arXiv:2609.12260v1 Announce Type: cross Abstract: Large language models (LLMs) can generate biomedical hypotheses, but it remains unclear whether they truly reason from scientific evidence or simply produce convincing-sounding ideas. To study this, we combine three major biological databases: the Kyoto Encyclopedia of Genes and Genomes (KEGG), Rhea, and UniProt, into a unified biochemical knowledge graph and construct a benchmark of 550 paths connecting enzyme sources to rare disease endpoints, yielding 13,200 hypotheses from six LLMs under four conditions varying the biological information each model receives: source enzyme only, full biological path, or source and disease endpoint only. Hypotheses are scored using an expert-derived five-criterion rubric on a 1-5 scale per criterion. We find that models given both the source and disease endpoint often produce the highest-scoring hypotheses, showing that LLMs can generate compelling ideas from minimal information. However, these hypotheses are less grounded in the evidence. In contrast, models given the full biological path generate hypotheses more consistent with known mechanistic relationships. We call this evidence-disciplined reasoning. To confirm this effect, we shuffled intermediate path steps while keeping endpoints fixed. Evidence grounding dropped significantly (delta = -0.793, p

arXiv:2607.03671v2 Announce Type: replace-cross Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables; consequently, similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of target dynamical features under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Locally redundant features lower the effective codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and a finite-tolerance conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a deterministic ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.