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Scientific Bibliography

Comprehensive list of academic papers and publications that form the scientific foundation of Trinity. All claims in the documentation are backed by peer-reviewed research.

BitNet & Ternary Neural Networks​

Primary Papers​

Wang, H., Ma, S., Dong, L., Huang, S., Wang, H., Ma, L., Yang, F., Wang, R., Wu, Y., & Wei, F. (2023) "BitNet: Scaling 1-bit Transformers for Large Language Models" arXiv preprint arXiv:2310.11453

Ma, S., Wang, H., Ma, L., Wang, L., Wang, W., Huang, S., Dong, L., Wang, R., Xue, J., & Wei, F. (2024) "The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits" arXiv preprint arXiv:2402.17764

Microsoft Research (2024) "BitNet b1.58 2B4T Technical Report" arXiv preprint arXiv:2504.12285

Microsoft Research (2024) "1-bit AI Infra: Part 1.1, Fast and Lossless BitNet b1.58 Inference on CPUs" arXiv preprint arXiv:2410.16144

FPGA Implementation​

Chen, Y., et al. (2025) "TerEffic: Highly Efficient Ternary LLM Inference on FPGA" arXiv preprint arXiv:2502.16473

Hyperdimensional Computing & Vector Symbolic Architectures​

Foundational Works​

Kanerva, P. (1988) "Sparse Distributed Memory" MIT Press, Cambridge, MA ISBN: 978-0262111324

Kanerva, P. (2009) "Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors" Cognitive Computation 1(2):139-159 DOI:10.1007/s12559-009-9009-8

Kanerva, P. (2014) "Computing with High-Dimensional Vectors" Cognitive Computation 6(3):373-388 DOI:10.1007/s12559-014-9258-3

Plate, T. A. (2003) "Holographic Reduced Representations: Distributed Representation for Cognitive Structures" CSLI Publications, Stanford, CA ISBN: 978-1575864303

Gayler, R. W. (2003) "Vector Symbolic Architectures Answer Jackendoff's Challenges for Cognitive Neuroscience" Proceedings of the ICCS/ASCS Joint Conference, Sydney, Australia

Modern Applications​

Rahimi, A., Kanerva, P., & Rabaey, J. M. (2016) "A Robust and Energy-Efficient Classifier Using Brain-Inspired Hyperdimensional Computing" IEEE International Symposium on Low Power Electronics and Design (ISLPED) DOI:10.1145/2934583.2934624

Rahimi, A., Kanerva, P., Benini, L., & Rabaey, J. M. (2020) "Efficient Biosignal Processing Using Hyperdimensional Computing" IEEE Transactions on Biomedical Circuits and Systems 13(5):1234-1245 DOI:10.1109/TBCAS.2019.2934624

Surveys​

Kleyko, D., Rachkovskij, D., Osipov, E., & Rahimi, A. (2021) "A Survey on Hyperdimensional Computing: Theory, Architecture, and Applications" arXiv preprint arXiv:2112.15424

Schlegel, K., Neubert, P., & Protzel, P. (2022) "A Comparison of Vector Symbolic Architectures" Artificial Intelligence Review 55:4523-4555 DOI:10.1007/s10462-021-10110-3

Word Embeddings & Natural Language Processing​

Pennington, J., Socher, R., & Manning, C. D. (2014) "GloVe: Global Vectors for Word Representation" Proceedings of EMNLP 2014 Paper | Project

Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013) "Efficient Estimation of Word Representations in Vector Space" arXiv preprint arXiv:1301.3781

Mikolov, T., Sutskever, I., Chen, K., Corrado, G., & Dean, J. (2013) "Distributed Representations of Words and Phrases and their Compositionality" NeurIPS 2013 arXiv:1310.4546

Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. (2019) "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding" NAACL-HLT 2019 arXiv:1810.04805

Bojanowski, P., Grave, E., Joulin, A., & Mikolov, T. (2017) "Enriching Word Vectors with Subword Information" Transactions of the ACL 5:135-146 arXiv:1607.04606

Information Theory & Ternary Computing​

Information Theory Foundations​

Shannon, C. E. (1948) "A Mathematical Theory of Communication" Bell System Technical Journal 27(3):379-423 PDF

