Set Of Inputs Research Articles

Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems

The problem of state estimation (reconstruction of the state vector) for a given class of biochemical systems under uncertain system dynamics has been addressed in this paper. In detail, the bioreactor at a water resource recovery facility represents the considered biochemical systems. The biochemical processes taking place in the bioreactor have been modelled using an activated sludge model. Based on this model, an appropriate utility model has been derived for estimation purposes. The internal dynamics of the model have been burdened with unstructured and parametric uncertainty due to the unknown reaction kinetics functions. Taking this uncertainty into account, an analysis of the observability and detectability of the utility model has been carried out. The utility model and the available set of inputs and measured outputs have been used to design a new robust non-linear observer that allows the estimation of state variables in the presence of uncertainty. In the synthesis of the observer, the asymptotic observer methodology has been combined with a second-order sliding mode observer, a so-called super twisting algorithm. The developed observer generates not only robust and stable estimates of the state variables but also enables the reconstruction of unknown kinetic functions. The stability of the designed observer has been proven using the Lyapunov stability theory. The observer has been implemented in the Matlab/Simulink environment. The comprehensive simulation studies carried out show the high efficiency of the estimation process using the developed state observer.

Navigating the Dynamics of Squeeze Film Dampers: Unraveling Stiffness and Damping Using a Dual Lens of Reynolds Equation and Neural Network Models for Sensitivity Analysis and Predictive Insights

The squeeze film damper (SFD) is proven to be highly effective in mitigating rotor vibration as it traverses the critical speed, thus making it extensively utilized in the aeroengine domain. In this paper, we investigate the stiffness and damping of SFD using the Reynolds equation and neural network models. Our specific focus includes examining the structural and operating parameters of SFDs, such as clearance, feed pressure of oil, rotor whirl, and rotational speed. Firstly, the pressure distribution analytical model of the oil film inside the SFD based on the hydrodynamic lubrication theory is established, as described by the Reynolds equation. It obtained oil film forces, pressure, stiffness, and damping values under various sets of structural, lubrication, and operating parameters, including length, clearance, boundary pressure at both sides, rotational speed, and whirling motion, by applying difference computations to the Reynolds equation. Secondly, according to the significant analyses of the obtained oil film stiffness and damping, the following three parameters of the most significance are found: clearance, rotational speed, and rotor whirl. Furthermore, neural network models, including GA-BP and decision tree models, are established based on the obtained results of difference computation. The numerical simulation and calculation of these models are then applied to show their validity with all given parameters and the three significant parameters separately as two sets of model input. Regardless of either set of model inputs, these established neural network models are capable of predicting the nonlinear stiffness and damping of the oil film inside an SFD. These sensitive parameters merely require measurement, followed by the utilization of a neural network to predict stiffness and damping instead of the Reynolds equation. This process serves structural enhancement, facilitates parameter optimization in SFDs, and provides crucial support for refining the design parameters of SFDs.

SISS-MCO: large scale sparsity-induced spot selection for fast and fully-automated robust multi-criteria optimisation of proton plans

Objective. Intensity modulated proton therapy (IMPT) is an emerging treatment modality for cancer. However, treatment planning for IMPT is labour-intensive and time-consuming. We have developed a novel approach for multi-criteria optimisation (MCO) of robust IMPT plans (SISS-MCO) that is fully automated and fast, and we compare it for head and neck, cervix, and prostate tumours to a previously published method for automated robust MCO (IPBR-MCO, van de Water 2013). Approach. In both auto-planning approaches, the applied automated MCO of spot weights was performed with wish-list driven prioritised optimisation (Breedveld 2012). In SISS-MCO, spot weight MCO was applied once for every patient after sparsity-induced spot selection (SISS) for pre-selection of the most relevant spots from a large input set of candidate spots. IPBR-MCO had several iterations of spot re-sampling, each followed by MCO of the weights of the current spots. Main results. Compared to the published IPBR-MCO, the novel SISS-MCO resulted in similar or slightly superior plan quality. Optimisation times were reduced by a factor of 6 i.e. from 287 to 47 min. Numbers of spots and energy layers in the final plans were similar. Significance. The novel SISS-MCO automatically generated high-quality robust IMPT plans. Compared to a published algorithm for automated robust IMPT planning, optimisation times were reduced on average by a factor of 6. Moreover, SISS-MCO is a large scale approach; this enables optimisation of more complex wish-lists, and novel research opportunities in proton therapy.

