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Statistical Complexity of Quantum Learning

Abstract Learning problems involve settings in which an algorithm has to make decisions based on data, and possibly side information such as expert knowledge. This study has two main goals. First, it reviews and generalizes different results on the data and model complexity of quantum learning, where the data and/or the algorithm can be quantum, focusing on information‐theoretic techniques. Second, it introduces the notion of copy complexity, which quantifies the number of copies of a quantum state required to achieve a target accuracy level. Copy complexity arises from the destructive nature of quantum measurements, which irreversibly alter the state to be processed, limiting the information that can be extracted about quantum data. As a result, empirical risk minimization is generally inapplicable. The paper presents novel results on the copy complexity for both training and testing. To make the paper self‐contained and approachable by different research communities, an extensive background material is provided on classical results from statistical learning theory, as well as on the distinguishability of quantum states. Throughout, the differences between quantum and classical learning are highlighted by addressing both supervised and unsupervised learning, and extensive pointers are provided to the literature.

97 MATHEMATICS AND COMPUTING↗

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.

97 MATHEMATICS AND COMPUTING↗

Making Games Not Work: Paradoxes Embedded in Game-Based Training and Concepts for Overcoming Them

An interest in game-based training solutions is natural. All one has to do is watch someone fully engaged in a modern game to see the potential of harnessing that attention for training. However, the reality of game-based training has not fully satisfied these expectations. This paper explains two paradoxes that must be overcome for games to support training. These paradoxes are a result of the realities of the basic human condition clashing with the requirements of learning theory. 80th paradoxes arise from the concept of "engagement" that is central to games. The first comes from a more robust definition of engagement, which is the condition of Flow or Optimal Experience. Flow is the state game developers want to see in users. One aspect of Flow is loss of sense of self as the individual becomes immersed in the experience. The paradox arises because this loss of self directly contradicts the learning requirement of self-reflection. The second paradox comes from theories of play, which state in part that play requires a level of individual freedom. The contradiction arises when game-based play must be harnessed to an organizational training program or regimen. The paper will discuss these paradoxes in the context of an effort to design a game-based training modality to train combat medics and will close with a review of compensating strategies identified by the designers. The paper will provide information important to anyone interested in conceptualizing and designing game-based training.

Jones, Phillip N.↗

Learnability of Red-Green Opponency

Lennie, Haake, and Williams found that in the lateral geniculate nucleus (LGN), parvocellular unit responses are consistent with the hypothesis that their input connectivity is blind to the difference between middle-wavelength-sensitive (MWS) and long-wavelength-sensitive (LWS) cones. Most of their cells have a total MWS input weight opposite in sign and similar in magnitude to their total LWS input weight. If these weights are exactly balanced, the construction of a red-green opponent system from such units is simple: such units need only be aligned so the signs of their outputs agree. Ahumada and Mulligan described an associative learning process which can accomplish this alignment. If the units are not balanced (carry some luminance information), the strong overlap between the MWS and LWS spectral responses can cause units to agree more on the basis of luminance, and the associative process fails to produce red-green opponency. The learning theory requires that the LGN units be nearly balanced (more strongly encode chromaticity than luminance) and quantitatively expresses the requirement: the principal component of the LGN outputs must be in the red-green rather than the luminance direction. We show that the cone weights of the monkey LGN cells measured by Derrington, Krauskopf, and Lennie can satisfy this learnability criterion even if the MWS spectral response is close to the LWS spectral response, simulating anomalous trichromacy. The learnability theory provides a source of visual system variation for explaining why different anomalous trichromats may make the same average anomaloscope match (same pigments), but have either narrow (good opponent learning) or wide (poor learning) ranges of acceptable matches.

Ahumada, Albert J., Jr.↗

Learning-based position control of a closed-kinematic chain robot end-effector

A trajectory control scheme whose design is based on learning theory, for a six-degree-of-freedom (DOF) robot end-effector built to study robotic assembly of NASA hardwares in space is presented. The control scheme consists of two control systems: the feedback control system and the learning control system. The feedback control system is designed using the concept of linearization about a selected operating point, and the method of pole placement so that the closed-loop linearized system is stabilized. The learning control scheme consisting of PD-type learning controllers, provides additional inputs to improve the end-effector performance after each trial. Experimental studies performed on a 2 DOF end-effector built at CUA, for three tracking cases show that actual trajectories approach desired trajectories as the number of trials increases. The tracking errors are substantially reduced after only five trials.

Nguyen, Charles C.↗

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Space Station Freedom - A resource for aerospace education

The role of the International Space Station in future U.S. aerospace education efforts is discussed from a NASA perspective. The overall design concept and scientific and technological goals of the Space Station are reviewed, and particular attention is given to education projects such as the Davis Planetarium Student Space Station, the Starship McCullough, the Space Habitat, the working Space Station model in Austin, TX, the Challenger Center for Space Life Education, Space M+A+X, and the Space Science Student Involvement Program. Also examined are learning-theory aspects of aerospace education: child vs adult learners, educational objectives, teaching methods, and instructional materials.

Brown, Robert W.↗

Two papers on feed-forward networks

Connectionist feed-forward networks, trained with back-propagation, can be used both for nonlinear regression and for (discrete one-of-C) classification, depending on the form of training. This report contains two papers on feed-forward networks. The papers can be read independently. They are intended for the theoretically-aware practitioner or algorithm-designer; however, they also contain a review and comparison of several learning theories so they provide a perspective for the theoretician. The first paper works through Bayesian methods to complement back-propagation in the training of feed-forward networks. The second paper addresses a problem raised by the first: how to efficiently calculate second derivatives on feed-forward networks.

