2. Yes, the LLMs explain their reasoning, and it makes sense They say what they saw in the graphical diagnostics and how it informed their choices. (Examples in the paper's appendix). Ablation tests confirm they really use the plots! This is what makes the search over equations practical.

Thanks Dan!
1. Combinatorial SR seems impractical because evaluating each function needs a non-convex gradient descent parameter search. We had the LLMs write functions estimating gradient search startpoints, which ablation tests showed was essential. Combinatorial SR couldn’t have done this.

10. Finally, some thoughts. The AI scientist excelled at equation discovery because its success could be quantified. AI scientists can now help with problems like this in any research field. Interpreting the results for now still required humans. Next year, who knows.

9. Because the AI system gave us an explicit equation, we could make exactly solvable models for the computational benefits and potential circuit mechanisms of high-dimensional coding. Humans did this part too!

8. We proved that when p<2, the tuning curves’ sharp peaks yield power-law PCA spectra of exponent 2(p+1). Most cells had p~1, explaining the observed exponent of ~4. The same model explained high-dimensional coding in head-direction cells. Humans did this part.

7. The equation the AI scientist found is simple and, in retrospect, we humans could have come up it with ourselves. But we didn’t. The AI scientist did. The key innovation was replacing the Gaussian power of 2 with a parameter p controlling the peak shape.

6. The AI scientist took 45 minutes and $8.25 in LLM tokens to find a new tuning equation that fits the data better, and predicts the population code’s high-dimensional structure – even though we had only tasked it to model single-cell tuning.

5. The LLM was given fit-quality scores for previous equations, and graphical diagnostics comparing the fits to raw data. It explained how it used these graphics to improve the equations, in the docstrings of the code it wrote.

4. Resolving this conundrum needs a new model for orientation tuning. We found one with AI science. Equations modelling tuning curves were encoded as Python programs, and a reasoning LLM repeatedly created new models improving on previous attempts.

3. Visual cortex encodes even low-dimensional stimuli like oriented gratings with high-dimensional power-law codes. But classical tuning models like the double Gaussian predict low-dimensional codes with exponential spectra.

2. Neural codes are most computationally powerful when they are high dimensional. In previous work with @computingnature and @marius10p, we showed that visual cortex uses high-dimensional codes whose PCA spectra follow a power-law.
www.nature.com/articles/s41...