Improving the second-tier classification of methylmalonic acidemia patients using a machinelearning ensemble method.

Methylmalonic acidemia (MMA) is a disorder of autosomal recessive inheritance, with an estimated prevalence of 1:50,000. First-tier clinical diagnostic tests often return many false positives [five false positive (FP): one true positive (TP)]. In this work, our goal was to refine a classification model that can minimize the number of false positives, currently an unmet need in the upstream diagnostics of MMA. We developed machinelearning multivariable screening models for MMA with utility as a secondary-tier tool for false positives reduction. We utilized mass spectrometry-based features consisting of 11 amino acids and 31 carnitines derived from dried blood samples of neonatal patients, followed by additional ratio feature construction. Feature selection strategies (selection by filter, recursive feature elimination, and learned vector quantization) were used to determine the input set for evaluating the performance of 14 classification models to identify a candidate model set for an ensemble model development. Our work identified computational models that explore metabolic analytes to reduce the number of false positives without compromising sensitivity. The best results [area under the receiver operating characteristic curve (AUROC) of 97%, sensitivity of 92%, and specificity of 95%] were obtained utilizing an ensemble of the algorithms random forest, C5.0, sparse linear discriminant analysis, and autoencoder deep neural network stacked with the algorithm stochastic gradient boosting as the supervisor. The model achieved a good performance trade-off for a screening application with 6% false-positive rate (FPR) at 95% sensitivity, 35% FPR at 99% sensitivity, and 39% FPR at 100% sensitivity. The classification results and approach of this research can be utilized by clinicians globally, to improve the overall discovery of MMA in pediatric patients. The improved method, when adjusted to 100% precision, can be used to further inform the diagnostic process journey of MMA and help reduce the burden for patients and their families.

Investigation in optimization of process parameters in turning of mild steel using response surface methodology and modified deep neural network

The turning operation is a traditional and conventional process for machining cylindrical materials to achieve a desired shape. During machining in the turning process, the accuracy and quality of the end product mainly depend on its process parameters. Therefore, this study attempts to achieve a quality product from a conventional lathe machine by optimizing its process parameters for En2-BS970 mild steel. The experiments were designed with the help of response surface methodology (RSM). The most influential turning parameters, such as feed rate, spindle speed, cutting fluid flow rate, and cutting angle, are investigated experimentally. In addition, the machining responses, namely material removal rate (MRR), surface roughness (SR), cutting force (CF), and cutting time (CT), have been optimized using the RSM numerical optimization method. Furthermore, a deep neural network (DNN) machine learning prediction model based on the whale optimization algorithm (WOA) is developed for this experiment in order to predict turning performances for En2-BS970 material. The predicted DNN results showed an accuracy of about 90% compared to experimental results, indicating that the implementation of WOA significantly optimized the DNN weights during training. The RSM optimized responses are obtained as 14.608 mm3/min for MRR, 0.7504 µm for SR, 442.94 N for CF, and 2.48 seconds for CT during the turning operation with input settings of 0.24 mm/rev, 466.535 rpm, 0.075 ml/s and 60.18° for feed rate, spindle speed, cutting fluid flow rate and cutting edge angle respectively.

A Trip-Based Data-Driven Model for Predicting Battery Energy Consumption of Electric City Buses

The paper presents a novel approach for predicting battery energy consumption in electric city buses (e-buses) by means of a trip-based data-driven regression model. The model was parameterized based on the data collected by running a physical experimentally validated e-bus simulation model, and it consists of powertrain and heating, ventilation, and air conditioning (HVAC) system submodels. The main advantage of the proposed approach is its reliance on readily available trip-related data, such as travel distance, mean velocity, average passenger count, mean and standard deviation of road slope, and mean ambient temperature and solar irradiance, as opposed to the physical model, which requires high-sampling-rate driving cycle data. Additionally, the data-driven model is executed significantly faster than the physical model, thus making it suitable for large-scale city bus electrification planning or online energy consumption prediction applications. The data-driven model development began with applying feature selection techniques to identify the most relevant set of model inputs. Machine learning methods were then employed to achieve a model that effectively balances accuracy, simplicity, and interpretability. The validation results of the final eight-input quadratic-form e-bus model demonstrated its high precision and generalization, which was reflected in the R2 value of 0.981 when tested on unseen data. Owing to the trip-based, mean-value formulation, the model executed six orders of magnitude faster than the physical model.

