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.

Ergodicity and Mixing Rate of One-Dimensional Cellular Automata

One-and two-dimensional cellular automata which are known to be fault-tolerant are very complex. On the other hand, only very simple cellular automata have actually been proven to lack fault-tolerance, i.e., to be mixing. The latter either have large noise probability ε or belong to the small family of two-state nearest-neighbor monotonic rules which includes local majority voting. For a certain simple automaton L called the soldiers rule, this problem has intrigued researchers for the last two decades since L is clearly more robust than local voting: in the absence of noise, L eliminates any finite island of perturbation from an initial configuration of all 0's or all 1's. The same holds for a 4-state monotonic variant of L, K, called two-line voting. We will prove that the probabilistic cellular automata Kε and Lε asymptotically lose all information about their initial state when subject to small, strongly biased noise. The mixing property trivially implies that the systems are ergodic. The finite-time information-retaining quality of a mixing system can be represented by its relaxation time Relax(⋅), which measures the time before the onset of significant information loss. This is known to grow as (1/ε)^c for noisy local voting. The impressive error-correction ability of L has prompted some researchers to conjecture that Relax(Lε) = 2^(c/ε). We prove the tight bound 2^(c1log^21/ε) ＜ Relax(Lε) ＜ 2^(c2log^21/ε) for a biased error model. The same holds for Kε. Moreover, the lower bound is independent of the bias assumption. The strong bias assumption makes it possible to apply sparsity/renormalization techniques, the main tools of our investigation, used earlier in the opposite context of proving fault-tolerance.

3D Trajectory Recovery for Tracking Multiple Objects and Trajectory Guided Recognition of Actions

A mechanism is proposed that integrates low-level (image processing), mid-level (recursive 3D trajectory estimation), and high-level (action recognition) processes. It is assumed that the system observes multiple moving objects via a single, uncalibrated video camera. A novel extended Kalman filter formulation is used in estimating the relative 3D motion trajectories up to a scale factor. The recursive estimation process provides a prediction and error measure that is exploited in higher-level stages of action recognition. Conversely, higher-level mechanisms provide feedback that allows the system to reliably segment and maintain the tracking of moving objects before, during, and after occlusion. The 3D trajectory, occlusion, and segmentation information are utilized in extracting stabilized views of the moving object. Trajectory-guided recognition (TGR) is proposed as a new and efficient method for adaptive classification of action. The TGR approach is demonstrated using "motion history images" that are then recognized via a mixture of Gaussian classifier. The system was tested in recognizing various dynamic human outdoor activities; e.g., running, walking, roller blading, and cycling. Experiments with synthetic data sets are used to evaluate stability of the trajectory estimator with respect to noise.

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.