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I began experimenting with neural network code a number of months ago when I decided to implement a network capable of maze navigation. I had read about NNs but I wanted to have the level of understanding that comes with actually implementing such an algorithm. In this post I shall discuss the design of the NN framework, the NN intended to solve mazes, the problems with said design and my thoughts on NNs in general and connectionism. The code was all written in Common Lisp (SBCL) in Eclipse/CUSP on a Linux system.

The maze environment was realized as a 2D array of 0s and 1s where a 1 represented a wall. The mazes were randomly generated using a recursive spatial partitioning algorithm. There are some pretty pictures in the programming category of this blog. The decision to have mazes be the problem domain was somewhat arbitrary and introduced some complexity. In retrospect, finding efficient solutions to mazes was not the best problem to tackle with a simple NN. Although it seems totally doable with the right network design.

The implementation of the NN framework leveraged the Lisp object system allowing for simple extension of the algorithm. The default Neuron object was associated with a set of generic methods Activation, Learning and Propagation. A user wishing to change the Activation function could simply inherit from Neuron and override Activation for their Neuron type. Different types of Neurons and their associated functions could be easily intermixed within the same network without much explicit ‘glue’ code. The implementation also included an object/functional abstraction of a neural layer as used for feedforward networks. The highest level abstraction, feedforward-nn, encapsulated a set of neural layers, an explicit input layer and output layer, and user defined functions that specify the mapping from the problem domain to the input and output layers. At least from my own use, these abstractions facilitated very good flexibility and ease of reuse. They also map back intuitively to typical theoretical specifications of NNs.

I quickly discovered the difficult aspect of NNs is not the implementation of an NN framework but rather the design of a network to solve a particular problem. Initially, I considered ‘evolving’ a network using genetic algorithms. Indeed, this would have been neat especially if it worked. However, I felt that would divert my focus too much and require even more time. I settled on an intuitive design that included 9 input neurons and 8 output neurons; there were no intermediate layers. The neurons were wired in feed-forward fashion with this exception of the output layer feeding back into the input layer (more on this in a moment). The first 8 neurons of the input layer represented a ‘touch sense’ where the neuron was set to fire if a wall was present in that direction (8 possible directions for a 2D cellular environment). The output layer represented the direction to move where the sum of the output neuron’s activation levels was [0, 8]. The 9th neuron on the input layer was a ‘smell sense’ which fired if the agent was closer to the cheese/exit than it was on the previous pass. Now, in order to potentiate a ‘correct’ move, a move closer to the cheese, the agent must ‘remember’ the firing sequence of the output neurons from the last pass; hence the aforementioned feedback from the output layer to the input layer.

Unfortunately, this critter never does get to the cheese. Typically after a few moves it settles into a corner and never departs. After a direction is established, the critter becomes more and more determined to keep going that direction. To be successful, there must be some notion of de-potentiation after continued lack of stimulus on neuron 9. That way, it would eventually try another direction even when the input stimulus remains constant. Therefore, I believe some additional tweaking could produce a network capable of solving the mazes.

Regardless, I feel I’ve accomplished what I set out for which was to obtain a fundamental understanding of NNs, their potential and their limitations. Of particular interest to me when I started the project was to evolve my own opinion regarding the biological validity of NNs. I believe a major shortcoming of the current NN definitions, in the scope of biological simulation, is the total reliance on changes in ‘physical’ representation to map to changes in behavior. Given identical input to an NN you will have identical output until the weights, part of the physical representation, are altered. However, I’m skeptical that changes in biological behavior can be modeled purely from these representational changes. There are meta-representational aspects that must be considered such as firing frequency. More simply, you have the wire but you also have what is transmitted ‘over’ the wire. NNs appear to focus on changing the wires to produce changes in behavior. Indeed, it is known that long term potentiation does exist and it likely does produce changes in behavior. However, I assert that is likely not the only mode under which behavioral changes occur and NNs do not currently encompass any mode besides LTP. Rhetorically, how would one describe the behavior of working memory using a model dependent on LTP? To be clear, this is not to say that the necessary behavior can not ‘emerge’ from an NN. I’m merely stating that the current formalism, in of itself, doesn’t seem to allow for such behavior.

Another concern regarding the use of NNs to understand biological function is the potential complexity of the NN resulting from an attempt to model an abstract biological function such as the meaning of an object (I am assuming that the mind is ultimately reducible to the physical or computational realm). As I eluded in the previous paragraph, I assert that abstract concepts are meta-representational, or that one must look beyond a simple neural correlate snapshot to understand how the more complex areas of the mind function. If this is true, then a model at the level of an NN may prove to be as much as a mystery as the physical reality it was intended to model and resist proofs of its correctness.

