There was an interesting view on topology from: three blue one brown, "This open problem taught me what topology is". There was also a youtube video regarding the use of GPU for LLMs that used graphing the connections of related words and word combinations, I assume tokens, using the GPUs for three dimensional graphing for the inference of combinations of tokens. My thought is that the use of the three or possibly four dimensions for graphing inference would be equivalent to using Quantum states for computing and of course would be available using todays technology. Have a look at the videos and then comment. What are your thoughts? The following might even be better context of the above from ChatGPT: 1. Topology and "Three Blue, One Brown" Grant Sanderson’s video on topology, especially in the context of an open problem, is likely exploring how this branch of mathematics deals with the properties of space that are preserved under continuous deformations, such as stretching, twisting, or bending, but not tearing or gluing. One thing that is interesting about topology in a computational or machine learning context is its ability to model and understand the inherent structure of high-dimensional data without necessarily requiring a Euclidean metric or fixed dimensionality. Linking Topology with LLMs: Topological concepts like "homeomorphisms" (continuous deformations) or "manifolds" (spaces that locally resemble Euclidean space) are potentially useful in LLMs when trying to model the “structure” of data points (tokens) in a high-dimensional latent space. While topological data analysis (TDA) isn't a mainstream method for training LLMs, there’s growing interest in methods that analyze the shape and structure of data manifolds for better understanding and improving the efficiency of model training and inference. Topological spaces in this case might metaphorically represent how tokens are related and how language constructs can be continuously transformed or mapped onto each other. For example, this idea of "continuous deformations" could be a useful analogy when thinking about how language models can infer new word combinations or conceptual shifts through context or similarity rather than strict, discrete categorization. 2. Using GPUs for Multi-Dimensional Graphing of Tokens The idea you mentioned about using GPUs for "three-dimensional graphing" of tokens likely refers to the use of GPUs for large-scale computation tasks in training models, specifically in the context of large language models (LLMs) and the high-dimensional embeddings they use to represent words or tokens. Modern language models, like GPT, BERT, or other transformer-based models, map words or phrases into high-dimensional vector spaces (typically hundreds or thousands of dimensions) using embeddings. These embeddings aren't just simple word vectors; they capture nuanced relationships and can be thought of as points in a high-dimensional space. Graph Representation: In some advanced applications of graph theory and neural networks, the tokens might be viewed as nodes, and their relationships or contextual dependencies are the edges connecting them. Embeddings can be thought of as mapping these tokens into a space, potentially visualizable (though not necessarily in 3D) by advanced dimensionality reduction techniques like t-SNE or PCA. But, the GPUs are largely used to parallelize the matrix multiplication operations that happen in the model’s layers (especially in transformer models) rather than directly for visualizing graph embeddings in 3D or 4D space. Possibility of 3 or 4 Dimensions for Graphing Inference: You mentioned the possibility of using 3 or 4 dimensions to represent token relations, which is an interesting thought. It’s true that neural network embeddings exist in high-dimensional spaces-typically 300-1500 dimensions-but we visualize them in 2D or 3D for ease. If you're thinking in terms of quantum computing, that’s a different paradigm altogether. Quantum computing uses qubits, which can exist in a superposition of states and, as a result, allow the potential for exponentially more complex computation compared to classical bits. 3. Linking to Quantum States for Computation The idea of using quantum states for computation, especially in the context of quantum machine learning (QML), is an emerging field. Quantum computers exploit the principles of quantum mechanics, such as superposition and entanglement, to perform calculations that would be infeasible for classical computers. In quantum machine learning, it's hypothesized that quantum states could represent multidimensional data, allowing for the simultaneous exploration of multiple possibilities (as is the case with superposition), which might offer more efficient ways to model complex relationships between tokens or words in LLMs. However, the current state of quantum computing is far from being able to replace classical computing in tasks like language modeling. We are still in the "quantum advantage" phase-where quantum computers have demonstrated potential for specific tasks (like factorizing large numbers with Shor’s algorithm), but large-scale, general-purpose quantum computing is still a long way off. 4. Your Thought: Quantum Computing + LLMs + Multi-Dimensional Graphs To connect these ideas, you're suggesting that the use of multi-dimensional graphing (such as 3D or 4D embeddings) for LLMs could potentially mirror or be akin to quantum states in computation. In theory, the ability to model relationships in such a space with GPUs could be seen as using high-dimensional representations, which resemble the kind of "state superposition" we think about in quantum systems. Does this map to quantum computing? Not exactly, at least in the conventional sense. Quantum computing doesn’t currently “graph” relationships in the same way as a classical neural network. But if quantum computing were to be applied to natural language processing (NLP) or large language models, it could involve quantum-enhanced representations that explore multiple possibilities simultaneously-something like using quantum states to represent different potential word combinations and their relationships, evolving through the quantum circuit’s interference patterns. Thoughts: The multi-dimensional representations of tokens and the idea of leveraging quantum states share similarities in terms of being able to explore many possible states simultaneously (whether it’s high-dimensional embeddings or quantum superpositions). But they operate in different paradigms. GPUs for deep learning focus on optimizing the process of training and inference in models, whereas quantum computers have the potential (but are still in an experimental phase) to fundamentally change how computations are performed by using quantum mechanics. The intersection of quantum computing and neural networks (Quantum Neural Networks or QNNs) is an exciting area of research, but the real-world applications-especially for NLP-are still in early stages. What you’re touching on is a speculative, futuristic view where quantum computing may be used to model more complex, multi-dimensional relationships between tokens, but we’re not there yet. The overlap between topology, machine learning, and quantum computing is conceptually fascinating and could offer new ways to think about how models infer and generalize. We're already seeing a shift toward more holistic, geometrically-inspired models in machine learning, but full-fledged quantum integration into LLMs remains speculative at this point.

I remember reading that the Morse code was able to create 26 letters of the English alphabet and then the combination of those 26 letters has created 140000 words and those 140000 words has created so far 140 billion documents. And that is how I started to understand DNA. Now to try and figure out how to program for a Quantum computer where there are multiple states. Goodluck in your journey.

hi bro i hope your channel really grows well. I would suggest use better graphics in your Presentation or slides your video was truly intellectual. HAPPY NEW YEAR.💌

Congratulations on the talk Ioannis! Awesome explanation as always!

Thanks for sharing. Please check typo in the title "GPC"

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