Ramin, setting aside the math which is simple enough, I don't understand the conceptual intuition behind
". An intelligent agent is locally robust if the magnitude of the change in its decision is independent of the direction of an infinitesimal change in the input. " It seems naively that the magnitude of change in an intelligent system's decision SHOULD depend on the direction of change of its input (even if the change of input is small) ... I can't see why not... I have thought a bunch recently about the relationship btw cognitive logic and complex-variable algebra as well, see e.g. https://arxiv.org/abs/2101.07498 ben On Sat, Jun 12, 2021 at 6:24 AM Ramin Barati <[email protected]> wrote: > Thank you for sharing your work. I confess that I am not that versed in > mathematics, but I'm working on something for my PhD in the same line as to > what you propose here and was wondering if my initial understanding of your > proposal is correct. IMO, my proposal would go under the "How to do this > quickly, efficiently, effectively?" category. My proposal is that I want to > approach the problem in an axiomatic way. I am under the impression that > the term "axiomatic" is very controversial, so allow me to elaborate. > > So what do I mean by axioms? I certainly am not talking about axioms in > the sense of "facts". For example, "the thigh bone is connected to the hip > bone" is not an axiom in my mind. Another non-example would be the > "Resolution" law in logic. What I am looking for is the axioms by which we > define what constitutes the reactions of an "intelligent agent". For > example, "An intelligent agent should be stable in its decision making" is > an axiom in my view. Actually, this is more than an example and I want to > propose this as the first axiom of an "intelligent agent". To put it in > more precise terms, "there should not be adversarial examples for an > intelligent agent". Think of a mosquito, it is a very simple intelligent > agent that follows the sources of light (or heat, I'm not sure). But it is > not possible to produce an adversarial pattern of light (e.g. rapidly > blinking light) to convince the mosquito to NOT follow the light source. > > At the first glance, this axiom is not that helpful. But if we get > mathematical, it turns out that this axiom has profound consequences. I am > planning on uploading a paper on this topic in arxiv in the coming days. To > be able to continue the discussion though, I will put some of the math here > and am looking forward to getting your opinion on it. > > To put the axiom in mathematical terms, I propose a concept that I call > "local robustness". An intelligent agent is locally robust if the magnitude > of the change in its decision is independent of the direction of an > infinitesimal change in the input. To get a feel of the rationale behind > the definition, consider an image and its label. If I introduce some small > perturbation to the image, the change in the confidence of the label an > intelligent agent assigns to the perturbed image should be independent of > the "content" of the perturbation. In math form: > [image: local_rob.PNG] > The definition could be readily generalized to complex vectors. From > complex analysis we know that a function would satisfy the local robustness > condition if and only if it satisfies the Cauchy-Riemman equations. I > should mention that CR equations are defined for a scalar input, but it is > straightforward to generalize this to complex vectors. The functions that > satisfy the homogeneous CR equations are very special and they are called > "holomorphic" functions. These functions have other desirable properties as > well. A complex-valued function is analytic and complex differentiable if > and only if it is holomorphic (it's more nuanced than that, but I will > omit the discussion for brevity). It is proved that only complex-valued > functions of a complex vector could be holomorphic. In other words, it is > impossible to construct a holomorphic function of a real vector. So the > first consequence of the axiom would be "an intelligent agent uses a > complex-valued function of a complex vector for decision making". I can