Generalized planning as heuristic search: A new planning search-space that leverages pointers over objects

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not trivially extend to Generalized Planning (GP); GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in their number of objects, the initial and goal configuration of these objects and hence, in the number (and possible values) of the state variables. State-space search, as it is implemented by heuristic planners, becomes then impractical for GP. In this paper we adapt the planning as heuristic search paradigm to the generalization requirements of GP, and present the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines an upgraded version of our GP algorithm, called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space for GP. Lastly, the paper defines a set of evaluation and heuristic functions for BFGP that assess the structural complexity of the candidate GP solutions, as well as their fitness to a given input set of classical planning instances. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g. integers.

Online Guaranteed Reachable Set Approximation for Systems With Changed Dynamics and Control Authority

This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and control authority, given an a priori computed reachable set for the nominal system. The method functions by shrinking or inflating a precomputed reachable set based on prior knowledge of the system's trajectory deviation growth dynamics, depending on whether an inner approximation or outer approximation is desired. These dynamics determine an upper bound on the minimal deviation between two trajectories emanating from the same point that are generated by control inputs from the nominal and diminished set of control inputs, respectively. The dynamics depend on the given Hausdorff distance bound between the nominal set of admissible controls and the possibly unknown impaired space of admissible controls. Because of its computational efficiency compared to direct computation of the off-nominal reachable set, this procedure can be applied to on-board fault-tolerant path planning and failure recovery. In addition, the proposed algorithm does not require convexity of the reachable sets unlike our previous work, thereby making it suitable for general use. We raise a number of implementational considerations for our algorithm, and we present three illustrative examples, namely an application to the heading dynamics of a ship, a lower triangular dynamical system, and a system of coupled linear subsystems.

Text Summarization Using NLP

Abstract: This Project represents the work associated with Text Summarization. In this paper, we present a framework for summarizing the massive facts. The proposed framework depends on highlight extraction from internet, using each morphological element and semantic data. Presently, in which large facts is available on the internet, it's far maximum important to offer the improved approaches to extract the statistics quickly and most successfully. It may be very hard for human beings to manually extract the precis of a large document of text. There are lots of text substances to be had on the internet. So, there's a hassle of looking for related files from the quantity of documents to be had and absorbing associated statistics from it. In essence to determine out the previous issues, the automated textual content summarization could be very a whole lot essential. Text Summarization is the method of figuring out the most vital and significant information in a input report or set of related input files and compressing all the inputs into a shorter version preserving its normal goals.

A process-aware framework to support Process Mining from blockchain applications

Several studies were conducted to demonstrate the application of Process Mining (PM) techniques to Ethereum-compatible application event data. However, the availability of event data is constrained by the application’s process awareness, which is under-reported in the literature. Based on domain analysis, which identified several challenges to mining the business process from blockchain applications, a framework was designed, instantiated, and tested in this study. The framework supports identification of appropriate cases for PM and automates the generation of event logs from blockchain data. It consists of two modules, the Process Awareness Recognizer (PAR) and the Event Log Generator (ELG). PAR is a rule-based classifier to assess the process awareness of a given application. ELG is an automated batch processing model consisting of three methods: (1) Extractor: to retrieve event data from blockchains; (2) Decoder: to transform the extracted data to a human-readable format; and (3) Formatter: to produce event log files in a format compatible with PM tools. It was validated by implementing a proof-of-concept application with an input set of 201 real-world applications. The results prove the framework’s feasibility and applicability.

Evaluation of educational resource utilization efficiency, regional technological heterogeneity, and total factor productivity change in 35 European countries.

