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Inverse problems are solvable on real number signal processing hardware

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 2025年 74卷

作者： Boche, Holger Fono, Adalbert Kutyniok, Gitta Tech Univ Munich Inst Theoret Informat Technol TUM Sch Computat Informat & Technol Munich Germany Munich Ctr Quantum Sci & Technol MCQST Munich Germany Munich Quantum Valley MQV Munich Germany BMBF Res Hub 6G Life Dresden Germany Ludwig Maximilians Univ Munchen Dept Math Munich Germany Univ Tromso Dept Phys & Technol Tromso Norway Munich Ctr Machine Learning MCML Munich Germany DRL German Aerosp Ctr Inst Robot & Mechatron Tubingen Germany

Despite the success of Deep Learning (DL) serious reliability issues such as non-robustness persist. An interesting aspect is, whether these problems arise due to insufficient tools or fundamental limitations of DL. We study this question from the computability perspective by characterizing the limits the applied hardware imposes. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. On digital hardware, a conceptual barrier on the capabilities of DL for solving finite-dimensional inverse problems has in fact already been derived. This paper investigates the general computation framework of Blum-Shub-Smale (BSS) machines, describing the processing and storage of arbitrary real values. Although a corresponding real-world computing device does not exist, research and development towards real number computing hardware, usually referred to by "neuromorphic computing", has increased in recent years. In this work, we show that the framework of BSS machines does enable the algorithmic solvability of finite dimensional inverse problems. Our results emphasize the influence of the considered computing model in questions of accuracy and reliability.

关键词： Inverse problems Deep learning computing theory BSS machines

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Limitations of Deep Learning for Inverse Problems on Digital Hardware

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IEEE TRANSACTIONS ON INFORMATION theory 2023年第12期69卷 7887-7908页

作者： Boche, Holger Fono, Adalbert Kutyniok, Gitta Tech Univ Munich Inst Theoret Informat Technol D-80333 Munich Germany Ruhr Univ Bochum BMBF Res Hub 6G Life Excellence Cluster Cyber Secu D-44801 Bochum Germany Munich Ctr Quantum Sci & Technol MCQST D-80799 Munich Germany Munich Quantum Valley MQV D-80807 Munich Germany Ludwig Maximilians Univ Munchen Dept Math D-80539 Munich Germany Ludwig Maximilians Univ Munchen Dept Math D-80539 Munich Germany Munich Ctr Machine Learning MCML D-80538 Munich Germany

Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. Even more, our results introduce a lower bound on the accuracy that can be obtained algorithmically.

关键词： Neural networks Computational modeling Hardware Inverse problems Deep learning Approximation algorithms Task analysis computing theory deep learning signal processing turing machine

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Teach More, Not Less Computability theory in CS202X A Case for Teaching Multiple Representations of the Church-Turing Thesis 2022

Teach More, Not Less Computability Theory in CS202X A Case f...

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53rd Annual ACM SIGCSE Technical Symposium on Computer Science Education (SIGCSE)

作者： Blumenthal, Richard Regis Univ Denver Denver CO USA

ISBN: (纸本)9781450390705

This paper posits that the Algorithms and Complexity (AL) knowledge area in the Computer Science Curricular 2013 report contains several "flaws" concerning the teaching of computability theory that should be corrected in the upcoming CS202X curricular report. These flaws undermine the understanding and appreciation of computability theory that computer science graduates are expected to have. Specifically, it is argued that two of these flaws contribute to a theoretical knowledge gap in a significant percentage of CS graduates and a third contributes to a missed pedagogical opportunity to increase a graduate's understanding and appreciation of computability and the Church-Turing thesis. Evidence for the impact of these flaws is based on an existing survey of Bachelor of Science in Computer Science (BSCS) programs and a new study presented in this paper of required computation theory courses in five-hundred BSCS programs. Proposed resolutions to these flaws are presented as simple curricular changes for CS202X and the introduction of a two-tiered course unit, which utilizes a multiple external representation pedagogy to teach multiple models of computability and the Church-Turing thesis. This unit is derived from experience with using this approach in a Computation theory course.

关键词： computer science curricula computing theory computational models multiple representations computing pedagogy

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A Novel Parallel Processing Element Architecture for Accelerating ODE and AI

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TSINGHUA SCIENCE AND TECHNOLOGY 2025年第5期30卷 1954-1964页

作者： Yang, Kaiyuan Liu, Longchao Liu, Haotian Deng, Tiantai Univ Sheffield Dept Elect & Elect Engn Sheffield S13JD England

Transforming complex problems, such as transforming ordinary differential equations (ODEs) into matrix formats, into simpler computational tasks is key for AI advancements and paves the way for more efficient computing architectures. Systolic Arrays, known for their computational efficiency, low power use and ease of implementation, address AI's computational challenges. They are central to mainstream industry AI accelerators, with improvements to the Processing Element (PE) significantly boosting systolic array performance, and also streamlines computing architectures, paving the way for more efficient solutions in technology fields. This research presents a novel PE design and its integration of systolic array based on a novel computing theory - bit-level mathematics for Multiply-Accumulate (MAC) operation. We present 3 different architectures for the PE and provide a comprehensive comparison between them and the state-of-the-art technologies, focusing on power, area, and throughput. This research also demonstrates the integration of the proposed MAC unit design with systolic arrays, highlighting significant improvements in computational efficiency. Our implementations show a 2380952.38 times lower latency, yet 64.19 times less DSP48E1, 1.26 times less Look-Up Tables (LUTs), 10.76 times less Flip-Flops (FFs), with 99.63 times less power consumption and 15.19 times higher performance per PE compared to the state-of-the-art design.

