Top Gun taught us that the best and brightest pilots can perform some amazing aerobatics.  Nobody seems surprised that a good pilot, with some practice, can move seamlessly from the flight maneuvers used on a Boeing 747 to those featured in Blue Angels shows.  While computer autopilots have performed well in commercial aircraft for some time, however, getting an electronic computer to pull a plane successfully through an aerobatic maneuver is almost impossible, and is thus a relatively new field of research.

Though this information may surprise one at first, the example is but one of a string of revelations accompanying the journey of intelligence research.  Thirty years ago very few scientists expected to run into difficulties in building cameras that understood what they were ‘looking at’ similarly to a person, but the challenge remains.  The emerging theme from varied engineering projects is that biological intelligence trades off some performance abilities for adaptability to a wide range of difficult conditions.  Becoming a professional baseball pitcher may take a good fifteen to twenty years, but it doesn’t take long for someone to learn to play catch, throw trash away, flip a pancake, and so on.  One of the primary goals of neuromorphic technology is to fill in the spectrum between the mathematical but rigid perfection of traditional controllers (and models), and the messy, cheap and rugged heuristics of the animals.

Among the most likely reasons that vision, aerobatics, and many other complicated problems become difficult very quickly is the inherent nonlinearity of the relationship between the input and output of a control system.  Let’s say that someone wants to design a controller that regulates a car’s throttle and transfers power to the different wheels while driving.  The controller knows how fast the car is going, how hard the driver is turning the wheel, and the weather conditions.  The controller probably does a pretty good job of keeping the car from sliding when the road is dry and clean.  In the rain, however, the tires will be more prone to slipping, so the controller shouldn’t allow the throttle to drive the wheels as hard in case they break loose.  The rule ‘more rain → less throttle’ is a simple and linear relationship that could be easily trained into the controller .  During the first fifteen minutes of rain, however, the road is especially slick because rainwater brings oils to the surface of the asphalt, after which times it gets washed away.  In other words, the danger of slipping has a nonlinear relationship to the amount of water detected by the controller; it goes up for about fifteen minutes and then settles back down to something worse than a dry road.  This small difference might not be a problem for a conservative controller designed to keep a family safe, but what if its purpose is to maximize turning speed in a race?  If it were trained only on very dry and very rainy roads (which seems reasonable enough), then a linear controller couldn’t anticipate a good throttle position for the start of a rainstorm, and a small error in throttle could result in a huge difference for the driver!

Rain danger is an example of nonlinearity in a single input dimension, but the situation becomes more complicated with interacting conditions.  Turning quickly is safer on a cement road than uneven asphalt because the uneven surface allows for less traction; dry roads are safer than wet ones because of hydroplaning.  A wet asphalt road may be better than a wet cement road, however, because the uneven surface lifts the tire and allows water to escape from under it (unlikely, don’t test this).  Rather than two bad conditions simply adding together to become worse, the combination may actually be safer than either one alone.

(The situation is a contrived example of the XOR problem, which was shown to be impossible for a single layer perceptron by Minsky and Papert.  In a mathematical sense, all nonlinearities are expressed as multiplicative interacting terms; the previous single variable case arises from a variable’s interactions with itself.  There’s also an interesting connection between nonlinear interactions and the ability of people to categorize and structure the world hierarchically.  Hofstadter mentions that expert chess players, when performing a task of quickly memorizing and recalling chess boards, make recall errors with groups of pieces rather than the single piece errors that novices make.  The grouping process, the recognition that some arrangements of pieces affect the outcome of the game more than others, makes steps towards capturing the nonlinearity of such a complex system.)

A controller can either learn how the process it’s controlling (the plant) works, or it can learn the inverse plant.  Learning the inverse problem can be easier because the algorithm is straightforward to apply; the input to the network is the desired outcome and the output is the action for the controller to take.  This is exemplified in robotic models of inverse kinematics, where a controller must learn to rotate the joints of a limb to get the limb’s end to a particular place in space.  Undoing a process may be difficult, however, when the space of possible plant outcomes is much larger than the number of knobs the controller can twist; in that case learning the forward model may give better performance.  The DIRECT model is an example of how the human brain can act as a limb controller by learning both the forward and inverse plant for a wide range of motions.  An interesting hypothesis put forward here is that ‘babbling’, a childlike exploration of all kinds of movements to gain experience, is essential for fine tuning the network in preparation for precise movement.  For high performance movements, Marr and Albus independently both suggested that the cerebellum is a forward kinematic model of human movement which could be used to apply small corrective signals to those coming straight from the cortex to the muscles.  All of these are examples of neural networks that already exist as controllers in biological bodies, and their applicability both to specific high-performance and robust general-purpose tasks has only increased with continued research.