Why AI Struggles With the Hard Core of Science: A Three-Layer Map of Discovery

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Imagine two scientists working on the same hard problem. The first reads every paper ever written on the topic, memorizes the equations, and quickly suggests the most promising experiments based on what others have already tried. The second stares at the problem, decides that the entire way the field is framing it is wrong, and borrows a strange idea from a completely different discipline to reframe the question. Both are useful. Only one of them is doing what we historically call discovery.

Most of today's AI for science behaves like the first scientist. We celebrate systems that search vast chemical spaces, fold proteins, or surface relevant literature in seconds. These are real achievements. But we rarely stop to ask a sharper question: is the AI actually building new concepts, or is it just executing very fast moves inside a conceptual frame that humans handed it?

On June 11, 2026, Guojun Liao posted a paper on arXiv that tries to give this question a clean answer: A Three-Layer Framework for AI in Scientific Discovery. His argument is simple but surgical. Scientific discovery is not one monolithic computational task. It is a stack of three different capabilities, and conflating them is the reason we keep overestimating how close we are to autonomous science.

The anatomy of the three layers

Liao's framework partitions an AI scientist into three distinct functions. Each layer has a different job, a different failure mode, and a different relationship to creativity.

• Layer 1 — Search and Retrieval. This is the ability to parse, index, and recall existing human knowledge. It is the home turf of modern large language models. When an LLM stitches together findings from biology and chemistry to propose a promising starting compound, it is operating at Layer 1. Think of it as an extraordinarily fluent librarian: it can find, summarize, and recombine what already exists, but it cannot step outside the corpus it was trained on. Whatever was never written down, it cannot retrieve.
• Layer 2 — Model Formation. This is the engine of genuine discovery, and it is also the layer we understand least. Layer 2 is the capacity to notice that the current conceptual framework is structurally inadequate — not just imprecise — and to formulate a new one, often by importing structures from a neighboring field. It depends on qualitative reasoning, analogy, and taste, not on tuning parameters. This is where Einstein replaces absolute time with spacetime, or where a biologist suddenly sees a cell as an information-processing system rather than a chemical bag.
• Layer 3 — Execution and Optimization. This is the computational muscle. Once a model is on the table, Layer 3 runs the simulations, executes the code, and searches the parameter space to refine the hypothesis. Reinforcement learning that finds the optimal control policy for a robot arm, or molecular dynamics that locates the lowest-energy crystal configuration, are textbook Layer 3 work.

The bottleneck in today's AI is squarely at Layer 2. Search without model formation keeps us trapped inside inherited paradigms; execution without conceptual revision just gets us to the same dead end faster, with a nicer loss curve.

Why model formation cannot be reached by optimization alone

Why can't Layer 3, with enough compute, eventually produce Layer 2? The reason is geometric, not computational.

Optimization algorithms always operate inside a fixed coordinate system. They tune the values of variables that have already been defined, in order to minimize some loss function someone else wrote down. But when a scientific framework is structurally wrong, the solution is not a better point in the existing coordinate system — it lives in a coordinate system that has not been invented yet. No amount of gradient descent can discover a dimension that does not exist in the problem statement.

Liao illustrates this with a clean case from optimization theory itself. For years, proving the convergence rate of Nesterov's Accelerated Gradient method was a notoriously painful algebraic exercise. Researchers were stuck — not because they lacked computing power, but because they were asking the question in the wrong language. The breakthrough came from a qualitative reframing: a discrete optimization algorithm can be viewed as the discretization of a continuous dynamical system. In the continuous limit, the behavior of accelerated gradient methods is captured by a second-order ordinary differential equation:

Once you sit inside this continuous picture, the next move comes from yet another neighboring discipline. To prove convergence, researchers borrowed the idea of a Lyapunov energy function from control theory — a quantity that is guaranteed to decrease over time — and constructed:

Showing that decreases gives the convergence rate almost for free. None of this is a quantitative tweak. It is a qualitative leap: a new object, imported from a different field, that makes a previously intractable proof routine. This is the signature of Layer 2 thinking, and it is exactly what current optimization-driven AI cannot produce on demand.

Autonomous discovery in the wild

Can a machine ever pull off this kind of qualitative jump on its own? Liao points to one suggestive data point: OpenAI's autonomous disproof of the Erdős unit-distance conjecture in 2026. What is interesting about that episode is not that a machine generated counterexamples — Layer 3 systems have been doing brute-force search for decades. What is interesting is that the system seemed to recognize that the standard geometric formulation of the problem was not scaling, and reframed it by building a bridge into discrete graph structures in an unexpected mathematical neighborhood. That reframing — not the search that followed — is the Layer 2 move.

Whether this was a real instance of autonomous model formation or a well-prompted near-miss is still debated. But it shows what the target looks like: not faster search, not bigger models, but systems that can notice when their own conceptual scaffolding is the thing that needs to change.

Why this matters for engineers building production AI

This framework is not just philosophy. It changes how we should debug real systems.

In applied AI, we constantly mistake Layer 3 scale for intelligence. When a production pipeline underperforms — whether it is a legal automation stack reading Canadian federal-court rulings, a document intelligence system, or a physical model of a rehabilitation environment — the default engineering reflex is to throw more compute at Layer 3 or more context at Layer 1. We fine-tune. We run hyperparameter sweeps. We expand the vector database. We add another retrieval stage.

Sometimes that is the right move. Often it is not. If the underlying schema of the data is wrong, or the conceptual architecture of a multi-agent system carves the problem at the wrong joints, optimization will faithfully amplify the error. You will get a sharper, more confident, more expensive version of the same misunderstanding.

Building robust systems means explicitly designing for qualitative self-evaluation: components whose job is to ask whether the current model of the problem is even the right model, and to propose a different one when it is not. Without a dedicated mechanism for Layer 2 — model formation, not just model tuning — AI will remain a brilliant assistant that can read all of our past papers and run all of our calculations, but will never be the one who rewrites the textbook.

Sources

• A Three-Layer Framework for AI in Scientific Discovery — arXiv · cs.AI · 2026-06-11