The Non-Optimality of Scientific Knowledge: Path Dependence, Lock-In, and The Local Minimum Trap

Scientific progress depends on sequences of enabling contributions, yet existing AI4Science benchmarks largely focus on citation prediction, literature retrieval, or idea generation rather than the dependencies that make progress possible. In this paper, we introduce discovery pathway forecasting: given a target scientific contribution and the prior literature available at a specified time, the task is to (1) identify the enabling contributions required to realize it and (2) ground each in prior work when such prior work exists. We present SciPaths, a benchmark of 262 expert-annotated gold pathways and 2,444 silver pathways constructed from machine learning and natural language processing papers, where each pathway records enabling contributions, roles, rationales, and prior-work groundings or unmapped decisions. Evaluating frontier and open-weight language models, we find that the best model reaches only 0.189 F1 under strict semantic matching, with core methodological dependencies hardest to recover. Prior-work grounding improves substantially when gold enabling contributions are provided, showing that decomposition quality is a major bottleneck for end-to-end pathway recovery. SciPaths therefore shifts evaluation toward a missing capability in scientific forecasting: reasoning backward from a target contribution to the enabling scientific building blocks and prior-work dependencies that make it feasible.

Scientific reasoning rarely stops at what is directly observable; it often requires uncovering hidden structure from data. From estimating reaction constants in chemistry to inferring demand elasticities in economics, this latent structure recovery is what distinguishes scientific reasoning from curve fitting. Large language models (LLMs) can often recall and apply relevant scientific formulas, but we show that this ability is surprisingly easy to suppress. We show that adding in-context examples makes models rely less on pretrained domain knowledge, even when those examples are generated by the very same formula. Rather than reinforcing knowledge-driven derivation, examples shift computation toward empirical pattern fitting. We document this knowledge displacement on 60 latent structure recovery tasks across five scientific domains, 6,000 trials, and four models. This displacement is consistent across domains, but its accuracy consequences depend on how the displaced strategy compares to the one that replaces it: the same shift can lower accuracy, leave it unchanged, or appear to improve it. In all cases, however, the model shifts away from knowledge-driven reasoning. For practitioners deploying LLMs on scientific tasks, the message is cautionary: in-context examples may displace, rather than reinforce, the knowledge they are intended to support.

Can scientific discovery be made arbitrarily easy by choosing the right representation, collecting enough data, and deploying sufficiently powerful algorithms? This paper argues that the answer is fundamentally negative. We introduce the Existential Theory of Research (ETR), a formal framework that models discovery as the recovery of structured explanations under constraints of representation, observation, and computation. Within this framework, we show that these three components cannot be simultaneously optimized: no method can guarantee universally simple explanations, arbitrarily compressed observations, and efficient exact inference. This limitation is not model-specific, but arises from a synthesis of uncertainty principles in sparse representation, sample complexity bounds in high-dimensional recovery, and the computational hardness of exact inference. We further show that representation mismatch alone can inflate intrinsic simplicity into apparent complexity, rendering otherwise tractable problems observationally and computationally prohibitive. To quantify these effects, we introduce an uncertainty functional that captures the joint difficulty of discovery. The results suggest that scientific difficulty is not accidental, but a structural consequence of the geometry and complexity of inference.