ARTICLE Communicated by Terrence Sejnowski Face Representations via Tensorfaces of Various Complexities Sidney R. Lehky sidney.lehky@riken.jp Cognitive Brain Mapping Laboratory, RIKEN Center for Brain Science, Wako-shi, Saitama 351-0198, Japan, and Computational Neurobiology Laboratory, Salk Institute, La Jolla, Californie 92037, U.S.A. Anh Huy Phan a.phan@skoltech.ru Center for Computational and Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology, 143026 Moscow, Russia; and Institute of Global

LETTER Communicated by Nakul Verma Safe Triplet Screening for Distance Metric Learning Tomoki Yoshida yoshida.t.mllab.nit@gmail.com Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan Ichiro Takeuchi takeuchi.ichiro@nitech.ac.jp Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, 466-8555, Japan; National Institute for Materials Science, Sengen, Tsukuba, Ibaraki, 305-0047, Japan; and RIKEN Center for Advanced Intelligence Project, Nihonbashi, Chuo-ku, Tokyo, 103-0012, Japan Masayuki Karasuyama karasuyama@nitech.ac.jp Nagoya Institute

ARTICLE Communicated by Simon Shaolei Du Every Local Minimum Value Is the Global Minimum Value of Induced Model in Nonconvex Machine Learning Kenji Kawaguchi kawaguch@mit.edu MIT, Cambridge, MA 02139, U.S.A. Jiaoyang Huang jiaoyang@math.harvard.edu Harvard University, Cambridge, MA 02138, U.S.A. Leslie Pack Kaelbling lpk@csail.mit.edu MIT, Cambridge, MA 02139, U.S.A. For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal

ARTICLE Communicated by Christopher Buckley A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition Ahmadreza Ahmadi ar.ahmadi62@gmail.com Okinawa Institute of Science and Technology, Okinawa, Japan 904-0495, and School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea Jun Tani* tani1216jp@gmail.com Okinawa Institute of Science and Technology, Okinawa, Japan 904-0495 This study introduces PV-RNN, a novel variational RNN

LETTER Communicated by Karl Friston A Minimum Free Energy Model of Motor Learning B. UN. Mitchell brian_a_mitchell@engineering.ucsb.edu Department of Computer Science, Université de Californie, Santa Barbara, Santa Barbara, Californie 931056, U.S.A. N. Lauharatanahirun nina.lauharatanahirun.civ@mail.mil Human Research and Engineering Directorate, The CCDC Army Research Laboratory, Aberdeen Proving Ground, MARYLAND 21005, USA., and Annenberg School for Communication, University of Pennsylvania, Philadelphia, Pennsylvanie 19104, U.S.A. J.. Ô. Garcia

LETTER Communicated by Razvan Pascanu Effect of Depth and Width on Local Minima in Deep Learning Kenji Kawaguchi kawaguch@mit.edu MIT, Cambridge, MA 02139, U.S.A. Jiaoyang Huang jiaoyang@math.harvard.edu Harvard University, Cambridge, MA 02138, U.S.A. Leslie Pack Kaelbling lpk@csail.mit.edu MIT, Cambridge, MA 02139, U.S.A. In this paper, we analyze the effects of depth and width on the quality of local minima, without strong overparameterization and simplification assumptions

LETTER Communicated by Hugo G. Schnack Brain Morphometry Methods for Feature Extraction in Random Subspace Ensemble Neural Network Classification of First-Episode Schizophrenia Roman Vyškovský vyskovsky@iba.muni.cz Daniel Schwarz schwarz@iba.muni.cz Masaryk University, Faculty of Medicine, Institute of Biostatistics and Analyses, 625 00, Brno, Czech Republic Tomáš Kašpárek tkasparek@fnbrno.cz Masaryk University and University Hospital Brno, Département de psychiatrie, 625 00, Brno, Czech Republic Machine learning (ML) is a

LETTER Communicated by Karl Friston Systems of Bounded Rational Agents with Information-Theoretic Constraints Sebastian Gottwald sebastian.gottwald@uni-ulm.de Daniel A. Braun daniel.braun@uni-ulm.de Institute of Neural Information Processing, Faculty of Engineering, Computer Science and Psychology, University of Ulm, Ulm, Baden-Württemberg, 89081 Germany Specialization and hierarchical organization are important features of efficient collaboration in economical, artificial, and biological systems. Ici, we investigate the hypothesis that both features can be

ARTICLE Communicated by Anne Steinemann Diplomats’ Mystery Illness and Pulsed Radiofrequency/Microwave Radiation Beatrice Alexandra Golomb bgolomb@ucsd.edu UC San Diego School of Medicine, La Jolla, Californie 92093, U.S.A. Importance: A mystery illness striking U.S. and Canadian diplomats to Cuba (and now China) “has confounded the FBI, the State Department and US intelligence agencies” (Lederman, Weissenstein, & Lee, 2017). Sonic explanations for the so-called health attacks have

