Multi-Area Visuotopic Map Complexes in Macaque Striate and Extra-striate Cortex

We propose that a simple, closed-form mathematical expression--the Wedge-Dipole mapping--provides a concise approximation to the full-field, two-dimensional topographic structure of macaque V1, V2, and V3. A single map function, which we term a map complex, acts as a simultaneous descriptor of all three areas. Quantitative estimation of the Wedge-Dipole parameters is provided via 2DG data of central-field V1 topography and a publicly available data set of full-field macaque V1 and V2 topography. Good quantitative agreement is obtained between the data and the model presented here. The increasing importance of fMRI-based brain imaging motivates the development of more sophisticated two-dimensional models of cortical visuotopy, in contrast to the one-dimensional approximations that have been in common use. One reason is that topography has traditionally supplied an important aspect of "ground truth", or validation, for brain imaging, suggesting that further development of high-resolution fMRI will be facilitated by this data analysis. In addition, several important insights into the nature of cortical topography follows from this work. The presence of anisotropy in cortical magnification factor is shown to follow mathematically from the shared boundary conditions at the V1-V2 and V2-V3 borders, and therefore may not causally follow from the existence of columnar systems in these areas, as is widely assumed. An application of the Wedge-Dipole model to localizing aspects of visual processing to specific cortical areas--extending previous work in correlating V1 cortical magnification factor to retinal anatomy or visual psychophysics data--is briefly discussed.

Space, Time and Learning in the Hippocampus: How Fine Spatial and Temporal Scales Are Expanded into Population Codes for Behavioral Control

The hippocampus participates in multiple functions, including spatial navigation, adaptive timing, and declarative (notably, episodic) memory. How does it carry out these particular functions? The present article proposes that hippocampal spatial and temporal processing are carried out by parallel circuits within entorhinal cortex, dentate gyrus, and CA3 that are variations of the same circuit design. In particular, interactions between these brain regions transform fine spatial and temporal scales into population codes that are capable of representing the much larger spatial and temporal scales that are needed to control adaptive behaviors. Previous models of adaptively timed learning propose how a spectrum of cells tuned to brief but different delays are combined and modulated by learning to create a population code for controlling goal-oriented behaviors that span hundreds of milliseconds or even seconds. Here it is proposed how projections from entorhinal grid cells can undergo a similar learning process to create hippocampal place cells that can cover a space of many meters that are needed to control navigational behaviors. The suggested homology between spatial and temporal processing may clarify how spatial and temporal information may be integrated into an episodic memory.

Simulating Effects of Learning and Lesions with a Model of Intrinsic and Synaptically Gated Responses of Striatal Cholinergic Interneurons

The giant cholinergic interneurons of the striatum are tonically active neurons (TANs) that respond with characteristic pauses to novel events and to appetitive and aversive conditioned stimuli. Fluctuations in acetylcholine release by TANs modulate performance- and learning-related dynamics in the striatum. Whereas tonic activity emerges from intrinsic properties of these neurons, glutamatergic inputs from thalamic centromedian-parafascicular nuclei, and dopaminergic inputs from midbrain, are required for the generation of pause responses. No prior computational models encompass both intrinsic and synaptically-gated dynamics. We present a mathematical model that robustly accounts for behavior-related electrophysiological properties of TANs in terms of their intrinsic physiological properties and known afferents. In the model, balanced intrinsic hyperpolarizing and depolarizing currents engender tonic firing, and glutamatergic inputs from thalamus (and cortex) both directly excite and indirectly inhibit TANs. If the latter inhibition, presumably mediated by GABAergic interneurons, exceeds a threshold, its effect is amplified by a KIR current to generate a prolonged pause. In the model, the intrinsic mechanisms and external inputs are both modulated by learning-dependent dopamine (DA) signals and our simulations revealed that many learning-dependent behaviors of TANs are explicable without recourse to learning-dependent changes in synapses onto TANs. The "teaching signal" that modulates reinforcement learning at cortico-striatal synapses may be a sequence composed of an adaptively scaled DA burst, a brief ACh burst, and a scaled ACh pause. Such an interpretation is consistent with recent data on cholinergic control of LTD of cortical synapses onto striatal spiny projection neurons.

