Sara A. Solla

A statistical approach to learning and generalization in layered neural networks

A general statistical description of the problem of learning from examples is presented. Learning in layered networks is posed as a search in the network parameter space for a network that minimizes an additive error function of a statistically independent examples. By imposing the equivalence of the minimum error and the maximum likelihood criteria for training the network, the Gibbs distribution on the ensemble of networks with a fixed architecture is derived. The probability of correct prediction of a novel example can be expressed using the ensemble, serving as a measure to the networks generalization ability. The entropy of the prediction distribution is shown to be a consistent measure of the networks performance. The proposed formalism is applied to the problems of selecting an optimal architecture and the prediction of learning curves. >

Top-down laminar organization of the excitatory network in motor cortex

Cortical layering is a hallmark of the mammalian neocortex and a major determinant of local synaptic circuit organization in sensory systems. In motor cortex, the laminar organization of cortical circuits has not been resolved, although their input-output operations are crucial for motor control. Here, we developed a general approach for estimating layer-specific connectivity in cortical circuits and applied it to mouse motor cortex. From these data we computed a laminar presynaptic → postsynaptic connectivity matrix, Wpost,pre, revealing a complement of stereotypic pathways dominated by layer 2 outflow to deeper layers. Network modeling predicted, and experiments with disinhibited slices confirmed, that stimuli targeting upper, but not lower, cortical layers effectively evoked network-wide events. Thus, in motor cortex, descending excitation from a preamplifier-like network of upper-layer neurons drives output neurons in lower layers. Our analysis provides a quantitative wiring-diagram framework for further investigation of the excitatory networks mediating cortical mechanisms of motor control.

Self-Sustained Activity in a Small-World Network of Excitable Neurons

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

Dopamine modulation in the basal ganglia locks the gate to working memory

The prefrontal cortex and basal ganglia are deeply implicated in working memory. Both structures are subject to dopaminergic neuromodulation in a way that exerts a critical influence on the proper operation of working memory. We present a novel network model to elucidate the role of phasic dopamine in the interaction of these two structures in initiating and maintaining mnemonic activity. We argue that neuromodulation plays a critical role in protecting memories against both internal and external sources of noise. Increases in cortical gain engendered by prefrontal dopamine release help make memories robust against external distraction, but do not offer protection against internal noise accompanying recurrent cortical activity. Rather, the output of the basal ganglia provides the gating function of stabilization against noise and distraction by enhancing select memories through targeted disinhibition of cortex. Dopamine in the basal ganglia effectively locks this gate by influencing the stability of up and down states in the striatum. Dopamine’s involvement in affective processing endows this gating with specificity to motivational salience. We model a spatial working memory task and show that these combined effects of dopamine lead to superior performance.

Toward the Restoration of Hand Use to a Paralyzed Monkey: Brain-Controlled Functional Electrical Stimulation of Forearm Muscles

Loss of hand use is considered by many spinal cord injury survivors to be the most devastating consequence of their injury. Functional electrical stimulation (FES) of forearm and hand muscles has been used to provide basic, voluntary hand grasp to hundreds of human patients. Current approaches typically grade pre-programmed patterns of muscle activation using simple control signals, such as those derived from residual movement or muscle activity. However, the use of such fixed stimulation patterns limits hand function to the few tasks programmed into the controller. In contrast, we are developing a system that uses neural signals recorded from a multi-electrode array implanted in the motor cortex; this system has the potential to provide independent control of multiple muscles over a broad range of functional tasks. Two monkeys were able to use this cortically controlled FES system to control the contraction of four forearm muscles despite temporary limb paralysis. The amount of wrist force the monkeys were able to produce in a one-dimensional force tracking task was significantly increased. Furthermore, the monkeys were able to control the magnitude and time course of the force with sufficient accuracy to track visually displayed force targets at speeds reduced by only one-third to one-half of normal. Although these results were achieved by controlling only four muscles, there is no fundamental reason why the same methods could not be scaled up to control a larger number of muscles. We believe these results provide an important proof of concept that brain-controlled FES prostheses could ultimately be of great benefit to paralyzed patients with injuries in the mid-cervical spinal cord.

