My bet is models can already do all these things. Useful math such as this is likely to emerge and be refined as part of training, assuming they’re discoverabl

My bet is models can already do all these things. Useful math such as this is likely to emerge and be refined as part of training, assuming they’re discoverable via gradient descent or whatever the cool kids are using these days. Reinforcement learning should then retain and refine anything useful once discovered. If something like a Kalman filter or Gaussian filter is discovered by the training process, it’d be put to use and refined, and maybe this is part of “grokking” phenomenon - a decent explanation is here: https://medium.com/generative-ai-revolution-ai-native-transformation/grokking-the-hidden-path-to-agis-implicit-reasoning-breakthrough-1bae5579af5b https://medium.com/generative-ai-revolution-ai-native-transf.... DeepSeek talked about “aha moments” in https://arxiv.org/pdf/2501.12948#page9 https://arxiv.org/pdf/2501.12948#page9 where under RL the model learned to backtrack and correct itself, for example. Makes one wonder what neat math we can find in models - eg. In May 2024, researchers at Anthropic found the Golden Gate Bridge and created a modified Claude that couldn’t stop talking about the bridge: https://www.anthropic.com/news/golden-gate-claude https://www.anthropic.com/news/golden-gate-claude Kind of like the bitter lesson of AI in reverse - instead of us trying to outsmart AI with hand-rolled tricks, why not let it tell us what tricks are out there to be discovered :-)