Texture Segregation By Visual Cortex: Perceptual Grouping, Attention, and Learning

A neural model is proposed of how laminar interactions in the visual cortex may learn and recognize object texture and form boundaries. The model brings together five interacting processes: region-based texture classification, contour-based boundary grouping, surface filling-in, spatial attention, and object attention. The model shows how form boundaries can determine regions in which surface filling-in occurs; how surface filling-in interacts with spatial attention to generate a form-fitting distribution of spatial attention, or attentional shroud; how the strongest shroud can inhibit weaker shrouds; and how the winning shroud regulates learning of texture categories, and thus the allocation of object attention. The model can discriminate abutted textures with blurred boundaries and is sensitive to texture boundary attributes like discontinuities in orientation and texture flow curvature as well as to relative orientations of texture elements. The model quantitatively fits a large set of human psychophysical data on orientation-based textures. Object boundar output of the model is compared to computer vision algorithms using a set of human segmented photographic images. The model classifies textures and suppresses noise using a multiple scale oriented filterbank and a distributed Adaptive Resonance Theory (dART) classifier. The matched signal between the bottom-up texture inputs and top-down learned texture categories is utilized by oriented competitive and cooperative grouping processes to generate texture boundaries that control surface filling-in and spatial attention. Topdown modulatory attentional feedback from boundary and surface representations to early filtering stages results in enhanced texture boundaries and more efficient learning of texture within attended surface regions. Surface-based attention also provides a self-supervising training signal for learning new textures. Importance of the surface-based attentional feedback in texture learning and classification is tested using a set of textured images from the Brodatz micro-texture album. Benchmark studies vary from 95.1% to 98.6% with attention, and from 90.6% to 93.2% without attention.

Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.

The Art of Seeing and Painting

The human urge to represent the three-dimensional world using two-dimensional pictorial representations dates back at least to Paleolithic times. Artists from ancient to modern times have struggled to understand how a few contours or color patches on a flat surface can induce mental representations of a three-dimensional scene. This article summarizes some of the recent breakthroughs in scientifically understanding how the brain sees that shed light on these struggles. These breakthroughs illustrate how various artists have intuitively understand paradoxical properties about how the brain sees, and have used that understanding to create great art. These paradoxical properties arise from how the brain forms the units of conscious visual perception; namely, representations of three-dimensional boundaries and surfaces. Boundaries and surfaces are computed in parallel cortical processing streams that obey computationally complementary properties. These streams interact at multiple levels to overcome their complementary weaknesses and to transform their complementary properties into consistent percepts. The article describes how properties of complementary consistency have guided the creation of many great works of art.

From Synapse to Self: Spikes, Synchrony, and Attentive Learning by Laminar Thalamocortical Circuits

How do our brains transform the "blooming buzzing confusion" of daily experience into a coherent sense of self that can learn and selectively attend to important information? How do local signals at multiple processing stages, none of which has a global view of brain dynamics or behavioral outcomes, trigger learning at multiple synaptic sites when appropriate, and prevent learning when inappropriate, to achieve useful behavioral goals in a continually changing world? How does the brain allow synaptic plasticity at a remarkably rapid rate, as anyone who has gone to an exciting movie is readily aware, yet also protect useful memories from catastrophic forgetting? A neural model provides a unified answer by explaining and quantitatively simulating data about single cell biophysics and neurophysiology, laminar neuroanatomy, aggregate cell recordings (current-source densities, local field potentials), large-scale oscillations (beta, gamma), and spike-timing dependent plasticity, and functionally linking them all to cognitive information processing requirements.

ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network

This article introduces a new neural network architecture, called ARTMAP, that autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success. This supervised learning system is built up from a pair of Adaptive Resonance Theory modules (ARTa and ARTb) that are capable of self-organizing stable recognition categories in response to arbitrary sequences of input patterns. During training trials, the ARTa module receives a stream {a^(p)} of input patterns, and ARTb receives a stream {b^(p)} of input patterns, where b^(p) is the correct prediction given a^(p). These ART modules are linked by an associative learning network and an internal controller that ensures autonomous system operation in real time. During test trials, the remaining patterns a^(p) are presented without b^(p), and their predictions at ARTb are compared with b^(p). Tested on a benchmark machine learning database in both on-line and off-line simulations, the ARTMAP system learns orders of magnitude more quickly, efficiently, and accurately than alternative algorithms, and achieves 100% accuracy after training on less than half the input patterns in the database. It achieves these properties by using an internal controller that conjointly maximizes predictive generalization and minimizes predictive error by linking predictive success to category size on a trial-by-trial basis, using only local operations. This computation increases the vigilance parameter ρa of ARTa by the minimal amount needed to correct a predictive error at ARTb· Parameter ρa calibrates the minimum confidence that ARTa must have in a category, or hypothesis, activated by an input a^(p) in order for ARTa to accept that category, rather than search for a better one through an automatically controlled process of hypothesis testing. Parameter ρa is compared with the degree of match between a^(p) and the top-down learned expectation, or prototype, that is read-out subsequent to activation of an ARTa category. Search occurs if the degree of match is less than ρa. ARTMAP is hereby a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success. As a result, rare but important events can be quickly and sharply distinguished even if they are similar to frequent events with different consequences. Between input trials ρa relaxes to a baseline vigilance pa When ρa is large, the system runs in a conservative mode, wherein predictions are made only if the system is confident of the outcome. Very few false-alarm errors then occur at any stage of learning, yet the system reaches asymptote with no loss of speed. Because ARTMAP learning is self stabilizing, it can continue learning one or more databases, without degrading its corpus of memories, until its full memory capacity is utilized.

