What is computational neuroscience? (XXX) Is the brain a computer?

It is sometimes stated as an obvious fact that the brain carries out computations. Computational neuroscientists sometimes see themselves as looking for the algorithms of the brain. Is it true that the brain implements algorithms? My point here is not to answer this question, but rather to show that the answer is not self-evident, and that it can only be true (if at all) at a fairly abstract level.

One line of argumentation is that models of the brain that we find in computational neuroscience (neural network models) are algorithmic in nature, since we simulate them on computers. And wouldn’t it be a sort of vitalistic claim that neural networks cannot be (in principle) simulated on computer?

There is an important confusion in this argument. At a low level, neural networks are modelled biophysically as dynamical systems, in which the temporality corresponds to the actual temporality of the real world (as opposed to the discrete temporality of algorithms). Mathematically, those are typically differential equations, possibly hybrid systems (i.e. coupled by timed pulses), in which time is a continuous variable. Those models can of course be simulated on computer using discretization schemes. For example, we choose a time step and compute the state of the network at time t+dt, from the state at time t. This algorithm, however, implements a simulation of the model; it is not the model that implements the algorithm. The discretization is nowhere to be found in the model. The model itself, being a continuous time dynamical system, is not algorithmic in nature. It is not described as a discrete sequence of operations; it is only the simulation of the model that is algorithmic, and different algorithms can simulate the same model.

If we put this confusion aside, then the claim that neural networks implement algorithms becomes not that obvious. It means that trajectories of the dynamical system can be mapped to the discrete flow of an algorithm. This requires: 1) to identify states with representations of some variables (for example stimulus properties, symbols); 2) to identify trajectories from one state to another as specific operations. In addition to that, for the algorithmic view to be of any use, there should be a sequence of operations, not just one operation (ie, describing the output as a function of the input is not an algorithmic description).

A key difficulty in this identification is temporality: the state of the dynamical system changes continuously, so how can this be mapped to discrete operations? A typical approach is neuroscience is to consider not states but properties of trajectories. For example, one would consider the average firing rate in a population of neurons in a given time window, and the rate of another population in another time window. The relation between these two rates in the context of an experiment would define an operation. As stated above, a sequence of such relations should be identified in order to qualify as an algorithm. But this mapping seems only possible within a feedforward flow; coupling poses a greater challenge for an algorithmic description. No known nervous system, however, has a feedforward connectome.

I am not claiming here that the function of the brain (or mind) cannot possibly be described algorithmically. Probably some of it can be. My point is rather that a dynamical system is not generically algorithmic. A control system, for example, is typically not algorithmic (see the detailed example of Tim van Gelder, What might cognition be if not computation?). Thus a neural dynamical system can only be seen as an algorithm at a fairly abstract level, which can probably address only a restricted subset of its function. It could be that control, which also attaches function to dynamical systems, is a more adequate metaphor of brain function than computation. Is the brain a computer? Given the rather narrow application of the algorithmic view, the reasonable answer should be: quite clearly not (maybe part of cognition could be seen as computation, but not brain function generally).

8 réflexions au sujet de « What is computational neuroscience? (XXX) Is the brain a computer? »

      • In the sense that the brain computes things that are not related to itself, but for example to the external world (eg. the location of a sound source).
        In my opinion, it can be said that neurons perform a computation on their inputs (eg. integration, coincidence-detection etc.), and the result of this computation is reflected in their outputs, which will trigger other computations in other neurons.
        Of course, it's us, as observers, who assign meaning to the values that are computed. The neurons themselves have no idea what they are doing.
        But still I think a description of the neural mechanisms in terms of (analog) computation can be insightful, more than describing the dynamics only.

        • When you say: "the result of this computation (...) will trigger other computations", you are making an algorithmic description indeed, but that's precisely what is problematic. Try to formalize what "result" means in terms of the variables of the dynamical system, and whether you can map the dynamics of the system to a mapping from one result to another result. Possible in principle with a feedforward network (because you have a composition of mappings between functions of time), generally not as soon as you have cycles.

          ps: there's a logical problem in your first statement (it's a computer because there are things it computes that have some property; your conclusion is in the premises)

  1. Ping : What is computational neuroscience? (XXXIV) Is the brain a computer (2) | Romain Brette

  2. It is believed that spacetime will have to be discretized to gain the final unified physics. Expect continuity to be nothing more than a useful approximation. In any case the temporal dynamics of real world systems do not have infinite precision continuous transition. True continuity demands infinite precision, it is unlikely to exist.

    Regards analog computation, real analog computers have finite precision, and thus are no more capable than digital computers. True analog would have infinite precision, such is not physically possible.

    Quantum computation is said does not exceed the capacity of digital computation, and even regards some of their sped up algorithms algorithms with similar degree of speed up have been found. In any case it is not believed the brain does computation.

    Several high profile researchers believe that physics is computable, and the brain being a physical object is computable.

    • To clarify what I meant in the last comment is that it is not believed the brain does quantum computation.

      As for algorithms with similar speed up as some sped up quantum algorithms, this refers to algorithms for digital computers.

    • As I pointed out in this post, the point discussed here is not whether the brain can be simulated. There are different ways to simulate a model; discrete, analog. The question is about the nature of the model; is it a sequence of manipulations of symbols or not (cf computational view of the mind).

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