Analysis of ECAN data: integrated information, strange attractors, etc.

[Ben Goertzel]

Matt,

Thinking about how to analyze time-series data from ECAN, I thought it
might be cool to look for interactions between IIT (Phi) and strange
attractor structure in the attentional focus...

I found this code which lets us analyze data using Integrated
Information Theory (Tononi's Phi)

https://figshare.com/articles/phi_toolbox_zip/3203326

This has gotten some acceptance as a "measure of consciousness", so if
we could show that some ECAN parameters or aspects correlate with
"degree of consciousness" as measured by Phi, this would let us
publish a wizzy and popular paper.... For instance, what if the
system was more conscious (higher Phi) when it connected a sentence
with background knowledge, than when it parsed a sentence but was
unable to connect it with background knowledge...


On the other hand, another interesting thing to do would be to look at
a delay-embedding of the dynamics...

Long ago I used the TISEAN toolkit for nonlinear time series analysis

What I am thinking here is: If we are loading in Atoms from a bunch of
texts, we could run PLSI or similar (latent semantic indexing) on the
texts (Eyob could help with that, he's a master of PLSI), to create a
dimensional space. At any moment in time, the WordNodes and named
ConceptNodes in the AttentionalFocus would then assign the AF a
certain point in the dimensional space defined by the PLSI factors.

This would turn the AF into a trajectory in n-dimensional space...

One could then use some approach to figure out the optimal delay and
do a delay-embedding of this trajectory, hopefully revealing the
underlying attractor structure...

TISEAN seems only to do delay embedding from 1D time series

https://www.pks.mpg.de/~tisean/Tisean_3.0.1/index.html

but there are papers explaining how to do it from multi-D time series

https://arxiv.org/pdf/nlin/0609029.pdf

https://arxiv.org/pdf/1409.5974.pdf

Showing that the AF contents occupy a certain strange attractor --
maybe shifting which strange attractor over time, or shifting the
shape of the strange attractor over time, would be interesting

Some association between the Phi (IIT) value and some property of the
inferred attractor would also be interesting...

-- Ben




--
Ben Goertzel, PhD
http://goertzel.org

"I am God! I am nothing, I'm play, I am freedom, I am life. I am the
boundary, I am the peak." -- Alexander Scriabin

[Matthew Ikle]

Yes all of this makes a lot of sense and could be exciting, especially the connection to Phi. Could be an extremely interesting paper — but a lot will depend upon parameter tuning as well as creating an appropriate experiment.

Before we begin setting up the experiment to look for connections between Phi and strange attractor structure, though, we obviously must first ensure basic ECAN implementation as follows:

Step 1: Ensure that ECAN works correctly and fulfills basic design criteria;
Step 2: Run poison experiment and retune parameters.

I feel confident that after Misgana makes the minor changes we discussed in HK, ECAN should work correctly. Only after we have run through the two steps above, though. should we proceed with the next (IIT) step and perform additional parameter tuning.

At some point (probably after all of the above), we should also enable HebbianLink updating and run experiments testing the three updating equations we have developed and setting the stage for yet another set of parameter tuning.

—matt

[Ben Goertzel]

Yes, agreed...

[Matt Ikle]

Hi Ben,

I've been thinking a lot about how to actually create experiments for connecting ECAN with Phi.

It seems to me that a simple pre-experiment we could run builds upon the insecticide experiment as follows. We could load the insecticide experiment background knowledge and then stimulate the atoms for poison and insects just as before. We can track STI values for these three atoms over time and calculate IIT time series values from the STI time series values. To do this means making only some minor modifications to the practical_phi toolbox Matlab code to find IIT.

We may even be able to, though I am more unsure about this, build upon this simple experiment to detect attractor formations within ECAN dynamics prior to looking at the larger ECAN dynamics using PLSI to reduce the space.

Just trying to create a simple first set of experiments. Thoughts?

--matt

Sent from my iPhone

[Ben Goertzel]

Yes, that would be a meaningful experiment to start with, though
obviously not a substitute for an experiment that gauges the
integrated information of the dynamics more broadly...

[Matthew Ikle]

Of course — that is why I called it a pre-experiment. There are some subtle mechanics (distribution determination, system partitioning) that we need to work out in the actual calculations for phi (or phi*) and the approach I outline will allow us to concentrate on figuring these out. Once we know how to perform these calculations for this simple pre-experiment, then we can more easily add complexity to it by extending and modifying it to the AF and/or WA. And of course connecting IIT with strange attractor formation would be the “holy grail” of the entire pipeline of experiments,

—matt

[Linas Vepstas]

Matt, Ben,

FYI,

I've been developing a suite of tools/API's that might be useful for this. Getting tonini phi is "easy" .. or hard depending on what exactly you want.  So...

at the core, there's an API to expose a portion of the atomspace as a matrix.  You can think of it as a correlation matrix, covariance matrix, adjacency matrix of a graph, etc.

The "adjacency matrix of a graph" is the viewpoint you want for IIT.

A set of stuff you can do with the matrix, including computing it's entropy, MI,various RMS deviations.  Doing PCA to it. Also, cutting it in various aways: Currently, I'm using the cuts to filter out noise and junk data, but you could use the cuts to perform the tonini cuts.

The "hard part" is that computing entropy for a 30K x 30K matrix can take hours... so that limits just how many cuts you can explore.

To use this toolset, you need to write a shim that specifies how to get the matrix element (i,j) and some related info: the atom type of all the i's the atom type of all the j's, the atom type of the pair (i,j), and where to store per-row and per-column data (for subtotals of various kinds)

I'm actively hacking this now, so its a bit unstable and maybe buggy. Code is here.

https://github.com/opencog/atomspace/tree/master/opencog/matrix

--linas

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[Linas Vepstas]

Also:

if you just want a single number out of curiosity: here's what i've got: for just-plain word pairs, I get an entropy of about 18, an MI of -2 (that's a minus sign there) and a sparsity of about 15 (i.e. only 1 in 2^15 entries in the adjacency matrix are non-zero)    I don't yet know what these numbers will be like, when I cut out the noise; I have to fix a few bugs first.

For the word-disjunct datasets, I get entropies around 21 and MI of minus 4. and similar sparsities.

doubling the size of the dataset has very little effect on these numbers: they might rise by maybe 0.1 or 0.2, but that's it.  Fixing bugs that lead to low quality data had the biggest effect: e.g handling punctuation marks correctly helped increase both entropy and MI.

p.s. both of those papers make a fundamental error: they state that phi is bounded below by zero.  That's clearly and patently false, which would be obvious to the authors if they'd ever applied their formulas to actual data. Boo and big negative marks for making such a basic mistake.

--linas