Towards Error-Centric Intelligence II: Energy-Structured Causal Models

TL;DR

This paper proposes Energy Structured Causal Models (ESCMs) to make internal mechanisms of machine learning models manipulable and interpretable through energy-based constraints, enabling causal explanations and interventions.

Contribution

It introduces ESCMs as a novel framework for causal reasoning in machine learning, shifting from explicit mappings to energy-based constraints for better interpretability and intervention.

Findings

ESCMs allow for local interventions on model mechanisms.

Empirical risk minimization leads to entangled, non-causal representations.

Under mild conditions, ESCMs recover standard SCM semantics.

Abstract

Contemporary machine learning optimizes for predictive accuracy, yet systems that achieve state of the art performance remain causally opaque: their internal representations provide no principled handle for intervention. We can retrain such models, but we cannot surgically edit specific mechanisms while holding others fixed, because learned latent variables lack causal semantics. We argue for a conceptual reorientation: intelligence is the ability to build and refine explanations, falsifiable claims about manipulable structure that specify what changes and what remains invariant under intervention. Explanations subsume prediction but demand more: causal commitments that can be independently tested and corrected at the level of mechanisms. We introduce computational explanations, mappings from observations to intervention ready causal accounts. We instantiate these explanations with Energy Structured Causal Models (ESCMs), in which mechanisms are expressed as constraints (energy functions or vector fields) rather than explicit input output maps, and interventions act by local surgery on those constraints. This shift makes internal structure manipulable at the level where explanations live: which relations must hold, which can change, and what follows when they do. We provide concrete instantiations of the structural-causal principles LAP and ICM in the ESCM context, and also argue that empirical risk minimization systematically produces fractured, entangled representations, a failure we analyze as gauge ambiguity in encoder energy pairs. Finally, we show that under mild conditions, ESCMs recover standard SCM semantics. Building on Part I's principles (LAP, ICM, CAP) and its definition of intelligence as explanation-building under criticism, this paper offers a formal language for causal reasoning in systems that aspire to understand, not merely to predict.