Structured Flow on Neural Manifolds (Jirsa et al, 2019)

As I try to develop a vocabulary for an ecological neuroscience, I am looking for two things. First, I'm looking for help from existing methods to help identify real neural parts and processes; so far I've ruled the FEP out for that. Second, I'm looking for an existing dynamical framing to help express whatever ecological psychology figures out about the brain. The jury is still out on whether the FEP is that framing; another option is a development of Kelso's coordination dynamics that invokes structured flow on manifolds. (This paper by Jirsa, McIntosh & Huys was a contribution to the special issue on Ecological Neuroscience). 

As I review the paper, I am going to be trying to figure out if this mathematical framing is going to help. It's not going to be a guide to real neural parts, but it might be the right way to formally describe the real parts we identify by other means. 

The first thing that Jirsa et al note is that your theory of brains simply must be grounded in the right description of behaviour. I agree, as did all the contributors to the special issue and has become a fairly mainstream idea now (see the important paper by Krakauer et al, 2017). They lean heavily into the coordination dynamics of Kelso, Haken, and others as being the right characterisation of the behavioural scale (there are some issues here, specifically whether these dynamical models can explain, but Jirsa et al do a good job of applying the work carefully). 

Broadly, they work carefully towards a formal language for describing neural states that is intimately connected to the dynamics of the behavioural scale. Where they end up also entails taking a task-specific approach, rather than the more broad strokes Kelso dynamical modelling approach. and they decide that this should be a feature and not a bug. Again, I agree - task specificity is a key move. 

Structured Flows on Manifolds

Behavioural systems are very, very high dimensional; we have redundant degrees of freedom at pretty much every scale and this issue is even more pronounced at the neural scale. The task-specific analysis says that we need to identify a way to take this system and temporarily softly-assemble it into a much, much lower dimensional system that can successfully operate in the current task and that can also be controlled effectively. 

(This should all sound familiar: it is the essence of Bingham's task-specific devices, and it is the driving principle behind all the motor abundance analysis methods such as Uncontrolled Manifold Analysis, TNC analysis, and optimal feedback control theory. I don't think any of this coincidence is an accident, and I think that joining the dots across multiple scales will rely on this kind of maths - this is why SFM is interesting to me!)

In this formalism, dimension reduction to a manifold gives you flow at two time scales. The slow time scale is the flow field that defines all the possible ways behaviour can unfold across the manifold. The fast time scale is the flow field that defines attractor states that govern particular instances of behaviour allowed on the manifold. 

This is where task-specificity becomes key - it's not possible to define a manifold that defines all possible behaviours the organism can ever possibly do, but it is possible to define a manifold that defines all the possible ways a specific task might unfold. Again, this is the key to making UCM etc work! A second implication is that these manifolds must be transient; they must be created and annihilated and recreated as the task demands swing in and out and back in. This is, I suspect, going to connect nicely with Anderson's Transient Assembled Local Neural Subsystems (TALoNS); more on that later. 

Some other nice features come with this formalism that suit an ecological neuroscience. First, there are natural ways to work information into the formalism as the driving force for the fast dynamics. Second, redundancy/degeneracy are baked in; you can get topologically equivalent slow timescale flow (task specific device) when, say, the same task requires coupling to visual vs auditory information sources. This accords nicely with some recent empirical work I'm doing on task dynamics, which I will get into later. 

Summary

Jirsa et al wrote a really good paper. They did an amazing job keeping the math doing the modelling distinct from the system being modelled (for example, they explicitly note that this formulation is not the only option, but then provided reasons to prefer it given the needs of an ecological neuroscience. Not doing this has been a big criticism of the FEP.). They worked very hard to develop their formalism with respect to the ecological behavioural scale; in other words, they took their own challenge to heart and grounded their neuroscience in behaviour. 

At this point, my tentative conclusion is that this framework will not help pick out real neural parts, but that it could very well provide the mathematical vocabulary required to implement the real neural parts (such as TALoNS?) we find by other means.