How to detect that sequence of points belong to some model of first order theory?

Assume that every neural network can be recast to the sequence of layers (https://arxiv.org/abs/2106.14587 has chapter how to do this). Assume that layer U has N neurons. The set of possible activities of layer U forms the N-dimensional vector space. Each concrete state of layer U (in the sense of activities) can be described by N-dimensional vector (point) in this space.

Assume, that NN functions or learns and assume that some First Order Theory (set of variables and functions and set of predicates/relations (Boolean valued functions) over them) exists (or gradually evolves) at layer U. Each FO theory can have one or more models in some semantic space https://en.wikipedia.org/wiki/First-order_logic#First-order_structures. Essentailly - model is the full or partial assignment: 1) values to the variables; 2) concrete mappings from D to D to each function symbol; 3) concrete mappings from D to Boolean to each predicate or n-ary predicate (relation) symbol.

Obviously, if layer U contains some theory then the sequence of N-dimensional vectors (points) that are sampled during the functioning of the neural network from this layer U, those points belong to one or other model of the same theory (depending on the input data for the concrete instance of functioning).

My question is: is there algorithm/approach/efforts/theory how to detect that sequence of points belongs to one or different models of the same theory and is there algorithm/approach how to recover this theory (apparently in the symbolic form modulos the language or language expressions) from the sequence of points that belong to one or different models of this theory?

I am not sure - maybe my problem is already considered in the literature (e.g. as rule induction, as inductive logic programming or as program synthesis in general) and I should only consider the re-application of the algorithms of the considered problem in my case? Or maybe my case is generalization that is not feasible to be handled? In any case my question stands open about the detection and recovery of theory.

There are topological methods of poing cloud analysis (e.g. computing the presistent homologies from the point set), maybe such algebraic topological invariants that ar computed from the point set can discriminate among the theories or even can help to recover theory?

There is promising book about such themes https://www.routledge.com/A-Functorial-Model-Theory-Newer-Applications-to-Algebraic-Topology-Descriptive/Nourani/p/book/9781774633106 but it seems to be fruit of predatory publishing and I am not sure about its reputation, I believe it may have low reputation although some ideas, insights and connections can be fantastically relevant and worthy.