ARTICLE Communicated by Ruoyu Sun Critical Point-Finding Methods Reveal Gradient-Flat Regions of Deep Network Losses Charles G. Frye cfrye59@gmail.com Redwood Center for Theoretical Neuroscience and Helen Wills Neuroscience Institute, Universität von Kalifornien, Berkeley, CA 94720, USA. James Simon james.simon@berkeley.edu Redwood Center for Theoretical Neuroscience and Department of Physics, Universität von Kalifornien, Berkeley, CA 94720, USA. Neha S. Wadia neha.wadia@berkeley.edu Andrew Ligeralde ligeralde@berkeley.edu Redwood Center for

ARTICLE Communicated by Shun-ichi Amari On the Achievability of Blind Source Separation for High-Dimensional Nonlinear Source Mixtures Takuya Isomura takuya.isomura@riken.jp Laboratory for Neural Computation and Adaptation and Brain Intelligence Theory Unit, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan Taro Toyoizumi taro.toyoizumi@riken.jp Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan, and Department of Mathematical Informatics, Graduate School

ARTICLE Communicated by Stefano Panzeri The Refractory Period Matters: Unifying Mechanisms of Macroscopic Brain Waves Corey Weistuch corey.weistuch@stonybrook.edu Laufer Center for Physical and Quantitative Biology and Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, USA. Lilianne R. Mujica-Parodi lilianne.strey@stonybrook.edu Laufer Center for Physical and Quantitative Biology, Departments of Biomedical Engineering and of Physics and Astronomy, Program in Neuroscience, and Department

LETTER Communicated by Raoul-Martin Memmesheimer The Remarkable Robustness of Surrogate Gradient Learning for Instilling Complex Function in Spiking Neural Networks Friedemann Zenke friedemann.zenke@fmi.ch Centre for Neural Circuits and Behaviour, Universität Oxford, Oxford OX1 3SR, VEREINIGTES KÖNIGREICH., and Friedrich Miescher Institute for Biomedical Research, 4058 Basel, Switzerland Tim P. Vogels tim.vogels@ist.ac.at Centre for Neural Circuits and Behaviour, Universität Oxford, Oxford OX1 3SR, VEREINIGTES KÖNIGREICH., and Institute

LETTER Communicated by Terrence Sejnowski Whence the Expected Free Energy? Beren Millidge beren@millidge.name School of Informatics, University of Edinburgh, Edinburgh, EH8 9AB, VEREINIGTES KÖNIGREICH. Alexander Tschantz tschantz.alec@gmail.com Sackler Center for Consciousness Science, School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1 9RH, VEREINIGTES KÖNIGREICH. Christopher L. Buckley C.L.Buckley@sussex.ac.uk Evolutionary and Adaptive Systems Research Group, School of Engineering and Informatics, University of Sussex, Falmer, Brighton, BN1

ARTICLE Communicated by Alain Destexhe From Biophysical to Integrate-and-Fire Modeling Tomas Van Pottelbergh tmjv2@cam.ac.uk Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, VEREINIGTES KÖNIGREICH. Guillaume Drion gdrion@ulg.ac.be Department of Electrical Engineering and Computer Science, University of Liège, 4000 Liège, Belgium Rodolphe Sepulchre r.sepulchre@eng.cam.ac.uk Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, VEREINIGTES KÖNIGREICH. This article proposes a methodology to extract a low-dimensional integrate-and-fire model from

ARTICLE Communicated by Dirk Ostwald Learning in Volatile Environments With the Bayes Factor Surprise Vasiliki Liakoni* vasiliki.liakoni@epfl.ch Alireza Modirshanechi* alireza.modirshanechi@epfl.ch Wulfram Gerstner wulfram.gerstner@epfl.ch Johanni Brea johanni.brea@epfl.ch École Polytechnique Fédérale de Lausanne, School of Computer and Communication Sciences and School of Life Sciences, 1015 Lausanne, Switzerland Surprise-based learning allows agents to rapidly adapt to nonstationary stochastic environments characterized by sudden changes. We show that exact Bayesian

LETTER Communicated by Ian Robertson Deeply Felt Affect: The Emergence of Valence in Deep Active Inference Casper Hesp* c.hesp@uva.nl Department of Psychology and Amsterdam Brain and Cognition Centre, University of Amsterdam, 1098 XH Amsterdam, Niederlande; Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, Niederlande; and Wellcome Centre for Human Neuroimaging, University College London, London WC1N 3BG, VEREINIGTES KÖNIGREICH. Ryan Smith* RSmith@laureateinstitute.org Laureate Institute for

