Concept Curve Paradigm - A new approach to Knowledge representation in the AI era (v2)
Description
Abstract
Current knowledge representation techniques in Artificial Intelligence, particularly high dimensional embeddings, face significant limitations when handling complex, structured information like extensive narratives or large bodies of knowledge.
Representing rich semantic structures as single vectors often leads to information compression, loss of meaning, and potential hallucinations in generative models. This paper introduces the Concept Curve Paradigm, a novel approach that redefines knowledge representation by modeling concepts, stories, and reasoning sequences not as isolated points, but as dynamic networks or trajectories of interrelated concepts within a semantic space.
This new paradigm preserves the inherent structure and relationships within information, overcoming the constraints of static embeddings. We detail Concept Curve Embeddings Indexation (CC-EI), a practical method derived from this paradigm, which indexes information fragments based on their key conceptual interconnections rather than compressing them into dense vectors.
The Concept Curve approach offers numerous benefits, including eliminating redundancy, enabling flexible conceptual connections, enhancing AI reasoning, facilitating unlimited context input and output, improving computational efficiency, and potentially shifting AI bottlenecks away from compute constraints.
Overall, the Concept Curve Paradigm offers a new foundation for more scalable, interpretable, and capable AI systems.
All methods described in this paper are publicly implemented and freely available through open source code and documentation.
The paper will be divided into two sections:
In the First Section
1. Embeddings: A Journey from Their Origins to Their Limits - we explore Embeddings from their origins to the present day and their limitations.
2. The Birth of the Concept Curve Paradigm - we introduce the proposed solution to current state of the art limitations.
3. The Concept Curve Embeddings Indexation - we explain a new model-agnostic indexing method for the future of AI, the Concept Curve Embeddings Indexation (CC-EI).
4. Conclusion
5. Note on Benchmarks
6. References
In the Second Section we present a series of explanatory appendices on the practical use of the Concept Curve paradigm (Examples and Details).
Annex 1 – Unlimited Size Input Context
Annex 2 – Computational Savings in Query Processing
Annex 3 – Unlimited Size Output
Annex 4 – Computational Savings in Output Processing
Annex 5 – No Longer Compute Constrained
Annex 6 – A Solution to Visual Stickiness in AI Image Outputs.
Annex 7 – Advanced Image Recognition and Semantic Explanation
Annex 8 – Real Time Knowledge Updating
Annex 9 – Neuro-Symbolic AIs: A Journey from Limitations to Structural Solutions
Annex 10 – Concept Clouds or Graphs: What is the optimal representation?
Files
CC_Paper-Final_Release.pdf
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Additional details
Identifiers
Dates
- Submitted
-
2025-08-16firs version was published 2025, May 11
Software
- Repository URL
- https://github.com/Daniel-codi/Concept_Curve_Embeddings_Indexation
- Programming language
- JavaScript, HTML
- Development Status
- Active
References
- Bengio, Y., Ducharme, R., Vincent, P., & Jauvin, C. (2003). A Neural Probabilistic Language Model. Journal of Machine Learning Research, 3(Feb), 1137–1155. https://www.jmlr.org/papers/volume3/bengio03a/bengio03a.pdf
- Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013). Efficient Estimation of Word Representations in Vector Space. https://arxiv.org/abs/1301.3781
- Google Inc. (2013). Word2Vec: Tool for Computing Continuous Distributed Representations of Words. Google Code Project (archived). https://code.google.com/p/word2vec
- Lewis, P., Perez, E., Piktus, A., Petroni, F., Karpukhin, V., Goyal, N., … & Riedel, S. (2020). Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks. https://arxiv.org/abs/2005.11401
- Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., … & Polosukhin, I. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems, 30. https://arxiv.org/abs/1706.03762
- Lipton, Z. C. (2018). The Mythos of Model Interpretability. Communications of the ACM, 61(10), 36–43. https://arxiv.org/abs/1606.03490
- Bistman, D. (2025). Concept Curve Method demonstration – Source Code and Documentation. https://github.com/Daniel-codi/Concept_Curve_Embeddings_Indexation
- Bistman, D. (2025). Supporting materials for Concept Curve Paradigm. Google Drive folder. https://drive.google.com/drive/folders/1_4i_9M6U1JJ6_kVjmlNljPTvWwD8_4ks
- Zhang, H., Duan, Z., Wang, X., Zhao, Y., Lu, W., Di, Z., Xu, Y., Chen, Y., & Zhang, Y. (2025). Nexus-Gen: A Unified Model for Image Understanding, Generation, and Editing
- Bistman, D. (2025). Concept Curve Paradigm – Presentation Short Video. YouTube. https://www.youtube.com/watch?v=8XhS3kaHKc8