Context:

I am a Sixth Form student from the UK interested in the application of mathematics to real-world problems.

During a fellowship with Leaf (The mathematics of morality — Leaf), I began researching moral weights and the use of neural proxies in cross-species comparisons. 

Continuing this as an Extended Project (Level 3 Qualification), I recently completed a project exploring an alternative to neuron counts.

Neuron counts are convenient and widely used, but they don't account for network organisation. Two brains with identical neuron counts can potentially have very different capacities for integrated and efficient information processing. 

Purpose of this post:

1) If you are interested in mathematical approaches to consciousness/sentience proxies I hope you'll find this research interesting. I would greatly appreciate any feedback, thoughts or advice you may have to offer about this project.

2) If you have experience in moral weights research, graph theory or connectome data, I'm seeking answers to a few specific questions:

• Is my output likely to be adapted and applied by researchers, and how could I improve this work to make it more accessible or actionable?
• Is it possible to make stronger mathematical links between exact derivations of properties and closed-form predictive equations found using regression?
• How should I support my weighting and combination of properties with philosophical consideration?
• How might the input parameters be derived directly from empirical data? Would it be sensible to consider techniques like electron microscopy?

My project:

I model animal brains abstractly as combinations of multiple generative graph models. The code generates hybrid graphs based on inputs such as neuron count, number of connections, graph model specific parameters, and the proportions of each graph model. My full project report is linked in this post.

I use statistical graph theory and PySR (physics informed symbolic regression) to obtain predictive equations for the key properties of these graphs (e.g. average shortest path length, clustering) in closed form, based on their input parameters. 

The properties can then be combined, normalised, and weighted appropriately, according to their theorized links to sentience. The result is a mathematical equation that outputs a single value, which could be used as a direct alternative or complementary proxy to neuron counts in quantitative measures of moral weight.

In future, the input parameters to this equation could be determined for different species directly from empirically derived animal data.

Main goal:

The objective of this project is to motivate moral weights researchers to consider the arrangement, behaviour and efficiency of animal neural networks rather than simply their neuron count.

The most useful and actionable output of this project is the Python code, which is in essence a complete and flexible tool for creating a neural proxy for direct use in moral weighing.  My hope is for the code to be copied and adapted by experts with access to connectome data.

The changes that should be made to the code to increase accuracy are clearly outlined and should not be difficult to implement. I also highlight some areas in which additional philosophical consideration would be beneficial.

Acknowledgements:

Thank you to @Jonah Boucher at Leaf Courses for inspiring this work, and helping me to strengthen and develop my idea. Thank you also to @Bob Fischer and @vicky_cox for interviewing with me, and for your very useful insights and advice.