LETTER Communicated by Mark Van Rossum CosMIC: A Consistent Metric for Spike Inference from Calcium Imaging Stephanie Reynolds stephanie.reynolds09@imperial.ac.uk Department of Electrical and Electronic Engineering and Centre for Neurotechnology, Imperial College London, London SW7 2AZ, ROYAUME-UNI. Therese Abrahamsson therese.abrahamsson@gmail.com Per Jesper Sjöström jesper.sjostrom@mcgill.ca Centre for Research in Neuroscience, Brain Repair and Integrative Neuroscience Program, Department of Neurology and Neurosurgery, Research Institute of the McGill University

ARTICLE Communicated by Jeremy Manning The Discrete and Continuous Brain: From Decisions to Movement—And Back Again Thomas Parr thomas.parr.12@ucl.ac.uk Karl J. Friston k.friston@ucl.ac.uk Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, WC1N 3BG, ROYAUME-UNI. To act upon the world, creatures must change continuous variables such as muscle length or chemical concentration. In contrast, decision making is an inherently discrete process, involving the

LETTER Communicated by Alexander Schwing Deep Restricted Kernel Machines Using Conjugate Feature Duality Johan A. K. Suykens johan.suykens@esat.kuleuven.be KU Leuven ESAT-STADIUS, B-3001 Leuven, Belgium The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel ma- chines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are

LETTER Communicated by Yoshua Bengio An Approximation of the Error Backpropagation Algorithm in a Predictive Coding Network with Local Hebbian Synaptic Plasticity James C. R.. Whittington james.whittington@ndcn.ox.ac.uk MRC Brain Network Dynamics Unit, University of Oxford, Oxford, OX1 3TH, U.K., and FMRIB Centre, Nuffield Department of Clinical Neurosciences, University of Oxford, John Radcliffe Hospital, Oxford, OX3 9DU, ROYAUME-UNI. Rafal Bogacz rafal.bogacz@ndcn.ox.ac.uk MRC Brain Network Dynamics Unit,

LETTER Communicated by Mika Rubinov Comparison of Different Generalizations of Clustering Coefficient and Local Efficiency for Weighted Undirected Graphs Yu Wang Eshwar Ghumare eshwargorakhnath.ghumare@kuleuven.be Laboratory for Cognitive Neurology, Department of Neurosciences, KU Leuven, Leuven 3000, Belgium Rik Vandenberghe rik.vandenberghe@uzleuven.be Laboratory for Cognitive Neurology, Department of Neurosciences, KU Leuven, Leuven 3000, Belgium, and Alzheimer Research Centre, KU Leuven, Leuven Institute for Neuroscience and Disease, KU Leuven,

LETTER Communicated by Jurgen Schmidhuber Continuous Online Sequence Learning with an Unsupervised Neural Network Model Yuwei Cui ycui@numenta.com Subutai Ahmad sahmad@numenta.com Jeff Hawkins jhawkins@numenta.com Numenta, Inc. Redwood City, Californie 94063, U.S.A. The ability to recognize and predict temporal sequences of sensory in- puts is vital for survival in natural environments. Based on many known properties of cortical neurons, hierarchical temporal memory (HTM) avec- quence memory

LETTER Communicated by Peter K ¨onig Integrator or Coincidence Detector: A Novel Measure Based on the Discrete Reverse Correlation to Determine a Neuron’s Operational Mode Jacob Kanev jkanev@zoho.com Institute of Software Engineering and Theoretical Computer Science, Technische Universit¨at Berlin, Berlin 10587, Germany Achilleas Koutsou achilleas.k@cs.ucy.ac.cy Chris Christodoulou cchrist@cs.ucy.a.cy Department of Computer Science, University of Cyprus, 1678 Nicosia, Cyprus Klaus Obermayer klaus.obermayer@mailbox.tu-berlin.de Institute of Software Engineering

LETTER Communicated by Eric Halgren Effect of Reference Scheme on Power and Phase of the Local Field Potential Vinay Shirhatti vinay@cns.iisc.ernet.in Ayon Borthakur borthakur.ayon@gmail.com Supratim Ray sray@cns.iisc.ernet.in Centre for Neuroscience, Indian Institute of Science, Bangalore, India, 560012 Brain signals are often analyzed in the spectral domain, where the power spectral density (PSD) and phase differences and consistency can reveal important information about the network. Cependant,

LETTER Communicated by S. Sathiya Keerthi Accuracy and Efficiency in Fixed-Point Neural ODE Solvers Michael Hopkins michael.hopkins@manchester.ac.uk Steve Furber steve.furber@manchester.ac.uk School of Computer Science, APT Group, University of Manchester, Manchester M13 9PL, ROYAUME-UNI. Simulation of neural behavior on digital architectures often requires the solution of ordinary differential equations (ODEs) at each step of the simulation. For some neural models, this is a significant computational burden,