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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Trainability of ReLU networks and Data-dependent Initialization

Here, in this paper, we study the trainability of rectified linear unit (ReLU) networks at initialization. A ReLU neuron is said to be dead if it only outputs a constant for any input. Two death states of neurons are introduced–tentative and permanent death. A network is then said to be trainable if the number of permanently dead neurons is sufficiently small for a learning task. We refer to the probability of a randomly initialized network being trainable as trainability. We show that a network being trainable is a necessary condition for successful training, and the trainability serves as an upper bound of training success rates. In order to quantify the trainability, we study the probability distribution of the number of active neurons at initialization. In many applications, overspecified or overparameterized neural networks are successfully employed and shown to be trained effectively. With the notion of trainability, we show that overparameterization is both a necessary and a sufficient condition for achieving a zero training loss. Furthermore, we propose a data-dependent initialization method in an overparameterized setting. Numerical examples are provided to demonstrate the effectiveness of the method and our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Subtleties in the trainability of quantum machine learning models

A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called quantum machine learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called variational quantum algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work, we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we call dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer’s output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed. Here our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Investigating parameter trainability in the SNAP-displacement protocol of a qudit system

Here, in this study, we explore the universality of Selective Number-dependent Arbitrary Phase (SNAP) and Displacement gates for quantum control in qudit-based systems. However, optimizing the parameters of these gates poses a challenging task. Our main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. We analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz we consider consists of blocks, where each block is composed of hardware operations, namely SNAP and Displacement gates [Fösel et al 2020 Efficient cavity control with snap gates arXiv:2004.14256]. Applying Variational Quantum algorithm (VQA) with observable and gate cost functions, we utilize techniques similar to those in [McClean et al 2018 Barren plateaus in quantum neural network training landscapes Nat. Commun.9 1–6] and [Cerezo et al 2021 Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun.12 1–12] along with the concept of t − design. Through this analysis, we make the following key observations: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) By leveraging the first and second moments properties of Haar measures, we establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, we identify a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Investigating parameter trainability in the SNAP-Displacement protocol of a qudit system.

Our main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. We analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz we consider consists of SNAP -Displacement blocks. We utilize techniques similar to those in [8] and [2] along with the concept of $t-$design. Through this analysis, we make the following key observations: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) using Haar measure properties, we establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, we identify a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Arbitrary Polynomial Separations in Trainable Quantum Machine Learning

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.

Anschuetz, Eric R. [California Institute of Techno↗
NASA NTRS1995

Trainable Cataloging for Digital Image Libraries with Applications to Volcano Detection

Users of digital image libraries are often not interested in image data per se but in derived products such as catalogs of objects of interest. Converting an image database into a usable catalog is typically carried out manually at present. For many larger image databases the purely manual approach is completely impractical. In this paper we describe the development of a trainable cataloging system: the user indicates the location of the objects of interest for a number of training images and the system learns to detect and catalog these objects in the rest of the database. In particular we describe the application of this system to the cataloging of small volcanoes in radar images of Venus. The volcano problem is of interest because of the scale (30,000 images, order of 1 million detectable volcanoes), technical difficulty (the variability of the volcanoes in appearance) and the scientific importance of the problem. The problem of uncertain or subjective ground truth is of fundamental importance in cataloging problems of this nature and is discussed in some detail. Experimental results are presented which quantify and compare the detection performance of the system relative to human detection performance. The paper concludes by discussing the limitations of the proposed system and the lessons learned of general relevance to the development of digital image libraries.

digital image libraries, trainable cataloging↗
DOE OSTI2021

Efficient Trainability of Linear Optical Modules in Quantum Optical Neural Networks

The existence of “barren plateau landscapes” for generic discrete-variable quantum neural networks, which obstructs efficient gradient-based optimization of cost functions defined by global measurements, would be surprising in the case of generic linear optical modules in quantum optical neural networks due to the tunability of the intensity of continuous variable states and the relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light in m modes can be generically compiled efficiently if the total intensity scales sublinearly with m, and extend this result to cost functions based on homodyne, heterodyne, or photon detection measurement statistics, and to noisy cost functions in the presence of attenuation. Here, we further demonstrate efficient trainability of m mode linear optical quantum circuits for variational mean field energy estimation of positive quadratic Hamiltonians for input states that do not have energy exponentially vanishing with m.

47 OTHER INSTRUMENTATION↗
NASA NTRS2000

Trainable Gene Regulation Networks with Applications to Drosophila Pattern Formation

This chapter will very briefly introduce and review some computational experiments in using trainable gene regulation network models to simulate and understand selected episodes in the development of the fruit fly, Drosophila melanogaster. For details the reader is referred to the papers introduced below. It will then introduce a new gene regulation network model which can describe promoter-level substructure in gene regulation. As described in chapter 2, gene regulation may be thought of as a combination of cis-acting regulation by the extended promoter of a gene (including all regulatory sequences) by way of the transcription complex, and of trans-acting regulation by the transcription factor products of other genes. If we simplify the cis-action by using a phenomenological model which can be tuned to data, such as a unit or other small portion of an artificial neural network, then the full transacting interaction between multiple genes during development can be modelled as a larger network which can again be tuned or trained to data. The larger network will in general need to have recurrent (feedback) connections since at least some real gene regulation networks do. This is the basic modeling approach taken, which describes how a set of recurrent neural networks can be used as a modeling language for multiple developmental processes including gene regulation within a single cell, cell-cell communication, and cell division. Such network models have been called "gene circuits", "gene regulation networks", or "genetic regulatory networks", sometimes without distinguishing the models from the actual modeled systems.

Mjolsness, Eric↗
DOE OSTI2021

An end-to-end trainable hybrid classical-quantum classifier

Abstract We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according to the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

A new generation of intelligent trainable tools for analyzing large scientific image databases

The focus of this paper is on the detection of natural, as opposed to human-made, objects. The distinction is important because, in the context of image analysis, natural objects tend to possess much greater variability in appearance than human-made objects. Hence, we shall focus primarily on the use of algorithms that 'learn by example' as the basis for image exploration. The 'learn by example' approach is potentially more generally applicable compared to model-based vision methods since domain scientists find it relatively easier to provide examples of what they are searching for versus describing a model.

Fayyad, Usama M.↗
NASA NTRS1994

A New Generation of Intelligent Trainable Tools for Analyzing Large Scientific Image Databases

In a variety of scientific disciplines two-dimensional digital image data is now relied on as a basic component of routine scientific investigation. The proliferation of image acquisition hardware such as multi-spectral remote-sensing platforms, medical imaging sensors, and high-resolution cameras have led to the widespread use of image data in fields such as atmospheric studies, planetary geology, ecology, agriculture, glacielogy, forestry, astronomy, diagnostic medicine, to name but a few.

machine↗
DOE OSTI2026

Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al ., npj Quantum Inf. 10 , 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. Here, in this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.

Algebraic structures↗