www.lesswrong.com/posts/NbQR95tgonXW2xMcQ/your-causal-variables-are-irreducibly-...
1 correction found
Without extensions like Beckers, Halpern, & Hitchcock's (2023) "Causal Models with Constraints," we don't even have a well-formed causal model at the neural network level
This is incorrect: standard structural causal model frameworks already include deterministic causal models, so deterministic neural computations do not by themselves make neural-network-level causal models ill-formed. Beckers et al. (2023) extends SCMs to handle constraint relations, not to make deterministic systems representable.
Full reasoning
The cited sentence says deterministic neural computations are not even a well-formed causal model unless one uses Beckers, Halpern, & Hitchcock (2023). But the mechanistic-interpretability literature it cites elsewhere already formalizes deterministic causal models directly.
- Geiger et al. (JMLR 2025), Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability, explicitly defines "a (deterministic) causal model" and uses that framework as the basis for causal abstraction in mechanistic interpretability.
- Mooij, Janzing, and Schölkopf explicitly study deterministic Structural Causal Models in From Ordinary Differential Equations to Structural Causal Models: the deterministic case.
- Beckers, Halpern, & Hitchcock (2023) say their extension is needed for constraints on settings of variables (their example is the algebraic relation
LDL + HDL = TOT), i.e. for non-causal constraints that standard SCMs cannot express under ordinary intervention semantics. Their abstract does not say the extension is needed merely because a system is deterministic.
So the problem with ordinary SCMs is not "neural networks are deterministic, therefore no well-formed causal model exists." Deterministic SCMs are already standard. Beckers et al. adds expressive power for constrained-variable settings, which is a different issue.
3 sources
- Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability
The paper formalizes mechanistic interpretability with causal abstraction and includes the definition: "A (deterministic) causal model is a pair ..." It presents this as a theoretical foundation for mechanistic interpretability.
- From Ordinary Differential Equations to Structural Causal Models: the deterministic case
Abstract: "We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM)."
- Causal Models with Constraints
Abstract: the goal is "to extend standard causal models to allow for constraints on settings of variables" because some non-causal relationships among variables cannot be represented in standard causal models. The motivating issue is constraints, not mere determinism.