Generative AI

Testing whether a time series is a martingale using Black-Scholes simulation, permutation entropy, and Welch's PSD method.

The math behind diffusion models: Chapman-Kolmogorov, Kramers-Moyal, Ito's lemma, and the forward/reverse SDEs.

How GRPO turns next-token prediction into a reinforcement learning objective, derived step by step from the Transformer forward pass.

A design sketch for combining Titan's surprise-based memory with Transformer² SVD fine-tuning, with the math worked out and no experiments run yet.

How SakanaAI's Transformer² adapts LLM weights at inference time via SVD fine-tuning, RL, and expert weight combination, mapped from paper to code.