Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, in the last century it has also become an increasingly important part of theoretical physics. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.
This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines?
In Spring 2019, CMSA will host a 3 day workshop that aims to bring together a set of scientists working on geometry as it applies to sensation, action and cognition. The aim is to revisit some old problems in these subjects using a modern lens, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.
As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019. The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
For a list of lodging options convenient to the Center, please visit our recommended lodgings page.
Tentative Speaker List:
More information to follow.