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Uncertainty Quantification in Working Memory via Moment Neural Networks

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arXiv 2024年

作者： Ma, Hengyuan Lu, Wenlian Feng, Jianfeng Institute of Science and Technology for Brain-inspired Intelligence Fudan University Shanghai200433 China Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence Fudan University Ministry of Education China School of Mathematical Sciences Fudan University No. 220 Handan Road Shanghai200433 China Shanghai Center for Mathematical Sciences No. 220 Handan Road Shanghai200433 China Shanghai Key Laboratory for Contemporary Applied Mathematics No. 220 Handan Road Shanghai200433 China Key Laboratory of Mathematics for Nonlinear Science No. 220 Handan Road Shanghai200433 China Department of Computer Science University of Warwick CoventryCV4 7AL United Kingdom

Humans possess a finely tuned sense of uncertainty that helps anticipate potential errors, vital for adaptive behavior and survival. However, the underlying neural mechanisms remain unclear. This study applies moment neural networks (MNNs) to explore the neural mechanism of uncertainty quantification in working memory (WM). The MNN captures nonlinear coupling of the first two moments in spiking neural networks (SNNs), identifying firing covariance as a key indicator of uncertainty in encoded information. Trained on a WM task, the model demonstrates coding precision and uncertainty quantification comparable to human performance. Analysis reveals a link between the probabilistic and sampling-based coding for uncertainty representation. Transferring the MNN’s weights to an SNN replicates these results. Furthermore, the study provides testable predictions demonstrating how noise and heterogeneity enhance WM performance, highlighting their beneficial role rather than being mere biological byproducts. These findings offer insights into how the brain effectively manages uncertainty with exceptional accuracy. © 2024, CC BY.

关键词： Neural networks

Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the 2s − 3s or 2s − 4s transition in hydrogen

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arXiv 2023年

作者： Li, Jiguang Derevianko, Andrei Elliott, D.S. Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Physics University of Nevada RenoNV89557 United States Department of Physics and Astronomy Purdue University West LafayetteIN47907 United States School of Electrical and Computer Engineering Purdue University West LafayetteIN47907 United States Purdue Quantum Science and Engineering Institute Purdue University West LafayetteIN47907 United States

We explore the feasibility of extracting electroweak observables from a measurement of atomic parity violation in hydrogen. Our proposed quantum-control scheme focuses on the 2s−3s or 2s−4s transitions in hydrogen. This work is motivated by the recently observed anomaly in the W-boson mass, which may substantially modify the Standard Model value of the proton weak charge. We also study the accuracy of the previously employed approximations in computing parity-violating effects in hydrogen. © 2023, CC BY.

关键词： Hydrogen

Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs

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arXiv 2023年

作者： Balewski, Jan Amankwah, Mercy G. Van Beeumen, Roel Bethel, E. Wes Perciano, Talita Camps, Daan National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Mathematics Case Western Reserve University ClevelandOH United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Computer Science Department San Francisco State University San FranciscoCA United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States

Compact quantum data representations are essential to the emerging field of quantum algorithms for data analysis. We introduce two new data encoding schemes, QCrank and QBArt, which have a high degree of quantum parallelism through uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits, allowing for high storage density. QBArt directly embeds a binary representation of the data in the computational basis, requiring fewer quantum measurements and lending itself to well-understood arithmetic operations on binary data. We present several applications of the proposed encodings for different types of data. We demonstrate quantum algorithms for DNA pattern matching, Hamming weight calculation, complex value conjugation, and retrieving an O(400) bits image, all executed on the Quantinuum QPU. Finally, we use various cloud-accessible QPUs, including IBMQ and IonQ, to perform additional benchmarking experiments. Copyright © 2023, The Authors. All rights reserved.

关键词： Digital storage

RL Perceptron: Generalization Dynamics of Policy Learning in High Dimensions

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Physical Review X 2025年第2期15卷 021051-021051页

作者： Nishil Patel Sebastian Lee Stefano Sarao Mannelli Sebastian Goldt Andrew Saxe Gatsby Computational Neuroscience Unit University College London Gower Street London WC1E 6BT United Kingdom Imperial College London Exhibition Road South Kensington London SW7 2AZ United Kingdom Data Science and AI Computer Science and Engineering Chalmers University of Technology and University of Gothenburg Gothenburg Sweden School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa International School of Advanced Studies (SISSA) Via Bonomea 265 34136 Trieste Italy Sainsbury Wellcome Centre University College London 25 Howland Street London W1T 4JG United Kingdom

Reinforcement learning (RL) algorithms have transformed many domains of machine learning. To tackle real-world problems, RL often relies on neural networks to learn policies directly from pixels or other high-dimensional sensory input. By contrast, many theories of RL have focused on discrete state spaces or worst-case analysis, and fundamental questions remain about the dynamics of policy learning in high-dimensional settings. Here, we propose a solvable high-dimensional RL model that can capture a variety of learning protocols, and we derive its typical policy learning dynamics as a set of closed-form ordinary differential equations. We obtain optimal schedules for the learning rates and task difficulty—analogous to annealing schemes and curricula during training in RL—and show that the model exhibits rich behavior, including delayed learning under sparse rewards, a variety of learning regimes depending on reward baselines, and a speed-accuracy trade-off driven by reward stringency. Experiments on variants of the Procgen game “Bossfight” and Arcade Learning Environment game “Pong” also show such a speed-accuracy trade-off in practice. Together, these results take a step toward closing the gap between theory and practice in high-dimensional RL.