Educational resource utilization efficiency (ERUE) and productivity growth are considered current global challenges that the modern world faces. This study evaluates the educational resource utilization efficiency, dynamic productivity change, and regional discrepancies in technologies involved in educational resource utilization in 35 European countries and four regions. DEA Super SBM, Meta frontier analysis, and Malmquist productivity index are employed to gauge the ERUE, technology gap ratio (TGR), and total factor education resources productivity change. A set of inputs and outputs is used from 35 European countries for the study period of 1998-2021. Results revealed that the average ERUE in European countries is 0.6312, Which indicates a 36.88% improvement potential in educational resource utilization. Southern Europe continuously exhibits superior average ERUE scores (0.6871) compared to other regions, indicating a higher efficiency in using educational resources. Luxembourg (1.0813), Czechia (0.9356), and Slovenia (0.8984) are found to be the top three performers in terms of ERUE level. The technology gap ratio value is highest in Southern Europe. It demonstrates that southern European countries used the most advanced technology in education resource utilization. The average Malmquist Index (MI) in European countries is 1.0349. It Indicates a 3.49% growth in educational resource utilization. Technology is the primary determinant of productivity growth, as Technological change is higher than efficiency change. Southern European countries showed the highest MI of 1.0542. Italy, Lithuania, and Serbia were found to have higher average MI scores over the study period (1998-2021). Finally, the Kruskal Wallis test proved that ERUE and TGR in 4 different regions of Europe are heterogeneous. In contrast, the MI in European regions isn't found to be significantly different.

Tropical cyclone intensity forecasting using model knowledge guided deep learning model

This paper developed a deep learning (DL) model for forecasting tropical cyclone (TC) intensity in the Northwest Pacific. A dataset containing 20 533 synchronized and collocated samples was assembled, which included ERA5 reanalysis data as well as satellite infrared (IR) imagery, covering the period from 1979 to 2021. The u-, v- and w-components of wind, sea surface temperature, IR satellite imagery, and historical TC information were selected as the model inputs. Then, a TC-intensity-forecast-fusion (TCIF-fusion) model was developed, in which two special branches were designed to learn multi-factor information to forecast 24 h TC intensity. Finally, heatmaps capturing the model’s insights are generated and applied to the original input data, creating an enhanced input set that results in more accurate forecasting. Employing this refined input, the heatmaps (model knowledge) were used to guide TCIF-fusion model modeling, and the model-knowledge-guided TCIF-fusion model achieved a 24 h forecast error of 3.56 m s−1 for Northwest Pacific TCs spanning 2020–2021. The results show that the performance of our method is significantly better than the official subjective prediction and advanced DL methods in forecasting TC intensity by 4% to 22%. Additionally, compared to operational approaches, model-guided knowledge methods can better forecast the intensity of landfalling TCs.

STSR-INR: Spatiotemporal super-resolution for multivariate time-varying volumetric data via implicit neural representation

Implicit neural representation (INR) has surfaced as a promising direction for solving different scientific visualization tasks due to its continuous representation and flexible input and output settings. We present STSR-INR, an INR solution for generating simultaneous spatiotemporal super-resolution for multivariate time-varying volumetric data. Inheriting the benefits of the INR-based approach, STSR-INR supports unsupervised learning and permits data upscaling with arbitrary spatial and temporal scale factors. Unlike existing GAN- or INR-based super-resolution methods, STSR-INR focuses on tackling variables or ensembles and enabling joint training across datasets of various spatiotemporal resolutions. We achieve this capability via a variable embedding scheme that learns latent vectors for different variables. In conjunction with a modulated structure in the network design, we employ a variational auto-decoder to optimize the learnable latent vectors to enable latent-space interpolation. To combat the slow training of INR, we leverage a multi-head strategy to improve training and inference speed with significant speedup. We demonstrate the effectiveness of STSR-INR with multiple scalar field datasets and compare it with conventional tricubic+linear interpolation and state-of-the-art deep-learning-based solutions (STNet and CoordNet).

A new input design framework for asymptotic active fault diagnosis with application to integrated diagnosis and control

This paper proposes a new input design framework for set-based asymptotic active fault diagnosis and then applies it to integrated design of active fault diagnosis and control. First, a new input design method is proposed for asymptotic active fault diagnosis by maximizing a newly-defined excluding degree of the origin from all healthy and faulty residual zonotopes. Second, an input set is constructed based on the mathematical expression of the excluding degree at each time instant such that any input out of the input set can be used for active fault diagnosis. Third, an optimal input is designed out of the input set at each time instant for simultaneous active fault diagnosis and control. Besides, an optimal input can also be designed out of the input set to achieve integrated design of active fault diagnosis and other objectives (e.g., minimal input energy to reduce harm to the system, etc.). At the end of this paper, several examples are used to illustrate the effectiveness of the proposed methods.

