Modeling motor cortical operations by an attractor network of stochastic neurons

Working memory, attention, and salience in active inference

The psychological concepts of working memory and attention are widely used in the cognitive and neuroscientific literatures. Perhaps because of the interdisciplinary appeal of these concepts, the same terms are often used to mean very different things. Drawing on recent advances in theoretical neurobiology, this paper tries to highlight the correspondence between these established psychological constructs and the formal processes implicit in mathematical descriptions of brain function. Here, we consider attention and salience from the perspective offered by active inference. Using variational principles and simulations, we use active inference to demonstrate how attention and salience can be disambiguated in terms of message passing between populations of neurons in cortical and subcortical structures. In brief, we suggest that salience is something that is afforded to actions that realise epistemic affordance, while attention per se is afforded to precise sensory evidence - or beliefs about the causes of sensations.

The active construction of the visual world

What we see is fundamentally dependent on where we look. Despite this seemingly obvious statement, many accounts of the neurobiology underpinning visual perception fail to consider the active nature of how we sample our sensory world. This review offers an overview of the neurobiology of visual perception, which begins with the control of saccadic eye movements. Starting from here, we can follow the anatomy backwards, to try to understand the functional architecture of neuronal networks that support the interrogation of a visual scene. Many of the principles encountered in this exercise are equally applicable to other perceptual modalities. For example, the somatosensory system, like the visual system, requires the sampling of data through mobile receptive epithelia. Analysis of a somatosensory scene depends on what is palpated, in much the same way that visual analysis relies on what is foveated. The discussion here is structured around the anatomical systems involved in active vision and visual scene construction, but will use these systems to introduce some general theoretical considerations. We will additionally highlight points of contact between the biology and the pathophysiology that has been proposed to cause a clinical disorder of scene construction - spatial hemineglect.

Neurobiological studies of chronic pain and analgesia: Rationale and refinements

Chronic pain is a complex condition for which the need for specialized research and therapies has been recognized internationally. This review summarizes the context for the international call for expansion of pain research to improve our understanding of the mechanisms underlying pain in order to achieve improvements in pain management. The methods for conducting sensory assessment in animal models are discussed and the development of animal models of chronic pain is specifically reviewed, with an emphasis on ongoing refinements to more closely mimic a variety of human pain conditions. Pharmacological correspondences between pre-clinical pain models and the human clinical experience are noted. A discussion of the 3Rs Framework (Replacement, Reduction, Refinement) and how each may be considered in pain research is featured. Finally, suggestions are provided for engaging principal investigators, IACUC reviewers, and institutions in the development of strong partnerships to simultaneously expand our knowledge of the mechanisms underlying pain and analgesia while ensuring the humane use of animals in research.

Robust Working Memory in an Asynchronously Spiking Neural Network Realized with Neuromorphic VLSI

We demonstrate bistable attractor dynamics in a spiking neural network implemented with neuromorphic VLSI hardware. The on-chip network consists of three interacting populations (two excitatory, one inhibitory) of leaky integrate-and-fire (LIF) neurons. One excitatory population is distinguished by strong synaptic self-excitation, which sustains meta-stable states of “high” and “low”-firing activity. Depending on the overall excitability, transitions to the “high” state may be evoked by external stimulation, or may occur spontaneously due to random activity fluctuations. In the former case, the “high” state retains a “working memory” of a stimulus until well after its release. In the latter case, “high” states remain stable for seconds, three orders of magnitude longer than the largest time-scale implemented in the circuitry. Evoked and spontaneous transitions form a continuum and may exhibit a wide range of latencies, depending on the strength of external stimulation and of recurrent synaptic excitation. In addition, we investigated “corrupted” “high” states comprising neurons of both excitatory populations. Within a “basin of attraction,” the network dynamics “corrects” such states and re-establishes the prototypical “high” state. We conclude that, with effective theoretical guidance, full-fledged attractor dynamics can be realized with comparatively small populations of neuromorphic hardware neurons.

Self-organization of multiple spatial and context memories in the hippocampus

One obstacle to understanding the exact processes unfolding inside the hippocampus is that it is still difficult to clearly define what the hippocampus actually does, at the system level. Associated for a long time with the formation of episodic and semantic memories, and with their temporary storage, the hippocampus is also regarded as a structure involved in spatial navigation. These two independent perspectives on the hippocampus are not necessarily exclusive: proposals have been put forward to make them fit into the same conceptual frame. We review both approaches and argue that three critical developments need consideration: (a) recordings of neuronal activity in rodents, revealing beautiful spatial codes expressed in entorhinal cortex, upstream of the hippocampus; (b) comparative behavioral results suggesting, in an evolutionary perspective, qualitative similarity of function across homologous structures with a distinct internal organization; (c) quantitative measures of information, shifting the focus from who does what to how much each neuronal population expresses each code. These developments take the hippocampus away from philosophical discussions of all-or-none cause-effect relations, and into the quantitative mainstream of modern neural science.

