Efficient Higher Order Derivatives of Objective Functions Composed of Matrix Operations

This paper is concerned with the efficient evaluation of higher-order derivatives of functions $f$ that are composed of matrix operations. I.e., we want to compute the $D$-th derivative tensor $\nabla^D f(X) \in \mathbb R^{N^D}$, where $f:\mathbb R^{N} \to \mathbb R$ is given as an algorithm that consists of many matrix operations. We propose a method that is a combination of two well-known techniques from Algorithmic Differentiation (AD): univariate Taylor propagation on scalars (UTPS) and first-order forward and reverse on matrices. The combination leads to a technique that we would like to call univariate Taylor propagation on matrices (UTPM). The method inherits many desirable properties: It is easy to implement, it is very efficient and it returns not only $\nabla^D f$ but yields in the process also the derivatives $\nabla^d f$ for $d \leq D$. As performance test we compute the gradient $\nabla f(X)$ % and the Hessian $\nabla_A^2 f(A)$ by a combination of forward and reverse mode of f(X) = \trace (X^{-1}) in the reverse mode of AD for $X \in \mathbb R^{n \times n}$. We observe a speedup of about 100 compared to UTPS. Due to the nature of the method, the memory footprint is also small and therefore can be used to differentiate functions that are not accessible by standard methods due to limited physical memory

Digital electric field induced switching of plasmonic nanorods using an electro-optic fluid fiber

We demonstrate the digital electric field induced switching of plasmonic nanorods between 1 and 0 orthogonal aligned states using an electro-optic fluid fiber component. We show by digitally switching the nanorods, that thermal rotational diffusion of the nanorods can be circumvented, demonstrating an approach to achieve submicrosecond switching times. We also show, from an initial unaligned state, that the nanorods can be aligned into the applied electric field direction in 110 nanoseconds. The high-speed digital switching of plasmonic nanorods integrated into an all-fiber optical component may provide novel opportunities for remote sensing and signaling applications

Creating exotic condensates via quantum-phase-revival dynamics in engineered lattice potentials

In the field of ultracold atoms in optical lattices a plethora of phenomena governed by the hopping energy $J$ and the interaction energy $U$ have been studied in recent years. However, the trapping potential typically present in these systems sets another energy scale and the effects of the corresponding time scale on the quantum dynamics have rarely been considered. Here we study the quantum collapse and revival of a lattice Bose-Einstein condensate (BEC) in an arbitrary spatial potential, focusing on the special case of harmonic confinement. Analyzing the time evolution of the single-particle density matrix, we show that the physics arising at the (temporally) recurrent quantum phase revivals is essentially captured by an effective single particle theory. This opens the possibility to prepare exotic non-equilibrium condensate states with a large degree of freedom by engineering the underlying spatial lattice potential.Comment: 9 pages, 6 figure

A computational method for key-performance-indicator-based parameter identification of industrial manipulators

We present a novel derivative-based parameter identification method to improve the precision at the tool center point of an industrial manipulator. The tool center point is directly considered in the optimization as part of the problem formulation as a key performance indicator. Additionally, our proposed method takes collision avoidance as special nonlinear constraints into account and is therefore suitable for industrial use. The performed numerical experiments show that the optimum experimental designs considering key performance indicators during optimization achieve a significant improvement in comparison to other methods. An improvement in terms of precision at the tool center point of 40% to 44% was achieved in experiments with three KUKA robots and 90 notional manipulator models compared to the heuristic experimental designs chosen by an experimenter as well as 10% to 19% compared to an existing state-of-the-art method

Improving Traceability Link Recovery Using Fine-grained Requirements-to-Code Relations

Traceability information is a fundamental prerequisite for many essential software maintenance and evolution tasks, such as change impact and software reusability analyses. However, manually generating traceability information is costly and error-prone. Therefore, researchers have developed automated approaches that utilize textual similarities between artifacts to establish trace links. These approaches tend to achieve low precision at reasonable recall levels, as they are not able to bridge the semantic gap between high-level natural language requirements and code. We propose to overcome this limitation by leveraging fine-grained, method and sentence level, similarities between the artifacts for traceability link recovery. Our approach uses word embeddings and a Word Mover\u27s Distance-based similarity to bridge the semantic gap. The fine-grained similarities are aggregated according to the artifacts structure and participate in a majority vote to retrieve coarse-grained, requirement-to-class, trace links. In a comprehensive empirical evaluation, we show that our approach is able to outperform state-of-the-art unsupervised traceability link recovery approaches. Additionally, we illustrate the benefits of fine-grained structural analyses to word embedding-based trace link generation

Roger that! Learning How Laypersons Teach New Functions to Intelligent Systems

Intelligent systems are rather smart today but still limited to built-in functionality. To break through this barrier, future systems must allow users to easily adapt the system by themselves. For humans the most natural way to communicate is talking. But what if users want to extend the systems’ functionality with nothing but natural language? Then intelligent systems must understand how laypersons teach new skills. To grasp the semantics of such teaching sequences, we have defined a hierarchical classification task. On the first level, we consider the existence of a teaching intent in an utterance; on the second, we classify the distinct semantic parts of teaching sequences: declaration of a new function, specification of intermediate steps, and superfluous information. We evaluate twelve machine learning techniques with multiple configurations tailored to this task ranging from classical approaches such as naı̈ve-bayes to modern techniques such as bidirectional LSTMs and task-oriented adaptations. On the first level convolutional neural networks achieve the best accuracy (96.6%). For the second task, bidirectional LSTMs are the most accurate (98.8%). With the additional adaptations we are able to improve both classifications distinctly (up to 1.8%)

Towards Programming in Natural Language: Learning New Functions from Spoken Utterances

Systems with conversational interfaces are rather popular nowadays. However, their full potential is not yet exploited. For the time being, users are restricted to calling predefined functions. Soon, users will expect to customize systems to their needs and create own functions using nothing but spoken instructions. Thus, future systems must understand how laypersons teach new functionality to intelligent systems. The understanding of natural language teaching sequences is a first step toward comprehensive end-user programming in natural language. We propose to analyze the semantics of spoken teaching sequences with a hierarchical classification approach. First, we classify whether an utterance constitutes an effort to teach a new function or not. Afterward, a second classifier locates the distinct semantic parts of teaching efforts: declaration of a new function, specification of intermediate steps, and superfluous information. For both tasks we implement a broad range of machine learning techniques: classical approaches, such as Naïve Bayes, and neural network configurations of various types and architectures, such as bidirectional LSTMs. Additionally, we introduce two heuristic-based adaptations that are tailored to the task of understanding teaching sequences. As data basis we use 3168 descriptions gathered in a user study. For the first task convolutional neural networks obtain the best results (accuracy: 96.6%); bidirectional LSTMs excel in the second (accuracy: 98.8%). The adaptations improve the first-level classification considerably (plus 2.2% points)