General Background

Negative Feedback Neural Net Diagrams

Defines symbols:





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Idealized Trial and Error Learning:


Symbolizes being stimulated until trials (new synapses) are made:
Only those trial connections that stop the stimulation are kept.
For example: one would remember only the last trial that stopped hunger.



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Idealized Imitation Learning:


Imitation is designed to be consistent with a successful 'trial and Error':
Internal connections are made if they reduce the number of external stimulations required to make the same result.
For learning an inhibitory connection, the potentially inhibited nerve should stop being stimulated after the potential inhibitor is stimulated.
For learning a 'reinforcing' connection, the potentially 'reinforced' nerve should be stimulated after the potential 'reinforcer' is.
For example: If one first sees a book, then hears the word 'book' and then doesn't see the book; this system would connect the nerve stimulated by the sight of the book to the nerve that causes the sound 'book'.
For efficiency, one would have to have first 'learned' to make distinct groups of nerves separately stimulated by various common objects;
and one would have to have first made distinct groups of nerves connected to make various common word sounds.
These groups would have to be large enough and interleaved so there are all possible parings between images and sounds so the 'right' pairs are close enough to be connected by 'trial and error' or 'imitation'. See 'seek & join' below.
Also, after each success, the lesson would have to be repeated so the correct response would be 'locked in' so subsequent lessons would not easily change earlier correct memories.


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However, this example shows some need for modifications:

1. The student has to first learn to repeat the words after the teacher says them.
   
2. Since the spoken words are not continuous-constant stimulations, and brain measurements show lots of spikes, I propose that the nerves(verticals) stay stimulated-sensitive slightly longer than they are affected by sharp stimulation from a synapse(horizontals). And a stimulated-sensitive nerve outputs sharp spike pulse stimulations.
   
3. For 'weighted summation'(Hopfield) type firing let the stimulation state of a nerve follow from weighted synapses (repeated successes in the above sense giving greater weight).
   



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'nor', nor formula & activation:


In -nn, a nor is a separately stimulated nerve(output) that has 1 or more inhibitory connections(inputs). Its 'separately stimulated nerve' is its 'activation'; otherwise its inputs have no effect. A 'nor formula' is those nors commonly 'activated' by branch nerves from one stimulated root nerve. I want each nor to have a separate 'activation' nerve so it may be individually named or inhibited so part of the formula may be deactivated or new parts easily added.


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Named Nerves:

(a gif is planned)
To communicate with an external teacher or even one's self, it helps to have an easier way to stimulate a particular nerve than to put ones self in that actual particular environment which would stimulate it. That is, names and symbols help to build models. See 'seek & join' and 'models' below. In particular for simple 'seek & join', the activation(output nerve) of a 'nor' is named by being inhibited when its name nerve is stimulated so a single nor in a nor formula may be selected(activated) by stimulating the names of all the other nors.


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Seek & join, Backward Connection:

(a gif & javascript is planned)
Keep only a continuously connected subset of the massive number of temporarily connected and stimulated nerves needed to find and connect an old nor's output to a new nor's input. (This search is necessary since for generality we need to be able to connect any nerves. See use of nerve types below: new) This output has to have a new 'named nerve' to individually inhibit it's activation so the process may be repeated.
This Seek & join feature of -nn was suggested by efficient construction needs to prove for -nn the possible adding of another 'nor' AT ANY PLACE in any nor formula. (I believe any nor formula may be constructed by adding one nor at a time since one could conceptually remove one nor at a time from the end of any nor formula. I say 'conceptually' since once a formula in a -nn is locked, connections cannot be physically removed). It is also necessary to cause any one nerve to make arbitrarily many branch extension connections from it and to individually control the stimulation of any other nerve to be connected to one of these extensions (I have had to propose the use of special nerves at the end of a nerve chain. These special nerves retain their ability to grow new branches; the nerves between loose it when their use in a chain is repeated.).
'seek' is the protracted stimulation of a new name while the -nn is set to readily make new trial stimulations without the normal small time limit for considering the trial is an error. (This sensitization may be similarly done in the human brain by something like increased adrenaline.) Thus many more than the usual number of 'trial & error' connections are made. This should be increased until one of these 'new name' branches reaches the new nor's stimulated activation output and so inhibits it by the -nn trial & error' rule. This "new nor's stimulated activation nerve" may be any unused branch from the nor formula's activation root; these 'unused branches' may be added by 'trial & error' as the root is normally stimulated. Also to avoid these seek nerves being inhibitorily connected back onto themselves, I propose the stimulation to have a unique(a random selection of starting time) spike pattern from root through branches (like the human brain seems to have) so nerves are NOT connected to ones that have this synchronized spike pattern stimulation. But, damn it, just after this upload, I investigated a nagging feeling of problems getting the new output activator branches for inhibitory connection to old ones: they would have the same spike pattern since they come from the same root; so I further need to assume the newly inhibited branch activator nerve resulting from a 'seek & join' will desynchronize the spike trains in it so an old branch of the formula activation may be connected to a new one generated by 'seek' from the same root!
'join' in -nn is then a strengthened connection ONLY to each nerve connected between this new name and the stimulated new nor activation nerve. This may be done by a 'backward connection' from this inhibition connection through the inhibitor nerve through the nerve which has a trial stimulation(reinforcement) connection to it and then the one that stimulated that one etc. Each such 'backward connection' is strengthened so when the name stimulation is stopped all the other trials are erased and fewer nerves are wasted. Also to aid connection to an individual nerve at the end of a 'join', I propose that the intermediate nerves in the 'backward connection' cease to make new connections or branches
(Here I think the use of 2 types of nerves solves the problem: the net has potential 'end' nerves scattered among many 'join' type nerves. Assuming a given nor formula has 'end' nerves for the end of each nor activator, each nor name, and the root activator, with 'join' nerves elsewhere, we then consider adding another nor: The root is stimulated until it activates many new join nerves and possibly some 'end' nerves. Then the new nor activator name is stimulated long enough for its join nerves to find one of these new stimulated potential end nerves and inhibit it. This inhibition is assumed to cause the joining back to the root. Timely destimulation should complete this joining of root end to new nor activator end and its name and incidentally release the many 'seek' nerves. Testing this could be done with the attempt to join other nor outputs to it.)
For greater efficiency in the seek, I propose the use of 2 intensity levels of stimulation so in seeking a stimulated 'end' type nerve, unstimulated 'end' type nerves are bypassed:
strong stimulation causes trial connections to only stimulated 'end' type nerves and weak stimulation causes trial connection to only unstimulated 'end' type nerves; intensity is to be independent of time period of stimulation.
Any other nor's output may be similarly inhibitively connected to this new nor output by stimulating the root activation of the nor formula and inhibiting by name all the other nor activation nerves for a new 'seek & join '.
A good test of this would be to program it in a general purpose computer. However I have an intermediate example: Javascript -nn (2 pages: netscape2)
I hope someone has the interest to do a more complete job; please contact me.

Definitions based on -NN: artificial logic/philosophy:

1. Cause and effect environments:
   Those environments where the connection patterns in -nns stabilize. This may take thousands of years over sequences of many communicating -nns. Like Human history(see 'ultimate model' below). Chaos identifies environments without enough repetition for a large -nn to be able to detect and stop it. Chaos( maximal variety) should not motivate a well learned -nn to do anything different.
   
2. Consciousness:
   The stimulations occurring during the TIME of 'trial and error'; when the same stimulation is protracted beyond a 'time threshold' enough to cause new connections and stimulate other nerves so possibly previously learned or new responses are tried. Mere repetition of using previously successful responses is considered automatic and unconscious . This 'time threshold' I propose is about 1/2 second as measured by Benjamin Liebt as the gap between stimulation and consciousness; I was encouraged by this measurement instead of like Roger Penrose("Shadows of the Mind" 1994, page 385). Also the activities during 'unconsciousness' are properly faster and only need to be modified by "consciousness" when automatic reactions fail( do not stop the stimulation during the time threshold). Also for -nn, "imitation" may be faster and 'unconscious'.
   