Buntine, Wray L.↗

MODSIM World 2007 Conference and Expo: Select Papers and Presentations from the Education and Training Track

This NASA Conference Publication features select papers and PowerPoint presentations from the Education and Training Track of MODSIM World 2007 Conference and Expo. Invited speakers and panelists of national and international renown, representing academia, industry and government, discussed how modeling and simulation (M&S) technology can be used to accelerate learning in the K-16 classroom, especially when using M&S technology as a tool for integrating science, technology, engineering and mathematics (STEM) classes. The presenters also addressed the application ofM&S technology to learning and training outside of the classroom. Specific sub-topics of the presentations included: learning theory; curriculum development; professional development; tools/user applications; implementation/infrastructure/issues; and workforce development. There was a session devoted to student M&S competitions in Virginia too, as well as a poster session.

Pinelli, Thomas E.↗

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

Using a Support Vector Machine and a Land Surface Model to Estimate Large-Scale Passive Microwave Temperatures over Snow-Covered Land in North America

A support vector machine (SVM), a machine learning technique developed from statistical learning theory, is employed for the purpose of estimating passive microwave (PMW) brightness temperatures over snow-covered land in North America as observed by the Advanced Microwave Scanning Radiometer (AMSR-E) satellite sensor. The capability of the trained SVM is compared relative to the artificial neural network (ANN) estimates originally presented in [14]. The results suggest the SVM outperforms the ANN at 10.65 GHz, 18.7 GHz, and 36.5 GHz for both vertically and horizontally-polarized PMW radiation. When compared against daily AMSR-E measurements not used during the training procedure and subsequently averaged across the North American domain over the 9-year study period, the root mean squared error in the SVM output is 8 K or less while the anomaly correlation coefficient is 0.7 or greater. When compared relative to the results from the ANN at any of the six frequency and polarization combinations tested, the root mean squared error was reduced by more than 18 percent while the anomaly correlation coefficient was increased by more than 52 percent. Further, the temporal and spatial variability in the modeled brightness temperatures via the SVM more closely agrees with that found in the original AMSR-E measurements. These findings suggest the SVM is a superior alternative to the ANN for eventual use as a measurement operator within a data assimilation framework.

Modeling↗

Seeding picoscale solutions for social macro goals: complex thinking in projects for vulnerable communities

This chapter presents lessons learned from two experiences of implementing sociopoliticalsustainability strategies to achieve environmental and economic sustainability.The projects were carried out in rural communities in Guinea-Bissau andJamaica, which are both vulnerable to climate change. Each experience, developedfrom a systemic perspective and under two frameworks (the water–food–energynexus and ‘Appropriate Technology’), is described in four phases (problemcharacterization, solution design, solution pre-evaluation, and implementation),with the significant findings made by the team in terms of challenges, rewards, andessential conditions for development. Both deal with environment-friendly solutionsthat solve the problems of water and energy provision. Based on complex thinking,the experiences are analyzed from the social inclusion, participation, empowerment,and learning theory viewpoints. Finally, the insights gained by the team arehighlighted: communication requirements, the level of dependency of industrializedsolutions, budget constraints, training, testing, and planning recommendations, thediversity of interaction with the communities, and partners’ skills. As a result, futureactions can exploit these experiences and contribute to the success of subsequentprojects.

Pereira Pinto, Joao↗

A HPC Theory-Guided Machine Learning Cyberinfrastructure for Communicating Hydrometeorological Data Across Scales

High-resolution predictions of hydrometeorological variables are critical for supporting hydropower generation decisions and flood control at hydroelectric power plants. Traditional climate and hydrologic models rely on the numerical simulation of detailed physical processes. Therefore, running these simulations is time-, labor-, and computation-intensive. Improving the spatial and temporal resolution in these modeling outputs could lead to cubic increases in both the simulation time and computational demands, rendering high-resolution hydrometeorological predictions expensive and impractical. Many past studies apply the super resolution (SR) technique to downscale climate models using deep learners. However, deep learners are deemed “black-boxes,” as their derivation processes from low-resolution outputs to high-resolution outputs are often hidden. Their results are difficult for domain scientists to interpret and validate. Thus, there is a need for an exploratory machine learning approach that can partially integrate domain-specific theory and knowledge into the data-driven mapping process between simulation outputs of different spatial scales. The domain-specific theory and knowledge can be incorporated into the data model through an inductive approach in which process-related environmental variables are used and analyzed as key drivers (i.e., environmental surrogates) to reflect the complex physical processes. Many of these variables, such as land use land cover, soil types, topography, digital elevation, air temperature, and various watershed characteristics, can be directly measured through sensors or remote sensing techniques. Additionally, SR applications that can downscale hydrological and hydrodynamics models to efficiently produce high-resolution (1 m) flood depth grids are still rare. Since the flood depth grid can be used to support critical decisions for flood control operation at hydroelectric power plants, it is crucial to enable an SR-based capability for interpolating high-resolution flood inundation maps.

13 HYDRO ENERGY↗

Model-free estimation of completeness, uncertainties, and outliers in atomistic machine learning using information theory

Abstract An accurate description of information is relevant for a range of problems in atomistic machine learning (ML), such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.

36 MATERIALS SCIENCE↗