关键词： Differential equations

PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems

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arXiv 2023年

作者： Mao, Shunyuan Dong, Ruobing Lu, Lu Yi, Kwang Moo Wang, Sifan Perdikaris, Paris Department of Physics and Astronomy University of Victoria VictoriaBCV8P 5C2 Canada Department of Chemical and Biomolecular Engineering University of Pennsylvania PhiladelphiaPA19104 United States Department of Computer Science University of British Columbia VancouverBCV6T 1Z4 Canada Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk-planet interactions in protoplanetary disks in real-time. We base our tool on Deep Operator Networks (DeepONets), a class of neural networks capable of learning non-linear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk-planet system - the Shakura & Sunyaev viscosity α, the disk aspect ratio h0, and the planet-star mass ratio q - to steady-state solutions of the disk surface density, radial velocity, and azimuthal velocity. We demonstrate the accuracy of the PPDONet solutions using a comprehensive set of tests. Our tool is able to predict the outcome of disk-planet interaction for one system in less than a second on a laptop. A public implementation of PPDONet is available at https://***/smao-astro/PPDONet. Copyright © 2023, The Authors. All rights reserved.

关键词： Open source software

Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

Quantum Computing: Vision and Challenges

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arXiv 2024年

作者： Gill, Sukhpal Singh Cetinkaya, Oktay Marrone, Stefano Claudino, Daniel Haunschild, David Schlote, Leon Wu, Huaming Ottaviani, Carlo Liu, Xiaoyuan Machupalli, Sree Pragna Kaur, Kamalpreet Arora, Priyansh Liu, Ji Farouk, Ahmed Song, Houbing Herbert Uhlig, Steve Ramamohanarao, Kotagiri School of Electronic Engineering and Computer Science Queen Mary University of London London United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Dipartimento di Matematica e Fisica Università della Campania "Luigi Vanvitelli" Italy Quantum Information Science Section Oak Ridge National Laboratory Oak RidgeTN United States Detecon International GmbH Munich Germany DB Cargo Berlin Germany Center for Applied Mathematics Tianjin University Tianjin China Department of Computer Science York Centre for Quantum Technologies University of York York United Kingdom Fujitsu Research of America Inc. Santa ClaraCA United States Information Networking Institute Carnegie Mellon University United States Cymax Group Technologies BC Canada Microsoft Schiphol Netherlands Mathematics and Computational Research Division Argonne National Laboratory IL United States Department of Computer Science Faculty of Computers and Artificial Intelligence South Valley University Hurghada Egypt Baltimore United States The University of Melbourne VIC Australia

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many complex problems that cannot be solved otherwise with conventional computing methods. These problems include modeling quantum mechanics, logistics, chemical-based advances, drug design, statistical science, sustainable energy, banking, reliable communication, and quantum chemical engineering. The last few years have witnessed remarkable progress in quantum software and algorithm creation and quantum hardware research, which has significantly advanced the prospect of realizing quantum computers. It would be helpful to have comprehensive literature research on this area to grasp the current status and find outstanding problems that require considerable attention from the research community working in the quantum computing industry. To better understand quantum computing, this paper examines the foundations and vision based on current research in this area. We discuss cutting-edge developments in quantum computer hardware advancement and subsequent advances in quantum cryptography, quantum software, and high-scalability quantum computers. Many potential challenges and exciting new trends for quantum technology research and development are highlighted in this paper for a broader debate. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum computers

Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems

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arXiv 2025年

作者： Scherbela, Michael Gao, Nicholas Grohs, Philipp Günnemann, Stephan Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 ViennaA-1090 Austria Department of Computer Science Munich Data Science Institute Technical University of Munich Germany Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstrasse 69 Linz4040 Austria

We present finite-range embeddings (FiRE), a novel wave function ansatz for accurate large-scale ab-initio electronic structure calculations. Compared to contemporary neural-network wave functions, FiRE reduces the asymptotic complexity of neural-network variational Monte Carlo (NN-VMC) by ∼ nel, the number of electrons. By restricting electron-electron interactions within the neural network, FiRE accelerates all key operations – sampling, pseudopotentials, and Laplacian computations – resulting in a real-world 10× acceleration in now-feasible 180-electron calculations. We validate our method’s accuracy on various challenging systems, including biochemical compounds, conjugated hydrocarbons, and organometallic compounds. On these systems, FiRE’s energies are consistently within chemical accuracy of the most reliable data, including experiments, even in cases where high-accuracy methods such as CCSD(T), AFQMC, or contemporary NN-VMC fall short. With these improvements in both runtime and accuracy, FiRE represents a new ‘gold-standard’ method for fast and accurate large-scale ab-initio calculations, potentially enabling new computational studies in fields like quantum chemistry, solid-state physics, and material design. Copyright © 2025, The Authors. All rights reserved.

关键词： Organometallics

Rejoinder: Gaussian differential privacy

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arXiv 2021年

作者： Dong, Jinshuo Roth, Aaron Su, Weijie J. Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Computer and Information Sciences University of Pennsylvania United States Department of Statistics The Wharton School University of Pennsylvania United States

We warmly thank Editor Paul Smith for selecting our paper for discussion and are extremely grateful to all the discussants for taking their valuable time to provide engaging and stimulating feedback on our work. These insights situate our work in context and provide promising directions for future research. We are excited to see that thoughts about theoretical complements and new applications are already emerging. A general view, shared by all discussants, is that privacy is a first-order concern in many data science problems. We are very pleased to learn that our statistics community welcomes new foundational development and methodological contributions that allow for privacy protections in statistical data analysis. In this rejoinder, we aim to address two broad issues that cover most comments made in the discussion. First, we discuss some theoretical aspects of our work and comment on how this work might impact the theoretical foundation of privacy-preserving data analysis. Taking a practical viewpoint, we next discuss how f-differential privacy (f-DP) and Gaussian differential privacy (GDP) can make a difference in a range of applications. © 2021, CC BY.

关键词： Privacy-preserving techniques