i think its time i move with reinforcement algorithms and define some templates to reinforcement algorithm to catch. 

hmm i would start with geometry of positions of nonempty entries in matrix its geometrical patterns I would investigate.

they say prime numbers are unique? I think every integer is unique and having a unique geometry? or are there templates?  

time to investigate some numpy analysis with geometric shapes similarity of integers yupp.

not as simplicial complex euler number like counts type topological criterion it would follow but ah i wished i finished topology study that i would take templates from there alike simplicial complex numbers. 

hmm but the topic of reinforcement algorithm is to have define own template. 

or should i use a generalization neural network structure to investigate shape commonalities without going in to details of some advanced templating to build first then rebuild own templates with generative algos like reinforcement learning?

its time i cancel my own effort to investigate structure study since i couldnt find myself, but its now time to move this daunting task to neural networks to do investigate better/faster than me that as I myself couldnt find out any pattern in structure of integers yet.

ah i wish i finished topology study so now i have better templating power. or i wish i started algebraic topology and geometry book also there also might enable better templates design for this structure/pattern analysis. 

but i just cant move on to any other topic before investigating integers. cause its very important. i mean if there is structure there that could be defined utilized it is really important imho.  

i just need to understand if there are patterns/structures beforehand moving from this integer study topic of abstract algebra revising study in ai project.

but maybe i now give a brief break to study to revise basic topology knowledge in fast study pace to check out whether if i could find other template design improvision matter from there alike simplicial complex number i mean but rather not specifically like that either.  

its like having insight of patterns of integers if we consider them analogous to concepts like limiting dimensions of the topic of how dimension increase changes the structure of the underlying group operations there how it evolves its like i wish to see how chqange of dimensionality of that group impacts its structure initially and if there are patterns with high dimensions (high integers) or is there any pattern at all maybe there is not.

to give brief example of its group wise properties for a domain of some dimension take a physical operator  of any kind e.g some hamiltoninan equation etc etc there if you know the structure's some behavior for some oif its equivalence classes it might give more insights of the expected hamiltonian behavior in this new sense of solution of hamiltonian there. of having some insight of how it could behave. 

so before that one needs to see the evolution of the structure how its structured if there are any patterns for any integer to figure out then to any hamiltonian solution parts of the equations dynamic evolution  could be known before solving it type goals it has. to not take integers as integers but rather a group there with some group structure and having knowledge about how that groups behaves in several conditions to have an nisight of a physical operator without even solving it. 

to create a new alternative framework of arithmetic using such constituents of patterns/structure to have insight of how equations would behave. wihtout using the just number concept but its group patterns structures if exists.

maybe this is not accomplishable but I just want to explore this structure of integers topic.

maybe there is nopattern in structures of integers. if thats so i would at least learn that. i just cant move on from this topic until i figure out if there is structures or not. kind of fixated to this task whilst this task itself were wondered during abstract algebra revising study. 

yaayyy so before defining templates some topology fun starts now|! 

but actually if generalization seeking neural networks were used topology knowledge would be unnecessary actually. 

but still since iw ould both also have generative neural networks/algoithms investigating this problem twhich might actually need initial set of templates which needs topology information. thereby i resume revising of topology information now awhile at the same time would revise generalization doer neural networks to define such to investigate structure. 

but it would be like i would need to also with big data maybe until 100000 generate structure of integers then feed neural network with that. 

so thereby first task might be creating the smple data to network and how to define encode the data. that which it would auto search structure. e.g. dimension bare dimension of it might be like 100000 * 100000 how to encode this information and feed to neural network is one other topic to resolve.

ah i need to also revise neural networks knowledge since i had not stuied for a while. its been a lot while i had not studied neural networks topics/methods. 

so let his study part begin.  of neural networks assisted patterns in structure study.