In ‘Is coding a relevant metaphor for the brain?’(2018) Romain Brette argues that the causal structure of neural codes (linear, atemporal) is incongruent with the causal structure of the brain (circular, dynamic). While he clearly explains how neural codes are inappropriate theoretical constructs for behavioural neuroscience experiments it's immediately clear what he means by causal structure.
On the 18th page he explains that:
The causal structure of the brain is sketched on Figure 9A. At a coarse description level, the brain is a dynamical system coupled to the environment by circular causality. At a finer description level, the brain is itself made of neurons, which are themselves dynamical systems coupled together. To a first approximation, the coupling is mediated by spikes, which are timed events. In a dynamical system, state variables have a causal role by construction; examples of state variables in this physical system are membrane potential and the state of ionic channels. Spikes have causal effect, but being events they are not state variables; a spike is something that happens, not a property of the system.
which is incongruent with concept of a neural code since:
Neural codes abstract time away, but temporality is critical to the operation of a dynamical system.
It's worth noting that Judea Pearl and other computer scientists have developed practical methods for causal inference  but no rigorous notion of causality. For this reason, I think evidence of the brain's causal structure would require a practical dynamical model of the brain on which we can perform causal inference to answer questions in behavioural neuroscience.
This leads me to a couple questions:
- Are there biologically-plausible dynamical systems models that would qualify? (Might brain network models be sufficient? Ex: )
- Assuming such models exist, what methods may we use to perform causal inference on these dynamical systems?
After further reflection upon comments due to Bryan Krause I think these two questions may be combined to form a single question:
Are there biologically plausible models for causal inference in the human brain?
Dynamical Systems that build upon neural coding theory:
Brette's notion of causal structure for the brain appears to be in direct opposition with that of Karl Friston's Free Energy Principle  whose formalism builds upon neural coding theory:
Learning under the free-energy principle can be formulated in terms of optimizing the connection strengths in hierarchical models of the sensorium. This rests on associative plasticity to encode causal regularities and appeals to the same synaptic mechanisms as those underlying cell assembly formation.
However, in  Karl Friston argues that a dynamical system like the brain can encode sequences of events via attractors:
...the basic idea is that the environment unfolds as an ordered sequence of spatio-temporal dynamics, whose equations of motion induce attractor manifolds that contain sensory trajectories. Critically, the shape of the manifold generating sensory data is itself changed by other dynamical systems that could have their own attractors. If we consider the brain has a generative model of these coupled attractors, then we would expect to see attractors in neuronal dynamics that are trying to predict sensory input. In a hierarchical setting, the states of a high-level attractor enter the equations of motion of a low-level attractor in a nonlinear way, to change the shape of its manifold.
This is a plausible hypothesis which suggests that a more sophisticated notion of encoding might be used by the brain where state variables emerge from temporal sequences via attractors. Having said that, Brette's critique of the conventional interpretation of neuronal codes by the majority of behavioural neuroscientists still holds.
Causal Inference vs the metaphysics of Causality:
We can't know the brain itself, only models of the brain that we may use to do experiments. To clarify my first question: Brette says that models based on notions of neural coding wouldn't qualify so what are concrete examples of dynamical systems models that do? My questions are very much designed to move the discussion beyond theory and what could be useful to behavioural neuroscientists. Furthermore, I suspect that it's not possible to define causality without going into metaphysics. This is probably why Judea Pearl chose to develop a theory of causal inference and not a theory of causal methods. Using methods from causal inference you can argue that two causal structures are distinct if: (1) there is a method for causal inference that is applicable to struct A but not struct B (2) there is a method for causal inference for which struct A and struct B give different answers.
- Romain Brette. Is coding a relevant metaphor for the brain? BioArxiv. 2018.
- Robert R. Tucci. Introduction to Judea Pearl's Do-Calculus. 2013.
- Christopher W. Lynn & Danielle S. Bassett. The physics of brain network structure, function and control. Nature. 2019.
- Karl Friston. The free-energy principle: a unified brain theory? 2010.
- Karl Friston and Stefan Kiebel. Predictive coding under the free-energy principle. Phil. Trans. R. Soc. B. 2009.
- The Metaphysics of Causation. Stanford Encyclopedia of Philosophy. 2016.