关键词： Power demand AI accelerators Computer architecture Throughput Systolic arrays Computational efficiency Table lookup Sparse matrices Resource management Low latency communication arallel MAC Unit Processing Element (PE) FPGA implementation computing theory

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Mathematical Foundation of Cognitive computing Based Artificial Intelligence 5th

Mathematical Foundation of Cognitive Computing Based Artific...

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5th RAAI Summer School on Artificial Intelligence

作者： Gergely, Tamas Ury, Laszlo Appl Log Lab Budapest Hungary

ISBN: (纸本)9783030332747;9783030332730

Today Cognitive computing and Artificial Intelligence (AI) face the same challenges namely, simulate human thought processes and mimic the way human brain works. The main difference between Cognitive computing and AI is: (i) AI models various functions of human intelligence, where computer is one of the modelling means though often the most important one, i.e. intelligence is in the focus while (ii) Cognitive computing models human thought processes and simulates the hypothetical way human brain works as computation. Our aim is to develop a theoretically and methodologically well-founded theory of AI together with a unified computational theory, which will provide specific tools and methods for Cognitive computing. To achieve our goal we follow a methodology triangle, consisting of a conceptual-philosophical, a system theoretical and a logical-mathematical component. computing will play a fundamental role in both system-theoretical and logical-mathematical methodological components. Hereby we concentrate on the development of the logical-mathematical foundation in detail by the use of category theory, which provides an excellent frame for defining all notions necessary for developing a universal theory for computing, specification, cognitive reasoning, information, knowledge and their various combinations. Foundation theory is by the use of the so-called constitutions, the mathematical basis for the cognitive computation. Logical foundation will be developed as a special constitution and cognitive computing processes are defined by using situations, infons and information. The main properties are discussed with some examples.

关键词： Categorical theoretical foundation Cognitive computing Specification theory Cognitive reasoning computing theory Logic programming

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A computing theory for collaborative and transparent decision making under time constraint

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INFORMATION SYSTEMS FRONTIERS 2011年第2期13卷 207-220页

作者： Sasaki, Hideyasu Ritsumeikan Univ Dept Informat Sci & Engn Shiga 5250045 Japan

In this paper, we present a computing theory on the accelerated critical point of selection of proper strategies between collaboration and competition and its mathematical analysis for collaborative and transparent decision making under "time constraint", i.e., cost of time pressure, which decision makers face in negotiation. Web 2.0 provides a useful digital environment to support various time-stressed human behaviors for collaborative decision making. However, little research has examined the collaborative behavior under time constraint on the Internet in its designs and implementations on electronically supported decision making. Those systems are implemented in black boxes so that we need transparent designs of decision support systems to promote collaboration by time-stressed decision makers. The essential problem on collaborative decision making under time constraint is the discovery and evaluation on the critical point of selection of proper strategies between collaboration and competition. Most of the current decision support systems accept the half of maximum acceptable time for negotiation as a critical point, a priori, though that conventional point is often late for proper decision making. The proposed theory shows that a critical point is to be accelerated at the one-third of maximum acceptable time for negotiation. We have formulated the proposed computing theory based on mathematical formulation, and checked its feasibility in its applications to a case study. The proposed theory promotes collaborative and transparent decision making in consideration of the properties of stakes under time pressure by selecting the strategy of collaboration or competition at the much earlier stage.

关键词： computing theory Collaboration Transparency Decision making Time constraint Mathematical formulation

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Antonio Monteiro: a pioneer of theoretical computational studies in Argentina

Antonio Monteiro: a pioneer of theoretical computational stu...

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38th Latin America Conference on Informatics (CLEI)

作者： Carnota, Raul Rodriguez, Ricardo Proyecto SAMCA Salvando Memoria Computac Argentin Buenos Aires DF Argentina UBA Fac Ciencias Exactas & Nat Dept Computac Buenos Aires DF Argentina

ISBN: (纸本)9781467307932;9781467307949

The well known portuguese mathematician Antonio Monteiro (1907-1980), founder of the prestigious mathematics school at the National University of the South (UNS), actively manifested his interest in computation beginning in the late 1950s. This interest, directed primarily at theoretical aspects, also manifested itself in an attempt to create a new focus amongst mathematicians as well as seeking support for technological projects. Nevertheless, his efforts to establish a top notch computation center at UNS were not realized and to this day remain unappreciated. In light of new documents and testimonies it is clear that Monteiro was a pioneer in the development of theoretical computational studies in Argentina, where he sought to develop the field and encourage students to make their careers in it. The reticence to recognize this role can be interpreted as a conflict in models for the development of computer science. We also propose a multicausal explanation for the failure of this particular academic endeavor.

关键词： component Antonio Monteiro computing theory Bahia Blanca Argentina Latin America computing History Informatics History Universidad Nacional del Sur Bernard Vauquois

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computing theory with relevance 04

Computing theory with relevance

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Conference on Australasian computing Education

作者： Wayne Brookes University of Technology Sydney NSW

In computer science education, the topic of computing theory is one that is commonly not well received by students. Career-oriented students often view the topic as irrelevant, and would rather learn new skills and technologies that they perceive will improve their future employment prospects. This paper outlines an approach that attempts to blend these two apparent extremes by using "popular" technologies, including XML, to motivate and illustrate concepts of computing theory in a first-year undergraduate computing subject.

关键词： computing theory computer science education extensible markup language Students theories

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