There are at least five general spectrums upon which all models of the nervous system must lie, and there are trade-offs to being on either end of each of these spectrums.
Global vs. Local Computations: Global propagation posits that certain computations occur at “lower” levels of the nervous system and lend their suggestions in the form of neural signals to “higher” levels of the nervous system who aggregate and act on these signals. On the other side of the spectrum, we have strictly local computations with no overseer. The global propagation standpoint has the advantage of being easier to explain complex phenomena, and being more intuitive to humans due to its organized framework. The local computation standpoint has the advantages of being more evolutionarily plausible and currently having more evidence, as scientists have yet to locate an obvious supervisor region of the brain. An example of global computation is error recognition in the medial frontal cortex, while an example of local computation is BCM synaptic modification in the visual system. Advantage: Local.
Recurrent vs. One-Shot Feedback: Recurrent feedback models have the advantage of being able to handle more complex situations with fewer nodes while one-shot feedback has the advantage of less computation necessary per input, because the weights don’t have to converge to a steady state. As Douglas Hofstadter explains, recursive computation can lead to strange loops that never converge on an answer, however, our brains must have some way of handling this uncertainty. Ultimately, the number of neurons in the brain is probably the most important bottleneck evolutionarily, and therefore recurrent feedback is more likely. An example of a one-shot feedback system is a linear associator network while an example of a recurrent feedback system is the Hopfield model. Advantage: Recurrent.
Undirected vs. Directed Trees: Markov networks are undirected, while Bayesian networks are directed. Directed networks are built such that through each connection from one node to another must also specify a direction, with a parent and a child node. Undirected networks make no such distinction. The advantages of the directed network are that it can infer extra dependency relationships among the variables based simply on the topology, but the disadvantage is that it cannot logically express all the dependencies that an undirected network can. The causal nature of the directed network makes it more plausible and intuitive to a human audience, but of course neurons themselves are not human. If you really want to know the answer, go ask your local math professor. Advantage: Directed (according to Judea Pearl).
Immutable vs. Plastic Networks: There are many different biologically revelant types of brain plasticity, including new nodes (through neurogenesis), more connections between existing nodes (through the outgrowth of neurites), and altering the weights of existing connections (through long-term potentation). The advantage of including plasticity in your model of the nervous system is that it is more realistic, but the disadvantage is that we are not exactly sure how this plasticity works and you may end up coding processes that would accomplish lots of cool stuff but that don’t actually occur. For example, it currently seems that neurogenesis may yield a benefit cells around them through chaperone effects and then die off themselves, but how would you formalize that? Advantage: Plastic, but approach with care.
Empirical vs. Abstract Pathways: This dichotomy could be applied to science in general; it is not applicable simply to models of the brain. The advantages of predicting abstract pathways is that you can have a more parsimonious answer to complex questions. The disadvantage of attempting to guess without solid proof is that you may waste your time without solving any important puzzles. Most of what gets published in the top journals is empirical, while most of what your roommate tells you at 2:30 am is abstract. However, there have been many instances where pure, abstract theory has helped to advance the science; for example, see Hebbian Learning. Advantage: Thomas Kuhn.
This was inspired by the first of Caltech’s 100 Questions for Cognitive Scientists: “Models of the nervous system come in many forms and types; from abstract to highly realistic (e.g. Hopfield model vs. biophysical detailed networks). Use specific examples to discuss the tradeoffs.” Feel free to offer your own answer or thoroughly trash mine in the comments.