3. Pleasure:
   When these new trials are successful( the stimulations which caused them cease).
   
4. Pain:
   The widespread and protracted stimulation for which 'trial and error' is unsuccessful.
   
5. Honest communication:
   The stimulation sequence by one -nn of another -nn so it learns the same responses.
   
6. Names:
   Like book or x. A stimulus either verbal or visual is maintained (for trial & error) until the teacher receives correct responses or (for imitation) until after the teacher has presented and removed the desired response. For a logical variable like p or x there should be several examples. So in teaching formulas or models, when the variable is mentioned a large variety of nerves are stimulated so some may have branches near the outputs of earlier learned parts of the formula which may also be stimulated in the sequence needed to connect the variable name to the output so it may be stimulated by the name when needed to construct another part.
7. Models:
   Sets of connections(nor formulas) which can be separately activated or tested by stimulations from externally stimulated nerves or internal nerves. Some models may be used to represent the causal relations in the external world (the physical laws of the universe). Others may represent possible responses of the -nn to the external world or to internal models of it (these are internal response models: controllers of the external world: anti-models). The ultimate model must be that of a self contained universe in which this -nn exists in a 'cause and effect' environment ( the model is also self contained). (see General Background above).
   The anti-model (I would like some help here too) could be the 'mental' analog of the anti-something required for each something for a self contained universe. It is a part of the ultimate model which generates the output of the net. The use of the anti-model with its ultimate model makes continual automatic successful changes and the -nn is 'unconscious' (nirvana); conceivably the mental analog of the nothing of the self contained, self caused universe's creator. Please see 'Conclusions' below for examples.
   
8. Free Will:
   The automatic probabilistic selection between one's self constructed anti-models by one's own universe model. The 'probability' is proportional to the number of experiences that the anti-models successfully resolve. However, the members of a society will have greater contributions to the variety of the universe if they have a system of interacting which optimizes their potential: partner insurance democracy (2 pages)
   
9. Practical language:
   A system of smaller or elemental models which can be easily recombined to make many larger models. A language may be used for external communication when it is affected by and affects other -NNs; practically cheaply like with spoken or printed words. See below how names are used to aid learning.
   
10. Practical art:
    Efficient use of the particular sensitivities (biases) of a particular -NN to maximize communication and effect on it. Abstract art like instrumental music may be organized to shake the senses out of habitual perceptual ruts so one is more creative in any field.
11. Generalization:
    Generalizations have a probability to be learned and used. This probability is in proportion to the fewer 'trial and error' connections needed to achieve 'success' in learning and using the generalization than needed individually for all the particular cases they represent.
    Logical ideas or math may be 'generalized' by making new definitions or theorems that have less restrictive requirements or conditions; maybe to the extent that the some theorems become part of a simple definition ( generalized calculus & -nn (5 pages)).
    Each old or new experience may be 'generalized' by searching for related experiences and considering extreme variations and searching for common logical analysis. Then a prototypical input should be constructed for each group of experiences. It should have significant parts named so different combinations of names will make it generate identical stimulation patterns for each generalized member of the group. The prototypical input is of use in logic formulas - see below.
    Tautologies are nor formulas whose output is stimulated regardless of which input stimulation pattern is made. Thus, to simplify a nor formula, one should at least remove any parts of it which are tautologies when the formula is copied elsewhere. Tautologies may not be removed from 'locked' formulas.
    An example of using the general principle of conserved energy is the compound bow shown under 'mechanical inventions' at start of 'home page': I asked myself 'what is most important for arrow flight?' Arrow's energy. 'How does it get its energy?' force times distance. But in old style bows, the greatest force is at the maximum pull distance where one must hold it most steady for aiming. 'How can one generate a better force curve?' 'Examples?' Lock pliers use another hinge so try to find a way of adding a hinge to a bow.

