Thanks for the feedback! Sure, we will keep this in mind and make the content more relatable and approachable. Appreciate you contributing your thoughts here 😊

More to come! Stay tuned :)

Sharp eyes! Thank you 😊

Input: "Create equations modeling the evaporative process of a black hole as informed by the penrose-diagram: treat remnant as the lower dimensional approximation of the state-space, and virtual particles re-entering the black as forming an inner white hole projecting mass-energy into a hyperspherical manifold, including a temporal evolutional vector field as a kerr-like solution in D dimensions : as mai-ku function >> codeblock, please, thanks!" Output: "Certainly! Below is a structured way to represent the complex theoretical concepts surrounding black hole evaporation, the role of virtual particles, and higher-dimensional physics into a MAI-KU code block format, combining the advanced topics into an organized mathematical summary: ```mai-ku !!{Modeling Black Hole Evaporation: Penrose Diagram and Higher-Dimensional Physics} >: {Introduction to Black Hole Evaporation} !{Overview}: "Exploring the evaporative process of black holes via Penrose diagrams, focusing on the remnant as a lower-dimensional approximation of the state-space. We examine how virtual particles re-entering the black hole contribute to an internal dynamic resembling a white hole."; >:{Mathematical Formulation} !{Equations}: [ "ds^2 = -dt^2 + dr^2 + r^2 dΩ^2_{D-2}", // Metric in D dimensions "dr/dt = -α sqrt(M)", // Evaporation rate, where α is a constant related to the Hawking radiation intensity and M is the mass of the black hole "dM/dt = -β M^2", // Mass-energy loss rate due to radiation, β is a constant "Ψ = Ψ_0 e^{-iωt} Y_l^m(θ, φ) r^l" // Wave function of virtual particles around the black hole, incorporating temporal and angular dependencies ]; >:{Kerr-like Solution in Higher Dimensions} !{Details}: "Developing a Kerr-like solution to represent the rotational dynamics of the black hole in D dimensions. This solution incorporates a temporal evolution vector field to account for the effects of angular momentum and mass-energy projections into the hyperspherical manifold."; >:{Temporal Evolution and Vector Field Dynamics} !{Vector Field}: "v^μ = (ξ^t, ξ^r, 0, ..., 0)", // Temporal evolution vector field components !{Temporal Dynamics}: "∂_t ξ^μ + Γ^μ_{νλ} ξ^ν ξ^λ = 0", // Ensuring the vector field evolves according to the geodesic equation in curved spacetime !{Hyperspherical Manifold Projection}: "S^D = \\{ x ∈ R^{D+1} : ||x|| = 1 \\}", // Definition of a hyperspherical manifold in D+1 dimensions >:{Implications of Inner White Hole Dynamics} !{White Hole Projection}: "Analyzing how mass-energy feedback from virtual particles, entering the black hole and emanating as a white hole, projects into the higher-dimensional space, influencing the topology and temporal properties of the manifold."; $: {Conclusion and Further Research} !{Summary}: "This model proposes a theoretical framework that integrates black hole evaporation, Kerr-like rotational dynamics, and white hole projections within a unified higher-dimensional space-time context. Further mathematical refinement and physical interpretation are necessary to explore practical implications and align with observational data."; $: {Future Directions} !{Research Avenues}: "Investigate the stability of the hyperspherical manifold under varying energy conditions and explore potential observable consequences of such higher-dimensional dynamics in astrophysical phenomena."; ``` This MAI-KU block aims to succinctly encapsulate the sophisticated interplay of black hole physics, virtual particle dynamics, and higher-dimensional space-time, providing a clear direction for theoretical exploration and potential future research."