Vector Associative Maps: Unsupervised Real-time Error-based Learning and Control of Movement Trajectories

This article describes neural network models for adaptive control of arm movement trajectories during visually guided reaching and, more generally, a framework for unsupervised real-time error-based learning. The models clarify how a child, or untrained robot, can learn to reach for objects that it sees. Piaget has provided basic insights with his concept of a circular reaction: As an infant makes internally generated movements of its hand, the eyes automatically follow this motion. A transformation is learned between the visual representation of hand position and the motor representation of hand position. Learning of this transformation eventually enables the child to accurately reach for visually detected targets. Grossberg and Kuperstein have shown how the eye movement system can use visual error signals to correct movement parameters via cerebellar learning. Here it is shown how endogenously generated arm movements lead to adaptive tuning of arm control parameters. These movements also activate the target position representations that are used to learn the visuo-motor transformation that controls visually guided reaching. The AVITE model presented here is an adaptive neural circuit based on the Vector Integration to Endpoint (VITE) model for arm and speech trajectory generation of Bullock and Grossberg. In the VITE model, a Target Position Command (TPC) represents the location of the desired target. The Present Position Command (PPC) encodes the present hand-arm configuration. The Difference Vector (DV) population continuously.computes the difference between the PPC and the TPC. A speed-controlling GO signal multiplies DV output. The PPC integrates the (DV)·(GO) product and generates an outflow command to the arm. Integration at the PPC continues at a rate dependent on GO signal size until the DV reaches zero, at which time the PPC equals the TPC. The AVITE model explains how self-consistent TPC and PPC coordinates are autonomously generated and learned. Learning of AVITE parameters is regulated by activation of a self-regulating Endogenous Random Generator (ERG) of training vectors. Each vector is integrated at the PPC, giving rise to a movement command. The generation of each vector induces a complementary postural phase during which ERG output stops and learning occurs. Then a new vector is generated and the cycle is repeated. This cyclic, biphasic behavior is controlled by a specialized gated dipole circuit. ERG output autonomously stops in such a way that, across trials, a broad sample of workspace target positions is generated. When the ERG shuts off, a modulator gate opens, copying the PPC into the TPC. Learning of a transformation from TPC to PPC occurs using the DV as an error signal that is zeroed due to learning. This learning scheme is called a Vector Associative Map, or VAM. The VAM model is a general-purpose device for autonomous real-time error-based learning and performance of associative maps. The DV stage serves the dual function of reading out new TPCs during performance and reading in new adaptive weights during learning, without a disruption of real-time operation. YAMs thus provide an on-line unsupervised alternative to the off-line properties of supervised error-correction learning algorithms. YAMs and VAM cascades for learning motor-to-motor and spatial-to-motor maps are described. YAM models and Adaptive Resonance Theory (ART) models exhibit complementary matching, learning, and performance properties that together provide a foundation for designing a total sensory-cognitive and cognitive-motor autonomous system.

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.

Emergence of Tri-Phasic Muscle Activation from the Non-linear Interactions of Central and Spinal Neural Network Circuits

The origin of the tri-phasic burst pattern, observed in the EMGs of opponent muscles during rapid self-terminated movements, has been controversial. Here we show by computer simulation that the pattern emerges from interactions between a central neural trajectory controller (VITE circuit) and a peripheral neuromuscularforce controller (FLETE circuit). Both neural models have been derived from simple functional constraints that have led to principled explanations of a wide variety of behavioral and neurobiological data, including, as shown here, the generation of tri-phasic bursts.

A Neural Network Model for the Spatial and Temporal Response of Retinal Ganglion Cells

This article introduces a quantitative model of early visual system function. The model is formulated to unify analyses of spatial and temporal information processing by the nervous system. Functional constraints of the model suggest mechanisms analogous to photoreceptors, bipolar cells, and retinal ganglion cells, which can be formally represented with first order differential equations. Preliminary numerical simulations and analytical results show that the same formal mechanisms can explain the behavior of both X (linear) and Y (nonlinear) retinal ganglion cell classes by simple changes in the relative width of the receptive field (RF) center and surround mechanisms. Specifically, an increase in the width of the RF center results in a change from X-like to Y-like response, in agreement with anatomical data on the relationship between α- and