Levels of analysis
The goal of the Axon model is to provide a coherent theoretical framework for the overall field of Computational Cognitive Neuroscience (CCN), which involves three different levels of analysis:
• Neuroscience provides the “lowest level” grounding of the underlying biological mechanisms of the brain.
• Cognitive Psychology provides a higher level understanding of what the brain actually does at a functional level: how do people and animals actually think, and how can we understand the relationship between these cognitive functions and the underlying mechanisms from neuroscience?
• Computation provides a tool to build the bridges between neuroscience and cognition in a formal and precise way: instead of building a theory only on the basis of words and concepts, we also build it out of computer programs that implement very specific mathematical and algorithmic mechanisms that attempt to describe what the neural mechanisms are doing.
These different levels of analysis in the CCN field can be mapped onto the levels of analysis articulated by David Marr (Marr, 1977), which are based on the source domain of computer science, where a given computational device can be understood at three different levels:
• Computational is the highest level, characterizing the overall computations that are being performed, and the abstract nature of the information that is being processed. For example, a sorting algorithm can be described as accomplishing the computational outcome of ordering items in a list according to a given metric, where the italicized terms represent the critical computational-level parameters associated with this level of computation.
• Algorithmic is the next level down, providing a more detailed description of the underlying information processing steps required to accomplish a given computation. Given the universal nature of a turing machine computational device, this algorithmic description can be provided in any suitable high level language such as Python, C, Go, or pseudocode which tends to look a bit like Python.
• Implementational is the hardware level of description, in terms of the actual bits of silicon that actually implement the turing machine, typically using a Von Neumann architecture that underlies all modern computers.
It is essential to recognize that Marr’s levels depend critically on the level-spanning role of the turing machine and Von Neumann architecture, which provide an abstract theoretical tool that bridges between these levels. Once you have this kind of abstract theoretical mechanism that accurately describes what the underlying hardware is actually doing at the implementational level, and provides the basis for your algorithmic-level description, then everything is very straightforward from a conceptual level.
However, we know for certain that the brain is not a turing machine at the level of neurons, although it may end up operating like one at an emergent, higher level through the interactions of multiple brain systems, and likely only in humans. Therefore, Marr’s specific levels, which provide such a compelling source analogy, are not directly applicable to understanding the brain.
Instead, we need to find an alternative abstract theoretical mechanism that accurately describes what the underlying hardware of the brain is doing, and how this hardware accomplishes all of the higher-level cognitive functionality.
In short, Marr’s levels are not some kind of automatic feature of nature, but really are a consequence of having an accurate level-bridging theory that allows our brains to construct descriptions of nature at these different levels. In reality, there is only the implementational level: the underlying neurochemical soup of the brain, or the electrical circuits of a computer.
This kind of level-bridging theory is precisely what the Axon framework is intended to provide, through a highly accurate (though still abstracted) mechanistic implementation of the neural mechanisms of the neocortex and other brain areas (see the Rubicon model for details), that has a clear computational-level basis in terms of error-driven predictive learning and the many functional properties of bidirectional connectivity, etc. The models built from these mechanisms then provide an accurate explanation of a wide range of cognitive phenomena.