Hi everyone, I've been following the AGI list for a while, but this is my first post. Here is a little bit about my background in artificial neural networks from MANY years ago (see my PhD thesis on using artificial neural network-based vision to drive a car: https://books.google.com/books?id=7pvbBwAAQBAJ) and from more recent research on brain-computer interfaces (see: http://www.computerworld.com/article/2521888/app-development/intel--chips-in-brains-will-control-computers-by-2020.html) to help introduce myself and ground this post.
On Tue, 16 Jun 2015 15:24:04, Matt Mahoney wrote: > There is a lot of evidence that neurons in the brain are performing a > type of computation that is simulated in artificial neural networks. > Specifically, that a neuron computes a weighted sum of inputs followed > by a clipping or threshold function. The quantity of interest is the > firing rate, which is represented as a real-valued activation level > that varies on the order of tens or hundreds of milliseconds.... > > In any case, the computation is O(n), where n is the number of > synapses. This is in P. There is growing evidence in neuroscience that there is more to neural computation than simply neurons computing a weighted sum of their inputs. And from my read of that evidence, a reasonable argument can be made that recreating such computation on a digital computer may be NP-hard / NP-complete. Below is a sketch of one argument as to why this might be the case. The question hinges on what level a Whole Brain Emulation (WBE) would/will need to operate to recreate the key aspects of brain dynamics in order to recreate human thinking/consciousness - will it require emulation at the level of cortical columns, individual neurons, neurotransmitter molecules, atomic or possibly even quantum interactions? This will determine to a great extent how feasible it will be to create such emulations in a digital computer. Here is an analogy that sometimes makes me pessimistic about the feasibility of whole brain emulation. Consider the problem of predicting how long, linear strings of amino acids (i.e. proteins) fold to create the bioactive 3D structure of protein molecules that are critical for all life. Proteins fold incredibly fast into the same, extremely complex 3D structures - see this video (https://www.youtube.com/watch?v=qs3xONv548I) for an animation of the 3D structure of hemoglobin. Despite knowing the exact sequence of amino acids in the protein molecules like hemoglobin, and knowing how to compute the local forces between various adjacent/nearby amino acids that contribute to the molecule's ultimate 3D shape, even the fastest computers are not able to accurately predict the 3D shape of a folded protein from its amino acid sequence alone. In fact, the protein folding problem has been shown to be NP-hard ( http://www.brown.edu/Research/Istrail_Lab/papers/robustproofs.pdf), in fact, even worse, NP-complete - see this paper http://www.ncbi.nlm.nih.gov/pubmed/9541869). To quote from the paper above: "Exhaustive search of a protein's conformational space is clearly not a feasible algorithmic strategy. The number of possible conformations is exponential in the length of the protein sequence, and powerful computational hardware would not be capable of searching this space for even moderately large proteins." The relevance of the protein folding problem to the brain emulation problem stems from the reason why predicting a protein's 3D shape is so hard. The reason is due to non-local interactions. The reason its so hard is that each new amino acid added to the protein not only has local effects on the shape of the resulting manifold, but has long range, non-linear influence on how far distant parts of the protein interact. For example, a slight change in a bond angle at one location in the amino acid chain has the potential to bring far distant amino acids in the chain into a new spacial configuration relative to one another, changing their individual bond angles which in turn induce more long-range impacts in a ever expanding ripple effect. So adding (or modifying) one amino acid to the chain requires a combinatorially explosive additional amount of computation to predict the impact on the 3D structure if using a digital simulation of the protein and the folding process. In other words, elements of the system (in this case amino acids) engage in non-local, long-range interactions with other elements of the system in ways that are intractable to predict/simulate without an incredibly detailed (and therefore computationally intractable) model of the physics of the system. What does this have to do with how the brain works? Its becoming increasingly clear in neuroscience that important aspects of neural processing (especially consciousness, see https://en.wikipedia.org/wiki/Gamma_wave) occur as a result of long range interactions between populations of neurons mediated by neural oscillations (https://en.wikipedia.org/wiki/Neural_oscillation) which in turn are largely generated and propagated by what are called Local Field Potentials (LFPs see https://en.wikipedia.org/wiki/Local_field_potential), which are an electrophysiological signal generated by the summed electric current flowing from multiple nearby neurons within a volume of brain tissue. The details aren't that important. The key thing to understand is that the firing of a single neuron doesn't just influence the downstream neurons it is directly connected to via synapses. The firing of a single neuron is an electrochemical event, which contributes to altering the brain's electrical field at various scales. Changes to the electrical field in turn influence the tendency (probability) of neuron's within that field to fire (see http://www.ncbi.nlm.nih.gov/pubmed/8985893 for evidence), which in turn will change the electrical field further, causing other neurons to change their tendency to fire, creating a cascade of influence that is *independent of the direct synaptic connectivity pattern.* Here is a good 2010 paper (see http://www.ncbi.nlm.nih.gov/pubmed/20130201 ) by Buzsáki & Koch (two leaders in the field of neuroscience) providing evidence that 'digital' neural spiking and 'analog' spatially varying electric field potentials in the brain are interdependent - mutually influencing each other to form a feedback loop. To quote from the abstract "These findings imply that local electric fields, generated by the cooperative action of brain cells, can influence the timing of neural activity." And here is where the analogy between protein folding and brain emulation becomes apparent. If changes in a neuron's firing behavior can have long-range impact on the firing behavior of other neurons to which it is not directly (or even indirectly) connected via its influence on the brain's electrical field, this could set in motion the kind of cascade of non-local influences that made the protein folding problem theoretically (not to mention practically) intractable. In other words, if this type of long-range, non-linear, synapse-independent interaction is indeed happening and is important for information processing in the brain, then it may be intractable to accurately predict brain activity at time T+1 from brain activity at time T based solely on the synaptic connectivity pattern between neurons - which most researchers into whole brain emulation seem to assume will be possible. In short, growing evidence supporting the importance of cortical oscillations in neural processing suggests that this sort of analog/digital feedback loop might be critical to how the brain works, and that such interactions might be very hard (possible intractably hard) to model accurately (i.e. emulation vs. merely crude simulation) on a digital computer, in a similar way to how protein folding is intractable to model on a digital computer. I hope this isn't the case, since IMO the most likely path to a transhumanist future for today's middle age people is mind uploading, given the progress being made towards accurate whole brain preservation, as documented by recent steps towards winning the Brain Preservation Prize (see: http://blog.brainpreservation.org/2015/05/26/may-2015-bpf-prize-update/). Thanks, --Dean ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
