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Exploring biologically inspired mechanisms of adversarial robustness

Neural computing and Applications 2025年 1-12页

作者： Holzhausen, Konstantin Merlid, Mia Torvik, Håkon Olav Malthe-Sørenssen, Anders Lepperød, Mikkel Elle Department of Physics University of Oslo Sem Sælands vei 24 Fysikkbygningen Oslo0371 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway

Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike artificial models, biological neurons adjust connectivity based on neighboring cell activity. Understanding the biological mechanisms of robustness can pave the way toward building trustworthy and safe systems. Robustness in neural representations is hypothesized to correlate with the smoothness of the encoding manifold. Recent work suggests power law covariance spectra, which were observed studying the primary visual cortex of mice, to be indicative of a balanced trade-off between accuracy and robustness in representations. Here, we show that unsupervised local learning models with winner takes all dynamics learn such power law representations, providing upcoming studies a mechanistic model with that characteristic. Our research aims to understand the interplay between geometry, spectral properties, robustness, and expressivity in neural representations. Hence, we study the link between representation smoothness and spectrum by using weight, Jacobian and spectral regularization while assessing performance and adversarial robustness. Our work serves as a foundation for future research into the mechanisms underlying power law spectra and optimally smooth encodings in both biological and artificial systems. The insights gained may elucidate the mechanisms that realize robust neural networks in mammalian brains and inform the development of more stable and reliable artificial systems. © The Author(s) 2025.

关键词： Generative adversarial networks

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Modeling stochastic eye tracking data: A comparison of quantum generative adversarial networks and Markov models

Modeling stochastic eye tracking data: A comparison of quant...

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2024 Genetic and Evolutionary Computation Conference Companion, GECCO 2024 Companion

作者： Bhandari, Shailendra Lencastre, Pedro Lind, Pedro Department of Computer Science OsloMet - Oslo Metropolitan University OsloN-0130 Norway Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo0164 Norway

ISBN: (纸本)9798400704956

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics. © 2024 is held by the owner/author(s).

关键词： Generative adversarial networks

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Correction: Exploring biologically inspired mechanisms of adversarial robustness(Neural computing and Applications, 10.1007/s00521-025-11019-6)

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Neural computing and Applications 2025年 1-2页

In this article, panel (b) of Fig. 6 was inadvertently printed in black and white instead of colour;the figure should have appeared as shown below. (Figure presented.) Norm of the Jacobian of latent activations h^ (upper panel) and decision landscape (lower panel) of studied models. Similarly to [12], the displayed planes are created by grid sampling from a random plane projection in the model’s input space The original article has been corrected. © The Author(s) 2025.

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Learning Place Cell Representations and Context-Dependent Remapping 38

Learning Place Cell Representations and Context-Dependent Re...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Pettersen, Markus Rogge, Frederik Lepperød, Mikkel Elle Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Kristian Augusts Gate 23 Oslo Norway Department of Biosciences University of Oslo Blinderveien 31 Oslo Norway

Hippocampal place cells are known for their spatially selective firing patterns, which has led to the suggestion that they encode an animal's location. However, place cells also respond to contextual cues, such as smell. Furthermore, they have the ability to remap, wherein the firing fields and rates of cells change in response to changes in the environment. How place cell responses emerge, and how these representations remap is not fully understood. İn this work, we propose a similarity-based objective function that translates proximity in space, to proximity in representation. We show that a neural network trained to minimize the proposed objective learns place-like representations. We also show that the proposed objective is easily extended to include other sources of information, such as context information, in the same way. When trained to encode multiple contexts, networks learn distinct representations, exhibiting remapping behaviors between contexts. The proposed objective is invariant to orthogonal transformations. Such transformations of the original trained representation (e.g. rotationsİ, therefore yield new representations distinct from the original, without explicit relearning, akin to remapping. Our findings shed new light on the formation and encoding properties of place cells, and also demonstrate an interesting case of representational reuse. © 2024 Neural information processing systems foundation. All rights reserved.

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SCALABLE APPROXIMATION AND SOLVERS FOR IONIC ELECTRODIFFUSION IN CELLULAR GEOMETRIES

arXiv

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arXiv 2024年

作者： Benedusi, Pietro Ellingsrud, Ada J. Herlyng, Halvor Rognes, Marie E. Department for Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

The activity and dynamics of excitable cells are fundamentally regulated and moderated by extracellular and intracellular ion concentrations and their electric potentials. The increasing availability of dense reconstructions of excitable tissue at extreme geometric detail pose a new and clear scientific computing challenge for computational modelling of ion dynamics and transport. In this paper, we design, develop and evaluate a scalable numerical algorithm for solving the time-dependent and nonlinear KNP-EMI equations describing ionic electrodiffusion for excitable cells with an explicit geometric representation of intracellular and extracellular compartments and interior interfaces. We also introduce and specify a set of model scenarios of increasing complexity suitable for benchmarking. Our solution strategy is based on an implicit-explicit discretization and linearization in time, a mixed finite element discretization of ion concentrations and electric potentials in intracellular and extracellular domains, and an algebraic multigrid-based, inexact block-diagonal preconditioner for GMRES. numerical experiments with up to 108 unknowns per time step and up to 256 cores demonstrate that this solution strategy is robust and scalable with respect to the problem size, time discretization and number of *** Codes 65F10, 65N30, 65N55, 68U20, 68W10, 92-08, 92C20 © 2024, CC BY-SA.

