Black-box Representation Research Articles

Graph-Based Similarity of Deep Neural Networks

Understanding the enigmatic black-box representations within Deep Neural Networks (DNNs) is an essential problem in the community of deep learning. An initial step towards tackling this conundrum lies in quantifying the degree of similarity between these representations. Various approaches have been proposed in prior research, however, as the field of representation similarity continues to develop, existing metrics are not compatible with each other and struggling to meet the evolving demands. To address this, we propose a comprehensive similarity measurement framework inspired by the natural graph structure formed by samples and their corresponding features within the neural network. Our novel Graph-Based Similarity (GBS) framework gauges the similarity of DNN representations by constructing a weighted, undirected graph based on the output of hidden layers. In this graph, each node represents an input sample, and the edges are weighted in accordance with the similarity between pairs of nodes. Consequently, the measure of representational similarity can be derived through graph similarity metrics, such as layer similarity. We observe that input samples belonging to the same category exhibit dense interconnections within the deep layers of the DNN. To quantify this phenomenon, we employ a motif-based approach to gauge the extent of these interconnections. This serves as a metric to evaluate whether the representation derived from one model can be accurately classified by another. Experimental results show that GBS gets state-of-the-art performance in the sanity check. We also extensively evaluate GBS on downstream tasks to demonstrate its effectiveness, including measuring the transferability of pretrained models and model pruning.

Combining physics and deep learning to learn continuous-time dynamics models

Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of physics or robotics. Especially for learning dynamics models, these black-box models are not desirable as the underlying principles are well understood and the standard deep networks can learn dynamics that violate these principles. To learn dynamics models with deep networks that guarantee physically plausible dynamics, we introduce physics-inspired deep networks that combine first principles from physics with deep learning. We incorporate Lagrangian mechanics within the model learning such that all approximated models adhere to the laws of physics and conserve energy. Deep Lagrangian Networks (DeLaN) parametrize the system energy using two networks. The parameters are obtained by minimizing the squared residual of the Euler–Lagrange differential equation. Therefore, the resulting model does not require specific knowledge of the individual system, is interpretable, and can be used as a forward, inverse, and energy model. Previously these properties were only obtained when using system identification techniques that require knowledge of the kinematic structure. We apply DeLaN to learning dynamics models and apply these models to control simulated and physical rigid body systems. The results show that the proposed approach obtains dynamics models that can be applied to physical systems for real-time control. Compared to standard deep networks, the physics-inspired models learn better models and capture the underlying structure of the dynamics.

Cost-aware Resource Recommendation for DAG-based Big Data Workflows: An Apache Spark Case Study

The era of personal resources being sufficient for enterprise big data computations has passed. As computations are executed in the cloud, small policy changes of cloud operators may cause considerable changes in operational costs. Carefully choosing the amount of resources for a given application is thus of great importance. This, however, requires a priori knowledge of the application's performance under different configurations. Creating a performance prediction model needs to account for the heterogeneity of resources and the diversity in application workflows. Previous approaches for heterogeneous environments consider a black-box representation of the application which results in single-purpose models. This paper addresses the problem with two gray-box prediction models using linear programming (LP) and mixed-integer linear programming (MILP). Given a set of available resources, the models consider Apache Spark applications and their Directed Acyclic Graph (DAG) of workflow running on top of a Hadoop-YARN cluster. We then propose a configuration recommendation algorithm to optimize the cost-performance trade-offs when renting machine instances. The accuracy of the proposed models is evaluated with real-world executions of several representative applications on the Wikipedia dataset and the TPC-DS benchmark. The average error of only 3.28% for the proposed prediction models demonstrates the practicality of the proposed approach in handling cost-performance trade-offs.

Developing two dynamic Malmquist-Luenberger productivity indices: An illustrated application for assessing productivity performance of Indian banks

In the presence of undesirable output(s) in the production process, the Malmquist-Luenberger productivity index (MLPI) has emerged as a standard tool to measure total factor productivity change and its distinct components, namely efficiency change and technical change. Notwithstanding, the standard version of MLPI has certain genuine downsides, particularly the commonness of infeasibility while computing cross-period directional distance functions with negative data values and the black-box representation of the production technology. For overcoming these downsides, this paper advances two extensions of the standard MLPI. Specifically, we propose dynamic Malmquist-Luenberger and dynamic sequential Malmquist-Luenberger productivity indices to measure the productivity change in a system that can be represented by a dynamic network production structure. The proposed indices take a holistic view of production technology that connects several divisions internally by intermediate processes and use the carryovers flow over time to add a temporal dimension to it. To exhibit the capability of the proposed extensions of MLPI, we model a three-stage dynamic network structure for Indian banks and compute the indices of productivity change, efficiency change, and technical change for forty-two banks for the period from 2010 to 2017. The empirical findings elucidate that the observed productivity growth in the Indian banking industry is primarily driven by technical progress.

