model, we compute the error predicted by the state-space averaging method. It is found that the error for a polynomial input is bounded by two polynomials with the same order as that of the input. And the percentage error is bounded by a constant. Hence, if the acceptable level is within that constant, then the state-space averaging method can be applied. Similar analysis is carried out on a non-polynomial input. A sinusoidal function is chosen because of its wide applications on AC circuits. Although a similar result is obtained, the percentage error for the sinusoidal input is much greater than that of the polynomial input. Hence, the state-space averaging method may not be so good for the AC analysis

Input and Weight Space Smoothing for Semi-supervised Learning

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the minimality of the resulting representation, the other insensitivity to nuisance variability. We propose a method to perform such smoothing, which combines known input-space smoothing with a novel weight-space smoothing, based on a min-max (adversarial) optimization. The resulting Adversarial Block Coordinate Descent (ABCD) algorithm performs gradient ascent with a small learning rate for a random subset of the weights, and standard gradient descent on the remaining weights in the same mini-batch. It achieves comparable performance to the state-of-the-art without resorting to heavy data augmentation, using a relatively simple architecture

Finding a boundary between valid and invalid regions of the input space

In the context of robustness testing, the boundary between the valid and invalid regions of the input space can be an interesting source of erroneous inputs. Knowing where a specific software under test (SUT) has a boundary is essential for validation in relation to requirements. However, finding where a SUT actually implements the boundary is a non-trivial problem that has not gotten much attention. This paper proposes a method of finding the boundary between the valid and invalid regions of the input space. The proposed method consists of two steps. First, test data generators, directed by a search algorithm to maximise distance to known, valid test cases, generate valid test cases that are closer to the boundary. Second, these valid test cases undergo mutations to try to push them over the boundary and into the invalid part of the input space. This results in a pair of test sets, one consisting of test cases on the valid side of the boundary and a matched set on the outer side, with only a small distance between the two sets. The method is evaluated on a number of examples from the standard library of a modern programming language. We propose a method of determining the boundary between valid and invalid regions of the input space and apply it on a SUT that has a non-contiguous valid region of the input space. From the small distance between the developed pairs of test sets, and the fact that one test set contains valid test cases and the other invalid test cases, we conclude that the pair of test sets described the boundary between the valid and invalid regions of that input space. Differences of behaviour can be observed between different distances and sets of mutation operators, but all show that the method is able to identify the boundary between the valid and invalid regions of the input space. This is an important step towards more automated robustness testing.Comment: 10 pages, conferenc

Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives

In this paper we review the works related to muscle synergies that have been carried-out in neuroscience and control engineering. In particular, we refer to the hypothesis that the central nervous system (CNS) generates desired muscle contractions by combining a small number of predefined modules, called muscle synergies. We provide an overview of the methods that have been employed to test the validity of this scheme, and we show how the concept of muscle synergy has been generalized for the control of artificial agents. The comparison between these two lines of research, in particular their different goals and approaches, is instrumental to explain the computational implications of the hypothesized modular organization. Moreover, it clarifies the importance of assessing the functional role of muscle synergies: although these basic modules are defined at the level of muscle activations (input-space), they should result in the effective accomplishment of the desired task. This requirement is not always explicitly considered in experimental neuroscience, as muscle synergies are often estimated solely by analyzing recorded muscle activities. We suggest that synergy extraction methods should explicitly take into account task execution variables, thus moving from a perspective purely based on input-space to one grounded on task-space as well

SINVAD: Search-based Image Space Navigation for DNN Image Classifier Test Input Generation

The testing of Deep Neural Networks (DNNs) has become increasingly important as DNNs are widely adopted by safety critical systems. While many test adequacy criteria have been suggested, automated test input generation for many types of DNNs remains a challenge because the raw input space is too large to randomly sample or to navigate and search for plausible inputs. Consequently, current testing techniques for DNNs depend on small local perturbations to existing inputs, based on the metamorphic testing principle. We propose new ways to search not over the entire image space, but rather over a plausible input space that resembles the true training distribution. This space is constructed using Variational Autoencoders (VAEs), and navigated through their latent vector space. We show that this space helps efficiently produce test inputs that can reveal information about the robustness of DNNs when dealing with realistic tests, opening the field to meaningful exploration through the space of highly structured images