go > on about the other consequences of the axiom, but bringing them up would be > futile if you find the approach not satisfactory or relevant. > > > > On Sat, Jun 12, 2021 at 1:31 AM Tofara Moyo <[email protected]> wrote: > >> Think of a song in music . that will illustrate this method of >> orthogonality better. In music if a musical instrument plays with fast >> changes for a bit the next thing it will do is go orthogonal and perform >> slow moves. This happens with all instruments. but at the same time, if the >> base is moving fast the higher instruments must be in their slower phase >> for it to sound pleasing. if the verse has low energy the chorus must be >> orthogonal and have higher energy. If the verse and chorus are too coupled >> then a bridge will add the needed orthoganaility. in drums if the kick is >> slow the hats must be faster, every now and then there must be a drum roll >> to go orthogonal. if a song has alot of low frequency sounds there must be >> orthogonality produced by having some higher frequency sounds as well. A >> well made song is one that uses orthogonality to its fullest potential. >> this is true of science and philosophy. scientific movements are defined by >> being orthogonal to each other. a well made proof makes statements in >> orthogonal moves. Intelligence can be optimised by choosing optimal >> configurations. If we started off with the axioms of set theory we could >> recreate all of modern mathematics and more by moving in orthoganal steps >> that involve combining infomrtion from these axioms. >> >> Now music theory doesn't just have the chromatic scale. It has majors and >> minors which each have their role. If we had a reality graph we may choose >> to move in majors along it or some other scale. then if we wanted to ramp >> this up we would perform chromatic progressions where we borrow notes or >> chords from different scales. We could be even more detailed and choose to >> move in such a way that in one scale we have moved in 4ths perhaps but in >> another we really moved in 5ths, then reverse that. treating reality as a >> graph lends itself to its own type of music theory if we consider the >> circle of fifths and the chromatic scale as a type of graph. >> >> So it's not enough just to move in orthogonal steps. There is a world of >> nuance and detail that can be added to create more and more pleasing >> progressions. just as music producers can be better than others based on >> their use of orthogonality, an agent that treats realitys graph as a music >> instrument would think much more advanced if it implemented all the tricks >> available to it. So if you have a thought. The best next thought should be >> orthogonal and if it isn't then you are setting yourself up for a greater >> resolution later on where you will finally go orthogonal to both thoughts >> at once in a large step. In order to go orthogonal to this there are >> plenty of options . the more sophisticated ones could be said to use all >> the bells and whistles of graph "music" theory. >> >> On Fri, Jun 11, 2021 at 10:35 PM Tofara Moyo <[email protected]> >> wrote: >> >>> Yes you're right, implementation is key. I am not all that well versed >>> in mathematics but I believe your approach may yield better results than a >>> fractal based approach, though fractals is a mathematical topic itself. I >>> had the idea that if we placed a normal fractal in a fractal "space" then >>> all the repeating information coincides and we are left with just the one >>> shape. as we morph the space back to 2d all the redundant information >>> resurfaces. This would lead us to believe that in order to train an agent >>> to recognise the information found in reality we need to embed an axiomatic >>> shape into a 2d space, and then alter the dimensionality of that space >>> until it introduces redundant information and produces the fractal that >>> reality is composed of. I mentioned that the fractal is based on the axiom >>> of identity. What this means is that a series of similar tiles persists >>> until it is "time" for an orthogonal tile to be present. Then that new >>> grouping of the orthogonal tile and the originals persists