How the brain generates movement

In this study, we assume that the brain uses a general-purpose pattern generator to transform static commands into basic movement segments. We hypothesize that this pattern generator includes an oscillator whose complete cycle generates a single movement segment. In order to demonstrate this hypothesis, we construct an oscillator-based model of movement generation. The model includes an oscillator that generates harmonic outputs whose frequency and amplitudes can be modulated by external inputs. The harmonic outputs drive a number of integrators, each activating a single muscle. The model generates muscle activation patterns composed of rectilinear and harmonic terms. We show that rectilinear and fundamental harmonic terms account for known properties of natural movements, such as the invariant bell-shaped hand velocity profile during reaching. We implement these dynamics by a neural network model and characterize the tuning properties of the neural integrator cells, the neural oscillator cells, and the inputs to the system. Finally, we propose a method to test our hypothesis that a neural oscillator is a central component in the generation of voluntary movement.

Schema generation in recurrent neural nets for intercepting a moving target

The grasping of a moving object requires the development of a motor strategy to anticipate the trajectory of the target and to compute an optimal course of interception. During the performance of perception-action cycles, a preprogrammed prototypical movement trajectory, a motor schema, may highly reduce the control load. Subjects were asked to hit a target that was moving along a circular path by means of a cursor. Randomized initial target positions and velocities were detected in the periphery of the eyes, resulting in a saccade toward the target. Even when the target disappeared, the eyes followed the target's anticipated course. The Gestalt of the trajectories was dependent on target velocity. The prediction capability of the motor schema was investigated by varying the visibility range of cursor and target. Motor schemata were determined to be of limited precision, and therefore visual feedback was continuously required to intercept the moving target. To intercept a target, the motor schema caused the hand to aim ahead and to adapt to the target trajectory. The control of cursor velocity determined the point of interception. From a modeling point of view, a neural network was developed that allowed the implementation of a motor schema interacting with feedback control in an iterative manner. The neural net of the Wilson type consists of an excitation-diffusion layer allowing the generation of a moving bubble. This activation bubble runs down an eye-centered motor schema and causes a planar arm model to move toward the target. A bubble provides local integration and straightening of the trajectory during repetitive moves. The schema adapts to task demands by learning and serves as forward controller. On the basis of these model considerations the principal problem of embedding motor schemata in generalized control strategies is discussed.

Converging neuronal activity in inferior temporal cortex during the classification of morphed stimuli

How does the brain dynamically convert incoming sensory data into a representation useful for classification? Neurons in inferior temporal (IT) cortex are selective for complex visual stimuli, but their response dynamics during perceptual classification is not well understood. We studied IT dynamics in monkeys performing a classification task. The monkeys were shown visual stimuli that were morphed (interpolated) between pairs of familiar images. Their ability to classify the morphed images depended systematically on the degree of morph. IT neurons were selected that responded more strongly to one of the 2 familiar images (the effective image). The responses tended to peak approximately 120 ms following stimulus onset with an amplitude that depended almost linearly on the degree of morph. The responses then declined, but remained above baseline for several hundred ms. This sustained component remained linearly dependent on morph level for stimuli more similar to the ineffective image but progressively converged to a single response profile, independent of morph level, for stimuli more similar to the effective image. Thus, these neurons represented the dynamic conversion of graded sensory information into a task-relevant classification. Computational models suggest that these dynamics could be produced by attractor states and firing rate adaptation within the population of IT neurons.

Affine differential geometry analysis of human arm movements

Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the "two-thirds power law", which connects path curvature with velocity, and "local isochrony", which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan's moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants-equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production.

Progressive Transformation of Hippocampal Neuronal Representations in “Morphed” Environments

Hippocampal neural codes for different, familiar environments are thought to reflect distinct attractor states, possibly implemented in the recurrent CA3 network. A defining property of an attractor network is its ability to undergo sharp and coherent transitions between pre-established (learned) representations when the inputs to the network are changed. To determine whether hippocampal neuronal ensembles exhibit such discontinuities, we recorded in CA3 and CA1 when a familiar square recording enclosure was morphed in quantifiable steps into a familiar circular enclosure while leaving other inputs constant. We observed a gradual noncoherent progression from the initial to the final network state. In CA3, the transformation was accompanied by significant hysteresis, resulting in more similar end states than when only square and circle were presented. These observations suggest that hippocampal cell assemblies are capable of incremental plastic deformation, with incongruous information being incorporated into pre-existing representations.

