|diagram via: Monica Anderson|
Ambiguity in Systems
Ms. Anderson groups ambiguity with two other types of problems - incomplete information and incorrect information. These kinds of problems are not just limited to computerized systems. These same kinds of problems occur in written text, spoken language and video. Anderson proposes distributed representation as a better way for computer models to take these ambiguities into account:
A much better way is to design the model to allow for multiple possible interpretations to co-exist, in parallel, and to each allow analysis to progress along multiple paths until such a time that a selection of an alternative has significant support. "Distributed Representation" is one commonly used strategy that allows this. These systems are also resilient against incomplete and incorrect information. Handling parallel interpretations explicitly (by using other methods) may quickly become very complicated because of the curse of Dimensionality and the combinatorial explosion of dependencies.The "curse of dimensionality" may not be a term all our readers understand. We will try to explain it. It was Richard Bellman that first coined the phrase "Curse of dimensionality" in a 1957 report to the RAND corporation titled, Dynamic Programming. Eccles & Su in their 2004 lecture at the ISICT in 2004, in a paper titled, Illustrating The Curse of Dimensionality Numerically Through Different Data Distribution Models explains this curse as being that "...as the dimension of the vectors increases, the cost of retrieving data increases dramatically." Wikipedia provides a rather clear explanation of this "curse:"
There are multiple phenomena referred to by this name in domains such as sampling, combinatorics, machine learning and data mining. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. This sparsity is problematic for any method that requires statistical significance. In order to obtain a statistically sound and reliable result, the amount of data you need to support the result often grows exponentially with the dimensionality. Also organizing and searching data often relies on detecting areas where objects form groups with similar properties; in high dimensional data however all objects appear to be sparse and dissimilar in many ways which prevents common data organization strategies from being efficient.So according to this curse you will never have enough data as the system becomes more complex, since the data will grow exponentially along with the system's complexity or dimensions.
The distributed representation solution to this increasing complexity was first developed by Churchland and Sejnowski in 1992, in a book titled, The Computational Brain. The mind dictionary from the University of Waterloo defines distributed representation thusly:
The concept of distributed representation is a product of joint developments in the neurosciences and in connectionist work on recognition tasks (Churchland and Sejnowski 1992). Fundamentally, a distributed representation is one in which meaning is not captured by a single symbolic unit, but rather arises from the interaction of a set of units, normally in a network of some sort. In the case of the brain, the concept of ‘grandmother’ does not seem to be represented by a single ‘grandmother cell,’ but is rather distributed across a network of neurons (Churchland and Sejnowski 1992). This method of representation stands in direct opposition to the symbolic representation used by adherents of classical artificial intelligence (AI).The Stanford Encyclopedia of Philosophy further elucidates the contrast between this newer approach and the more classical approaches to AI:
The last forty years have been dominated by the classical view that (at least higher) human cognition is analogous to symbolic computation in digital computers. On the classical account, information is represented by strings of symbols, just as we represent data in computer memory or on pieces of paper. The connectionist claims, on the other hand, that information is stored non-symbolically in the weights, or connection strengths, between the units of a neural net. The classicist believes that cognition resembles digital processing, where strings are produced in sequence according to the instructions of a (symbolic) program. The connectionist views mental processing as the dynamic and graded evolution of activity in a neural net, each unit's activation depending on the connection strengths and activity of its neighbors, according to the activation function.Anderson would agree with the connectionist view when she states that,
...if these kinds of strategies are not adopted, then computer systems operating in ambiguous domains may display "brittle" behavior. When encountering ambiguous input, especially at the edges of the system's competence, the quality of the result will degrade rapidly.Self-reference, Paradoxes & Strange Loops
|Drawing Hands by Escher (1948)|
What I mean by "strange loop" is — here goes a first stab, anyway — not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in a hierarchy, and yet somehow the successive "upward" shifts turn out to give rise to a closed cycle. That is, despite one's sense of departing ever further from one's origin, one winds up, to one's shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop. (pp. 101-102)Opinions, Hypothesis & Multiple Points of View
These are more problems that arise in complex systems. Anderson explains this:
These three are again shades of each other. A hypothesis might be part of the input data but could also be a (typically temporary) assertion made by the system itself. Opinions are typically expressed one per agent. And one agent might simultaneously hold multiple persistent points of view on some issue, often depending on context.We will continue with Anderson's proposed solution to these issues in our next installment in this series.