till an >>> orthogonal tiling to those is met and so on. Consider the act of eating for >>> example. Each time you chew you are adding a chewing tile then when you >>> swallow that in some sense becomes an orthogonal tile.Then this tile >>> repeats tile it finds an orthoganal one to it In fact it can be said that >>> only things that are orthogonal in reality can stick out of nothingness in >>> order to participate in causality. >>> >>> Also we need to understand that concepts are a plagiarism of reality. >>> When you say "biden bridges the gap between the old and the young" the >>> "bridges" fits naturally in that sentence with all the other concepts >>> because natural bridges have exactly the same shape tile. In fact if you >>> examine that sentence a lot of it makes reference to things in objective >>> reality, Such as gap and between. Even old and young reference space. All >>> thinking is fitting together tiles from reality. Higher thinking involves >>> more sophisticated shape filling by better search methods for those shapes. >>> If we were to create a fractal space where a primitive shape in 2d space >>> describes realitys fractal in that fractal space all we would need to do to >>> act and think would be to move in orthogonal steps from a starting point. >>> All physical movement and conceptualisation would be taken care of at once. >>> >>> Note also that in a conversation the most informative reply is one that >>> is in some sense orthogonal to the utterance. this way it is more decoupled >>> from the utterance. In a game like Go , performing moves in orthogonal >>> steps along the graph of the game describes optimal play. This takes me to >>> music theory. A scale of 12 notes defines the most ( pleasing ) >>> orthogonal moves as moving in 5ths aka the circle of 5ths. This is related >>> to the fact that a scale would have the most pleasing harmonies and >>> progressions be defined as those that involve ratios with the lowest >>> denominator possible.i believe that the music scale is the most degenerate >>> application of this. if we had a scale with 30 notes orthogonality might >>> have been defined by a circle of 10ths or some other number so 5 is not >>> particularly special. >>> >>> if we have a graph things get even more interesting. rather than having >>> a single number define orthogonality we now have a vector. knowing that >>> vector is the best way to move along the graph. for instance with go. If we >>> were to reduce the game to a graph and find its vector of orthogonality we >>> would have greater search capabilities in order to perform moves. simply go >>> orthogonal. or if the last n moves have been coupled then the next n moves >>> should be orthogonal to those n moves but coupled among themselves for >>> example. >>> >>> So if we could start off with a primitive shape in 2d and morph it as we >>> change the space it is in to non interger dimensions we discover the >>> applicable vector that defines orthogonality and move in orthogonal >>> stepwise motion along it. >>> >>> On Fri, Jun 11, 2021 at 10:01 PM Linas Vepstas <[email protected]> >>> wrote: >>> >>>> Similar ideas have been circulating for decades or longer. Yes, the >>>> concept of fractals and tilings are similar. My goal here is to point out >>>> that these ideas can be implemented in software. I'm trying to drum up the >>>> practical conversation, the one of "how can we do this?" . >>>> >>>> On Fri, Jun 11, 2021 at 2:24 AM Tofara Moyo <[email protected]> >>>> wrote: >>>> >>>>> This is interesting. I came across similar ideas too and i posted them >>>>> on the AGI facebook page last year june. here they are for comparison. >>>>> >>>>> >>>>> this post is about the way things repeat and change in the world. in >>>>> short something repeats for a while , such as you passing houses while you >>>>> are walking down a road. So you pass house after house...then you get to >>>>> an >>>>> intersection and there are no more houses, but after that you then find >>>>> that the thing that repeats is "passing houses AND intersections"...so you >>>>> group the houses with the intersection and you pass this new grouping many >>>>> times before you get to