Approximating subset sum ratio via partition computations

AbstractWe present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to 1 as possible. Our scheme makes use of exact and approximate algorithms for Partition, and clearly showcases the close relationship between the two algorithmic problems. Depending on the relationship between the size of the input set n and the error margin $$\varepsilon $$ ε , we improve upon the best currently known algorithm of Melissinos and Pagourtzis [COCOON 2018] of complexity $$\mathcal {O} (n^4 / \varepsilon )$$ O ( n 4 / ε ) . In particular, the exponent of n in our proposed scheme may decrease down to 2, depending on the Partition algorithm used.

Strategies for deep learning-based attenuation and scatter correction of brain 18 F-FDG PET images in the image domain.

Attenuation and scatter correction is crucial for quantitative positron emission tomography (PET) imaging. Direct attenuation correction (AC) in the image domain using deep learning approaches has been recently proposed for combined PET/MR and standalone PET modalities lacking transmission scanning devices or anatomical imaging. In this study, different input settings were considered in the model training to investigate deep learning-based AC in the image space. Three different deep learning methods were developed for direct AC in the image space: (i) use of non-attenuation-corrected PET images as input (NonAC-PET), (ii) use of attenuation-corrected PET images with a simple two-class AC map (composed of soft-tissue and background air) obtained from NonAC-PET images (PET segmentation-based AC [SegAC-PET]), and (iii) use of both NonAC-PET and SegAC-PET images in a Double-Channel fashion to predict ground truth attenuation corrected PET images with Computed Tomography images (CTAC-PET). Since a simple two-class AC map (generated from NonAC-PET images) can easily be generated, this work assessed the added value of incorporating SegAC-PET images into direct AC in the image space. A 4-fold cross-validation scheme was adopted to train and evaluate the different models based using 80 brain 18 F-Fluorodeoxyglucose PET/CT images. The voxel-wise and region-wise accuracy of the models were examined via measuring the standardized uptake value (SUV) quantification bias in different regions of the brain. The overall root mean square error (RMSE) for the Double-Channel setting was 0.157±0.08 SUV in the whole brain region, while RMSEs of 0.214±0.07 and 0.189±0.14 SUV were observed in NonAC-PET and SegAC-PET models, respectively. A mean SUV bias of 0.01±0.26% was achieved by the Double-Channel model regarding the activity concentration in cerebellum region, as opposed to 0.08±0.28% and 0.05±0.28% SUV biases for the network that uniquely used NonAC-PET or SegAC-PET as input, respectively. SegAC-PET images with an SUV bias of -1.15±0.54%, served as a benchmark for clinically accepted errors. In general, the Double-Channel network, relying on both SegAC-PET and NonAC-PET images, outperformed the other AC models. Since the generation of two-class AC maps from non-AC PET images is straightforward, the current study investigated the potential added value of incorporating SegAC-PET images into a deep learning-based direct AC approach. Altogether, compared with models that use only NonAC-PET and SegAC-PET images, the Double-Channel deep learning network exhibited superior attenuation correction accuracy.

A New Approach to Identifying Sorghum Hybrids Using UAV Imagery Using Multispectral Signature and Machine Learning

Using multispectral sensors attached to unmanned aerial vehicles (UAVs) can assist in the collection of morphological and physiological information from several crops. This approach, also known as high-throughput phenotyping, combined with data processing by machine learning (ML) algorithms, can provide fast, accurate, and large-scale discrimination of genotypes in the field, which is crucial for improving the efficiency of breeding programs. Despite their importance, studies aimed at accurately classifying sorghum hybrids using spectral variables as input sets in ML models are still scarce in the literature. Against this backdrop, this study aimed: (I) to discriminate sorghum hybrids based on canopy reflectance in different spectral bands (SB) and vegetation indices (VIs); (II) to evaluate the performance of ML algorithms in classifying sorghum hybrids; (III) to evaluate the best dataset input for the algorithms. A field experiment was carried out in the 2022 crop season in a randomized block design with three replications and six sorghum hybrids. At 60 days after crop emergence, a flight was carried out over the experimental area using the Sensefly eBee real time kinematic. The spectral bands (SB) acquired by the sensor were: blue (475 nm, B_475), green (550 nm, G_550), red (660 nm, R_660), Rededge (735 nm, RE_735) e NIR (790 nm, NIR_790). From the SB acquired, vegetation indices (VIs) were calculated. Data were submitted to ML classification analysis, in which three input settings (using only SB, using only VIs, and using SB + VIs) and six algorithms were tested: artificial neural networks (ANN), support vector machine (SVM), J48 decision trees (J48), random forest (RF), REPTree (DT) and logistic regression (LR, conventional technique used as a control). There were differences in the spectral signature of each sorghum hybrid, which made it possible to differentiate them using SBs and VIs. The ANN algorithm performed best for the three accuracy metrics tested, regardless of the input used. In this case, the use of SB is feasible due to the speed and practicality of analyzing the data, as it does not require calculations to perform the VIs. RF showed better accuracy when VIs were used as an input. The use of VIs provided the best performance for all the algorithms, as did the use of SB + VIs which provided good performance for all the algorithms except RF. Using ML algorithms provides accurate identification of the hybrids, in which ANNs using only SB and RF using VIs as inputs stand out (above 55 for CC, above 0.4 for kappa and around 0.6 for F-score). There were differences in the spectral signature of each sorghum hybrid, which makes it possible to differentiate them using wavelengths and vegetation indices. Processing the multispectral data using machine learning techniques made it possible to accurately differentiate the hybrids, with emphasis on artificial neural networks using spectral bands as inputs and random forest using vegetation indices as inputs.