Conclusions:

1. Probably, general principles in an environment will be successfully modeled by large enough -nns; because good generalities increase the chance of effective connections by usefully extracting the common or repeatable responses of individual responses. See 'nor formulas' above. That internal model which repeats the output/input patterns caused by the external world is an effective 'test bed' for internal 'control' models(anti-models). By 'effective' I mean makes the -nn lock its connections as happens by repetition.
   
2. Logic:
   Logic is a model made from numerous nors. Nors may be learned at will in a -nn by learning one or more inhibitions of a stimulated nerve. See 'nor formulas' above. Learning may be aided by a teacher( external or internal).
   P implies Q: Where P and Q represent 2 nor formulas where all input stimulation patterns to P stimulate the same output nerves as they do to Q.
   Any truth value logic formula may be taught.
   Proof: The teacher adjusts the stimulation schedule so each stage of learning a logic model is the addition of only one more "nor". See 'nor formula' and 'seek & join' above. These 'nor formulas' may be called micro-agents after Marvin Minsky in his "Society of Mind".
   
3. -NNs make entropy greater over time.
   By 'entropy over time' I mean the accumulation(integral) of entropy over time. Any acceleration of entropy increases its accumulation over time: Acceleration simply makes the positive entropy curve higher sooner. (However I would ultimately like to see definitions of entropy and time in -nn terms. Perhaps it is adequate to simply define time as the 'trial and error' time threshold of a -nn or some multiple of the minimal existence of any complete state of the self contained universe. It might be based on the creation rate of virtual photons.) The -nn 'trial and error' system learns connections that cause fixed stimulations from the outside world to change sooner than otherwise. The -nn 'imitation' system causes learning relations that may be repeated and so cause the -nn to use up repetition biases and so increase entropy sooner. This changing of things that appear constant or repeat, is the basis for increasing entropy sooner.
   (Some more background: The 2nd law of thermodynamics is that any change in an environment increases its entropy. But the entropy of our energy sources will probably be the same in a billion years regardless of human existence. In particular, human burning of coal and oil increases entropy that would ultimately be increased anyway by earth crust movement exposing it to the air for oxidation. Humans just increase entropy sooner(accelerate it) by digging up coal and oil and using it to make and use better digging machines. Thus 'constructive' human action, sooner adds to the variety of this universe(large and small societies on earth and earlier carbon dioxide preceded by separate carbon and oxygen ) and is a required part of promptly reducing its bias(no large societies on earth and later carbon dioxide preceded by separate carbon and oxygen). Thus humans and the rest of the universe make themselves exist.)
   Entropy acceleration is greater where any 'cause and effect' patterns are discovered by the -NNs because a known, correct generality is more likely to be successfully tried and 'locked in' than all its many particular instances. For example, a successful trial of 'turning up the heat' is more likely than many trial inhibitions of all the cold sensing nerves of a normal body.
   
4. Stability cannot occur for unmodelable universes.
   Any gods or fantasies must be model able and reliable to be locked in a -nn. Stability only occurs when any particular stimulation 'picture' is responded to by outputs that stop that 'picture'. This suggests suicide(an anti-model of only the self ; not an anti-model of the universe). However, teachers realizing this, would divert that until enough other control principles are locked in by proper training. One who has an anti-model of the universe successfully changes(controls) most of one's perceptions of it. Here it is clear how the crudely evolved human senses could be made( by genetic engineering) more consistent with the universe so changing 'most' perceptions becomes changing ALL perceptions. For example, It should not be necessary to sugar-coat bitter-pills or pose sexy people with computer software, etc.
   

ai discussions (1 pages)
generalized calculus (5 pages)

E-mail author: R Massey for additions Oct 2003.
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