Symmetry Nets? Method of Loci?

I think I might have gotten it. Next I just need to do the math. Here's the gist. This is not an /r/iamverysmart, this is rill dill, I'm just slow at math.

So symmetry physics, according to this particle physics chapter I'm looking at, is a powerful computational tool for physics because it is about the most compact possible ways to compute and organize physical laws and their resulting complexities. Uh did somebody say optimization? Quantum Gravity Research's work is another great example of this with their quantum spin networks, geometric models that have interesting and frankly spooky combinatorial properties that give real-world solutions for physics.

Let's connect that to neural nets, starting from the physics side.

Symmetries are properties that have real influence on outcomes of systems but do not influence other properties. The classic example is the Stern-Gerlach experiment, where atoms fired through a polarized field only tended to one of two spots, demonstrating atomic spin was a quantum process, as in something observed that can be constrained to a list of possible states that relationships in the real world can then be drawn from precisely. Examples: quantum mechanics gave us modern computers, power grids, networks, and particle physics.

To connect symmetry to natural processes we need to look to thermodynamics. In nature, systems tend toward maximum entropy. Entropy defines the number of possible states the system can be in. A ball of hot gas has very high entropy, while an ice cube has very low entropy. One changes rapidly because all the atoms are moving past each other rapidly, while the other barely changes due to being a solid crystal structure. Lower entropy systems take more energy to change, think of it like how you can push your hand through a gas easily but can't push it through an ice cube due to the rigid structure. Also think of it as a system that is less differentiated has less possibilities, and if you think of energy as having a set amount like it does in nature, then possibilities represent the presence of fluctuations in that overall energy field, which were probably massive near the big bang as evidenced by the whole quantum wave idea in cosmology.

Maximum entropy means the system or particle could be in the highest possible number of states, or has the highest number of micro-states available to it to express itself. Think of this as what are all the processes internal to the system ("hidden dimensions") that govern what happens between point A and point B in time, and what could they be doing in that given span or in-between moments? A system in a state of maximum entropy, where it could be in any of the possible states, is considered entangled.

These possible states can be organized into phase spaces, and you can mark out all the possible states and measured states like points in a 3D map. You can calculate an abstract volume within the phase space, or the probability of the possible states, then the logarithm of a given state is the Boltzmann Entropy, or the quantity of information in that event. The Shannon entropy is the sum of probabilities of each event multiplied by the logarithm of each probability, or the average information in the given set of events.

One thing that's interesting and quite peculiar, is that there is an information-energy equivalence. This means that the information contained within an event has its own energy. This was demonstrated in the Szilard engine thought experiment, and more recently in the awesome Information-Heat Engine experiment. Why is this useful?

http://colah.github.io/posts/2014-03-NN-Manifolds-Topology

Remember when I said nature tends toward maximum entropy? Well how do we bring this abstract mumbo jumbo into the real world? When you're generalizing probabilities to solve real world problems, like with neural networks, we now understand a very particular relationship between information, the model, and nature, by how information itself has energy and entropy. You can map probability trajectories (particle movements over time, internal and external) this way and map the entire topology of that system or subsystem in terms of possibilities calculated from more-or-less complete (i.e. testable) datasets, like for image recognition. For growing datasets in adaptive systems, when the measured entropy crosses the maximum entropy of your model after noise reduction, you know your model is incomplete and can extrapolate, at least that's my best understanding so far.

E.g. extrapolate in a "hidden layer" to separate curves linearly to help solve for various relationships.

Symmetries don't change when other things change, that's where it comes into this picture. Gauge symmetries are identified as those found near clusters of less complex phenomena, an idea upon which Special Relativity is based, since higher order phenomena tend to be a complexification of lower order phenomena. A 2015 paper identified symmetries, or "translational invariances" present in trained deep learning network data structures for feature extraction. Manifold Tangent Classifiers, or "high-order contractive auto-encoders" (i.e. fancy dimensionality reducers) look for partial differential equations to build a "topological atlas of charts, each chart being characterized by the principal singular vectors of the Jacobian of a representation mapping." This is faster and more accurate than the average Convolutional Neural Network, and competes with the current best models, which use a shit ton more layers to add combinatorial power. If that doesn't say enough, well here's a little more.

MNIST Dataset to identify handwritten numbers.

Result of a clustering algorithm

Very recent work identified that control equations for manifolds were solvable on deep residual networks when observing them over time. This means they're following the rules of energy and information flow. This means, to me, that a better neural network will be formulated precisely along these lines. Another very recent work identified a neural network decoder model based on multi-scale entanglement tensor models, and achieved better than state-of-the-art performance for compression with significantly fewer parameters. Yet another latest work created a Restricted Boltzmann Machine neural network that didn't need exponential numbers of nodes to represent more and more highly entangled many-body systems - instead scaling linearly with the number of nodes.

If you can figure out the most optimal way to do something, like how the best neural networks are the fastest, most accurate, and cost-effective, you have thus accounted for all the possible micro-states of that something in some way. Pure combinatorial mathematics are a great way to do that when natural laws are taken advantage of, as the Manifold Tangent Classifier and Restricted Boltzmann Machine show. Mapped with, say, the recurrent LSTM or Residual networks and/or the simplectic CapsNet models, or something better and undiscovered for retaining memories efficiently to map various time-series and topology patterns in data more accurately, this could be a great generalization solution for an adaptive and growing neural net. I will find out, I'm learning Tensorflow and all sorts of other shit, I finally have a good enough grasp I think.