a mall, then you group all three things together >>>>> and you keep walking past this new grouping untill you get outside the >>>>> city, then you group the city and the country side and you start passing >>>>> many cities and country sides as you go, then this becomes counries and >>>>> continents and planets and solar systems and galaxies...in short this >>>>> process describes reality, from the way a piece of wood bark is rough to >>>>> the way we even think >>>>> >>>>> in mathematics there is a topic called fractals that describes shapes >>>>> that look the same at different scales,here is a fractal shape that looks >>>>> the same even when you zoom in. So as you walk past houses , think of that >>>>> as zooming in to different scales and finding the same object you started >>>>> with, house after house represents scale after scale. this is more >>>>> complicated however because after the first set of scales we change focus, >>>>> and then zoom in on this new grouping/focus as if that was the fractal.... >>>>> >>>>> There are other type of fractal like shapes or at least objects that >>>>> follow the principle that are more applicable to this. Called tilings. >>>>> These are tiles or identical shapes that are placed side by side and fill >>>>> a >>>>> space with no gaps in between them. So the steps you take while walking >>>>> would each be a tile , while when you stop that becomes a tile of a >>>>> different shape from the stepping tiles that you join to them...then this >>>>> new grouping of tiles becomes the shape that you are tiling, when this >>>>> changes you tile the combination of the change with the original tiles. >>>>> this is a multi shape tiling that is binary in nature. Even the stepping >>>>> tiling can be broken into two different tiles, one for each leg...and so >>>>> on. >>>>> >>>>> A meriology is something that is made of parts. A chair is made of >>>>> parts that are made of parts all the way down to atoms and even further. >>>>> the parts of a chair are separated by space and time. The parts of the >>>>> tiling above may be seperated by space and time such as walking or the >>>>> texture of a surface, but it can also be seperated by something even >>>>> stranger. think of the tiling where you are left handed while everyone >>>>> else >>>>> is right handed. What separtes the lefties as a group from the righties. >>>>> it >>>>> cant be the normal space or time as they are not litteraly seperated by a >>>>> demarcation placed somewhere. If we could specify a type of space that >>>>> these two tiles are filling wouldnt that simply be a conceptual space? and >>>>> if we were to tile a space with concepts would that not be thinking? So we >>>>> already have a way to use this in AI. >>>>> >>>>> >>>>> >>>>> On Fri, Jun 11, 2021 at 2:33 AM Linas Vepstas <[email protected]> >>>>> wrote: >>>>> >>>>>> I just wrote up a new blog post on ... well, the usual topic. I'm >>>>>> cc'ing the Link Grammar mailing list, as it has been instrumental in >>>>>> waking >>>>>> me to these ideas. >>>>>> >>>>>> -- Linas >>>>>> >>>>>> ---------- Forwarded message --------- >>>>>> From: OpenCog Brainwave <[email protected]> >>>>>> Date: Thu, Jun 10, 2021 at 6:55 PM >>>>>> Subject: [New post] Everything is a Network >>>>>> To: <[email protected]> >>>>>> >>>>>> >>>>>> Linas Vepstas posted: "The goal of AGI is to create a thinking >>>>>> machine, a thinking organism, an algorithmic means of knowledge >>>>>> representation, knowledge discovery and self-expression. There are two >>>>>> conventional approaches to this endeavor. One is the ad hoc assembly of >>>>>> assorted" >>>>>> >>>>>> New post on *OpenCog Brainwave* >>>>>> <https://blog.opencog.org/?author=5> Everything is a Network >>>>>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/> by Linas >>>>>> Vepstas <https://blog.opencog.org/?author=5> >>>>>> >>>>>> The goal of AGI >>>>>> <https://en.wikipedia.org/wiki/Artificial_general_intelligence> is >>>>>> to create a thinking machine, a thinking organism, an algorithmic means >>>>>> of knowledge >>>>>> representation >>>>>> <https://en.wikipedia.org/wiki/Knowledge_representation_and_reasoning>, >>>>>> knowledge discovery >>>>>> <https://en.wikipedia.org/wiki/Knowledge_extraction> and >>>>>> self-expression >>>>>> <https://en.wikipedia.org/wiki/Natural_language_generation>. There >>>>>> are two conventional approaches to this endeavor. One is the ad hoc >>>>>> assembly of assorted technology pieces-parts, >>>>>> <https://www.youtube.com/watch?v=y_oem9BqUTI> with the implicit >>>>>> belief that, after some clever software engineering, it will just come >>>>>> alive. The other approach is to propose some grand over-arching >>>>>> theory-of-everything that, once implemented in software, will just come >>>>>> alive and become the Singularity >>>>>> <https://en.wikipedia.org/wiki/Technological_singularity>. >>>>>> >>>>>> This blog post is a sketch of the second case. As you read what >>>>>> follows, your eyes might glaze over, and you might think to yourself, "oh >>>>>> this is silly, why am I wasting my time reading this?" The reason for >>>>>> this >>>>>> is that, to say what I need to say, I must necessarily talk in such >>>>>> generalities, and provide such silly, childish examples, that it all >>>>>> seems >>>>>> a bit vapid. The problem is that a theory of everything must necessarily >>>>>> talk about everything, which is hard to do without saying things that >>>>>> seem >>>>>> obvious. Do not be fooled. What follows is backed up by some deep and >>>>>> very >>>>>> abstract mathematics that few have access to. I'll try to summon a basic >>>>>> bibliography at the end, but, for most readers who have not been studying >>>>>> the mathematics of knowledge for the last few decades, the learning curve >>>>>> will be impossibly steep. This is an expedition to the Everest of >>>>>> intellectual pursuits. You can come at this from any (intellectual) race, >>>>>> creed or color; but the formalities may likely exhaust you. That's OK. If >>>>>> you have 5 or 10 or 20 years, you can train and work out and lift >>>>>> weights. >>>>>> You can get there. And so... on with the show. >>>>>> >>>>>> The core premise is that "everything is a network >>>>>> <https://en.wikipedia.org/wiki/Network_theory>" -- By "network", I >>>>>> mean a graph >>>>>> <https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)>, >>>>>> possibly with directed edges, usually with typed >>>>>> <https://en.wikipedia.org/wiki/Type_theory> edges, usually with >>>>>> weights, numbers, and other data on each vertex or edge. By "everything" >>>>>> I >>>>>> mean "everything". Knowledge, language, vision, understanding, facts, >>>>>> deduction, reasoning, algorithms, ideas, beliefs ... biological >>>>>> molecules... everything. >>>>>> >>>>>> A key real-life "fact" about the "graph of everything" is it consists >>>>>> almost entirely of repeating sub-patterns. For example, "the thigh >>>>>> bone is connected to the hip bone >>>>>> <https://en.wikipedia.org/wiki/Dem_Bones>" -- this is true >>>>>> generically for vertebrates >>>>>> <https://en.wikipedia.org/wiki/Vertebrate>, no matter which animal >>>>>> it might be, or if it's alive or dead, it's imaginary or real. The >>>>>> patterns >>>>>> may be trite, or they may be complex. For images/vision, an example might >>>>>> be "select all photos containing a car >>>>>> <https://en.wikipedia.org/wiki/CAPTCHA>" -- superficially, this >>>>>> requires knowing how cars look alike, and what part of the pattern is >>>>>> important (wheels, windshields) and what is not (color, parked in a lot >>>>>> or flying >>>>>> through space <https://where-is-tesla-roadster.space/live>). >>>>>> >>>>>> The key learning task is to find such recurring patterns, both in >>>>>> fresh sensory input (what "the computer" is seeing/hearing/reading right >>>>>> now) and in stored knowledge (when processing a dataset - >>>>>> previously-learned, remembered knowledge - for example, a dataset of >>>>>> medical symptoms). The task is not just "pattern recognition >>>>>> <https://en.wikipedia.org/wiki/Pattern_recognition>" identifying a >>>>>> photo of a car, but of pattern discovery >>>>>> <https://en.wikipedia.org/wiki/Frequent_pattern_discovery> -- >>>>>> learning that there are things in the universe called "cars", and that >>>>>> they >>>>>> have wheels and windows -- extensive and intensive