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arXiv 2023年

作者： de Oliveira, Arthur Castello Branco Siami, Milad Sontag, Eduardo D. Department of Electrical & Computer Engineering Northeastern University BostonMA02115 United States Departments of Bioengineering Northeastern University BostonMA02115 United States

— Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models – contrary to classical statistical belief. This phenomenon, sometimes known as "benign overfitting", raises questions regarding in what other ways might overparameterization affect the properties of a learning problem. In this work, we investigate the effects of overfitting on the robustness of gradient-descent training when subject to uncertainty on the gradient estimation. This uncertainty arises naturally if the gradient is estimated from noisy data or directly measured. Our object of study is a linear neural network with a single, arbitrarily wide, hidden layer and an arbitrary number of inputs and outputs. In this paper we solve the problem for the case where the input and output of our neural-network are one-dimensional, deriving sufficient conditions for robustness of our system based on necessary and sufficient conditions for convergence in the undisturbed case. We then show that the general overparametrized formulation introduces a set of spurious equilibria which lay outside the set where the loss function is minimized, and discuss directions of future work that might extend our current results for more general formulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

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Why should autoencoders work?

arXiv

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arXiv 2023年

作者： Kvalheim, Matthew D. Sontag, Eduardo D. Department of Mathematics and Statistics University of Maryland Baltimore CountyMD United States Departments of Electrical and Computer Engineering Bioengineering Northeastern University BostonMA United States

Deep neural network autoencoders are routinely used computationally for model reduction. They allow recognizing the intrinsic dimension of data that lie in a k-dimensional subset K of an input Euclidean space Rn. The underlying idea is to obtain both an encoding layer that maps Rn into Rk (called the bottleneck layer or the space of latent variables) and a decoding layer that maps Rk back into Rn, in such a way that the input data from the set K is recovered when composing the two maps. This is achieved by adjusting parameters (weights) in the network to minimize the discrepancy between the input and the reconstructed output. Since neural networks (with continuous activation functions) compute continuous maps, the existence of a network that achieves perfect reconstruction would imply that K is homeomorphic to a k-dimensional subset of Rk, so clearly there are topological obstructions to finding such a network. On the other hand, in practice the technique is found to "work" well, which leads one to ask if there is a way to explain this effectiveness. We show that, up to small errors, indeed the method is guaranteed to work. This is done by appealing to certain facts from differential topology. A computational example is also included to illustrate the ideas. Copyright © 2023, The Authors. All rights reserved.

关键词： Deep neural networks

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Sensor and Actuator Scheduling in Bilinear Dynamical Networks

Sensor and Actuator Scheduling in Bilinear Dynamical Network...

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IEEE Conference on Decision and Control

作者： Arthur Castello B. De Oliveira Milad Siami Eduardo D. Sontag Department of Electrical & Computer Engineering Northeastern University Boston MA USA Departments of Bioengineering Northeastern University Boston MA USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

In this paper, we investigate the problem of finding a sparse sensor and actuator (S/A) schedule that minimizes the approximation error between the input-output behavior of the fully sensed/actuated bilinear system and the system with the scheduling. The quality of this approximation is measured by an ℋ 2 -like metric, which is defined for a bilinear (time-varying) system with S/A scheduling based on the discrete Laplace transform of its Volterra kernels. First, we discuss the difficulties of designing S/A schedules for bilinear systems, which prevented us from finding a polynomial time algorithm for solving the problem. We then propose a polynomial-time S/A scheduling heuristic that selects a fraction of sensors and node actuators at each time step while maintaining a small approximation error between the input-output behavior of the fully sensed/actuated system and the one with S/A scheduling in this ℋ 2 -based sense. Numerical experiments illustrate the good approximation quality of our proposed methods.