关键词： Electric potential

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A SPLITTING, DISCONTINUOUS GALERKIN SOLVER FOR THE CELL-BY-CELL ELECTRONEUTRAL NERNST-PLANCK FRAMEWORK

arXiv

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arXiv 2024年

作者： Ellingsrud, Ada J. Kuchta, Miroslav Department for Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

Mathematical models for excitable tissue with explicit representation of individual cells are highly detailed and can, unlike classical homogenized models, represent complex cellular geometries and local membrane variations. However, these cell-based models are challenging to approximate numerically, partly due to their mixed-dimensional nature with unknowns both in the bulk and at the lower-dimensional cellular membranes. We here develop and evaluate a novel solution strategy for the cell-based KNP-EMI model describing ionic electrodiffusion in and between intra- and extracellular compartments with explicit representation of individual cells. The strategy is based on operator splitting, a multiplier-free formulation of the coupled dynamics across sub-regions, and a discontinuous Galerkin discretization. In addition to desirable theoretical properties, such as local mass conservation, the scheme is practical as it requires no specialized functionality in the finite element assembly and order optimal solvers for the resulting linear systems can be realized with black-box algebraic multigrid preconditioners. numerical investigations show that the proposed solution strategy is accurate, robust with respect to discretization parameters, and that the parallel scalability of the solver is close to optimal – both for idealized and realistic two and three dimensional *** Codes 65M60, 65F10, 65M55, 68U20, 92-08, 92C37 © 2024, CC BY.

关键词： Linear systems

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Stability of step size control based on a posteriori error estimates

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Computational Science and Engineering 2024年第1期1卷 1-23页

作者： Ranocha, Hendrik Giesselmann, Jan Institute of Mathematics Johannes Gutenberg University Mainz Mainz Germany Numerical Analysis and Scientific Computing Technical University of Darmstadt Darmstadt Germany

A posteriori error estimates based on residuals can be used for reliable error control of numerical methods. Here, we consider them in the context of ordinary differential equations and Runge-Kutta methods. In particular, we take the approach of Dedner & Giesselmann (2016) and investigate it when used to select the time step size. We focus on step size control stability when combined with explicit Runge-Kutta methods and demonstrate that a standard I controller is unstable while more advanced PI and PID controllers can be designed to be stable. We compare the stability properties of residual-based estimators and classical error estimators based on an embedded Runge-Kutta method both analytically and in numerical experiments.

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THE MODELLING ERROR IN MULTI-DIMENSIONAL TIME-DEPENDENT SOLUTE TRANSPORT MODELS

arXiv

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arXiv 2023年

作者： Masri, Rami Zeinhofer, Marius Kuchta, Miroslav Rognes, Marie E. Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Norway

Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations under suitable assumptions on the domain velocity. Moreover, we quantify the associated modelling errors by establishing a-priori estimates in evolving Bochner spaces. In particular, we show that the modelling error decreases with the characteristic vessel diameter and thus vanishes for infinitely slender vessels. numerical tests in idealized geometries corroborate and extend upon our theoretical *** Codes 35K45, 65G99, 65J08, 65M15, 92-10 © 2023, CC BY-NC-SA.

关键词： Solute transport

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Regularity for Diffusion Equations with Non-smooth Data

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Results in Mathematics 2023年第4期78卷 1-22页

作者： Dondl, Patrick Zeinhofer, Marius Department of Applied Mathematics University of Freiburg Freiburg im Breisgau Germany Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway

We prove an $$L^p(I,C^\alpha (\Omega ))$$ regularity result for a diffusion equation with mixed boundary conditions, $$L^\infty $$ coefficients and an $$L^{ q }$$ initial condition. We provide explicit control of the $$L^p(I,C^\alpha (\Omega ))$$ norm with respect to the data. To prove our result, we first establish $$C^\alpha (\Omega )$$ control of the stationary equation, extending a result by Haller-Dintelmann et al. (Appl Math Optim 60(3):397–428, 2009).

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From low-rank retractions to dynamical low-rank approximation and back

arXiv

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arXiv 2023年

作者： Séguin, Axel Ceruti, Gianluca Kressner, Daniel Institute of Mathematics LausanneCH-1015 Switzerland University of Innsbruck Numerical Analysis and Scientific Computing Innsbruck Austria

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds. This is closely related to dynamical low-rank approximation (DLRA) techniques. In fact, any retraction leads to a numerical integrator and, vice versa, certain DLRA techniques bear a direct relation with retractions. As an example for the latter, we introduce a new retraction, called KLS retraction, that is derived from the so-called unconventional integrator for DLRA. We also illustrate how retractions can be used to recover known DLRA techniques and to design new ones. In particular, this work introduces two novel numerical integration schemes that apply to differential equations on general manifolds: the accelerated forward Euler (AFE) method and the Projected Ralston–Hermite (PRH) method. Both methods build on retractions by using them as a tool for approximating curves on manifolds. The two methods are proven to have local truncation error of order three. numerical experiments on classical DLRA examples highlight the advantages and shortcomings of these new *** Codes 65L05, 65L29 Copyright © 2023, The Authors. All rights reserved.

关键词： Differential equations

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