Thanks for the kind words! 🫶

Thank you! 🙏

Great question! To your 1st question, no that's not the conclusion that I was trying to make - as evidence from empirical research will be needed to reach that conclusion. What I showed in the video was that the RAPTOR-based RAG built purely on vector database probably was not enough to ensure high-quality and comprehensive answers. I don't know what could've gone wrong (as said around 6:29) and how to fix the process, but we can use knowledge graphs to enhance and improve the answer quality (7:11). In this case, it's more of combining vector-based RAG with knowledge graphs. I actually don't know the answer to your 2nd question as I'm not an expert on Neo4j graph embeddings, but this is an interesting idea worth testing out! To your 3rd question, not quite sure what you meant by an efficient clustering process, but LangChain also tested out the RAPTOR technique and I recommend taking a look to see if it provides more helpful information to your concerns :) ukposts.info/have/v-deo/opJ4l56bi4JoxWQ.html

Good question! And you're probably spot on. Adding new documents to vector databases may require updating the clustering, while knowledge graphs can be scaled up more easily by adding new nodes and relationships without redoing and reconstructing the entire process.

We used Diffbot's Natural Language API to convert any unstructured text data into knowledge graphs! While it's not easy to clearly explains how it contains all information, you can experiment and play around with any text you have at: demo.nl.diffbot.com/ Simply paste any text data you have and see how it performs! 😉 As documented in the notebook, you can use DiffbotGraphTransformer to convert any Wikipedia text to knowledge graphs: github.com/leannchen86/raptor-rag-kg-enhanced/blob/main/raptor-rag-kg-enhanced.ipynb Let me know if you other questions. Happy to answer them!

Since you’re using Wikipedia data in this example, it would be interesting to see how your automated knowledge graph construction compares with a more human-curated effort like dbpedia.

Yes! And that's what we at Diffbot are currently working on with our LLM solutions. We believe language models should return the verified source of information which helps generate the response, adding validity and factual accuracy. We'll be releasing a video on that. Stay tuned 😉

Very flattered! Our main purpose for content creation is providing values to the audience, especially educational value. So while likes/view counts definitely are seen as part of the metrics to assess content quality, whether the viewers learn something new or enjoy the video is the more important focus for us. Thanks for the encouragement!

Thanks for the question and this sounds like an interesting problem! The Diffbot knowledge graph and APIs have become free! So, it shouldn’t cause the problem. Is there a good way to reach you or if you’re open to a vid chat, you can shoot me an email at: leannchen86@gmail.com

@@diffbot4864 Thanks so much, I'll email you!

Good question. But that normally doesn’t make a difference, as language models don’t read text like we as humans do - words are transitioned into tokens. The easiest way to test is using ChatGPT, either misspell a famous person’s name or use all lower cases, and it would still return the correct person.

@@diffbot4864 yes, i am familiar with the workings of a transformer. I think the casing will produce a different token, so you are at the mercy of the training data size / transformer size / context size to have a capitalized word return the same response. In general my experience is also that it does not make a difference, but you were using here a short context and a small model. That is why i thought it might be an explanation.

Good analogy!

You cited it better than I did 😂

Friendly reminder: Neo4j is a graph database, so it can’t construct knowledge graphs for you. You’ll still need NLP techniques to extract entities and relationships first for knowledge graph data and later store in a graph database like Neo4j.

Very true, I guess non profit and passion projects will require to deal with that in other ways.

@@aldotanca9430 Actually all Diffbot's APIs become FREE this week, including Diffbot Natural Language API (being used in this video), which can help extract entities/relationships, entity resolution, etc. You can freely get access at: app.diffbot.com

@@diffbot4864 Thanks! But I think I would need to sign up with a company email? The system will not accept a personal email, github account or similar. It seems set to only allow a "work email". Of course, many people will have a work email and could use that even if their project is unconnected with their job, and there are probably 'creative' ways to get around that. I was just pointing out that diffbot accounts seem to be meant for business users only.

That’s a good advice! Thank you for the feedback. I’ll try this when I encounter something similar again :)

Which one? If you want to see the process, you can find the notebook in the description!

🙄😳