From causal models to models of learning

There is a second route into LINCS, through the causal revolution in statistics and artificial intelligence. Pearl’s critique of mainstream machine learning is not simply that its predictions can be inaccurate. It is that systems trained primarily on associations often lack an explicit model of the mechanisms that produced those associations, and therefore lack a principled object on which to perform an intervention [ Pearl , 2009b , 2018 , Pearl and Mackenzie , 2018 ] . A predictor can estimate \(P(Y\mid X=x)\) without representing what it would mean to replace the mechanism for \(X\), hold the other mechanisms invariant, and ask for \(P(Y\mid \operatorname {do}(X=x))\).

McCarthy posed an antecedent challenge in terms of appearance and reality [ McCarthy , 2007 ] . Sense data provide partial, view-dependent appearances; intelligence must reason about the comparatively stable objects and mechanisms that generate them. Recovering reality from appearance is an inverse problem and is generally non-unique. More fundamentally, the vocabulary of the explanation need not already occur in the observations. Atomic theory required theoretical objects that were not present as patterns in unaided sense data. Democritus proposed the ontological idea centuries before Dalton made atoms and molecules elements of a quantitatively constrained scientific theory.

McCarthy and Pearl therefore expose complementary limitations. Classification of appearances does not by itself construct a model of their hidden reality; conditioning on observations does not by itself determine how that reality would respond to action. A learning framework adequate to both challenges must permit theoretical objects behind appearances and controlled changes to the mechanisms connecting them.

Causal inference addresses this limitation by making a domain model explicit. Structural causal models, structural equation models, potential outcomes, and related formalisms specify enough structure to distinguish observation from action. Their variables and mechanisms are normally grounded in a domain such as epidemiology, biology, economics, or policy. Once that structure has been declared, an intervention can be represented as a controlled change to part of the model, followed by propagation through what remains invariant.

LINCS imports this methodological lesson into machine learning at a different level. Its primary model need not be a causal model of a biological or economic system. It is a model of the learning system itself: its objects, transformations, data flows, compositional obligations, observers, allowed edits, and admission tests. A learning sketch makes that system inspectable and actionable. Non-compositionality localizes a structural discrepancy; the repair language specifies what may be changed; and admission tests whether the proposed change preserves the promises that were not targeted.

The comparison also raises a proof-theoretic question. Causal models provide the semantics of intervention, while do-calculus supplies rules for transforming observational and interventional expressions under explicit graphical conditions. Chapter 1 develops the corresponding distinction for LINCS. Its axioms specify admissible structural-learning models. It begins with a Universal Obstruction Axiom: every admissible diagnostic factors uniquely through a typed obstruction object, whose triviality is equivalent to satisfaction of the declared compositional obligations. Additional structural laws govern tangent lift, descent, and repair; a candidate repair calculus then gives rules for observer substitution, presentation elimination, localization and gluing, tangent transport, target surgery, and conservative theory extension. These rules preserve declared structural judgments. They do not identify causal effects unless the learning sketch also carries the required causal semantics.

The analogy supports several scales of action. A parameter intervention moves within a fixed realization. A component intervention replaces a morphism, module, policy, adapter, warrant, or skill. An architectural intervention changes routes, interfaces, covers, or composition laws. A declaration intervention augments the sketch with new objects, arrows, probes, or axioms. Ordinary optimization usually occupies the first level. The later levels require an explicit language of structural change and stronger evidence that the unaffected obligations remain intact.

This does not make every LINCS repair causal in Pearl’s semantic sense. A repair becomes a causal intervention only when the relevant arrows denote mechanisms and the edit is connected to a realizable intervention protocol. Otherwise it is a more general structural intervention. Category theory supplies the typing, composition, and invariance conditions; domain knowledge and experimental design supply causal meaning. LINCS is therefore best understood as extending the discipline of causal modeling, not as declaring all learning to be causality.