Towards Error-Centric Intelligence II: Energy-Structured Causal Models
Marcus Thomas
TL;DR
This work develops Energy–Structured Causal Models (ESCMs) as an intervention-aware, energy-based layer for deep systems, enabling manipulable causal explanations that go beyond predictive accuracy. ESCMs represent mechanisms as energy constraints and interventions as local constraint edits, with abduction–intervention–prediction guiding counterfactual reasoning. The framework provides a Reduction Theorem to recover standard SCM semantics under mild locality assumptions and introduces Locality Autonomy (LAP) and Independent Causal Mechanisms (ICM) penalties to enforce modularity and separability. It also offers a geometric view of equilibria via a Riemannian metric, analyzes gauge freedom and fractured representations, and outlines integration paths with deep learning architectures through adaptors, mechanisms, actuators, and probes. The approach aims to produce explanations that are testable, editable, and robust to reparameterization, advancing error-centric intelligence that can generalize across tasks and domains.
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.