Re: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
This is exactly backward, and which makes using it as an unqualified presumption a little odd. Fetching an object from true RAM is substantially more expensive than executing an instruction in the CPU, and the gap has only gotten worse with time. That wasn't my point, which you may have missed. The point is that with our current technology track it's far cheaper to double your memory than to double your CPU speed. I'm not referring to the amount of memory bits processed by the CPU, but the total number of pigeonholes available. These are not one and the same. Therefore you can make gains in representational power by boosting the amount of RAM, and having each bit of memory be a more precise representation. You can afford to have, for example, a neuron encoding blue sofas and a neuron encoding red sofas. While a more restricted RAM approach would need to rely on a distributed representation, one with only sofa neurons and color neurons. (apologies for the poor example, but I'm in a hurry) Your points are correct, but refer to the bottleneck of getting information from RAM to the CPU, not on the total amount of RAM available. Back to the problem of the human brain, a big part of the problem in the silicon case is that the memory is too far from the processing which adds hard latency to the system. The human brain has the opposite problem, the processing is done in the same place as the memory it operates on (great for latency), but the operational speed of the processing architecture is fundamentally very slow. The reason the brain seems so fast compared to silicon for many tasks is that the brain can support a spectacular number of effective memory accesses per second that silicon can't touch. Both technologies have their advantages and disadvantages. The brain's memory capacity (in terms of number of addressable bits) cannot be increased easily while a computer's can be. I merely suggest that this fundamental difference is something to consider if one is intent on implementing AGI in a Neumann architechture. --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
Re: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Ben, you haven't given us an update on how things are going with the Novamente A.I. engine lately. Is this because progress has been slow and there is nothing much to report, or you don't want to get peoples hopes up while you are still so far from being done, or that you want to surprise us one day with, "Hey guys, guess what? The Singularity has arrived!" To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Brad, Hmmm... yeah, the problem you describe is actually an implementation issue, which is irrelevant to whether one does synchronoous or asynchronous updating. It's easy to use a software design where, when a neuron sends activation to another neuron, a check is done as to whether the target neuron is over threshold. If it's over threshold, then it's put on the ready to fire queue. Rather than iterating through all neurons in each cycle, one simply iterates through those neurons on the ready-to-fire queue. Of course, one can use this approach with either synchronous or asynchronous updating. We used this design pattern in Webmind, which had a neural net aspect to its design; Novamente is a bit different, so such a strategy isn't relevant. -- Ben G While I haven't read any of the documents in question, I'd like to expound a bit here. While you are certainly correct, I think Pei was referring to the wasted computational power of updating synapses that are inactive and have no chance of being activated in the near future. In our current Neumann architectures, memory is much cheaper than CPU cycles, which is not the case in the brain. So while the brain opts for minimal neurons, and keeps most of them active in any given situation, a silicon NN might have factors of 10 more neurons, but use very sparse encoding and a well optimized update algorithm. This setup would emphasize only spending CPU time updating neurons that have a chance of being active. -Brad --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED] --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Guess I'm too used to more biophysical models in which that approach won't work. In the models I've used (which I understand aren't relevant to your approach) you can't afford to ignore a neuron or its synapses because they are under threshold. Interesting dynamics are occurring even when the neuron isn't firing. You could ignore some neurons that are at rest and hadn't received any direct or modulatory input for some time, but then you'd need some fancy optimizations to ensure you're not missing anything. But in the situation you're referring to with a more abstract (and therefore more useful to AGI) implementation, these details are irrelevant. I just wanted to chime in and ramble a bit :) Very glad to hear things are going well with Novamente. Hope the holidays treat all of you well. -Brad --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Yep, you're right of course. The trick I described is workable only for simplified formal NN models, and for formal-NN-like systems such as Webmind. It doesn't work for neural nets that more closely simulate physiology, and it also isn't relevant to systems like Novamente that are less NN-like ben -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Brad Wyble Sent: Wednesday, December 24, 2003 11:59 AM To: [EMAIL PROTECTED] Subject: RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets Guess I'm too used to more biophysical models in which that approach won't work. In the models I've used (which I understand aren't relevant to your approach) you can't afford to ignore a neuron or its synapses because they are under threshold. Interesting dynamics are occurring even when the neuron isn't firing. You could ignore some neurons that are at rest and hadn't received any direct or modulatory input for some time, but then you'd need some fancy optimizations to ensure you're not missing anything. But in the situation you're referring to with a more abstract (and therefore more useful to AGI) implementation, these details are irrelevant. I just wanted to chime in and ramble a bit :) Very glad to hear things are going well with Novamente. Hope the holidays treat all of you well. -Brad --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED] --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