properties. >>>>>> >>>>>> Learning does not mean "training >>>>>> <https://en.wikipedia.org/wiki/Training,_validation,_and_test_sets>" >>>>>> -- of course, one can train, but AGI cannot depend on some pre-existing >>>>>> dataset, gathered by humans, annotated by humans. Learning really means >>>>>> that, starting from nothing at all, except one's memories, one's sensory >>>>>> inputs, and one's wits and cleverness, one discovers something new, and >>>>>> remembers it. >>>>>> >>>>>> OK, fine, the above is obvious to all. The novelty begins here: The >>>>>> best way to represent a graph with recurring elements in it is with >>>>>> "jigsaw >>>>>> puzzle <https://en.wikipedia.org/wiki/Jigsaw_puzzle> pieces". (and >>>>>> NOT with vertexes and edges!!) The pieces represent the recurring >>>>>> elements, >>>>>> and the "connectors" on the piece indicate how the pieces are allowed to >>>>>> join together. For example, the legbone has a jigsaw-puzzle-piece >>>>>> connector >>>>>> on it that says it can only attach to a hipbone. This is true not only >>>>>> metaphorically, but (oddly enough) literally! So when I say "everything >>>>>> is >>>>>> a network" and "the network is a composition of jigsaw puzzle pieces", >>>>>> the >>>>>> deduction is "everything can be described with these (abstract) jigsaw >>>>>> pieces." >>>>>> >>>>>> That this is the case in linguistics has been repeatedly rediscovered >>>>>> by more than a few linguists. It is explained perhaps the most clearly >>>>>> and >>>>>> directly in the original >>>>>> <https://www.cs.cmu.edu/afs/cs.cmu.edu/project/link/pub/www/papers/ps/tr91-196.pdf> >>>>>> Link >>>>>> Grammar >>>>>> <https://www.cs.cmu.edu/afs/cs.cmu.edu/project/link/pub/www/papers/ps/LG-IWPT93.pdf> >>>>>> papers, although I can point at some other writings as well; one from a >>>>>> "classical" >>>>>> (non-mathematical) humanities-department linguist >>>>>> <https://www.academia.edu/36534355/The_Molecular_Level_of_Lexical_Semantics_by_EA_Nida>; >>>>>> another from a hard-core mathematician - a category theorist - who >>>>>> rediscovered this from thin air >>>>>> <http://www.cs.ox.ac.uk/people/bob.coecke/NewScientist.pdf>. Once >>>>>> you know what to look for, its freakin everywhere. Say, in biology, the >>>>>> Krebs >>>>>> cycle <https://en.wikipedia.org/wiki/Citric_acid_cycle> (citric acid >>>>>> cycle) - some sugar molecules come in, some ATP goes out, and these >>>>>> chemicals relate to each other not only abstractly as jigsaw-pieces, but >>>>>> also literally, in that they must have the right shapes >>>>>> <https://en.wikipedia.org/wiki/Molecular_recognition>! The carbon >>>>>> atom itself is of this very form: it can connect, by bonds, in very >>>>>> specific ways. Those bonds, or rather, the possibility of those bonds, >>>>>> can >>>>>> be imagined as the connecting tabs on jigsaw-puzzle pieces. This is not >>>>>> just a metaphor, it can also be stated in a very precise mathematical >>>>>> sense. (My lament: the mathematical abstraction to make this precise puts >>>>>> it out of reach of most.) >>>>>> >>>>>> The key learning task is now transformed into one of discerning the >>>>>> shapes of these pieces >>>>>> <https://github.com/opencog/atomspace/blob/master/opencog/sheaf/docs/sheaves.pdf>, >>>>>> given a mixture of "what is known already" plus "sensory data". The >>>>>> scientific endeavor is then: "How to do this?" and "How to do this >>>>>> quickly, >>>>>> efficiently, effectively?" and "How does this relate to other theories, >>>>>> e.g. neural networks >>>>>> <https://en.wikipedia.org/wiki/Artificial_neural_network>?" I >>>>>> believe the answer to the last question is "yes, its related", and I >>>>>> can kind-of explain how >>>>>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/skippy.pdf>. >>>>>> The answer to the first question is "I have a provisional way of >>>>>> doing this <https://github.com/opencog/learn>, and it seems to work >>>>>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/connector-sets-revised.pdf>". >>>>>> The middle question - efficiency? Ooooof. This part is ... unknown. >>>>>> >>>>>> There is an adjoint task to learning, and that is expressing and >>>>>> communicating. Given