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Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation · 0 citations (OpenAlex)

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Introduces concept modulation models (CMMs), a conditional generative framework A→modulator→concept→feature, and shows via attribute potentials (log-density ratios) that feature agreement on observed attributes lifts to a latent transition and that extrapolation holds iff transported potential identities extend to unseen attributes.

Problem

Identifiability and extrapolation guarantees in conditional latent-variable models are model-specific, with separate analyses in nonlinear ICA, causal representation learning, and perturbation modeling.

Approach

Concept modulation models with structure A→modulator→concept→X; feature agreement on observed attributes lifts to a latent concept transition, expressed through attribute potentials (log-density ratios), which also control extrapolation to unseen attributes.

Key results

• Feature equivalence on observed attributes induces a latent concept transition in the intersection of valid mixing and concept transition sets.
• Agreement at unseen attributes holds exactly when attribute-potential identities extend to those attributes.
• Recovers affine identifiability for the exponential-family running example and perturbation identifiability up to orthogonal transformation under sufficient diversity.

Limitations

• Requires common-support assumption, excluding deterministic do-interventions and support-changing mechanisms.
• Extrapolation needs structural assumptions tying unseen attribute potentials to observed ones.
• Purely theoretical; no empirical validation reported.

Experimental setup

Builds on: transition-based identifiability framework nonlinear ICA with auxiliary variables iVAE

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