The paper argues that we are hitting a wall with current AI because we are obsessed with number crunching instead of structure.

Belabes posits that modern AI is too focused on statistical minimization and processing speed, which reduces everything to collections of numbers that inherently lack meaning. You lose the essence of what you are actually trying to model when you strip away the context to get raw data. The author suggests a pivot to Alexandre Grothendieck’s Topos theory, which provides a mathematical framework for understanding geometric forms and preserving the deep structure of data rather than just its statistical number crunching.

Topos theory focuses on finding a new style space that acts as a bridge between different mathematical objects. Instead of just looking at points in a standard space, a topos allows us to look at the relationships and sheaves of information over that space, effectively letting us transfer invariants from one idea to another. It creates a way to connect things that seem totally unrelated on the surface by identifying their common essence. Belabes links this to the idea of conceptual strata where something that looks like noise or insignificant data in one layer might actually be critical structure in another layer. It’s a move away from the binary notion of significant versus insignificant data and toward a relativistic view where significance depends on the conceptual layer you are analyzing.

The author uses literary examples like Homer and Dostoevsky to show that authentic meaning often precedes the words used to express it, whereas our current digital systems treat language as a closed loop where words define other words. Current AI essentially simulates discourse without the underlying voice or intent. By adopting a Topos-based approach, we might be able to build systems that respect these layers of meaning and read slowly to extract the actual shape of the information. It is basically a call to stop trying to brute force intelligence with bigger matrices and start modeling the actual geometry of thought.