关键词： Actuators Schedules Dynamic scheduling Approximation error Approximation algorithms Complexity theory Behavioral sciences

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Corrigendum to “Remarks on input to state stability of perturbed gradient flows, motivated by model-free feedback control learning” [Syst. Control Lett. 161 (2022) 105138]

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Systems & Control Letters 2024年 194卷

作者： Eduardo D. Sontag Bioengineering and Electrical and Computer Engineering Departments Northeastern University Boston MA USA

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Automating Knowledge-Driven Model Recommendation: Methodology, Evaluation, and Key Challenges

arXiv

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arXiv 2023年

作者： Butchy, Adam A. Telmer, Cheryl A. Miskov-Zivanov, Natasa The Department of Bioengineering University of Pittsburgh PittsburghPA15213 United States The Department of Biological Sciences Carnegie Mellon University PittsburghPA15213 United States The Departments of Electrical and Computer Engineering Bioengineering and Computational Biology University of Pittsburgh PittsburghPA15213 United States

There is significant interest in using existing repositories of biological entities, relationships, and models to automate biological model assembly and extension. Current methods aggregate human-curated biological information into executable, simulatable models, but these models do not resemble human curated models and do not recapitulate experimental results. Here, we outline the process of automated model assembly and extension, while demonstrating it on both synthetic models and human-curated models of biological signaling networks. We begin with an iterative, greedy, and combinatoric approach to automated assembly and demonstrate the key difficulties inherent to contextless assembly. We publicly release the software used in this paper to enable further exploration of this problem. Copyright © 2023, The Authors. All rights reserved.

关键词： Iterative methods

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Achieving BSREM image quality at the speed of OSEM reconstruction using the cGAN framework

Achieving BSREM image quality at the speed of OSEM reconstru...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： S. Nazari Farsani J. Fisher J. R. Kim M. Jafaritadi C. S. Levin Department of Radiology Stanford University Stanford California United States of America Department of Electrical Engineering Stanford University Stanford California United States of America Department of Computer Science Stanford University Stanford California United States of America Departments of Radiology Physics Electrical Engineering and Bioengineering Stanford University Stanford California United States of America

Positron emission tomography (PET) is an imaging method for cancer, heart disease, and neurological disorders. PET images are reconstructed from emitted positron data using complex mathematical algorithms, among which ordered subset algorithms, including ordered subset expectation maximization (OSEM) and block sequential regularized expectation maximization (BSREM), are commonly employed. OSEM provides faster image reconstruction but with higher noise, while BSREM offers improved image quality, and reduced noise, albeit at the cost of increased computational complexity. To improve the accuracy and quality of OSEM-reconstructed brain PET images while maintaining time efficiency, we utilized a generative adversarial network (GAN) to enhance OSEM images to a level of quality and accuracy comparable to that of images generated by the BSREM algorithm. We collected 18 FDG PET scans from Alzheimer’s disease patients, which were preprocessed into a list-mode format and reconstructed using OSEM with 2 iterations and 2 subsets, and BSREM with 25 iterations. We trained a cGAN model, consisting of a U-net generator and a discriminator that received OSEM-reconstructed PET images as input, BSREM images as the target, and generated higher quality and accuracy PET images as output. Results were evaluated using PSNR, SSIM, and NRMSE. Using the cGAN model, we improved the SNR and contrast of the OSEM-reconstructed PET images with a 17% enhancement in the PSNR and a 60% decrease in the NRMSE, although the SSIM was not significantly improved. Our findings show that the GAN model can convert low-SNR, low-contrast OSEM images to high-quality, high-accuracy images similar to those generated by the BSREM algorithm. This approach offers potential advantages in achieving the image quality and accuracy of BSREM with the shorter reconstruction time of OSEM.