Monotonicity and the Precision of Program Analysis

It is widely known that the precision of a program analyzer is closely related to intensional program properties, namely, properties concerning how the program is written. This explains, for instance, the interest in code obfuscation techniques, namely, tools explicitly designed to degrade the results of program analysis by operating syntactic program transformations. Less is known about a possible relation between what the program extensionally computes, namely, its input-output relation, and the precision of a program analyzer. In this paper we explore this potential connection in an effort to isolate program fragments that can be precisely analyzed by abstract interpretation, namely, programs for which there exists a complete abstract interpretation. In the field of static inference of numeric invariants, this happens for programs, or parts of programs, that manifest a monotone (either non-decreasing or non-increasing) behavior. We first formalize the notion of program monotonicity with respect to a given input and a set of numerical variables of interest. A sound proof system is then introduced with judgments specifying whether a program is monotone relatively to a set of variables and a set of inputs. The interest in monotonicity is justified because we prove that the family of monotone programs admits a complete abstract interpretation over a specific class of non-trivial numerical abstractions and inputs. This class includes all non-relational abstract domains that refine interval analysis (i.e., at least as precise as the intervals abstraction) and that satisfy a topological convexity hypothesis.

Effect of Time-Varying Multiplicative Noise on DNN- k WTA Model.

Among many k -winners-take-all ( k WTA) models, the dual-neural network (DNN- k WTA) model is with significantly less number of connections. However, for analog realization, noise is inevitable and affects the operational correctness of the k WTA process. Most existing results focus on the effect of additive noise. This brief studies the effect of time-varying multiplicative input noise. Two scenarios are considered. The first one is the bounded noise case, in which only the noise range is known. Another one is for the general noise distribution case, in which we either know the noise distribution or have noise samples. For each scenario, we first prove the convergence property of the DNN- k WTA model under multiplicative input noise and then provide an efficient method to determine whether a noise-affected DNN- k WTA network performs the correct k WTA process for a given set of inputs. With the two methods, we can efficiently measure the probability of the network performing the correct k WTA process. In addition, for the case of the inputs being uniformly distributed, we derive two closed-form expressions, one for each scenario, for estimating the probability of the model having correct operation. Finally, we conduct simulations to verify our theoretical results.

A Unified Approach to Coreset Learning.

Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets' construction is done in a problem-dependent manner and it could take years to design and prove the correctness of a coreset for a specific family of queries. This could limit coresets' use in practical applications. Moreover, small coresets provably do not exist for many problems. To address these limitations, we propose a generic, learning-based algorithm for construction of coresets. Our approach offers a new definition of coreset, which is a natural relaxation of the standard definition and aims at approximating the average loss of the original data over the queries. This allows us to use a learning paradigm to compute a small coreset of a given set of inputs with respect to a given loss function using a training set of queries. We derive formal guarantees for the proposed approach. Experimental evaluation on deep networks and classic machine learning problems show that our learned coresets yield comparable or even better results than the existing algorithms with worst case theoretical guarantees (that may be too pessimistic in practice). Furthermore, our approach applied to deep network pruning provides the first coreset for a full deep network, i.e., compresses all the networks at once, and not layer by layer or similar divide-and-conquer methods.