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Whether artificial neural nets can approximate ODE's and whether neural networks in nature actually do this is not clear. Biology citations please. EDIT: To th

Whether artificial neural nets can approximate ODE's and whether neural networks in nature actually do this is not clear. Biology citations please. EDIT: To the reply. None of those papers state that evolution causes naturally occurring neural networks to become ODE solvers.

yummyfajitas 16y ago
I usually hate to argue by authority, but in this case I'll make an exception. Perhaps you are familiar with the work that got Hodgkin and Huxley the 1963 Nobel Prize in Physiology and Medicine? Ok, I won't just be lazy. Here are the original papers: http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392219&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392213&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392209&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139220... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392212&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392413&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139241... By the way, the question is not whether ANN's approximate ODEs, but whether ODEs can approximate BNNs (or whatever other processes guide the honeybee dance). [edit in response to your edit: those papers show that a neuron's behavior is well described as an ODE solver. How it evolved is irrelevant.]
jerf 16y ago
You're badly missing the point. A neuron is not an ODE solver in the sense that you feed it some sort of mathematical specification of the ODE and it sits there and performs algebraic manipulations until there is some solution that pops out in the form of IEEE 754 floating point numbers. Neurons aren't Mathematica. A set of neurons is the ODE solver. If there is a set of ODEs that describes some neural system in terms of the solution to the ODE, then the neural system profoundly is an ODE solver. You're now asking for a demonstration of something that can't exist because having already demonstrated a reasonable isomorphism between some ODEs and some neural nets, there isn't another layer of some sort of "REALLY REAL isomorphism", that is only a product of human cognition and the failures it has thereof. (I mean that in general, not specific to one person, humans in general are surprisingly good at creating distinctions where there shouldn't be.) A system is what it does. If the activities of some set of neurons can be accurately described as a solution to an ODE, then it is an ODE solver. If the activities of a set of neurons can be accurately modeled by a clock function, then the neurons are a clock corresponding to that function. If the activities of a set of neurons can be accurately described as an edge-detection algorithm, then the neurons are edge detectors. (Both of my other examples here are real too, by the way, I didn't just make them up for didactic purposes.)
- swannodette 16y ago
  I didn't miss that point, and I didn't say neuron. What set of neurons in a bee's brain is the ODE solver? Can we provide our own inputs and experimentally show that that specific set of neurons actually occurring in nature do what is described? Again, all we have is a theory with no more evidence than the original article. Models that match our observations in the world are our means to reason about the world. But they are not the world, this why our models constantly to change or have to be refined. In fact the cited papers below are quite clear about that. This paper is illuminating on the usefulness and limitations of the H-H model: http://www.ncbi.nlm.nih.gov/pubmed/12392930 http://www.ncbi.nlm.nih.gov/pubmed/12392930
  - yummyfajitas 16y ago
    What set of neurons in a bee's brain is the ODE solver? I didn't claim to have evidence for my theory. All I claimed is that it was simpler and more plausible than Shipman's. Look, if you flick a switch on the wall, and a light goes on, the simplest explanation is that some configuration of electrical wires inside the wall caused the production of light from an electrically powered light bulb. You can postulate all sorts of other exotic mechanisms, e.g. levers snapping the glass in a chemical light. But the "occams razor explanation" (which is all I attempted to provide) is electricity in wires. Same thing with bee behavior - you should postulate some configuration of neurons with behavior modeled by an ODE solver long before you invoke quantum field theory.

yummyfajitas 16y ago

I usually hate to argue by authority, but in this case I'll make an exception. Perhaps you are familiar with the work that got Hodgkin and Huxley the 1963 Nobel Prize in Physiology and Medicine? Ok, I won't just be lazy. Here are the original papers: http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392219&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392213&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392209&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139220... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392212&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139221... http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1392413&blobtype=pdf http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=139241... By the way, the question is not whether ANN's approximate ODEs, but whether ODEs can approximate BNNs (or whatever other processes guide the honeybee dance). [edit in response to your edit: those papers show that a neuron's behavior is well described as an ODE solver. How it evolved is irrelevant.]

jerf 16y ago

You're badly missing the point. A neuron is not an ODE solver in the sense that you feed it some sort of mathematical specification of the ODE and it sits there and performs algebraic manipulations until there is some solution that pops out in the form of IEEE 754 floating point numbers. Neurons aren't Mathematica. A set of neurons is the ODE solver. If there is a set of ODEs that describes some neural system in terms of the solution to the ODE, then the neural system profoundly is an ODE solver. You're now asking for a demonstration of something that can't exist because having already demonstrated a reasonable isomorphism between some ODEs and some neural nets, there isn't another layer of some sort of "REALLY REAL isomorphism", that is only a product of human cognition and the failures it has thereof. (I mean that in general, not specific to one person, humans in general are surprisingly good at creating distinctions where there shouldn't be.) A system is what it does. If the activities of some set of neurons can be accurately described as a solution to an ODE, then it is an ODE solver. If the activities of a set of neurons can be accurately modeled by a clock function, then the neurons are a clock corresponding to that function. If the activities of a set of neurons can be accurately described as an edge-detection algorithm, then the neurons are edge detectors. (Both of my other examples here are real too, by the way, I didn't just make them up for didactic purposes.)

swannodette 16y ago
I didn't miss that point, and I didn't say neuron. What set of neurons in a bee's brain is the ODE solver? Can we provide our own inputs and experimentally show that that specific set of neurons actually occurring in nature do what is described? Again, all we have is a theory with no more evidence than the original article. Models that match our observations in the world are our means to reason about the world. But they are not the world, this why our models constantly to change or have to be refined. In fact the cited papers below are quite clear about that. This paper is illuminating on the usefulness and limitations of the H-H model: http://www.ncbi.nlm.nih.gov/pubmed/12392930 http://www.ncbi.nlm.nih.gov/pubmed/12392930
- yummyfajitas 16y ago
  What set of neurons in a bee's brain is the ODE solver? I didn't claim to have evidence for my theory. All I claimed is that it was simpler and more plausible than Shipman's. Look, if you flick a switch on the wall, and a light goes on, the simplest explanation is that some configuration of electrical wires inside the wall caused the production of light from an electrically powered light bulb. You can postulate all sorts of other exotic mechanisms, e.g. levers snapping the glass in a chemical light. But the "occams razor explanation" (which is all I attempted to provide) is electricity in wires. Same thing with bee behavior - you should postulate some configuration of neurons with behavior modeled by an ODE solver long before you invoke quantum field theory.