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F A Mussa-Ivaldi

Publications and source records attributed to F A Mussa-Ivaldi.

5 recordsLinked to original sources
PubMed1992

From basis functions to basis fields: vector field approximation from sparse data.

Recent investigations (Poggio and Girosi 1990b) have pointed out the equivalence between a wide class of learning problems and the reconstruction of a real-valued function from a sparse set of data. However, in order to process sensory information and to generate purposeful actions living organisms must deal not only with real-valued functions but also with vector-valued mappings. Examples of such vector-valued mappings range from the optical flow fields associated with visual motion to the fields of mechanical forces produced by neuromuscular activation. In this paper, I discuss the issue of vector-field processing from a broad computational perspective. A variety of vector patterns can be efficiently represented by a combination of linearly independent vector fields that I call "basis fields". Basis fields offer in some cases a better alternative to treating each component of a vector as an independent scalar entity. In spite of its apparent simplicity, such a component-based representation is bound to change with any change of coordinates. In contrast, vector-valued primitives such as basis fields generate vector field representations that are invariant under coordinate transformations.

Animals↗
PubMed1992

Vector field approximation: a computational paradigm for motor control and learning.

Recent experiments in the spinalized frog (Bizzi et al. 1991) have shown that focal microstimulation of a site in the premotor layers in the lumbar grey matter of the spinal cord results in a field of forces acting on the frog's ankle and converging to a single equilibrium position. These experiments suggested that the neural circuits in the spinal cord are organized in a set of control modules that "store" a few limb postures in the form of convergent force fields acting on the limb's end-point. Here, we investigate how such postural modules can be combined by the central nervous system for generating and representing a wider repertoire of control patterns. Our work is related to some recent investigations by Poggio and Girosi (1990a, b) who have proposed to represent the task of learning scalar maps as a problem of surface approximation. Consistent both with this view and with our experimental findings in the spinal frog, we regard the issue of generating motor repertoires as a problem of vector-field approximation. To this end, we characterize the output of a control module as a "basis field" (Mussa-Ivaldi 1992), that is as the vectorial equivalent of a basis function. Our theoretical findings indicate that by combining basis fields, the central nervous system may achieve a number of goals such as (1) the generation of a wide repertoire of control patterns and (2) the representation of these control patterns with a set of coefficients that are invariant under coordinate transformations.

Animals↗
PubMed1991

Computations underlying the execution of movement: a biological perspective.

To execute voluntary movements, the central nervous system must transform the neural representation of the direction, amplitude, and velocity of the limb, represented by the activity of cortical and subcortical neurons, into signals that activate the muscles that move the limb. This task is equivalent to solving an "ill-posed" computational problem because the number of degrees of freedom of the musculoskeletal apparatus is much larger than that specified in the plan of action. Some of the mechanisms and circuitry underlying the transformation of motor plans into motor commands are described. A central feature of this transformation is a coarse map of limb postures in the premotor areas of the spinal cord. Vectorial combination of motor outputs among different areas of the spinal map may produce a large repertoire of motor behaviors.

Animals↗