some knowledge, represented in terms of such jigsaw >>>>>> pieces, how can it be converted from its abstract form (sitting in RAM, >>>>>> on >>>>>> the computer disk), into communications: a sequence of words, sentences, >>>>>> or >>>>>> a drawing, painting? >>>>>> >>>>>> That's it. That's the meta-background. At this point, I imagine that >>>>>> you, dear reader, probably feel no wiser than you did before you started >>>>>> reading. So what can I say to impart actual wisdom? Well, lets try an >>>>>> argument >>>>>> from authority >>>>>> <https://en.wikipedia.org/wiki/Argument_from_authority>: a >>>>>> jigsaw-puzzle piece is an object in an (asymmetric) monoidal category >>>>>> <https://en.wikipedia.org/wiki/Monoidal_category>. The internal >>>>>> language of that category is ... a language ... a formal language >>>>>> <https://en.wikipedia.org/wiki/Formal_language> having a syntax >>>>>> <https://en.wikipedia.org/wiki/Syntax>. Did that make an impression? >>>>>> Obviously, languages (the set of all syntactically valid expressions) >>>>>> and model-theoretic >>>>>> theories <https://en.wikipedia.org/wiki/Model_theory> are dual to >>>>>> one-another (this is obvious only if you know model theory). The learning >>>>>> task is to discover the structure >>>>>> <https://en.wikipedia.org/wiki/Model_(model_theory)>, the collection >>>>>> of types <https://en.wikipedia.org/wiki/Type_(model_theory)>, given >>>>>> the language <https://en.wikipedia.org/wiki/Text_corpus>. There is >>>>>> a wide abundance of machine-learning software that can do this in narrow, >>>>>> specific domains. There is no machine learning software that can do this >>>>>> in >>>>>> the fully generic, fully abstract setting of ... jigsaw puzzle pieces. >>>>>> >>>>>> Don't laugh. Reread this blog post from the beginning, and everywhere >>>>>> that you see "jigsaw piece", think "syntactic, lexical element of a >>>>>> monoidal category", and everywhere you see "network of everything", think >>>>>> "model theoretic language". Chew on this for a while, and now think: "Is >>>>>> this doable? Can this be encoded as software? Is it worthwhile? Might >>>>>> this >>>>>> actually work?". I hope that you will see the answer to all of these >>>>>> questions is yes. >>>>>> >>>>>> And now for a promised bibliography. The topic both deep and broad. >>>>>> There's a lot to comprehend, a lot to master, a lot to do. And, ah, I'm >>>>>> exhausted from writing this; you might be exhausted from reading. A >>>>>> provisional bibliography can be obtained from two papers I wrote on this >>>>>> topic: >>>>>> >>>>>> - Sheaves: A Topological Approach to Big Data >>>>>> >>>>>> <https://github.com/opencog/atomspace/blob/master/opencog/sheaf/docs/sheaves.pdf> >>>>>> - Neural-Net vs. Symbolic Machine Learning >>>>>> >>>>>> <https://github.com/opencog/learn/blob/master/learn-lang-diary/skippy.pdf> >>>>>> >>>>>> The first paper is rather informal. The second invoked a bunch of >>>>>> math. Both have bibliographies. There are additional PDF's in each of the >>>>>> directories that fill in more details. >>>>>> >>>>>> This is the level I am currently trying to work at. I invite all >>>>>> interested parties to come have a science party, and play around and see >>>>>> how far this stuff can be made to go. >>>>>> *Linas Vepstas <https://blog.opencog.org/?author=5>* | June 10, 2021 >>>>>> at 11:55 pm | Categories: Uncategorized >>>>>> <https://blog.opencog.org/?taxonomy=category&term=uncategorized> | >>>>>> URL: https://wp.me/p9hhnI-cl >>>>>> >>>>>> Comment >>>>>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/#respond> >>>>>> See all comments >>>>>> <https://blog.opencog.org/2021/06/10/everything-is-a-network/#comments> >>>>>> >>>>>> Unsubscribe >>>>>> <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fsubscribe.wordpress.com%2F%3Fkey%3Da9a418716d1b232b4d6f1b1829be75ae%26email%3Dlinasvepstas%2540gmail.com%26b%3DIuFxBBRYbGv3Hprjfcb1nN1xTFHgj5HkuY-x-lT6QKxqkZMgov9AM8QuMvodMCGn32Q3oTFW0et24AFIz1oCUdSZiyQlYOmTn36q6nLoKLLJow%253D%253D&sr=1&signature=674cb680ce749d47971c3d661d17cd4d&user=3747872&_e=eyJlcnJvciI6bnVsbCwiYmxvZ19pZCI6MTM3MTA1NDE4LCJibG9nX2xhbmciOiJlbiIsInNpdGVfaWRfbGFiZWwiOiJqZXRwYWNrIiwiZW1haWxfbmFtZSI6ImVtYWlsX3N1YnNjcmlwdGlvbiIsIl91aSI6Mzc0Nzg3MiwiZW1haWxfaWQiOiJiYjI0YmQwYTQwZjE3YTRlY2EzZmU5OGQwNzBkZmE3YSIsImRhdGVfc2VudCI6IjIwMjEtMDYtMTAiLCJsb2NhbGUiOiJlbiIsImN1cnJlbmN5IjoiVVNEIiwiY291bnRyeV9jb2RlX3NpZ251cCI6IlVTIiwiZG9tYWluIjoiYmxvZy5vcGVuY29nLm9yZyIsImZyZXF1ZW5jeSI6IjAiLCJkaWdlc3QiOiIwIiwiaGFzX2h0bWwiOiIxIiwiYW5jaG9yX3RleHQiOiJVbnN1YnNjcmliZSIsIl9kciI6bnVsbCwiX2RsIjoiXC94bWxycGMucGhwP3N5bmM9MSZjb2RlYz1kZWZsYXRlLWpzb24tYXJyYXkmdGltZXN0YW1wPTE2MjMzNjkzNDIuNjM5NCZxdWV1ZT1zeW5jJmhvbWU9aHR0cHMlM0ElMkYlMkZibG9nLm9wZW5jb2cub3JnJnNpdGV1cmw9aHR0cHMlM0ElMkYlMkZibG9nLm9wZW5jb2cub3JnJmNkPTAuMDAxNCZwZD0wLjAwNDImcXVldWVfc2l6ZT00JmJ1ZmZlcl9pZD02MGMyYTY3ZTlhY2VlJnRpbWVvdXQ9MTUmZm9yPWpldHBhY2smd3Bjb21fYmxvZ19pZD0xMzcxMDU0MTgiLCJfdXQiOiJ3cGNvbTp1c2VyX2lkIiwiX3VsIjoibGluYXN2IiwiX2VuIjoid3Bjb21fZW1haWxfY2xpY2siLCJfdHMiOjE2MjMzNjkzNDYzMzAsImJyb3dzZXJfdHlwZSI6InBocC1hZ2VudCIsIl9hdWEiOiJ3cGNvbS10cmFja3MtY2xpZW50LXYwLjMiLCJibG9nX3R6IjoiMCIsInVzZXJfbGFuZyI6ImVuIn0&_z=z> >>>>>> to no longer receive posts from OpenCog Brainwave. >>>>>> Change your email settings at Manage Subscriptions >>>>>> <https://public-api.wordpress.com/bar/?stat=groovemails-events&bin=wpcom_email_click&redirect_to=https%3A%2F%2Fsubscribe.wordpress.com%2F%3Fkey%3Da9a418716d1b232b4d6f1b1829be75ae%26email%3Dlinasvepstas%2540gmail.com&sr=1&signature=ece1c66e405464c8308b765ebceb3f20&user=3747872&_e=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&_z=z>. >>>>>> >>>>>> >>>>>> *Trouble clicking?* Copy and paste this URL into your browser: >>>>>> https://blog.opencog.org/2021/06/10/everything-is-a-network/ >>>>>> >>>>>> >>>>>> >>>>>> -- >>>>>> Patrick: Are they laughing at us? >>>>>> Sponge Bob: No, Patrick, they are laughing next to us. >>>>>> >>>>>> >>>>>> -- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "opencog" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to [email protected]. >>>>>> To view this discussion on the web visit >>>>>> https://groups.google.com/d/msgid/opencog/CAHrUA34gQSDZnbkV1Mp7aEOSGoENOkQTAZoBBRVL6%3DwJWfJv%3DA%40mail.gmail.com >>>>>> <https://groups.google.com/d/msgid/opencog/CAHrUA34gQSDZnbkV1Mp7aEOSGoENOkQTAZoBBRVL6%3DwJWfJv%3DA%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>> . >>>>>> >>>>> -- >>>>> You received this message because you are subscribed to the Google >>>>> Groups "opencog" group. >>>>> To unsubscribe from this group and stop receiving emails from it, send >>>>> an email to [email protected]. >>>>> To view this discussion on the web visit >>>>> https://groups.google.com/d/msgid/opencog/CAFMxUd-PQnKC5-PfFQV1pJ3jRe1Y773nHzaL%2BcgtDUZQv5ypfQ%40mail.gmail.com >>>>> <https://groups.google.com/d/msgid/opencog/CAFMxUd-PQnKC5-PfFQV1pJ3jRe1Y773nHzaL%2BcgtDUZQv5ypfQ%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>> . >>>>> >>>> >>>> >>>> -- >>>> Patrick: Are they laughing at us? >>>> Sponge Bob: No, Patrick, they are laughing next to us. >>>> >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "opencog" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/opencog/CAHrUA36gKrP3mBeGd4kGHBFhZ-_gd_1G6NOvuTp9_Bq1nH2juw%40mail.gmail.com >>>> <https://groups.google.com/d/msgid/opencog/CAHrUA36gKrP3mBeGd4kGHBFhZ-_gd_1G6NOvuTp9_Bq1nH2juw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>> . >>>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "opencog" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/opencog/CAFMxUd9qLP%2BJFKWJ8JfP6eWmaQwax1AAngRi1K5HoQCutAz5YQ%40mail.gmail.com >> <https://groups.google.com/d/msgid/opencog/CAFMxUd9qLP%2BJFKWJ8JfP6eWmaQwax1AAngRi1K5HoQCutAz5YQ%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> > -- > You received this message because you are subscribed to the Google Groups > "opencog" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/CAHmauB5tow-ChczspaUEf4-CUzRLDFs2yUVovX%2BCx0Nc6G0rjg%40mail.gmail.com > <https://groups.google.com/d/msgid/opencog/CAHmauB5tow-ChczspaUEf4-CUzRLDFs2yUVovX%2BCx0Nc6G0rjg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- Ben Goertzel, PhD http://goertzel.org “He not busy being born is busy dying" -- Bob Dylan -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBcXAiDciS%2BOnL4S%2BdekriK3TSvQCJqO-EJj6yopgxhs1A%40mail.gmail.com.