Re: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Actually, in attractor neural nets it's well-known that using random asynchronous updating instead of deterministic synchronous updating does NOT change the dynamics of a neural network significantly. The attractors are the same and the path of approach to an attractor is about the same. The order of updating turns out not to be a big deal in ANN's. It may be a bigger deal in backprop neural nets and the like, but those sorts of neural nets are a lot further from anything I'm interested in... I'd rather get ride of the notion of attractor altogether. Though it may be useful for perception, in high-level cognition I don't see anything like it. Of course, some beliefs are more stable than others, but are they states to which all processes converge? Hmmm Pei, I don't see how to get NARS' truth value functions out of an underlying neural network model. I'd love to see the details If truth value is not related to frequency nor to synaptic conductance, then how is it reflected in the NN? What I mean is not that NARS, as a reasoning system, can be (partially or completely) implemented by a network, but that NARS can be seen as a network --- though different from conventional NN. I think NN is much better than traditional AI in its philosophy --- I like parallel processing, distributed representation (to a certain extent), incremental learning, competing results, and so on. However, ironically, the techniques of NN is less flexible than symbolic AI. I don't like NN when it uses fixed network topology, has no semantics (and even claims it to be an advantage), takes the goal of learning as converging to a function (mapping input to output), does global updating, uses activation for both logical and control purposes, and so on. My way to combine the two paradigms is not to build a hybrid system that is part symbolic and part connectionist, but to build a unified system which is similar to symbolic AI in certain aspects, and similar to NN in some other aspects. Pei --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Hi, Actually, in attractor neural nets it's well-known that using random asynchronous updating instead of deterministic synchronous updating does NOT change the dynamics of a neural network significantly. The attractors are the same and the path of approach to an attractor is about the same. The order of updating turns out not to be a big deal in ANN's. It may be a bigger deal in backprop neural nets and the like, but those sorts of neural nets are a lot further from anything I'm interested in... I'd rather get ride of the notion of attractor altogether. Though it may be useful for perception, in high-level cognition I don't see anything like it. Of course, some beliefs are more stable than others, but are they states to which all processes converge? You have a point, which si why I didn't use the term attractor in the Hebbian Logic paper. The results I cited about attractor neural nets have to do with attractors. But in the brain, or in a Hebbian Logic network, you don't have attractors -- what you have are probabilistically invariant subsets of state space, i.e. subsets of the system's state space with the property that, once a system gets in there, it's likely to stay there a while. Attractors are a limiting case of this kind of state-space-subset, and they're a limiting case that doesn't occur in the cognitive domain. Hmmm Pei, I don't see how to get NARS' truth value functions out of an underlying neural network model. I'd love to see the details If truth value is not related to frequency nor to synaptic conductance, then how is it reflected in the NN? What I mean is not that NARS, as a reasoning system, can be (partially or completely) implemented by a network, but that NARS can be seen as a network --- though different from conventional NN. I think NN is much better than traditional AI in its philosophy --- I like parallel processing, distributed representation (to a certain extent), incremental learning, competing results, and so on. However, ironically, the techniques of NN is less flexible than symbolic AI. I don't like NN when it uses fixed network topology, has no semantics (and even claims it to be an advantage), takes the goal of learning as converging to a function (mapping input to output), does global updating, uses activation for both logical and control purposes, and so on. My way to combine the two paradigms is not to build a hybrid system that is part symbolic and part connectionist, but to build a unified system which is similar to symbolic AI in certain aspects, and similar to NN in some other aspects. Firstly, Novamente is not a hybrid system that's part symbolic and part connectionist, either. Webmind was, but Novamente isn't anymore. There's no more association spreading or activation spreading; these NN-like processes have been replaced by specialized deployments of PTL (probabilistic reasoning Novamente-style). Novamente does hybridize a bunch of things: BOA learning, combinatory logic, PTL inference, etc. ... but not any NN stuff Second, I do not advocate neural nets as an approach to AI, either. I think the approach has its merits, but overall I think that NN's are a really inefficient way to use von Neumann hardware. If we knew enough to *really* emulate the brain's NN in software, then the guidance offered by the brain would be so valuable as to offset the inefficiency of implementing massively-parallel-wetware-oriented structures and algorithms on von Neumann hardware. But we don't know nearly enough about the brain to make brain-emulating NN's; and the currently popular NN architectures seem to satisfy neither the goal of brain emulation, nor the goal of efficient/effective AI. My point in articulating Hebbian Logic is NOT to propose it as an optimally effective approach to AI, but rather to propose it as a conceptual solution to the conceptual problem of: **How the hell do logical inference and related stuff emerge from neural networks and other brainlike stuff?** No one in cognitive science seems to have a good explanation of this, beyond the really vague handwaving level. I think that the Hebbian Logic approach provides a significantly better explanation than anyone else has given so far. Even given that it also involves a bunch of handwaving (since I didn't work out all the technical details, and probably won't do so soon due to my own time limitations). Hebbian Logic *might* be a decent approach to practical AI --- I don't think it would be a terribly stupid approach --- but I like the Novamente approach better... -- Ben --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
Re: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Ben, Some comments to this interesting article: *. S = space of formal synapses, each one of which is identified with a pair (x,y), with x Î N and y ÎNÈS. Why not x ÎNÈS? *. outgoing: N à S* and incoming: N - S* Don't you want them to cover higher-order synapses? *. standard neural net update and learning functions One thing I don't like in NN is globle updating, that is, all activations and weights are updated in every step. Even if it is biologically plausible (which I'm not sure), in an AI system it won't scale up. I know to drop this will completely change the dynamics of NN. *. AàI B, means that when B is present, A is also present What are A and B (outside the network)? Are they terms, sets, attributes, events, or propositions? What do you mean by present? *. probability P(A,t), defined as the probability that, at time t, a randomly chosen neuron xÎA is firing and the conditional probability P(A|B; t) = P(A ÇB,t)/ P(B,t) This is the key assumption made in your approach: to take the frequency of firing as the degree of truth. I need to explore further about its implications, though currently I feel uncomfortable. In my own network interpretation of NARS (for a brief description, see http://www.cogsci.indiana.edu/farg/peiwang/papers.html#thesis Section 7.5), I take activation/firing as a control parameter, indicate the recourse spends on the node, which is independent to the truth value --- I'm thinking about T and T is true are fundamentally different. Of course, the logic/control distinction is not in NN, where both are more or less reflected in activation value. When you map their notions into logic, such a distinction become tricky. *. Basic inference rules I don't see what is gained by a network implementation (compared to direct probabilistic calculation). *. Hebbian Learning The original Hebbian learning rule woks on symmetric links (similarity, not inheritance), because weight of a link is decrease when one end is activated and the other isn't, and which is which doesn't matter. What you does in Hebbian learning variant A is necessary, but it is not the original Hebbian learning rule. *. Section 6 I'm not sure I understand the big picture here. Which of the following is correct? (1) PTL is fully justified according to probability theory, and the NN mechanism is used to implement the truth value functions. (2) PTL is fully justified according to probability theory, and the truth value functions are directly calculated, but the NN mechanism is used to implement inference control, that is, the selection of rules and premises in each step. (3) The logic is partially justified/calculated according to probability theory, and partially according to NN (such as the Hebbian learning rule). *. In general, I agree that it is possible to unify Hebbian network with multi-valued term logic (with an experience-grounded semantics). NARS is exactly such a logic, where a statement is a link from one term to another, and its truth value is the accumulated confirmation/disconfirmation record about the relation. In NARS, Hebbian learning rule correspond to the comparison (with induction, abduction, and deduction as variants) plus revision. Activation spreading corresponds to (time) resource allocation. BTW, Pavlov's conditioning is similar to Hebbian learning, and can also be seen as special case of induction in (higher-order) multi-valued term logic. Pei - Original Message - From: Ben Goertzel [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, December 20, 2003 8:26 PM Subject: [agi] The emergence of probabilistic inference from hebbian learning in neural nets Hi, For those with the combination of technical knowledge and patience required to sift through some fairly mathematical and moderately speculative cog-sci arguments... some recent thoughts of mine have been posted at http://www.goertzel.org/dynapsyc/2003/HebbianLogic03.htm The topic is: **How to construct a neural network so that symbolic logical inference will emerge from its dynamics?** This is not directly relevant to my own current AI work (Novamente, www.agiri.org), which is not neural network based. However, it is conceptually related to Novamente; and more strongly conceptually related to Webmind, the previous AGI design with which I was involved. It is also loosely related to Pei Wang's NARS inference system. While my guess is that this is not the most effective path to AGI at present, I do think it's a very interesting area for research and an exploration-worthy potential path toward AGI. Apologies for the rough-draft-ish-in-places document formatting ;-) -- Ben --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED] --- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