Deforming the hippocampal map

To investigate conjoint stimulus control over place cells, Fenton et al. (J Gen Physiol 116:191-209, 2000a) recorded while rats foraged in a cylinder with 45 degrees black and white cue cards on the wall. Card centers were 135 degrees apart. In probe trials, the cards were rotated together or apart by 25 degrees . Firing field centers shifted during these trials, stretching and shrinking the cognitive map. Fenton et al. (2000b) described this deformation with an ad hoc vector field equation. We consider what sorts of neural network mechanisms might be capable of accounting for their observations. In an abstract, maximum likelihood formulation, the rat's location is estimated by a conjoint probability density function of landmark positions. In an attractor neural network model, recurrent connections produce a bump of activity over a two-dimensional array of cells; the bump's position is influenced by landmark features such as distances or bearings. If features are chosen with appropriate care, the attractor network and maximum likelihood models yield similar results, in accord with previous demonstrations that recurrent neural networks can efficiently implement maximum likelihood computations (Pouget et al. Neural Comput 10:373-401, 1998; Deneve et al. Nat Neurosci 4:826-831, 2001).

The anatomical and computational basis of the rat head-direction cell signal

As a rat navigates through space, neurons called head-direction (HD) cells provide a signal of the rat's momentary directional heading. Although partly guided by landmarks, the cells also show a remarkable ability to track directional heading based on angular head movement. Theoretical models suggest that the HD cells are linked together to form an attractor network, and that cells which signal angular velocity update the directional setting of the attractor. Recently, cell types similar to those required theoretically have been discovered in the lateral mammillary and dorsal tegmental nuclei. Lesion and anatomical data suggest these nuclei might constitute the postulated attractor-path integration mechanism, and that they provide the HD cell signal to cortical areas where it has been observed.

A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability

We report a computer simulation of the visuospatial delayed-response experiments of Funahashi et al. (1989), using a firing-rate model that combines intrinsic cellular bistability with the recurrent local network architecture of the neocortex. In our model, the visuospatial working memory is stored in the form of a continuum of network activity profiles that coexist with a spontaneous activity state. These neuronal firing patterns provide a population code for the cue position in a graded manner. We show that neuronal persistent activity and tuning curves of delay-period activity (memory fields) can be generated by an excitatory feedback circuit and recurrent synaptic inhibition. However, if the memory fields are constructed solely by network mechanisms, noise may induce a random drift over time in the encoded cue position, so that the working memory storage becomes unreliable. Furthermore, a "distraction" stimulus presented during the delay period produces a systematic shift in the encoded cue position. We found that the working memory performance can be rendered robust against noise and distraction stimuli if single neurons are endowed with cellular bistability (presumably due to intrinsic ion channel mechanisms) that is conditional and realized only with sustained synaptic inputs from the recurrent network. We discuss how cellular bistability at the single cell level may be detected by analysis of spike trains recorded during delay-period activity and how local modulation of intrinsic cell properties and/or synaptic transmission can alter the memory fields of individual neurons in the prefrontal cortex.

Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells

Physical variables such as the orientation of a line in the visual field or the location of the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which the physical variables are estimated from observed neural activity. Reconstruction is useful first in quantifying how much information about the physical variables is present in the population and, second, in providing insight into how the brain might use distributed representations in solving related computational problems such as visual object recognition and spatial navigation. Two classes of reconstruction methods, namely, probabilistic or Bayesian methods and basis function methods, are discussed. They include important existing methods as special cases, such as population vector coding, optimal linear estimation, and template matching. As a representative example for the reconstruction problem, different methods were applied to multi-electrode spike train data from hippocampal place cells in freely moving rats. The reconstruction accuracy of the trajectories of the rats was compared for the different methods. Bayesian methods were especially accurate when a continuity constraint was enforced, and the best errors were within a factor of two of the information-theoretic limit on how accurate any reconstruction can be and were comparable with the intrinsic experimental errors in position tracking. In addition, the reconstruction analysis uncovered some interesting aspects of place cell activity, such as the tendency for erratic jumps of the reconstructed trajectory when the animal stopped running. In general, the theoretical values of the minimal achievable reconstruction errors quantify how accurately a physical variable is encoded in the neuronal population in the sense of mean square error, regardless of the method used for reading out the information. One related result is that the theoretical accuracy is independent of the width of the Gaussian tuning function only in two dimensions. Finally, all the reconstruction methods considered in this paper can be implemented by a unified neural network architecture, which the brain feasibly could use to solve related problems.

Network models of the basal ganglia

Over the past year, a number of conceptual and mathematical models of the basal ganglia and their interactions with other areas of the brain have appeared in the literature. Even though the models each differ in significant ways, several computational principles, such as convergence, recurrence and competition, appear to have emerged as common themes of information processing in the basal ganglia. Simulation studies of these models have provoked new types of questions at the many levels of inquiry linking biophysics to behavior.

Cortical dynamic tuning: the role of intrinsic connections, as revealed by modeling

A current challenge in computational neuroscience is to elucidate the role of cortical circuitry in information processing and in generating motor output. Our understanding of the functional significance of specifically organized feedback connections is progressing rapidly as researchers establish the equivalence of theoretical models to biological neural circuits. Modeling studies of different neural structures, along with quantitative comparisons of model performance to biological data, have recently helped to identify the basic features of synaptic connectivity that may play important roles in cortical operations.