Multi-Locus Nonparametric Linkage Analysis of Complex Trait Loci with Neural Networks

Complex traits are generally taken to be under the influence of multiple genes, which may interact with each other to confer susceptibility to disease. Statistical methods in current use for localizing such genes essentially work under single-gene models, either implicitly or explicitly. In genomic screens for complex disease genes, some of the marker loci must be in tight linkage with disease susceptibility genes. We developed a general multi-locus approach to identify sets of such marker loci. Our approach focuses on affected sib pair data and employs a nonparametric pattern recognition technique using artificial neural networks. This technique analyzes all markers simultaneously in order to detect patterns of locus interactions. When applied to previously published sib pair data on type I diabetes, our approach finds the same genes as in the published report in addition to some new loci. For a specific two-locus model of inheritance, the power of our approach is higher than that of the currently used analysis standard.

Prediction of upper limb muscle activity from motor cortical discharge during reaching

Movement representation by the motor cortex (M1) has been a theoretical interest for many years, but in the past several years it has become a more practical question, with the advent of the brain-machine interface. An increasing number of groups have demonstrated the ability to predict a variety of kinematic signals on the basis of M1 recordings and to use these predictions to control the movement of a cursor or robotic limb. We, on the other hand, have undertaken the prediction of myoelectric (EMG) signals recorded from various muscles of the arm and hand during button pressing and prehension movements. We have shown that these signals can be predicted with accuracy that is similar to that of kinematic signals, despite their stochastic nature and greater bandwidth. The predictions were made using a subset of 12 or 16 neural signals selected in the order of each signals unique, output-related information content. The accuracy of the resultant predictions remained stable through a typical experimental session. Accuracy remained above 80% of its initial level for most muscles even across periods as long as two weeks. We are exploring the use of these predictions as control signals for neuromuscular electrical stimulation in quadriplegic patients.

Neural primitives for motion control

The neural control of movement requires the ability to deal with changes, both in the environment and in the parameters that characterize the mechanical structure of the organism. Here we discuss the three types of coordinate representations that sensory and motor systems use to generate and control movements, and argue that the intrinsic redundancy of the musculoeskeletal system can be exploited to implement control signals that result in successful task completion while allowing for variance in trajectory parameters not relevant to the task. We also argue that muscle synergies activated through the stimulation of specific loci along the spinal cord provide evidence for the existence of a vocabulary of motor primitives that can be combined, either simultaneously or sequentially, to generate a broad repertoire of complex movements.

Exhaustive learning

Exhaustive exploration of an ensemble of networks is used to model learning and generalization in layered neural networks. A simple Boolean learning problem involving networks with binary weights is numerically solved to obtain the entropy Sm and the average generalization ability Gm as a function of the size m of the training set. Learning curves Gm vs m are shown to depend solely on the distribution of generalization abilities over the ensemble of networks. Such distribution is determined prior to learning, and provides a novel theoretical tool for the prediction of network performance on a specific task.

Biomimetic Brain Machine Interfaces for the Control of Movement

Quite recently, it has become possible to use signals recorded simultaneously from large numbers of cortical neurons for real-time control. Such brain machine interfaces (BMIs) have allowed animal subjects and human patients to control the position of a computer cursor or robotic limb under the guidance of visual feedback. Although impressive, such approaches essentially ignore the dynamics of the musculoskeletal system, and they lack potentially critical somatosensory feedback. In this mini-symposium, we will initiate a discussion of systems that more nearly mimic the control of natural limb movement. The work that we will describe is based on fundamental observations of sensorimotor physiology that have inspired novel BMI approaches. We will focus on what we consider to be three of the most important new directions for BMI development related to the control of movement. (1) We will present alternative methods for building decoders, including structured, nonlinear models, the explicit incorporation of limb state information, and novel approaches to the development of decoders for paralyzed subjects unable to generate an output signal. (2) We will describe the real-time prediction of dynamical signals, including joint torque, force, and EMG, and the real-time control of physical plants with dynamics like that of the real limb. (3) We will discuss critical factors that must be considered to incorporate somatosensory feedback to the BMI user, including its potential benefits, the differing representations of sensation and perception across cortical areas, and the changes in the cortical representation of tactile events after spinal injury.