RE: [agi] The emergence of probabilistic inference from hebbian learning in neural nets
Pei, Thanks for your thoughtful comments! Here are some responses... - *. S = space of formal synapses, each one of which is identified with a pair (x,y), with x Î N and y ÎNÈS. Why not x ÎNÈS? - No strong reason -- but, I couldn't see a need for that degree of generality in a Hebbian Logic context... of course, there's no reason not to allow it in a formal model. --- *. outgoing: N à S* and incoming: N - S* Don't you want them to cover higher-order synapses? --- Yeah, you're right. However, I may remove higher-order synapses from the paper entirely, preferring to deal with higher-order relations via links to multi-neuron paths as discussed later on. - *. standard neural net update and learning functions One thing I don't like in NN is globle updating, that is, all activations and weights are updated in every step. Even if it is biologically plausible (which I'm not sure), in an AI system it won't scale up. I know to drop this will completely change the dynamics of NN. -- Actually, in attractor neural nets it's well-known that using random asynchronous updating instead of deterministic synchronous updating does NOT change the dynamics of a neural network significantly. The attractors are the same and the path of approach to an attractor is about the same. The order of updating turns out not to be a big deal in ANN's. It may be a bigger deal in backprop neural nets and the like, but those sorts of neural nets are a lot further from anything I'm interested in... --- *. probability P(A,t), defined as the probability that, at time t, a randomly chosen neuron xÎA is firing and the conditional probability P(A|B; t) = P(A ÇB,t)/ P(B,t) This is the key assumption made in your approach: to take the frequency of firing as the degree of truth. I need to explore further about its implications, though currently I feel uncomfortable. In my own network interpretation of NARS (for a brief description, see http://www.cogsci.indiana.edu/farg/peiwang/papers.html#thesis Section 7.5), I take activation/firing as a control parameter, indicate the recourse spends on the node, which is independent to the truth value --- I'm thinking about T and T is true are fundamentally different. Of course, the logic/control distinction is not in NN, where both are more or less reflected in activation value. When you map their notions into logic, such a distinction become tricky. --- Yeah, to make Hebbian Logic work, you need to assume that frequency of firing roughly corresponds to degree of truth -- at least, for those neural clusters that directly represent symbolic information. So, for instance, the cat cluster fires a lot when a real or imaginary cat is present to the mind. If the mind wants to allocate attention to the cat cluster, but there is no real cat present, it must then either -- find a way to stimulate other things logically related to cat -- create abstract quasi-perceptual stimuli that constitute a mock cat and fool the cat cluster into firing I think this is how the brain and human mind work. I agree it's not optimal, and that in an AI system it's nicer to make separate parameters for activation and truth value, as is done in both NARS and Novamente. - *. Basic inference rules I don't see what is gained by a network implementation (compared to direct probabilistic calculation). - Actually, I think there is no big advantage. This issue is discussed in the very last section of the paper. My view is that the brain uses a horribly inefficient mechanism to achieve probabilistic inference, and AI systems can achieve the same thing more efficiently. I prefer the Novamente implementation of PTL to a Hebbian Logic implementation. However, I think it's interesting to observe, theoretically, that a Hebbian Logic representation is possible. - *. Hebbian Learning The original Hebbian learning rule woks on symmetric links (similarity, not inheritance), because weight of a link is decrease when one end is activated and the other isn't, and which is which doesn't matter. What you does in Hebbian learning variant A is necessary, but it is not the original Hebbian learning rule. Oops, you are right. My variant A is fairly standard in the literature these days, but it's not the original one. I will correct that, thanks. *. Section 6 I'm not sure I understand the big picture here. Which of the following is correct? (1) PTL is fully justified according to probability theory, and the NN mechanism is used to implement the truth value functions. (2) PTL is fully justified according to probability theory, and the truth value functions are directly calculated, but the NN mechanism is used to implement inference control, that is, the selection of rules and premises in each step. (3) The logic is partially justified/calculated according to probability theory, and partially according to
