Iterative Addressing in a Virtual Memory for Conceptualisation

If we could build a lens , where we sample from spaces itteratively in order to generate a particular, we may have a model that simplifies the process. And aids in keeping the selection process a series of linear transformations. For example, if we would like to generate an entire video, we could train an algorithm , perhaps with a VAE to selct the priinciple components of videos and then sample from this distribution. It will be up to the system to learn these components on its own, but the axes of this distribution are not objects in their own right. A point on a manifold is selected that is defined by the information it contains, which is a complete instance of a video. The system proposed described separates features and creates a manifold for each. Each new manifold will be linked by a parameter for selecting from that space. For this paper I present these manifolds as euclidean spaces that are positioned within a cascade. What this means is that , during the process of generation, if a cat is in one of the scenes of the video, we will select features for the cat itteratively, starting from the "choice" of selecting a generic cat, which is paramatrecised in its own space, then branching of into particulars such as pose and position within the video. A simpler example will involve an NLP system such as a conversational interface that is augmented with these spaces.We could have a 2D descrete space in N^(2) where the axis contains a mapping of elements that are the words in a natural language such as english. This will be a finite space with the elements listed along the axis corresponding to a natural number untill the list is complete. We could represent an ordered tuple in this space as a two worded sentence. Some being sensible and some not. If we extended the number of dimensions in the space we could represent more and more sentecnes. but it soon becomes impractical. We would soon run into storage requirements for this database of ntuples that would not be practical. We solve this problem by defining the space as and when we need it. Each and every tuple possible in the space of N^(x) where x represents the number of words in the tuple will be accessable within the system for arbitrary values of x , and they will be uniquely defined by just two numbers. our work will be to define an Nth term within a space that is created when the numebr of words necessary is x. What this means is that the system will need to know firstly x, or how many words are in the sentence to be generated, then once that is known the algorithm finds the Nth term in that space defined within the context of an algorythm that sorts N^(x). That tuple that represents this Nth term will then be the snetecne that the NLP system generates .All this without needing to store an actual x dimensional space in memory, Now when traing a traditional neural network we only need to supply two numbers into the algorithm to represent an entire sentence, in both the first utterance and its response.We could further segment this (N,x) space and sample selectively the intersection of many sets, and get a tailor made response. We could even upon being given an utterance , generate the segment of all the sentences that are the result of the utterance, as in logically follow given previos utterances by segmenting after each utterance and either taking joins or intersections then sampling from this set in order to get a response.This represents a form of a database of what the algorythm knows as a set of tuples. These subsets could be trained for by for example a GAN that is restricted in what it can model. For instance a movie generating GAN set up would start by using the generator as a segmenter to define points in (N,x) of interest, mapping x to the number of pixels of an object and N to the point representing the object. Then during the generation process it will only be allowed to sample the (n,x) space in order to generate, and then only those samples and the neighborhood around the samples it learnt to classify. As is common with GANS binary noise will be added but it will only represent transformations of position within a scene and other details left in producing authentic scenes. It is my supposition that this would speed up convergence. Especially if we take the real images and use them to enrich the generator by adding their segments into it as training goes on. In the NLP setting , the GAN would relate different parts of (N,x) by selecting points across it according to the rule learnt or induced by the training set, i.e. the Real samples. Care must be taken to use the log of N during training to minimise the size of the numbers being used. Rather we will need a system of nested logs with different bgases for this. then this is parsed to the algorithm , with the bases. So 355274 could be the anti log to the base 2 of 355, then take this result and antilog it with base 7 and finaly take that result and antilog it with base 4. So the original number will be found by taking successive anti logs with those particular bases.The final algorythm will be responsible for picking up this additional information.