Full-wave black-box transmission line tower model for the assessment of lightning backflashover

In order to calculate the overvoltages across the insulator strings of overhead lines, electromagnetic transient (EMT)-type simulators require a model of the tower and its grounding system. In this paper, an electromagnetic field simulation model based on the solution of the full-wave frequency-domain Maxwell’s equations is established to obtain an EMT-compatible black-box representation of the transmission line tower for time-domain simulations. Details of the system, such as the grounding system consisting of counterpoise electrodes, shield wires, phase conductors, and tower cross arms and slant elements are considered in the simulation model. The frequency dependence of soil electrical parameters is included as well. The input data to the frequency-domain simulation model consists of the topology of the tower structure, grounding system, and the parameters of the surrounding medium. As a case study, the developed simulation model is applied to obtain the black-box representation (macromodel) of a 400kV double circuit tower, where the lightning current injected at the tower top is the input, and the output is the induced voltage across the insulator strings. The critical current leading to the flashover of the insulator strings is calculated according to various existing flashover models and two different first stroke lightning current waveforms. Finally, a probabilistic analysis is performed to obtain the percentage of downward negative first strokes leading to a backflashover.

Hierarchical control of DC microgrids combining robustness and smartness

This paper investigates the hierarchical control of DC microgrids. Compared to AC microgrids, DC microgrids encounter complicated converter-level control, and simplified system-level management. To address these characteristics, a new three-level control hierarchy is introduced. The converter control level encapsulates sophisticated converter topologies and inner control loops into a black-box representation. The voltage coordination level uses DC voltage signals to coordinate both static and transient power sharing. The energy management level optimizes the power flow and power quality in a broader scope through communication. This architecture lowers the focus of control to bottom levels. More functions are allocated to the converter control and voltage coordination levels. They can maintain basic microgrid performance with fully local control, thereby ensuring reliable power supply in case of communication failures. Moreover, taking advantage of DC microgrids' simplified system-level operation patterns, the energy management level uses straightforward algorithms to achieve intelligent functions. As a result, this architecture achieves both robust and smart control by exploring DC microgrids' critical features.

Invertible Network for Classification and Biomarker Selection for ASD.

Determining biomarkers for autism spectrum disorder (ASD) is crucial to understanding its mechanisms. Recently deep learning methods have achieved success in the classification task of ASD using fMRI data. However, due to the black-box nature of most deep learning models, it's hard to perform biomarker selection and interpret model decisions. The recently proposed invertible networks can accurately reconstruct the input from its output, and have the potential to unravel the black-box representation. Therefore, we propose a novel method to classify ASD and identify biomarkers for ASD using the connectivity matrix calculated from fMRI as the input. Specifically, with invertible networks, we explicitly determine the decision boundary and the projection of data points onto the boundary. Like linear classifiers, the difference between a point and its projection onto the decision boundary can be viewed as the explanation. We then define the importance as the explanation weighted by the gradient of prediction w.r.t the input, and identify biomarkers based on this importance measure. We perform a regression task to further validate our biomarker selection: compared to using all edges in the connectivity matrix, using the top 10% important edges we generate a lower regression error on 6 different severity scores. Our experiments show that the invertible network is both effective at ASD classification and interpretable, allowing for discovery of reliable biomarkers.

A hybrid method for synthesis of integrated water and regeneration networks with variable removal ratios

This work presents a systematic optimization framework that integrates graphical insights with mathematical modelling to reduce both model complexity and computational time. The graphical technique adopted in this work is Composite Table Algorithm (CTA), which is improved to determine an optimal regenerator removal ratio (RR) that simultaneously minimizes the freshwater requirement and wastewater generation within the water network. The improved CTA is demonstrated using literature examples for both fixed load and fixed flowrate problems. It is further adapted to solve a multiple contaminant problem using the reference contaminant approach. The mathematical model developed includes a detailed design of a reverse osmosis (RO) unit to allow for simultaneous optimization of water and energy used by the regenerator. This provides accurate cost estimation of the water network rather than the linear cost functions associated with the use of blackbox representations in graphical targeting. Upon integrating the graphical and mathematical techniques in this study, results show that there was a reduction of about 85% in CPU time. This implies that the model converges faster and therefore favours the use of insight-based techniques as a preprocessing step for mathematical modelling.

