Credit assignment in multiple goal embodied visuomotor behavior

The intrinsic complexity of the brain can lead one to set aside issues related to its relationships with the body, but the field of embodied cognition emphasizes that understanding brain function at the system level requires one to address the role of the brain-body interface. It has only recently been appreciated that this interface performs huge amounts of computation that does not have to be repeated by the brain, and thus affords the brain great simplifications in its representations. In effect the brain’s abstract states can refer to coded representations of the world created by the body. But even if the brain can communicate with the world through abstractions, the severe speed limitations in its neural circuitry mean that vast amounts of indexing must be performed during development so that appropriate behavioral responses can be rapidly accessed. One way this could happen would be if the brain used a decomposition whereby behavioral primitives could be quickly accessed and combined. This realization motivates our study of independent sensorimotor task solvers, which we call modules, in directing behavior. The issue we focus on herein is how an embodied agent can learn to calibrate such individual visuomotor modules while pursuing multiple goals. The biologically plausible standard for module programming is that of reinforcement given during exploration of the environment. However this formulation contains a substantial issue when sensorimotor modules are used in combination: The credit for their overall performance must be divided amongst them. We show that this problem can be solved and that diverse task combinations are beneficial in learning and not a complication, as usually assumed. Our simulations show that fast algorithms are available that allot credit correctly and are insensitive to measurement noise

Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

Higher Derivative Terms from Threebranes in F Theory

The computation of higher derivative corrections to the low energy effective actions of ${\cal N}=2$ gauge theories is considered. In particular, higher derivative corrections are computed for four dimensional ${\cal N}=2$ super Yang-Mills theory with gauge group SU(2) and $N_f=4$ hypermultiplets in the fundamental representation. The four derivative terms computed in an approach which realizes the gauge theory as the world volume theory of three branes in F theory are in agreement with the field theory result.Comment: 13 pages, uses harvmac, presentation improved, references adde