Hierarchy in semantic maps, with phase transitions as a function of information
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Big Data is utilized by many to interpret a situation and predict behavior. The core idea is that with Big Data we can construct models that provide a causative relationship between the sensory input and the target output behavior. This approach to Big Data assumes that causative models exist.
In addition in the world of deep learning the back propagation of supervised labels flatten the architecture of the system. The internal description represented in the hidden nodes of the network are biased by the target from one side and by the lowest level of input on the other side.
Thus to a degree many Big Data approaches utilize the data to discover the single underlying truth.
I would like to argue that Big Data should be employed differently, an unsupervised approach with more inherent flexibility will discover the scale dependent truths and the transitions between scale.
In a hierarchical semantic map at each layer there are well defined axiomatic truths. For example, a wheel and tire are well defined elements at the same scale. While a bicycle and car are well defined elements at a different scale than wheel and tire.
How do transitions occur between scales? How do I know that the elements of wheel and tire create an emergence of the element car? The argument is that as we increase information the number of possible interpretations decreases (Umberto Eco). Hence the increase in information at the lower level forces a phase transition to the higher level.
I call it a phase transition since there is no continuous function between the two scales. A tire when it grows up will never be a car. However a tire and a wheel might be parts of a car or might be parts of a bicycle. Who they are is a function of the information in the system.
The information increases linearly with more data and exponentially with more connections between data. Thus, if there are two tires and two wheels and the tires are clincher tires with inner tubes between them and the wheels, then a bicycle will emerge.
In the same fashion simpler elements of data are well defined. For example the readings of the mercury level in a thermometer provides facts. Truths. Each reading is accepted in of itself as a true element. However the higher level concept, the season summer or winter, is not readily accepted as a truth from a few independent readings.
This transition from accepted truth to disputed concept is due to the lack of information in the system. But by increasing the information in the system the higher level concept emerges. Big Data provides the data elements and we can derive relationships between them thus increasing the information. A hundred readings of the temperature associated with their respective dates provides a large data set of dependent data
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Two principles arise:
1. two truths from different levels in the hierarchy can not interact with each other.
2. The emergence is a classification/judgement and should only be done at the moment of maximum Information
All true. But the really interesting behavior emerges when the layers interact. When one side of a tire is visibly deformed to flat, the whole car is disabled. When a virus enters my nose, my immune system kicks in. When the moon passes directly between the sun and the earrh, populations panic at the sudden eclipse. Etc.
ReplyDelete1. the example with a tire describes a situation with the parts at the lower level are not connected tightly enough to provide enough information and hence fail to emerge as a whole.
Delete2. the example with a virus is a typical emergent behavior, the virus is attacked at the lower level by antibodies, the sum of all the lower level activity is your immune system
Agreed. And, i think these dispute your first conclusion which minimizes the possibility of interactions between layers.
ReplyDelete