Black Box Galois representations

We develop methods to study 2-dimensional 2-adic Galois representations ρ of the absolute Galois group of a number field K, unramified outside a known finite set of primes S of K, which are presented as Black Box representations, where we only have access to the characteristic polynomials of Frobenius automorphisms at a finite set of primes. Using suitable finite test sets of primes, depending only on K and S, we show how to determine the determinant det⁡ρ, whether or not ρ is residually reducible, and further information about the size of the isogeny graph of ρ whose vertices are homothety classes of stable lattices. The methods are illustrated with examples for K=Q, and for K imaginary quadratic, ρ being the representation attached to a Bianchi modular form.These results form part of the first author's thesis [2].

Visual interpretability for deep learning: a survey

This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance in various tasks, interpretability is always Achilles’ heel of deep neural networks. At present, deep neural networks obtain high discrimination power at the cost of a low interpretability of their black-box representations. We believe that high model interpretability may help people break several bottlenecks of deep learning, e.g., learning from a few annotations, learning via human–computer communications at the semantic level, and semantically debugging network representations. We focus on convolutional neural networks (CNNs), and revisit the visualization of CNN representations, methods of diagnosing representations of pre-trained CNNs, approaches for disentangling pre-trained CNN representations, learning of CNNs with disentangled representations, and middle-to-end learning based on model interpretability. Finally, we discuss prospective trends in explainable artificial intelligence.

A lumped parameter vane pump model for system stability analysis

This paper presents a semi-empirical lumped parameter model developed for analysing the dynamic stability and performance limitations of a pressure compensated vane pump for an automotive application with low-cost components. The model calculates continuous displacement chamber pressure profiles and inertial effects for the determination of the internal forces acting on the vane pump's pivoting cam. Measurements conducted on a custom test stand were used to define a nonlinearly progressive bias spring model and a black box representation of the pump control system valves. Analysis of the complete model reveals that the performance limitations imposed by the control system valves, in terms of system stability and achievable controller bandwidth, are more restrictive than the limitations imposed by the low-cost vane pump and limit the that bandwidth to 1.84 Hz. The control system also imposes limitations to the system performance based on resonance phenomena which may be significant in some applications.

Time-Discrete Modelling of Industrial Compressed Air Systems Based on Equivalent Circuits

Compressed air systems (CAS) on industrial plants consist of air compressors, compressed air reservoirs, compressed air lines and auxillaries as dehumidifiers, dust collectors, pneumatic oilers and pressure controllers. It is assumed that given suitable dimensioning, those industrial compressed-air systems can be used for demand side management purpose. In industrial CAS energy is transmitted by means of pressure difference and volumetric flow rate of the transmission medium compressed air. Alike electric circuits, they consist of various functional components which are flowed through by the compressed air. Furthermore the application of Kirchhoffs laws is possible to those systems. Hence, approximation of the behavior of industrial CAS is possible by arranging and connecting those components in an equivalent circuit diagram. As additional state variables of compressed air as humidity, temperature as well as contents of water, oil and dust are also to be considered, modeling of the individual components is more extensive. A general, abstract approach for the description of the individual components in the form of blackbox representations is outlined.

Formula omitted]-norm-based optimization for the identification of gray-box LTI state-space model parameters

In this paper, the challenging problem of determining the unknown parameters of an identifiable LTI state-space representation of a stable system is addressed by resorting to a specific H∞-norm-based optimization algorithm. More specifically, by assuming the availability of a reliable fully-parameterized representation of the system to identify, the algorithm developed herein consists in restructuring this initial black-box representation of the system dynamics via the optimization of a dedicated maximum eigenvalue-based criterion. This study shows that this H∞-norm-based approach can be seen as a good solution for the identification of gray-box LTI state-space representations and, by extension, as an interesting alternative or a reliable initialization step for the standard output-error techniques.

Multiharmonic Generator for Large-Signal-Network-Analyzer Verification

Since S-parameters were first used to describe linear microwave circuits in the 1960s, circuit designers, software developers, and instrument manufacturers have gradually come to an agreement on this blackbox representation, resulting in significant advancements in modeling, simulation, and measurement. As a mathematical language of high-frequency signal transmission and scattering, S-parameter stands for a unified form of the linear characteristics of microwave networks in the frequency domain. Subsequently, the vector network analyzer (VNA) was invented as the principal instrument to measure S-parameters and characterize the linear behavior of devices and components, including small-signal active circuits.