ARTICLE Communicated by Terrence Sejnowski A Cerebellar Computational Mechanism for Delay Conditioning at Precise Time Intervals Terence D. Sanger terry@sangerlab.net Departments of Biomedical Engineering, Neurologie, and Biokinesiology, Universität von Südkalifornien, Los Angeles, CA 90089, USA. Mitsuo Kawato kawato@atr.jp Brain Information Communication Research Laboratory Group, Advanced Telecommunications Research Institutes International, Kyoto 619-0288, Japan, and Center for Advanced Intelligence Project, RIKEN, Chuo-ku, Tokio, 103-0027, Japan The

LETTER Communicated by Justin Dauwels Reverse-Engineering Neural Networks to Characterize Their Cost Functions Takuya Isomura takuya.isomura@riken.jp Brain Intelligence Theory Unit, RIKEN Center for Brain Science, Wako, Saitama 351-0198, Japan Karl Friston k.friston@ucl.ac.uk Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London, WC1N 3AR, VEREINIGTES KÖNIGREICH. This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function

ARTICLE Communicated by Igor Goychuk Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics Shusen Pu sxp600@case.edu Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA. Peter J. Thomas pjthomas@case.edu Department of Mathematics, Applied Mathematics, and Statistics; Biology; Cognitive Science; and Electrical, Computer, and Systems Engineering: Case Western Reserve University, Cleveland, OH 44106, USA. Fox and Lu introduced a

ARTICLE Communicated by Diego Pazò A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation Richard Gast rgast@cbs.mpg.de Helmut Schmidt hschmidt@cbs.mpg.de Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Germany Thomas R. Knösche knoesche@cbs.mpg.de Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Deutschland, and Institute for Biomedical Engineering and Informatics, TU 98693 Ilmenau, Germany Bursting plays

ARTICLE Communicated by Tilo Schwalger Inference of a Mesoscopic Population Model from Population Spike Trains Alexandre René arene010@uottawa.ca Department of Physics, University of Ottawa, Ottawa K1N 6N5, Kanada; Max Planck Research Group Neural Systems Analysis, Center of Advanced European Studies and Research (caesar), Bonn 53175, Deutschland; and Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA-Institute Brain Structure-Function Relationships (INM-10),

ARTICLE Communicated by Ruben Moreno-Bote Heterogeneous Synaptic Weighting Improves Neural Coding in the Presence of Common Noise Pratik S. Sachdeva pratik.sachdeva@berkeley.edu Redwood Center for Theoretical Neuroscience and Department of Physics, Universität von Kalifornien, Berkeley, Berkeley, CA 94720 USA., and Biological Systems and Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Jesse A. Livezey jlivezey@lbl.gov Redwood Center for Theoretical Neuroscience, Universität von Kalifornien, Berkeley,

ARTICLE Communicated by Luca Mazzucato Nonequilibrium Statistical Mechanics of Continuous Attractors Weishun Zhong wszhong@mit.edu James Franck Institute, Universität von Chicago, Chicago, IL 60637, and Department of Physics, MIT, Cambridge, MA 02139, USA. Zhiyue Lu zhiyuelu@unc.edu James Franck Institute, Universität von Chicago, Chicago, IL 60637, USA. David J. Schwab dschwab@gc.cuny.edu Initiative for the Theoretical Sciences, CUNY Graduate Center, New York, New York 10016, and Center for the

ARTICLE Communicated by Shun-ichi Amari Center Manifold Analysis of Plateau Phenomena Caused by Degeneration of Three-Layer Perceptron Daiji Tsutsui d-tsutsui@cr.math.sci.osaka-u.ac.jp Osaka University, Toyonaka-shi, Osaka 560-0043, Japan A hierarchical neural network usually has many singular regions in the parameter space due to the degeneration of hidden units. Hier, we fo- cus on a three-layer perceptron, which has one-dimensional singular regions comprising both attractive and repulsive parts.

ARTICLE Communicated by Terrence Sejnowski Hidden Aspects of the Research ADOS Are Bound to Affect Autism Science Elizabeth B. Torres ebtorres@psych.rutgers.edu Psychology Department; Computer Science, Center for Biomedical Imagining and Modeling; and Rutgers University Center for Cognitive Science, Rutgers University, Piscataway, NJ 08854, USA. Richa Rai richarai9@gmail.com Psychology Department, Rutgers University, Piscataway, NJ 08854, USA. Sejal Mistry sejal.mistry@hsc.utah.edu Mathematics Department, Rutgers University, Piscataway, NJ 08854,

LETTER Communicated by Frederic Crevecoeur Model-Free Robust Optimal Feedback Mechanisms of Biological Motor Control Tao Bian tbian@nyu.edu Control and Networks Lab, Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Brooklyn, New York 11201, USA. Daniel M. Wolpert wolpert@columbia.edu Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, New York 10027, USA., and Department of Engineering, University of Cambridge, Cambridge