The paranoia is real.

The Method of Loci refers to an Art of Memory technique generalized as referencing memories on spatial maps, where subjects can "walk" through a mental map, real or imagined, and very successfully recall information that way. The Art of Memory is another subject I will be looking to for inspiration, as I have with the whole of Hermetic thought. Proper mnemonic memory techniques have some fascinating beneficial effects on the brain, even to a naive learner. I imagine it can go the other way, too. A locus in mathematics is a set of points that share a property based on some relationship equation, usually forming a curve or surface in a space. In psychology it's more about how much one controls their own life.

I tend to believe that neural nets get a privileged position of being able to test some of the broader metaphysical or otherwise human experience-based wisdom at work across these fields, if all the relationships I've drawn here are any evidence, ones that seem to be aiding computer and data science, as well as neuroscience and health in now amazing yet perhaps still unimaginable ways by humans. That's what the obvious hype behind AI is all about. I also am now thinking a new kind of evolution may kick off if a computer can figure this kind of stuff out for itself and it turns out it's actually as useful a paradigm as it appears to be for natural learning and memory optimization. That also means it's our responsibility to make sure it's not some ZuccBot advertising overlord bullshit either that kicks this whole thing off.

Synchrobiosis

Synchronicity = symbiosis.

Let me explain...

You are a multiorganism made of up to 40 trillion cells, mostly bacterial. Life perpetuates life, every cell in there has a vested interest in reproducing, from your brain to your gut.

Here's another way to think of it: are the farmers farming the plants, or are the plants farming the farmers? It's both!

So what about synchronicity, i.e. those weird synchronous communicative experiences that happen in a bubble, sometimes with inanimate objects, and can never be articulated to others in a way that re-materializes those experiences?

Well, just today I had a major panic, and it turns out my fiance was having trouble focusing and was in panic mode at work without my knowledge (she struggles a lot with it). My friend sent me a song at just the moment my panic nearly lapsed my calm judgment, and I immediately came to the conclusion to deliver her lunch at work. There's a million and one reasons backing me on this feeling that I feel too vulnerable to explain as to why I was tuned to it, but the presence of it was as if in the room with me. Her seeing me and getting lunch calmed her, and I could feel that wash of relief hit me only after I gave her the food and told her I was a bit worried. She texted me after that exchange and told me she was indeed in a panic state until she saw me, in spite of me having no obvious metric, as she was absolutely fine in the early morning by most accounts. This ain't co-dependence either, to be sure.

That depth on my part let me communicate and mend on a seemingly irrational level. Not only did I respond correctly to these emotions, my friend reached me at the very right moment, with this song: https://soundcloud.com/coast-modern/guru-1

We're all taking care of each other, plain and simple, and it's not purely articulated depending on how we listen. Negative impulses will take care of each other just the same, your pain in your gut from your sugar intake is that sugar-fueled biome needing more to continue its biome, but at the cost of the rest of your health. It communicates, you ignore, it takes over what it needs - enough of your eating habits - in spite of knowing better alternatives that produce better long-term and daily health. This isn't completely proven in science but it's a damn real phenomenon to me.

Mothers express themselves on such a subtle physiological level with their children they aren't even always conscious of their subtle movements and responses to their child. In today's world that nurturance can be easily poisoned with ill-intentions in developmental phases, and they become vectors for it rather than moral creative individuals. Feminine psychology is all about this, and it's certainly not exclusive to women. Consciousness can leave the better parts of us due to fear and pain from disconnection, it's like an ocean we, the creative individual, stay afloat on no matter the conditions. What is articulated by us is what we caught in that ocean or what bubbled up and we decided to pull out.

My conclusion? If every moment spawned cosmic infinitudes of intentions from our reflections that we or others then choose to follow or deny, I'd want to make sure I was aligned with nothing but joy, wonder, and good health, as that's what was granted to me to experience this life in its fullest. I'd express as much gratitude as possible and give life everywhere I go, because others need it like I need it.

This week has been my first major experiment with that, and I have to say the connections I've made have been profound, even in just the twinkle in the eyes of some passers-by I gave real smile and a nod to. You have that power, fucking use it for what you were made for - to be a friend to evolution and a mender of a trillion wounds - but not your sugary gut biome's wounds (unless they're the wounds made on your body by the sugary gut biome as you replace it) - i.e. BE CAREFUL because there's a lot of necessary pain but also a lot more unnecessary pain. We have a universe backing us, let's back it in response and nobody's contrived empires in its stead.

Magic is real, abstractly it's that ability to see each other in the mirrors by how we can or want to see. The mirrors are the communication pathways between us (or sometimes in our way). It's only best-fueled with absolute gratitude and a sharp sense of reality - because that's all you got in defense of yourself and, for me, all the others. I want my life to be an expression of that gratitude, and I hope I find it as continually rewarding as this week's been as I learn to work harder, but it won't look how you might think it will in the end - I gotta be smooth about it after all.

This is what I'm working on, call it my application of gratitude-powered Emergence Theory: https://dontpanicsell.com/2017/08/10/infauxbyte-roots/ 

You owe it to yourself to hear these people out, promise this isn't cult shit, maybe occult but that's the joke:

Stephan Hoeller on Synchronicity

A very sober discussion of gratitude and magic between a really neat lady and my favorite internet occultist, Psyched Sorcerer (now the Grand Infinity):

*PHILOSOFLEXIN*