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Identifying Steady State in the Network Dynamics of Spiking Neural Networks

SSRN

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SSRN 2022年

作者： George, Vivek Kurien Gupta, Arkin Silva, Gabriel A. Department of Bioengineering University of California La Jolla San DiegoCA92037 United States Department of Computer and Electrical Engineering University of California San Diego United States Departments of Bioengineering and Neurosciences University of California San Diego United States

Analysis of the dynamics of complex networks can provide valuable information. For example, the dynamics can be used to characterize and differentiate between different network inputs and configurations. However, without quantitatively delineating the network’s dynamic regimes, analysis of the network’s dynamics is based on heuristics and qualitative signatures of transient or steady-state regimes. This is not ideal because interesting phenomena can occur during the transient regime, steady-state regime, or at the transition between the two dynamic regimes. Moreover, for simulated and observed systems, precise knowledge of the network’s dynamical regime is imperative when considering metrics on minimal mathematical descriptions of the dynamics, otherwise either too much or too little data is analyzed. Here, we develop quantitative methods to ascertain the starting point and period of steady-state network activity. Using the precise knowledge of the network’s dynamic regimes, we build minimal representations of the network dynamics that form the basis for future work. We show applications of our techniques on idealized signals, on the dynamics of a biologically inspired spiking neural network, and on a wide class of deterministic complex networks. © 2022, The Authors. All rights reserved.

关键词： Complex networks

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Study of ASIC Readout Used for Detectors in an MR Compatible, RF-Penetrable TOF-PET Insert

Study of ASIC Readout Used for Detectors in an MR Compatible...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： Qian Dong Salar Sajedi Ilaria Sacco Peter Fischer Craig S. Levin Departments of Electrical Engineering and Radiology Stanford University Stanford CA USA Departments of Radiology Stanford University Stanford CA USA Department of Computer Science Heidelberg University Baden-Württemberg Germany Department of Radiology Electrical Engineering Bioengineering and Physics Stanford University Molecular Imaging Program at Stanford (MIPS) Stanford CA USA

Developing positron emission tomography (PET) systems with high channel number has driven the need for application-specific integrated circuits (ASICs) owing to their compactness, multi-channel readout capability, and excellent time and energy resolution performance. They can also be quite flexible by employing field-programmable gate arrays (FPGAs) in the readout circuit. In particular, the ASIC+FPGA approach provides a high performance and compact solution for TOF-PET applications. ASICs serve functions of extracting time and energy information from analog SiPM signals, and an FPGA is employed for other application-specific requirements like on-board chip configuration, communication with data acquisition (DAQ) systems, and system monitoring. Based on this foundation, we developed TOF-capable detector modules for our second generation RF-penetrable PET insert. During our previous experiments, we found that different trigger and readout methods lead to different noise pattern and intensity in MR environment, and also have different singles count loss ratio. This paper aims to study and compare different readout configurations for our MR-compatible detectors. We studied four trigger and readout methods: hit-standard, frequent-standard, hit-bypass, and frequent-bypass, and compared their singles count loss ratios with both theoretical models and experimental results. For all four methods, the theoretical results matched the experimental results well. The two methods which used bypass mode performed better than those using the standard mode approach. With the most optimized trigger and readout method (hit-bypass), we achieved 1.2% singles count loss ratio at a 20 kcps count rate per channel.

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Global linearization of asymptotically stable systems without hyperbolicity

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Systems & Control Letters 2025年 203卷

作者： Matthew D. Kvalheim Eduardo D. Sontag Department of Mathematics and Statistics University of Maryland Baltimore County MD USA Departments of Electrical and Computer Engineering and Bioengineering and affiliate of Departments of Mathematics and Chemical Engineering Northeastern University Boston MA USA

We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjugacy is (i) defined on the entire basin of attraction if the vector field is complete, and (ii) a C k ≥ 1 -diffeomorphism on the complement of the equilibrium if the vector field is C k and the underlying space is not 5-dimensional. We also show that the C k statement in the 5-dimensional case is equivalent to the 4-dimensional smooth Poincaré conjecture.

关键词： Linearization Hartman-Grobman theorem

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High-Fidelity Micro- and Nano-Scale Infrared Spectroscopic Imaging

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 562-562页

作者： Bhargava, Rohit Yeh, Kevin Kenkel, Seth Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign Urbana IL United States Departments of Bioengineering Chemical and Biomolecular Engineering Electrical and Computer Engineering Mechanical Science and Engineering University of Illinois at Urbana-Champaign Urbana IL United States Cancer Center at Illinois University of Illinois at Urbana- Champaign Urbana IL United States

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