In the end, NNs will probably continue to prove valuable to those researching at the granular level, neuroscientists, biopsychologists, etc. There is also the professional domain that can apply them to interesting problems regardless of their biological validity. However, I’m skeptical regarding the applicability to the investigation of abstract constructs such as the meaning of objects and reasoning.

I was first introduced to this term when I took a course in psychological research methods a few months ago. Essentially, it means defining a concept in such a way that it can be manipulated in objective space as opposed to subjective space. More simply, a a concept is defined in terms of measurable qualities rather than qualities for which no objective measure exists. Dealing with the objective and things defined operationally is key to scientific method in general and certainly not limited to psychology. Indeed, limiting rationality to the objective space has provided a framework under which great strides in discovery have been and are made feasible.

However, we must take care not to overextend the application of objective reasoning. Today, objectivity is applied almost without question to politics, social sciences and even the meaning of existance. It has been my personal experience that this far reaching application tends to be self-limiting at best and destructive at worst. On the limiting side of the spectrum, we can invoke the Marcusian notion of the operationalization of concepts lke “freedom,” where the objectification of freedom inherently limits what freedom ‘could’ be or mean. On the destructive end of the spectrum, we may postulate that the total absence of subjectivity leads to nihilism in that the limiting factors of objective definition become so pervasive that no room exists for personal discovery or growth.

In the strictest sense, an abstract operational definition would need to be a combination of other operational definitions eventually reducing to a set that are directly measurable. Therefore, a positivist may assert, “even very abstract concepts such as freedom and existence will eventually be explainable through operational definition via reduction of these concepts down to physical or computational laws.” However, the complexity of this model may not be graspable. That is, understanding the model may prove as difficult as understanding the physical manifestation the model was intended to represent. In other words, one would need to apply the same empirical methods to understand the model as they would to understand reality.

Furthermore, in the discourse of social and political sciences definitions are routinely established and used operationally that are not “pure” operational definitions. That is, they don’t reduce to directly measurable elements. This is an almost humorous constraint in these domains because they’re limited by a sense of objectivity which fails to truly be objective.

For better of for worse, objective thinking is so incredibly embedded in our thought processes at this point that it is overextended in attempts to tackle problems for which it is ill prepared. This over dependence opens the door to manipulation and limitations upon thought.

This year, Nov. 4th encompassed an atmosphere more reminiscent of a new year’s eve than an election day. Just as I was finishing the last sip of a tasty 0.5 liter Franziskaner at a neighborhood pub, the broadcast announced Obama as our president elect. The pub patrons howled and cheered as a dark chapter in American history begins to close.

The people finally realize they’ve been manipulated by an administration willing to rule by fear and they don’t want another leader with such ties. On the way, a man has demonstrated the American spirit in action and made skeptics, such as myself, consider a more optimistic attitude with respect to the political system and the people of this land.

As I walked home, there were cheers emitting from the windows of residences, packed bars full of merry making and at least one person running down the sidewalk clanking a ladle against a pot declaring the president elect. I was surprised and taken by the level of positive exuberance which I have never seen before in response to an election. Nov. 4th 2008 will indeed be a night remembered by many.

The blog Neuronarrative, http://neuronarrative.wordpress.com/, has an interesting post on “Identify Politics.” In sum, it’s the notion that politicians will present themselves as characters that a large demographic will relate with and thus will gain their vote. Indeed, this tactic worked well for Bush Jr. by presenting himself as a modest “good’ol boy” rather than the product of unmatched privilege.

I also notice this sort of posturing in the corporate environment, albeit a slightly different manifestation. Anyone wishing to “climb the ladder” must present themselves as being “compatible” with the culture of management in ways that are obviously outside the scope of work such as family, interests, politics and even alcohol tolerance (there are studies that correlate people who drink with co-workers with higher wages).

Ultimately, people make behavioral projections based on how close a perceived identity matches their own. The people you work with extrapolate what you may do in the future by identifying you with some preconceived generalization. In politics, if people feel they identify with the politician they’ll say, “I just know he’s going to do ‘this’ because he/she’s like me.”

When you don’t make an effort to present yourself as “a compatible identity,” and believe me I have some practice at ignoring this aspect of social dynamics, you’re seen at best eccentric or worse a loose cannon. Rather than an asset, you’re a liability because the people essentially “don’t get you” and feel that you’re less predictable than those the person(s) can identify with, regardless of actual behavior.

In day to day life, this particular social dynamic is probably necessary. It is certainly very ingrained in most people. However, politicians, advertisers and anyone else seeking gain can exploit this behavior characteristic without many people being aware of it at a conscious level. I find that dangerous and unethical.