Transfer of Learning in the Convolutional Neural Networks on Classifying Geometric Shapes Based on Local or Global Invariants

The convolutional neural networks (CNNs) are a powerful tool of image classification that has been widely adopted in applications of automated scene segmentation and identification. However, the mechanisms underlying CNN image classification remain to be elucidated. In this study, we developed a new approach to address this issue by investigating transfer of learning in representative CNNs (AlexNet, VGG, ResNet-101, and Inception-ResNet-v2) on classifying geometric shapes based on local/global features or invariants. While the local features are based on simple components, such as orientation of line segment or whether two lines are parallel, the global features are based on the whole object such as whether an object has a hole or whether an object is inside of another object. Six experiments were conducted to test two hypotheses on CNN shape classification. The first hypothesis is that transfer of learning based on local features is higher than transfer of learning based on global features. The second hypothesis is that the CNNs with more layers and advanced architectures have higher transfer of learning based global features. The first two experiments examined how the CNNs transferred learning of discriminating local features (square, rectangle, trapezoid, and parallelogram). The other four experiments examined how the CNNs transferred learning of discriminating global features (presence of a hole, connectivity, and inside/outside relationship). While the CNNs exhibited robust learning on classifying shapes, transfer of learning varied from task to task, and model to model. The results rejected both hypotheses. First, some CNNs exhibited lower transfer of learning based on local features than that based on global features. Second the advanced CNNs exhibited lower transfer of learning on global features than that of the earlier models. Among the tested geometric features, we found that learning of discriminating inside/outside relationship was the most difficult to be transferred, indicating an effective benchmark to develop future CNNs. In contrast to the “ImageNet” approach that employs natural images to train and analyze the CNNs, the results show proof of concept for the “ShapeNet” approach that employs well-defined geometric shapes to elucidate the strengths and limitations of the computation in CNN image classification. This “ShapeNet” approach will also provide insights into understanding visual information processing the primate visual systems.

Summing up Smart Transitions

Some of the most significant high-level properties of currencies are the sums of certain account balances. Properties of such sums can ensure the integrity of currencies and transactions. For example, the sum of balances should not be changed by a transfer operation. Currencies manipulated by code present a verification challenge to mathematically prove their integrity by reasoning about computer programs that operate over them, e.g., in Solidity. The ability to reason about sums is essential: even the simplest ERC-20 token standard of the Ethereum community provides a way to access the total supply of balances.Unfortunately, reasoning about code written against this interface is non-trivial: the number of addresses is unbounded, and establishing global invariants like the preservation of the sum of the balances by operations like transfer requires higher-order reasoning. In particular, automated reasoners do not provide ways to specify summations of arbitrary length.In this paper, we present a generalization of first-order logic which can express the unbounded sum of balances. We prove the decidablity of one of our extensions and the undecidability of a slightly richer one. We introduce first-order encodings to automate reasoning over software transitions with summations. We demonstrate the applicability of our results by using SMT solvers and first-order provers for validating the correctness of common transitions in smart contracts.

Goblint: Thread-Modular Abstract Interpretation Using Side-Effecting Constraints

Goblintis a static analysis framework for C programs specializing in data race analysis. It relies on thread-modular abstract interpretation where thread interferences are accounted for by means of flow-insensitive global invariants.

Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space

In this paper, for the orthogonal group G = O(2) and special orthogonal group G = O+(2) global G-invariants of plane paths and plane curves in two-dimensional Euclidean space E2 are studied. Using complex numbers, a method to detect G-equivalences of plane paths in terms of the global G-invariants of a plane path is presented. General evident form of a plane path with the given G-invariants are obtained. For given two plane paths x(t) and y(t) with the common G-invariants, evident forms of all transformations g ∈ G, carrying x(t) to y(t), are obtained. Similar results have obtained for plane curves.

Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space

Let [Formula: see text] be the [Formula: see text]-dimensional Euclidean space, [Formula: see text] be the group of all linear similarities of [Formula: see text] and [Formula: see text] be the group of all orientation-preserving linear similarities of [Formula: see text]. The present paper is devoted to solutions of problems of global [Formula: see text]-equivalence of paths and curves in [Formula: see text] for the groups [Formula: see text]. Complete systems of global [Formula: see text]-invariants of a path and a curve in [Formula: see text] are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.

Discrete Kinematic Geometry in Testing Axes of Rotation of Spindles

The accuracy of actual motion of the spindle of a machine tool, a key performance index, is measured at a series of positions, and evaluated using a discrete kinematic geometry model. The kinematic geometry model, or more precisely a novel mechanism, is presented for the first time in this paper and validated using an apparatus consisting of a spindle, an artifact with double master ball and five displacement sensors as per ASME codes and standards [1]. The six kinematic parameters of the spindle with a single rotor — three translations and three rotations are obtained using the novel mechanism and the measurements. The theory of discrete kinematic geometry is employed to reveal the intrinsic properties of the trajectories traced by the characteristic lines of the rotor. In order to avoid the influences caused by the locations and directions of the measuring coordinate systems, the invariants of a discrete line-trajectory, particularly the spherical image curve and the striction curve [2], are introduced to deal with the discrete measurements. The global invariants, the approximated moving axis and the approximated fixed axis of the rotor in the error motion, independent of the assembling position of the double master balls on the rotor, are proposed to evaluate the rotational accuracy of spindles. The discrete kinematic geometry provides a new perspective and a theoretical base for assessing the accuracy of the spindle motion.