alphabet: ABC, DEF, GHI, ... ABC: A, B, C DEF: D, E, F GHI: G, H, I ... pi: 3.14, 15, 92, 65, 35, ... 3.14: 3, ., 1, 4, 15: 1, 5 92: 9, 2 65: 6, 5 35: 3, 5 ...Given we already know how to learn sequences, this is easy to learn. Here is the code (using a constant chunk size of 3), here is the knowledge before learning, and after. I guess I should show a little of what that looks like. First the random (though in other uses, it would be preferable to use a more semantically similar encoding) encode stage:

full |range> => range(|1>,|2048>) encode |end of sequence> => pick[10] full |range> encode |A> => pick[10] full |range> encode |B> => pick[10] full |range> encode |C> => pick[10] full |range> encode |D> => pick[10] full |range> encode |E> => pick[10] full |range> encode |F> => pick[10] full |range> encode |G> => pick[10] full |range> encode |H> => pick[10] full |range> encode |I> => pick[10] full |range> encode |J> => pick[10] full |range> encode |K> => pick[10] full |range> encode |L> => pick[10] full |range> encode |M> => pick[10] full |range> encode |N> => pick[10] full |range> encode |O> => pick[10] full |range> encode |P> => pick[10] full |range> encode |Q> => pick[10] full |range> encode |R> => pick[10] full |range> encode |S> => pick[10] full |range> encode |T> => pick[10] full |range> encode |U> => pick[10] full |range> encode |V> => pick[10] full |range> encode |W> => pick[10] full |range> encode |X> => pick[10] full |range> encode |Y> => pick[10] full |range> encode |Z> => pick[10] full |range> encode |A B C> => pick[10] full |range> encode |D E F> => pick[10] full |range> encode |G H I> => pick[10] full |range> encode |J K L> => pick[10] full |range> encode |M N O> => pick[10] full |range> encode |P Q R> => pick[10] full |range> encode |S T U> => pick[10] full |range> encode |V W X> => pick[10] full |range> encode |Y Z> => pick[10] full |range> encode |3> => pick[10] full |range> encode |.> => pick[10] full |range> encode |1> => pick[10] full |range> encode |4> => pick[10] full |range> encode |5> => pick[10] full |range> encode |9> => pick[10] full |range> encode |2> => pick[10] full |range> encode |6> => pick[10] full |range> encode |8> => pick[10] full |range> encode |7> => pick[10] full |range> encode |3 . 1> => pick[10] full |range> encode |4 1 5> => pick[10] full |range> encode |9 2 6> => pick[10] full |range> encode |5 3 5> => pick[10] full |range> encode |8 9 7> => pick[10] full |range> encode |9 3 2> => pick[10] full |range> encode |3 8 4> => pick[10] full |range>The main thing to note here is that we are not just learning encodings for single symbols eg |A> or |3>, but also for chunks of symbols too. eg |A B C> and |3 . 1>. And in general, we can do similar encodings for anything we want to stuff into a ket. Once we have encodings for our objects we can learn their sequences. Here are a couple of them:

-- alphabet -- A B C, D E F, G H I, J K L, M N O, P Q R, S T U, V W X, Y Z start-node |alphabet> => random-column[10] encode |A B C> pattern |node 0: 0> => start-node |alphabet> then |node 0: 0> => random-column[10] encode |D E F> pattern |node 0: 1> => then |node 0: 0> then |node 0: 1> => random-column[10] encode |G H I> pattern |node 0: 2> => then |node 0: 1> then |node 0: 2> => random-column[10] encode |J K L> pattern |node 0: 3> => then |node 0: 2> then |node 0: 3> => random-column[10] encode |M N O> pattern |node 0: 4> => then |node 0: 3> then |node 0: 4> => random-column[10] encode |P Q R> pattern |node 0: 5> => then |node 0: 4> then |node 0: 5> => random-column[10] encode |S T U> pattern |node 0: 6> => then |node 0: 5> then |node 0: 6> => random-column[10] encode |V W X> pattern |node 0: 7> => then |node 0: 6> then |node 0: 7> => random-column[10] encode |Y Z> pattern |node 0: 8> => then |node 0: 7> then |node 0: 8> => append-column[10] encode |end of sequence> -- A B C -- A, B, C start-node |A B C> => random-column[10] encode |A> pattern |node 1: 0> => start-node |A B C> then |node 1: 0> => random-column[10] encode |B> pattern |node 1: 1> => then |node 1: 0> then |node 1: 1> => random-column[10] encode |C> pattern |node 1: 2> => then |node 1: 1> then |node 1: 2> => append-column[10] encode |end of sequence> -- D E F -- D, E, F start-node |D E F> => random-column[10] encode |D> pattern |node 2: 0> => start-node |D E F> then |node 2: 0> => random-column[10] encode |E> pattern |node 2: 1> => then |node 2: 0> then |node 2: 1> => random-column[10] encode |F> pattern |node 2: 2> => then |node 2: 1> then |node 2: 2> => append-column[10] encode |end of sequence> ...where we see both the high level sequence of the alphabet chunks (ABC)(DEF)..., and the lower sequences of single letters A, B, C and D, E, F. The pi sequence has identical structure, so I'll omit that. For the curious, see the pre-learning sw file.

