Diffusion learning reveals viable parameter manifolds and compensation geometry in biological dynamical systems

• URL: http://arxiv.org/abs/2607.03671v1
• Date: Sat, 04 Jul 2026 02:51:11 GMT
• Title: Diffusion learning reveals viable parameter manifolds and compensation geometry in biological dynamical systems
• Abstract summary: We formalize compatible parameter sets as emphviable parameter manifold: the inverse images of a system's target behaviors under a parameter-to-feature map.<n>We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets.<n>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.
• Score: 0.8373151777137791
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of a system's target dynamical behaviors 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. Co-varying features lower the 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 two-feature 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 recent ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and input-dependent 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.

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