Relevant bibliographies by topics / Infinite-width limit

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  1. Journal articles
  2. Dissertations / Theses
  3. Conference papers
  4. Reports

Academic literature on the topic 'Infinite-width limit'

Author: Grafiati
Published: 7 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Infinite-width limit"

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Bahri, Yasaman, Boris Hanin, Antonin Brossollet, et al. "Les Houches lectures on deep learning at large and infinite width*." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 10 (2024): 104012. http://dx.doi.org/10.1088/1742-5468/ad2dd3.

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Abstract These lectures, presented at the 2022 Les Houches Summer School on Statistical Physics and Machine Learning, focus on the infinite-width limit and large-width regime of deep neural networks. Topics covered include the various statistical and dynamical properties of these networks. In particular, the lecturers discuss properties of random deep neural networks, connections between trained deep neural networks, linear models, kernels and Gaussian processes that arise in the infinite-width limit, and perturbative and non-perturbative treatments of large but finite-width networks, at initi
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Pastur, L. "Eigenvalue distribution of large random matrices arising in deep neural networks: Orthogonal case." Journal of Mathematical Physics 63, no. 6 (2022): 063505. http://dx.doi.org/10.1063/5.0085204.

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This paper deals with the distribution of singular values of the input–output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent weight matrices alternate with diagonal matrices whose entries depend on the corresponding column of the nearest neighbor weight matrix. The problem has been considered in the several recent studies of the field for the Gaussian weights and biases and also for the weights that are Haar distributed orthogonal matrices and Gaussian biases. Based on a free probability argu
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Pacelli, R., S. Ariosto, M. Pastore, F. Ginelli, M. Gherardi, and P. Rotondo. "A statistical mechanics framework for Bayesian deep neural networks beyond the infinite-width limit." Nature Machine Intelligence 5, no. 12 (2023): 1497–507. http://dx.doi.org/10.1038/s42256-023-00767-6.

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Thorkildsen, Gunnar, and Helge B. Larsen. "X-ray diffraction in perfect t × l crystals. Rocking curves." Acta Crystallographica Section A Foundations of Crystallography 55, no. 5 (1999): 840–54. http://dx.doi.org/10.1107/s0108767399002986.

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A general formalism, based on the Takagi–Taupin equations, for calculating rocking curves in perfect t\times l crystals is presented. It includes nonsymmetrical scattering, refraction, and ordinary and anomalous absorption. t and l may be varied independently. In the limit of a semi-infinite crystal, the standard results from the fundamental theory are retrieved. For crystal dimensions less than the extinction length, the theory converges to the kinematical limit. Simulations for germanium and silicon show significant influence of crystal finiteness. When dynamical effects are prominent, the c
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Karr, D. G., J. C. Watson, and M. HooFatt. "Three-Dimensional Analysis of Ice Sheet Indentation: Limit Analysis Solutions." Journal of Offshore Mechanics and Arctic Engineering 111, no. 1 (1989): 63–69. http://dx.doi.org/10.1115/1.3257141.

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A method is presented for determining the collapse pressures of an ice sheet subjected to a uniformly distributed edge load by applying the upper-bound theorem of limit analysis. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. A quadratic anisotropic yield criterion is used to calculate the indentation pressures. The ice sheet consists of columnar ice and is assumed isotropic in the plane of the ice sheet. Upper-bound solutions are found by optimizing a three-dimensional discontinuous velocity field representing an assumed collapse pattern of the ice
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Landa, Haggai, Cecilia Cormick, and Giovanna Morigi. "Static Kinks in Chains of Interacting Atoms." Condensed Matter 5, no. 2 (2020): 35. http://dx.doi.org/10.3390/condmat5020035.

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We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1 . The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but
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AKHMEDIEV, N., J. M. SOTO-CRESPO, M. GRAPINET, and Ph GRELU. "DISSIPATIVE SOLITON PULSATIONS WITH PERIODS BEYOND THE LASER CAVITY ROUND TRIP TIME." Journal of Nonlinear Optical Physics & Materials 14, no. 02 (2005): 177–94. http://dx.doi.org/10.1142/s0218863505002645.

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We review recent results on periodic pulsations of the soliton parameters in a passively mode-locked fiber laser. Solitons change their shape, amplitude, width and velocity periodically in time. These pulsations are limit cycles of a dissipative nonlinear system in an infinite-dimensional phase space. Pulsation periods can vary from a few to hundreds of round trips. We present a continuous model of a laser as well as a model with parameter management. The results of the modeling are supported with experimental results obtained using a fiber laser.
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Bordelon, Blake, and Cengiz Pehlevan. "Dynamics of finite width Kernel and prediction fluctuations in mean field neural networks*." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 10 (2024): 104021. http://dx.doi.org/10.1088/1742-5468/ad642b.

