A neuronal device for the control of multi-step computations

We describe the operation of a neuronal device which embodies the computational principles of the `paper-and-pencil' machine envisioned by Alan Turing. The network is based on principles of cortical organization. We develop a plausible solution to implement pointers and investigate how neuronal circuits may instantiate the basic operations involved in assigning a value to a variable (i.e., x=5), in determining whether two variables have the same value and in retrieving the value of a given variable to be accessible to other nodes of the network. We exemplify the collective function of the network in simplified arithmetic and problem solving (blocks-world) tasks. Received: 14 June 2013,  Accepted: 9 July 2013;  Edited by: G. B. Mindlin;  DOI: http://dx.doi.org/10.4279/PIP.050006 Cite as: A Zylberberg, L Paz, P R Roelfsema, S Dehaene, M Sigman, Papers in Physics 5, 050006 (2013)

[1]  Philippe Pinel,et al.  Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus , 2004, Neuron.

[2]  S. Ullman.  Visual routines , 1984, Cognition.

[3]  S. Dehaene,et al.  Representation of number in the brain. , 2009, Annual review of neuroscience.

[4]  C. Gilbert,et al.  Brain States: Top-Down Influences in Sensory Processing , 2007, Neuron.

[5]  M. Shadlen,et al.  Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task , 2002, The Journal of Neuroscience.

[6]  M. Sigman,et al.  The human Turing machine: a neural framework for mental programs , 2011, Trends in Cognitive Sciences.

[7]  C. Gilbert,et al.  The Neural Basis of Perceptual Learning , 2001, Neuron.

[8]  Michael L. Platt,et al.  Neural correlates of decision variables in parietal cortex , 1999, Nature.

[9]  F. Hamker.  The role of feedback connections in task-driven visual search , 1999 .

[10]  T. Wiesel,et al.  Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis , 1986, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[11]  George Sperling,et al.  The information available in brief visual presentations. , 1960 .

[12]  Takeo Watanabe,et al.  Perceptual learning rules based on reinforcers and attention , 2010, Trends in Cognitive Sciences.

[13]  V. Lamme,et al.  The distinct modes of vision offered by feedforward and recurrent processing , 2000, Trends in Neurosciences.

[14]  Timothy D. Hanks,et al.  Neurobiology of decision making: An intentional framework , 2008 .

[15]  S. Thorpe,et al.  Speed of processing in the human visual system , 1996, Nature.

[16]  A. Newell.  Unified Theories of Cognition , 1990 .

[17]  R. O’Reilly.  Biologically Based Computational Models of High-Level Cognition , 2006, Science.

[18]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[19]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[20]  Pieter R. Roelfsema,et al.  Neurally Plausible Reinforcement Learning of Working Memory Tasks , 2012, NIPS.

[21]  Puiu F. Balan,et al.  Attention as a decision in information space , 2010, Trends in Cognitive Sciences.

[22]  Stanislas Dehaene,et al.  Development of Elementary Numerical Abilities: A Neuronal Model , 1993, Journal of Cognitive Neuroscience.

[23]  M. Tsodyks,et al.  Synaptic Theory of Working Memory , 2008, Science.

[24]  Mariano Sigman,et al.  Frontiers in Computational Neuroscience Computational Neuroscience Neurophysiological Bases of Exponential Sensory Decay and Top-down Memory Retrieval: a Model , 2022 .

[25]  Pieter R Roelfsema,et al.  Neuronal Activity in the Visual Cortex Reveals the Temporal Order of Cognitive Operations , 2010, The Journal of Neuroscience.

[26]  C. Lebiere,et al.  The Atomic Components of Thought , 1998 .

[27]  T. Wiesel,et al.  Targets of horizontal connections in macaque primary visual cortex , 1991, The Journal of comparative neurology.

[28]  Victor A. F. Lamme,et al.  The implementation of visual routines , 2000, Vision Research.

[29]  M. Konishi,et al.  A circuit for detection of interaural time differences in the brain stem of the barn owl , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[30]  Christian Lebiere,et al.  The dynamics of cognition: An ACT-R model of cognitive arithmetic , 1999, Kognitionswissenschaft.

[31]  G. Humphreys,et al.  Attention, spatial representation, and visual neglect: simulating emergent attention and spatial memory in the selective attention for identification model (SAIM). , 2003, Psychological review.

[32]  Allen Newell,et al.  Production Systems: Models of Control Structures , 1973 .

[33]  M N Shadlen,et al.  Motion perception: seeing and deciding. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[34]  C. Gilbert,et al.  On a common circle: natural scenes and Gestalt rules. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Rajesh P. N. Rao,et al.  How Prior Probability Influences Decision Making: A Unifying Probabilistic Model , 2012, NIPS.

[36]  Rodney J. Douglas,et al.  Feedback interactions between neuronal pointers and maps for attentional processing , 1999, Nature Neuroscience.

[37]  T. Wiesel,et al.  Lateral interactions in visual cortex. , 1990, Cold Spring Harbor symposia on quantitative biology.

[38]  C. Gilbert,et al.  Improvement in visual sensitivity by changes in local context: Parallel studies in human observers and in V1 of alert monkeys , 1995, Neuron.

[39]  J. Assad,et al.  A cognitive signal for the proactive timing of action in macaque LIP , 2006, Nature Neuroscience.

[40]  S Dehaene,et al.  A hierarchical neuronal network for planning behavior. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Emilio Salinas,et al.  Cognitive neuroscience: Flutter Discrimination: neural codes, perception, memory and decision making , 2003, Nature Reviews Neuroscience.

[42]  Jeffrey D. Schall,et al.  Neural basis of deciding, choosing and acting , 2001, Nature Reviews Neuroscience.

[43]  Mariano Sigman,et al.  From a single decision to a multi-step algorithm , 2012, Current Opinion in Neurobiology.

[44]  W. Newsome,et al.  Matching Behavior and the Representation of Value in the Parietal Cortex , 2004, Science.

[45]  J. Gold,et al.  The neural basis of decision making. , 2007, Annual review of neuroscience.

[46]  Xiao-Jing Wang,et al.  Introduction to Computational Neuroscience , 2006 .

[47]  John K. Slaney,et al.  Blocks World revisited , 2001, Artif. Intell..

[48]  Pieter R Roelfsema,et al.  Subtask sequencing in the primary visual cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[49]  L. Shastri,et al.  From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony , 1993, Behavioral and Brain Sciences.

[50]  Rajesh P. N. Rao,et al.  Embodiment is the foundation, not a level , 1996, Behavioral and Brain Sciences.

[51]  Jean,et al.  The Computer and the Brain , 1989, Annals of the History of Computing.

[52]  ● Pytorch,et al.  Attention! , 1998, Trends in Cognitive Sciences.

[53]  K. C. Anderson,et al.  Single neurons in prefrontal cortex encode abstract rules , 2001, Nature.

[54]  P. Roelfsema.  Elemental operations in vision , 2005, Trends in Cognitive Sciences.

[55]  M. Sigman,et al.  The dynamics of sensory buffers: geometric, spatial, and experience-dependent shaping of iconic memory. , 2008, Journal of vision.

[56]  F. Hamker.  A dynamic model of how feature cues guide spatial attention , 2004, Vision Research.

[57]  T. Shallice.  Specific impairments of planning. , 1982, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.