Eos

The idea behind Eos

We built Eos to investigate how discovery could become part of a model's continuing activity.

Recognising a relationship is one part of that work. A model must also be able to examine the relationship, establish where it applies and preserve something useful from the encounter.

Could the information a model encounters contribute to a growing foundation for discovery?

This question brings together recognising patterns, investigating relationships and carrying useful earlier work into later encounters.

From observation to a relationship

Recorded sequence experiments demonstrated that Eos could rediscover mathematical relationships within families of numerical patterns.

The successful cases included a known mathematical sequence, an arithmetic progression and a repeating sequence. In each case, the relationship identified from the supplied values supported the correct calculation of further values held aside for checking.

These experiments established concrete examples of recognition leading to computation. A pattern identified in the supplied values could be applied beyond the values used to establish it.

The relationship had become useful: it could produce a result that could be checked.

This provides a foundation for investigating how the range and complexity of those relationships can develop.

Recognising patterns across information

Eos also examined mathematical material across different subjects, including sequences, algebra, number theory and formal statements.

The recorded work demonstrated that it could form categories from the patterns encountered in these different materials. This gave the research a way to study what the model was distinguishing and how those distinctions accumulated.

The significance lies in making that developing organisation available for further investigation. Each encounter can add to the body of information the model carries.

Continuing from earlier work

A model's development depends on what remains available when the next encounter begins.

In a recorded experiment across different collections of mathematical material, earlier categories remained available alongside additional categories formed from the later material.

This demonstrated continuity across separate runs: earlier work could be retained and extended through a subsequent encounter.

What had already been established could become part of the starting point for what came next.

The research ahead

Eos brings these results into a wider investigation of continuing discovery.

The research direction is to broaden the relationships the model can investigate, deepen the connections between its observations and develop how what it retains contributes to later work.

Eos studies how discovery, checking and continuity support one another, so that each useful encounter contributes to a more capable foundation for the next.

Recognising patterns. Establishing relationships. Building upon what has been found.