The Grand Challenge Application Groups competition provides one mechanism for the support of multidisciplinary teams of scientists and engineers to meet the goals of the High Performance Computing and Communications (HPCC) Initiative in Fiscal Year 1992. The ideal proposal provided not only excellence in science: focussed problem with potential for substantial impact in a critical area of science and engineering) but also significant interactions between scientific and computational activities, usually involving mathematical, computer or computational scientists, that would have impact in high-performance computational activity beyond the specific scientific or engineering problem area(s) or discipline being studied. In the award to Berwick, Bizzi, Bulthoff, Jordan, Wexler, Poggio, Rivest, Winston, and Yang at MIT, the research project - High Performance Computing for Learning - has been designed explicitly to push the High Performance Computing algorithmic and architectural envelope via a CM-5 and VLSI testbed and to address many of the HPCC goals. It will advance new algorithms and software for a broad class of optimization and learning problems, tested on and directly driving operating system and architectural changes on the CM-5 (working with one of the CM-5's key architects). The learning problems addressed are essentially an entire class of modeling/optimization problems that intersect with nearly all HPCC Grand Challenge Problems.