Computational Graph Synthesis

The Core Question

Given a prompt P, an LLM response R, and no direct access to the actual internal algorithm, can we construct a plausible method that would have produced R?

The method does not need to be the true circuit. It needs to be useful: a route that can produce the answer when the right information sources are plugged in.

This is the archive sketch behind the longer essay: Methods, Librarians, and Learned Books.

The Librarian Analogy

Imagine observing a librarian answer a question. The librarian identifies the kind of request, walks to a shelf, selects a book, extracts the relevant material, writes it into a ledger, and produces an answer.

Even if we do not know the exact book or the exact internal thought process, the route is informative. It tells us the shape of the computation: query, source selection, retrieval, transformation, record, response.

Now replace the book with a learned book and the ledger with a learned ledger. The graph stays interpretable enough to carry useful bias, but its components can be optimized.

The Tradeoff

There is a scale between very specific and very general methods.

• A highly specific method needs less learned content.
• A very general method can accommodate many tasks, but must learn more.
• A black-box input-output model is maximally general and has the least built-in bias.

Bias becomes almost topological here: it is the shape of the routes the method makes easy.

Sketch Algorithm

1. Observe a problem-solving trace: a human response, an LLM response, or a multi-turn conversation.
2. Construct a plausible explanatory model of the method.
3. Abstract over that model into a reusable computational graph.
4. Identify the information interfaces the graph needs.
5. Replace those sources with learned modules.
6. Optimize the whole structure for the target class of tasks.

The open problem is interface discovery. Given only P and R, how do we infer which data sources the method needed?