Non-linear Control of Heave for an Unmanned Helicopter Using a Neural Network

This paper describes a new non-linear control technique applied to the heave control of an unmanned rotorcraft. First a hybrid plant model consisting of exactly known dynamics is combined with a black-box representation of the unknown dynamics. Desired trajectories are calculated to smoothly achieve a sequence of random step changes in desired height according to certain optimal criterion and plant limitations. Control inputs are then determined using the MATLAB® optimisation toolbox to achieve those desired trajectories for the plant heave model. Finally, a neural network is trained to mimic the control inputs resulting from the optimisation process. The neural network controller produces trajectories closely resembling the results from the optimisation process but with a much reduced computation time. Flight test results of control of the heave dynamics of a helicopter confirm the neural network controller's ability to operate in high disturbance conditions and outperform a proportional-derivative (PD) controller.

Modèle comportemental dans l'espace d'état d'un alternateur synchrone

This paper proposes a dynamic modeling approach of a synchronous generator in order to build simulators of embarked network. The developed model avoids the accessibility constraints to identify the rotor physical parameters. To reproduce temporal behavior of the rotor, a state space model of its black box representation is proposed. The parameters are identified by a particle swarm optimization algorithm using the results of SSFR tests. A current regulated static converter is proposed to replace the linear amplifier to do the measurements. This solution offer an inexpensive alternative to a linear power amplifier, especially for high power generator. Finally simulations and experimental results are compared in dynamic and steady states to validate the proposed approach.

Integration of hierarchical decomposition and mathematical programming for the synthesis of process flowsheets

Two of the main methods for performing the conceptual design of process flowsheets are (1) the mathematical programming approach using Mixed-Integer Nonlinear Programming (MINLP) techniques and (2) hierarchical decomposition. The objective of this paper is to develop a combined approach for flowsheet synthesis that exploits the advantages of each of these methods, while maintaining consistency with their fundamental tenets. In the proposed approach, the idea is to solve the entire flowsheet at each step of the decomposition using a multilevel tree search. Aggregated models, based on black-box (input-output) representations of the downstream subsystems, are used to account for interactions with the detailed MINLP model of the subsystem at the current level of decomposition. Thus a simultaneous optimization of the entire flowsheet is performed with a combination of simple and detailed models. This provides for better designs, tighter bounds, and a monotonic decrease in the profit as decomposition proceeds. The procedure continues until the entire flowsheet has been decomposed to the level of the detailed models. The profit of every alternative is compared to the base-case profit at each node in the multilevel tree search, allowing for early fathoming of uneconomical alternatives, through which exhaustive enumeration is avoided. Application of the proposed methodology is illustrated with one large example.

Design of hybrid distillation and vapor permeation processes

An explicit algebraic design model for vapor permeation systems is presented. The model is valid for binary mixtures, and is based on a black-box representation of the transport properties across the membrane. Based on this design model, some of the trade-offs in a hybrid distillation and vapor permeation process are illustrated through parametric studies.

Computing with polynomials given byblack boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators

Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show that within this representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and denominator of a rational function, can all be solved in random polynomial-time. Since we can convert black boxes efficiently to sparse format, problems with sparse solutions, e.g., sparse polynomial factorization and sparse multivariate rational function interpolation, are also in random polynomial time. Moreover, the black box representation is one of the most space efficient implicit representations that we know. Therefore, the output programs can be easily distributed over a network of processors for further manipulation, such as sparse interpolation.

Excretion-retention diagram to evaluate gas exchange properties of vertebrate respiratory systems.

Excretion [E = (PE - PI)/(PV - PI)] and retention [R = (Pa - PI)/(PV -PI)]are completely model-free defined variables which describe the dual input-output black-box representation of vertebrate respiratory systems under steady-state conditions. In the excretion-retention diagram (E-R diagram), E is plotted as a function of R. The application of the principle of mass conservation confines the possible combinations of E and R for a gas with a blood-gas partition coefficient, lambda, in a respiratory system with an overall ventilation, VT, and an overall perfusion, QT, to E = (lambda QT/VT) (1 - R). In general, E can be described as a continuous function of R. The mathematical formulation of this function depends on the configuration of the respiratory system. Easily recognizable curvatures are obtained for counter-cross, and cocurrent systems with and without parallel inhomogeneities. Visual inspection of actual E and R data displayed in an E-R diagram therefore allows the correct choice of the configuration of the respiratory system to be eventually used for further parameter estimation schemes. The E-R diagram is also a powerful tutorial tool for visualizing the complex relationships between the gas exchange of agents with different physical properties and the consequences of changes in ventilation and perfusion distribution within the respiratory system on gas transport.