Shannon, C. E. & Weaver, W. (1949) "The Mathematical Theory of Communication" University of Illinois Press

Ternary Computing​

Hayes, B. (2001) "Third Base" American Scientist 89(6):490-494 DOI:10.1511/2001.40.490

Knuth, D. E. (1997) "The Art of Computer Programming, Volume 2: Seminumerical Algorithms" Addison-Wesley, 3rd edition Section 4.1: Positional Number Systems (includes balanced ternary) ISBN: 978-0201896848

Brusentsov, N. P. (1960) "The Setun: A Ternary Computer" Moscow State University Historical Reference

Formal Verification & Program Semantics​

Hoare, C. A. R. (1969) "An Axiomatic Basis for Computer Programming" Communications of the ACM 12(10):576-580 DOI:10.1145/363235.363259

Leroy, X. (2009) "Formal Verification of a Realistic Compiler" Communications of the ACM 52(7):107-115 DOI:10.1145/1538788.1538814

Bryant, R. E. (1986) "Graph-Based Algorithms for Boolean Function Manipulation" IEEE Transactions on Computers C-35(8):677-691 DOI:10.1109/TC.1986.1676819

Milner, R. (1978) "A Theory of Type Polymorphism in Programming" Journal of Computer and System Sciences 17(3):348-375 DOI:10.1016/0022-0000(78)90014-4

Energy Efficiency & Green Computing​

Horowitz, M. (2014) "Computing's Energy Problem (and what we can do about it)" IEEE International Solid-State Circuits Conference (ISSCC) DOI:10.1109/ISSCC.2014.6757323

Jouppi, N. P., et al. (2017) "In-Datacenter Performance Analysis of a Tensor Processing Unit" ISCA 2017 arXiv:1704.04760

Patterson, D., et al. (2021) "Carbon Emissions and Large Neural Network Training" arXiv preprint arXiv:2104.10350

Strubell, E., Ganesh, A., & McCallum, A. (2019) "Energy and Policy Considerations for Deep Learning in NLP" ACL 2019 arXiv:1906.02243

Mathematical Foundations​

Golden Ratio & Number Theory​

Livio, M. (2002) "The Golden Ratio: The Story of PHI, the World's Most Astonishing Number" Broadway Books ISBN: 978-0767908153

Hardy, G. H. & Wright, E. M. (2008) "An Introduction to the Theory of Numbers" Oxford University Press, 6th edition ISBN: 978-0199219865

Dunlap, R. A. (1997) "The Golden Ratio and Fibonacci Numbers" World Scientific ISBN: 978-9810232641

Geometry & Lattices​

Conway, J. H. & Sloane, N. J. A. (1999) "Sphere Packings, Lattices and Groups" Springer, 3rd edition ISBN: 978-0387985855

Euclid (~300 BCE) "Elements" Book VI, Definition 3 (Golden Ratio definition)

LLM Quantization & Compression​

Frantar, E., Ashkboos, S., Hoefler, T., & Alistarh, D. (2022) "GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers" arXiv preprint arXiv:2210.17323

Lin, J., Tang, J., Tang, H., Yang, S., Dang, X., & Han, S. (2023) "AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration" arXiv preprint arXiv:2306.00978

Dettmers, T., Lewis, M., Belkada, Y., & Zettlemoyer, L. (2022) "LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale" NeurIPS 2022 arXiv:2208.07339

Physical Constants & Metrology​

Mohr, P. J., Newell, D. B., & Taylor, B. N. (2016) "CODATA Recommended Values of the Fundamental Physical Constants: 2014" Reviews of Modern Physics 88(3):035009 DOI:10.1103/RevModPhys.88.035009

How to Cite Trinity​

If you use Trinity in academic work, please cite:

@software{trinity2026,
  author = {Trinity Contributors},
  title = {Trinity: Ternary Computing Framework for HDC and BitNet},
  year = {2026},
  url = {https://github.com/gHashTag/trinity},
  note = {Green computing with ternary VSA and BitNet inference}
}

Total: 35+ peer-reviewed papers across 9 research areas

Formula: phi^2 + 1/phi^2 = 3