That's the learn stage taken care of, now the bit that took a little more work, code that recalls sequences, no matter how many layers deep. Though I've only so far tested it on a two-layer system. Here is the pseudo code:

next (*) #=> then clean select[1,1] similar-input[pattern] |_self> name (*) #=> clean select[1,1] similar-input[encode] extract-category |_self> print-sequence |*> #=> if not do-you-know start-node |_self>: return |_self> if name start-node |_self> == |_self>: -- prevent infinite loop when an object is its own sequence print |_self> return |> |node> => new-GUID |> current "" |node> => start-node |_self> while name current "" |node> != |end of sequence>: if not do-you-know start-node name current "" |node>: print name current "" |node> else: print-sequence name current "" |node> current "" |node> => next current "" |node> return |end of sequence>And the corresponding python:

def new_print_sequence(one,context,start_node=None): if start_node is None: # so we can change the operator name that links to the first element in the sequence. start_node = "start-node" if len(one.apply_op(context,start_node)) == 0: # if we don't know the start-node, return the input ket return one print("print sequence:",one) def next(one): return one.similar_input(context,"pattern").select_range(1,1).apply_sigmoid(clean).apply_op(context,"then") def name(one): return one.apply_fn(extract_category).similar_input(context,"encode").select_range(1,1).apply_sigmoid(clean) if name(one.apply_op(context,start_node)).the_label() == one.the_label(): print(one) # prevent infinte loop when an object is its own sequence. Maybe should have handled at learn stage, not recall? return ket("") current_node = one.apply_op(context,start_node) while name(current_node).the_label() != "end of sequence": if len(name(current_node).apply_op(context,start_node)) == 0: print(name(current_node)) else: new_print_sequence(name(current_node),context,start_node) current_node = next(current_node) return ket("end of sequence")And finally, put it to use:

$ ./the_semantic_db_console.py Welcome! sa: load chunked-alphabet-pi.sw sa: new-print-sequence |alphabet> print sequence: |alphabet> print sequence: |A B C> |A> |B> |C> print sequence: |D E F> |D> |E> |F> print sequence: |G H I> |G> |H> |I> print sequence: |J K L> |J> |K> |L> print sequence: |M N O> |M> |N> |O> print sequence: |P Q R> |P> |Q> |R> print sequence: |S T U> |S> |T> |U> print sequence: |V W X> |V> |W> |X> print sequence: |Y Z> |Y> |Z> |end of sequence> sa: new-print-sequence |pi> print sequence: |pi> print sequence: |3 . 1> |3> |.> |1> print sequence: |4 1 5> |4> |1> |5> print sequence: |9 2 6> |9> |2> print sequence: |6> |6> print sequence: |5 3 5> |5> |3> |5> print sequence: |8 9 7> |8> |9> |7> print sequence: |9 3 2> |9> |3> |2> print sequence: |3 8 4> |3> |8> |4> print sequence: |6> |6> |end of sequence>And we can print individual sub-sequences:

sa: new-print-sequence |D E F> print sequence: |D E F> |D> |E> |F> |end of sequence> sa: new-print-sequence |Y Z> print sequence: |Y Z> |Y> |Z> |end of sequence> sa: new-print-sequence |8 9 7> print sequence: |8 9 7> |8> |9> |7> |end of sequence>Some notes:

1) There are of course other ways to implement learning and recalling chunked sequences. In my implementation above, when a subsequence hits an "end of sequence" it escapes from the while loop, and the high level sequence resumes. But an alternative would be for the end of say the |8 9 7> subsequence to link back to the parent pi sequence, and then resume that sequence. In which case we would have this:

sa: new-print-sequence |8 9 7> print sequence: |8 9 7> |8> |9> |7> print sequence: |9 3 2> |9> |3> |2> print sequence: |3 8 4> |3> |8> |4> print sequence: |6> |6> |end of sequence>So, does |8 9 7> live as an independent sequence with no link to the parent sequence, or does the final |7> link back to the pi sequence? I don't know for sure, but I suspect it is independent, because consider the case where |8 9 7> is in multiple high level sequences. The |7> wouldn't know where to link back to.

2) I have had for a long time my similarity metric called simm, that returns the similarity of superpositions (1 for exact match, 0 for disjoint, values in between otherwise). But I have so far failed to implement a decent simm for sequences (aside from mapping strings to ngrams, and then running simm on that). I now suspect/hope chunking of sequences might be a key part.

3) presumably the chunking of sequences structure is used by the brain for more than just difficult passwords, eg perhaps grammar. Seems likely to me that if a structure is used somewhere by the brain, then it is used in many other places too. ie, if a structure is good, then reuse it.

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updated: 19/12/2016

by Garry Morrison

email: garry -at- semantic-db.org