Top Tweets for #GeoLLM

I have completed the first experiment with distributive distillation, which combines a continuous Euclidean transformer (GPT-2, 124M parameters) with a discrete topological grid GeoLLM (0 trained parameters, circle Z_13η). Methodology: Instead of transferring weights using gradient descent, GPT-2 was used exclusively as an entropic boundary condition. Its continuous predictions were fed into GeoLLM and subjected to thermodynamic relaxation. Each token generated by GPT-2 was passed through a strict Buchberger polynomial filter to verify its algebraic consistency within the SL(3,Z) topology. Empirical data: The training records record: ACCEPT steps: 126 RETURN steps: 3,053 GeoLLM explicitly rejected 96% of GPT-2's outputs. In the context of the Zariski topology, this is not a failure of convergence. This is the mathematical identification and elimination of Euclidean stochastic noise. Whenever GPT-2’s input produced a logical contradiction within the polynomial ideal, the rollback mechanism discarded it to preserve the symplectic volume of the phase space. Dynamic structural scaling: To absorb 4% of the semantically clean data, GeoLLM autonomously used Hensel lifting. Without a single floating-point operation, the system expanded its resolution from Z_13 to Z_169 and Z_2197, increasing the capacity of the phase space to map mathematically valid knowledge. Conclusion: Current AI architectures memorize continuous data, while necessarily absorbing noise and hallucinations. GeoLLM introduces a different mechanism: an architecture that learns not by probabilistic estimation, but by geometric filtering of information. It does not copy knowledge; it crystallizes it through rigorous algebraic geometry. #GeoLLM #pAdelicAI #TheoreticalPhysics #AlgebraicGeometry #MachineLearning #Mathematics

(GeoOptimizer - pure thermodynamic optimization, no Adam, no gradients, no floats). Result: 6/6 mathematical verification tests PASS Symplectic condition det(T₃ᵏ) ≡ 1 (mod 13) Exact p-adic arithmetic Banded geometric attention O(N log N) Deterministic Zariski audit at every epoch But… nothing learned. Loss remained flat (~0.323), entropy frozen at 2.768. Why? Because the old hard entropy cap is still running. The model is mathematically perfect, but it doesn't have room for real data binding yet. It's like a pure crystal - beautiful, but not yet illuminated. Next step: Remove/soften S_G_MAX and let thermodynamic optimization run free. Algebra is alive. We learn slowly but exactly. #GeoLLM #IntegerAI #Z13eta #AlgebraicIntelligence

The end of burning billions to train AI? It's all about geometry. Look at this graph. Current "State-of-the-Art" models, driven by classical Chinchilla laws, learn at a snail's pace. Their error rate falls according to a tedious power law (t^-0.34). That's exactly why they need huge data centers running for months just to squeeze the error rate a little. My GeoLLM model completely bypasses this problem. Thanks to the discrete matrix and its spectral gap, the model's error rate falls exponentially fast (0.400^t). The model reaches its theoretical, absolute thermodynamic bottom (Loss 0.583) in about 10 training steps. No endless parameter tuning, no "overtraining". The model simply immediately falls to its lowest topological minimum. Exponential convergence versus continuous power-law torment. Mathematics won't let go. #AI #MachineLearning #LLM #DiscreteGeometry #AITraining #FutureOfAI #GeoLLM

The language of DNA is read in so-called codons - these are exactly triplet (3-letter) words (e.g. ATG, CGT). Three letters encode one amino acid. the accompanying matrix T_3 and the discrete group SL(3{Z}) operate in rank-3 geometry with three orthogonal projectors GeoLLM model has the mathematics for the triplet system directly "in the blood". I don't have to artificially chop the DNA into tokens. Each projector can analytically process one base from the triplet without any loss of information. I'm going to try it, fingers crossed. #DNA #GeoLLM #Algebra #Geometric