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Abstract We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O ( 1 / width ) fluctuations of the dynamical mean field theory order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. We find that once the mean field/µP parameterization is adopted, the le
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Wang, Xu, Faning Dang, Xiaoshan Cao, Le Zhang, Jun Gao, and Haibin Xue. "Solution for Active and Passive Earth Pressure on Rigid Retaining Walls with Narrow Backfill." Applied Sciences 15, no. 4 (2025): 1750. https://doi.org/10.3390/app15041750.

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For a retaining wall adjacent to rock or rigid structures, existing model test results indicate that the slip soil in the limit state can be approximated as a trapezoidal slip wedge. Based on the static equilibrium condition of the slip wedge, a calculation method for active and passive earth pressures is proposed that considers the effect of backfill width through extreme value analysis. As the backfill width increases, the trapezoidal slip wedge transitions to a triangular slip wedge, introducing a critical width to distinguish between finite and semi-infinite soil conditions. For cohesionle
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Zeng, Y., and S. Weinbaum. "Stokes flow through periodic orifices in a channel." Journal of Fluid Mechanics 263 (March 25, 1994): 207–26. http://dx.doi.org/10.1017/s0022112094004088.

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This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratio B’/d’ and spacing D’. Here B’ is the half-height of the channel and d’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution
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Dissertations / Theses on the topic "Infinite-width limit"

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Hajjar, Karl. "A dynamical analysis of infinitely wide neural networks." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM001.

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Durant la dernière décennie, les réseaux de neurones ont eu un succès retentissant dans de nombreuses tâches en pratique, cependant les arguments théoriques derrière ce succès restent insuffisants et une théorie mathématique appropriée pour étudier rigoureusement ces objets fait toujours défaut. Les limites des réseaux de neurones à largeur infinie sont récemment apparues comme une façon d'éclaircir certains aspects du problème. Dans cette thèse, nous étudions la limite des réseaux de neurones de largeur infinie avec une renormalisation particulière souvent dénommée ''champ moyen'' dans la lit
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Conference papers on the topic "Infinite-width limit"

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Osinski, Marek, Mohammad Mojahedie, and Michael W. Prairie. "Density of states in finite-barrier quantum wells." In OSA Annual Meeting. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.mz4.

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Density of states in finite-barrier quantum wells is examined critically. In the infinite barrier limit, the two-dimensional (2D) density of states (DOS) has been shown to correspond to the bulk case.1 When finite wells are considered, this correspondence may no longer hold. In this paper, we propose a modification to the finite-well DOS, which retains the elegance of the infinite-well case while preserving the effects of the finite barrier. This is accomplished by either defining an effective infinite-well width that matches the parameters of the finite well or by defining a new effective mas
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Mukoyama, Hiroshi, Shigeyuki Shimachi, and Yoshihide Hakozaki. "Contact Pressure Estimates of Tooth Surfaces of Gear Couplings." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/ptg-14452.

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Abstract Recent demands for gear couplings are to reduce the backlash and to increase the shaft angle limit. On coping with these demands, the tooth contact pressure is recognized as the trade-off problem. In the traditional estimation of tooth contact pressure, the deflection of tooth is calculated by using the formula for spur gear that has long contact bearing in the face width direction, although gear coupling has it in the tooth depth direction. And, the Hertz depression of the tooth surface is estimated as that of the infinite plane. Additionally, the traditional methods don’t consider a
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Gordon, J. L., and D. P. Jones. "Application of a Sixth Order Generalized Stress Function for Determining Limit Loads for Plates with Triangular Penetration Patterns." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1298.

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The capability to obtain limit load solutions of plates with triangular penetration patterns using fourth order functions to represent the collapse surface has been presented in previous papers. These papers describe how equivalent solid plate elastic-perfectly plastic finite element capabilities are generated and demonstrate how such capabilities can be used to great advantage in the analysis of tubesheets in large heat exchanger applications. However, these papers have pointed out that although the fourth order functions can produce sufficient accuracy for many practical applications, there
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Reports on the topic "Infinite-width limit"

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Pasupuleti, Murali Krishna. Neural Computation and Learning Theory: Expressivity, Dynamics, and Biologically Inspired AI. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv425.

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Abstract: Neural computation and learning theory provide the foundational principles for understanding how artificial and biological neural networks encode, process, and learn from data. This research explores expressivity, computational dynamics, and biologically inspired AI, focusing on theoretical expressivity limits, infinite-width neural networks, recurrent and spiking neural networks, attractor models, and synaptic plasticity. The study investigates mathematical models of function approximation, kernel methods, dynamical systems, and stability properties to assess the generalization capa
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