Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSPs planar four-color graph coloring, maximum independent set, and Sudoku on this substrate, and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of non-saturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by non-linear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation, and also offer insight into the computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously -- elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala, and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow time scales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding "feeder" cortical regions show unstable, rapidly fluctuating dynamics likely crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.Comment: 35 pages, 6 figure

Modeling direction selectivity of simple cells in striate visual cortex within the framework of the canonical microcircuit

Nearly all models of direction selectivity (DS) in visual cortex are based on feedforward connection schemes, where geniculate input provides all excitatory synaptic input to both pyramidal and inhibitory neurons. Feedforward inhibition then suppresses feedforward excitation for nonoptimal stimuli. Anatomically, however, the majority of asymmetric, excitatory, synaptic contacts onto cortical cells is provided by other cortical neurons, as embodied in the Canonical Microcircuit of Douglas and Martin (1991). In this view, weak geniculate input is strongly amplified in the preferred direction by the action of intracortical excitatory connections, while in the null direction inhibition reduces geniculate-induced excitation. We investigate analytically and through biologically realistic computer simulations the functioning of a cortical network based on massive excitatory, cortico-cortical feedback. The behavior of this network is compared to physiological data as well as to the behavior of a purely feedforward model of DS based on nonlagged input. Our model explains a number of puzzling features of direction selective simple cells, including the small somatic input conductance changes that have been measured experimentally during stimulation in the null direction, and the persistence of DS while fully blocking inhibition in a single cell. Although the operation at the heart of our network is amplification, the network passes the linearity test of (Jagadeesh et al., 1993). We make specific predictions concerning the effect of selective blockade of cortical inhibition on the velocity-response curve

A Neural Model of Visually Guided Steering, Obstacle Avoidance, and Route Selection

A neural model is developed to explain how humans can approach a goal object on foot while steering around obstacles to avoid collisions in a cluttered environment. The model uses optic flow from a 3D virtual reality environment to determine the position of objects based on motion discotinuities, and computes heading direction, or the direction of self-motion, from global optic flow. The cortical representation of heading interacts with the representations of a goal and obstacles such that the goal acts as an attractor of heading, while obstacles act as repellers. In addition the model maintains fixation on the goal object by generating smooth pursuit eye movements. Eye rotations can distort the optic flow field, complicating heading perception, and the model uses extraretinal signals to correct for this distortion and accurately represent heading. The model explains how motion processing mechanisms in cortical areas MT, MST, and VIP can be used to guide steering. The model quantitatively simulates human psychophysical data about visually-guided steering, obstacle avoidance, and route selection.Air Force Office of Scientific Research (F4960-01-1-0397); National Geospatial-Intelligence Agency (NMA201-01-1-2016); National Science Foundation (NSF SBE-0354378); Office of Naval Research (N00014-01-1-0624

Adaptive Neural Networks for Control of Movement Trajectories Invariant under Speed and Force Rescaling

This article describes two neural network modules that form part of an emerging theory of how adaptive control of goal-directed sensory-motor skills is achieved by humans and other animals. The Vector-Integration-To-Endpoint (VITE) model suggests how synchronous multi-joint trajectories are generated and performed at variable speeds. The Factorization-of-LEngth-and-TEnsion (FLETE) model suggests how outflow movement commands from a VITE model may be performed at variable force levels without a loss of positional accuracy. The invariance of positional control under speed and force rescaling sheds new light upon a familiar strategy of motor skill development: Skill learning begins with performance at low speed and low limb compliance and proceeds to higher speeds and compliances. The VITE model helps to explain many neural and behavioral data about trajectory formation, including data about neural coding within the posterior parietal cortex, motor cortex, and globus pallidus, and behavioral properties such as Woodworth's Law, Fitts Law, peak acceleration as a function of movement amplitude and duration, isotonic arm movement properties before and after arm-deafferentation, central error correction properties of isometric contractions, motor priming without overt action, velocity amplification during target switching, velocity profile invariance across different movement distances, changes in velocity profile asymmetry across different movement durations, staggered onset times for controlling linear trajectories with synchronous offset times, changes in the ratio of maximum to average velocity during discrete versus serial movements, and shared properties of arm and speech articulator movements. The FLETE model provides new insights into how spina-muscular circuits process variable forces without a loss of positional control. These results explicate the size principle of motor neuron recruitment, descending co-contractive compliance signals, Renshaw cells, Ia interneurons, fast automatic reactive control by ascending feedback from muscle spindles, slow adaptive predictive control via cerebellar learning using muscle spindle error signals to train adaptive movement gains, fractured somatotopy in the opponent organization of cerebellar learning, adaptive compensation for variable moment-arms, and force feedback from Golgi tendon organs. More generally, the models provide a computational rationale for the use of nonspecific control signals in volitional control, or "acts of will", and of efference copies and opponent processing in both reactive and adaptive motor control tasks.National Science Foundation (IRI-87-16960); Air Force Office of Scientific Research (90-0128, 90-0175

Precis of neuroconstructivism: how the brain constructs cognition

Neuroconstructivism: How the Brain Constructs Cognition proposes a unifying framework for the study of cognitive development that brings together (1) constructivism (which views development as the progressive elaboration of increasingly complex structures), (2) cognitive neuroscience (which aims to understand the neural mechanisms underlying behavior), and (3) computational modeling (which proposes formal and explicit specifications of information processing). The guiding principle of our approach is context dependence, within and (in contrast to Marr [1982]) between levels of organization. We propose that three mechanisms guide the emergence of representations: competition, cooperation, and chronotopy; which themselves allow for two central processes: proactivity and progressive specialization. We suggest that the main outcome of development is partial representations, distributed across distinct functional circuits. This framework is derived by examining development at the level of single neurons, brain systems, and whole organisms. We use the terms encellment, embrainment, and embodiment to describe the higher-level contextual influences that act at each of these levels of organization. To illustrate these mechanisms in operation we provide case studies in early visual perception, infant habituation, phonological development, and object representations in infancy. Three further case studies are concerned with interactions between levels of explanation: social development, atypical development and within that, developmental dyslexia. We conclude that cognitive development arises from a dynamic, contextual change in embodied neural structures leading to partial representations across multiple brain regions and timescales, in response to proactively specified physical and social environment

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Neural Models of Normal and Abnormal Behavior: What Do Schizophrenia, Parkinsonism, Attention Deficit Disorder, and Depression Have in Common?

Defense Advanced Research Projects Agency and Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333