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Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle

Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by alternating ansätze, to obliviously transform the singular values of subsystems of unitary matrices by polynomial functions; these algorithms are numerically stable and analytically well-understood. That said, QSP/QSVT require consistent access to a single oracle, saying nothing about computing joint properties of two or more oracles; these can be far cheaper to determine given an ability to pit oracles against one another coherently. This work introduces a corresponding theory of QSP over multiple variables: M-QSP. Surprisingly, despite the non-existence of the fundamental theorem of algebra for multivariable polynomials, there exist necessary and sufficient conditions under which a desired stable multivariable polynomial transformation is possible. Moreover, the classical subroutines used by QSP protocols survive in the multivariable setting for non-obvious reasons, and remain numerically stable and efficient. Up to a well-defined conjecture, we give proof that the family of achievable multivariable transforms is as loosely constrained as could be expected. The unique ability of M-QSP to obliviously approximate joint functions of multiple variables coherently leads to novel speedups incommensurate with those of other quantum algorithms, and provides a bridge from quantum algorithms to algebraic geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Case Study: Analysis of Autonomous Center line Tracking Neural Networks

Deep neural networks have gained widespread usage in a number of applications. However, limitations such as lack of explainability and robustness inhibit building trust in their behavior, which is crucial in safety critical applications such as autonomous driving. Therefore, techniques which aid in understanding and providing guarantees for neural network behavior are the need of the hour. In this paper, we present a case study applying a recently proposed technique, Prophecy, to analyze the behavior of a neural network model, provided by our industry partner and used for autonomous guiding of airplanes on taxi runways. This regression model takes as input an image of the runway and produces two outputs, cross-track error and heading error, which represent the position of the plane relative to the center line. We use the Prophecy tool to extract neuron activation patterns for the correctness and safety properties of the model. We show the use of these patterns to identify features of the input that explain correct and incorrect behavior. We also use the patterns to provide guarantees of consistent behavior. We explore a novel idea of using sequences of images (instead of single images) to obtain good explanations and identify regions of consistent behavior.

Deep Neural Networks↗

Understanding and Verifying Neural Networks

Deep Neural Networks (DNNs) have gained immense popularity in recent times and have widespread use in applications such as image classification, sentiment analysis, speech recognition and also in safety-critical applications such as autonomous driving. However, they suffer limitations such as lack of explainability and robustness which raise safety and security concerns in their usage. Further, the complex structure and large input spaces of DNNs act as an impediment to thorough verification and testing. The SafeDNN project at the Robust Software Engineering (RSE) group at NASA aims at exploring techniques to ensure that systems that use deep neural networks are safe, robust and interpretable. In this talk, I will be presenting our technique Prophecy that automatically infers formal properties of deep neural network models. The tool extracts patterns based on neuron activations as preconditions that imply certain desirable output properties of the model. I would be highlighting case studies that use Prophecy in obtaining explanations for network decisions, understanding correct and incorrect behavior, providing formal guarantees wrt safety and robustness, and debugging neural network models. We have applied the tool on image classification networks, neural network controllers providing turn advisories in unmanned aircrafts, regression models used for autonomous center-line tracking in aircrafts and neural network object detectors

Deep Neural Networks↗

FUTURE EXPLORATION AND UTILIZATION OF OUTER SPACE

The assessment of the future of astronautics is the task of a prophet, a profession not recognized as an established branch of science. Prophecy is an art rather than a profession and there are no established methods of procedure. Knowledge of specific developments in progress and past experience give a reasonable basis for extrapolating a few years ahead. For the more distant future, imagination, intuition, and faith are the only tools, and these are inevitably colored by the nature and environment of the prophet. He may be naturally an optimist or a pessimist. The seeker for financial support and the salesman will see the future very differently than the engineer responsible for the success of launching vehicles on difficult missions. Some of the problems of predicting future developments may be appreciated by looking backward in time by 52 years.

ECHO I SATELLITE↗

Future Exploration and Utilization of Outer Space

The assessment of the future of astronautics is the task of a prophet, a profession not recognized as an established branch of science. Prophecy is an art rather than a profession and there are no established methods of procedure. Knowledge of specific developments in progress and past experience give a reasonable basis for extrapolating a few years ahead. For the more distant future, imagination, intuition, and faith are the only tools, and these are inevitably colored by the nature and environment of the prophet. He may be naturally an optimist or a pessimist. The seeker for financial support and the salesman will see the future very differently than the engineer responsible for the success of launching vehicles on difficult missions. Some of the problems of predicting future developments may be appreciated by looking backward in time by 52 years.

Dryden, H. L.↗

About an Element of Human Greatness

One of the things Dr. von Braun instinctively knew was that it was as nearly important to explain why we should go into space as to build the machines to take us there. He wrote books and magazine articles, spoke to everyone he could formally and informally, and spent his life to his dying day seeking to educate everyone on the importance of and need for spaceflight. Why should we go? I think there are actually two principle reasons: 1) Because the solar system is filled with cheap, clean energy, and we need to go get it, and, 2) this one may well be even more important, because we need a purpose for ourselves and our country. I think we need an eternal frontier to push up against, our purpose to conquer and settle it. The nice thing about doing that is the solar system is a very rich place, filled with not only mineral wealth but energy, a nearly inexhaustible supply. And if there s one thing this country and this planet desperately needs and is willing to pay for now and forever is energy. The solar system is where it is. We've got to go after it. I believe, then, that Americans have both a self-interest and a patriotic duty to convince ourselves it is time to take another giant step into space. The way to do that is to do what Dr. von Braun did, cut metal and start flying. Success engenders success. Dr. von Braun s grand dream need never die. NASA can spark a twenty-first-century revolution in transportation and energy that could fundamentally change the way we fly through space, power the world, even care for the sick if we do it right. All those things require cheap and clean energy. It exists in the solar system in a variety of forms. Solar energy is the most obvious form, but there are others, including helium-3, which may be the perfect fuel for fusion reactors, and also just happens to cover the Moon. I believe we must go after it. We just need to believe in ourselves and our purpose. I call on all of you here today to join together, get things moving again, and get serious about conquering space. If we do, we'll assure the country s prosperity, and the world s survival, too, for centuries. Along the way, maybe we ll finally understand why my old preacher thought St. Peter s comment about looking for new heavens was so important. According to His promise, it s a big challenge, a huge responsibility, to try to fulfill such a promise and prophecy.

Hickam, Homer↗

Principles of Sociology in Systems Engineering

Systems engineering involves both the integration of the system and the integration of the disciplines which develop and operate the system. Integrating the disciplines is a sociological effort to bring together different groups, often with different terminology, to achieve a common goal, the system. The focus for the systems engineer is information flow through the organization, between the disciplines, to ensure the system is developed and operated with all relevant information informing system decisions. Robert K. Merton studied the sociological principles of the sciences and the sociological principles he developed apply to systems engineering. Concepts such as specification of ignorance, common terminology, opportunity structures, role-sets, and the reclama (reconsideration) process are all important sociological approaches that should be employed by the systems engineer. In bringing the disciplines together, the systems engineer must also be wary of social ambivalence, social anomie, social dysfunction, insider-outsider behavior, unintended consequences, and the self-fulfilling prophecy. These sociological principles provide the systems engineer with key approaches to manage the information flow through the organization as the disciplines are integrated and share their information. This also helps identify key sociological barriers to information flow through the organization. This paper will discuss this theoretical basis for the application of sociological principles to systems engineering.

Watson, Michael D.↗