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]
