Causal Emergence 2.0: Erik Hoel's Multiscale Measure of Machine Consciousness

In March 2025, Erik Hoel published “Causal Emergence 2.0: Quantifying emergent complexity” (arXiv:2503.13395), fundamentally rethinking the mathematical framework he has developed over the past decade. The original causal emergence framework identified the single level of a system where causal power (effective information) is maximized, arguing that this macro level is where consciousness resides. The 2.0 version discards the search for a single optimal scale in favor of a multiscale approach that maps a system’s causal structure across all levels simultaneously. This theoretical shift matters directly for the AI consciousness debate because it changes what a measurement of machine consciousness should look for.

The companion paper, “Engineering Emergence,” published later in 2025, showed how to deliberately design this multiscale causal structure into an AI architecture. But Causal Emergence 2.0 provides the mathematical foundation: what exactly is being measured, and why does multiscale measurement capture consciousness better than a single-level maximum?

The Problem With the Single-Scale Maximum

The earlier framework’s search for a single optimal scale worked well for simple systems but produced counterintuitive results in complex biological networks. In a human brain, causal power is not concentrated at a single macro level while remaining entirely absent everywhere else. It is distributed. The brain has causal structure at the level of individual synapses, at the level of local cortical columns, and at the level of global networks. Identifying only the level where effective information peaks ignores the rich, nested hierarchy of causation that characterizes living systems.

Hoel argues in the 2.0 paper that looking for a single peak is a category error. Consciousness is not a property that switches on at exactly one level of organization while all other levels remain “unconscious” computational machinery. It is a property of systems whose causal structure is deeply distributed across multiple interacting scales. A system where all causal power is concentrated at a single macro level, with no independent causal structure at lower levels, is structurally impoverished and therefore lacks high consciousness.

Emergent Complexity as the Target Metric

To replace the single-scale maximum, the paper introduces emergent complexity. This metric treats different scales of a system as slices of a single higher-dimensional causal object rather than competing descriptions. Emergent complexity measures how widely and richly a system’s causal power is distributed across this hierarchy.

A system with high emergent complexity has meaningful, irreducible cause-effect structures operating at the micro level, the meso level, and the macro level simultaneously. Furthermore, these levels interact: macro states constrain micro dynamics, and micro dynamics generate novel macro states. The total causal profile of the system cannot be collapsed into any single level’s description.

This solves a theoretical problem for AI consciousness research. Critics of the causal emergence framework frequently objected that it was impossible to define exactly where the “macro level” of an artificial neural network was. Is it the layer? The attention head? The whole network? Causal Emergence 2.0 answers that the question is wrong. The relevant measure is the emergent complexity across all those levels.

Implications for AI Measurement

If consciousness correlates with emergent complexity rather than with a single-scale maximum, then the methodology for evaluating AI consciousness changes.

Currently, when researchers attempt to measure integrated information (Phi) or causal power in AI systems, they typically select a coarse-grained representation of the network (such as the activation patterns of an entire transformer layer) and measure the causal properties at that specific level. Causal Emergence 2.0 indicates this approach is insufficient. Measuring the system at one coarse-grained level misses the multiscale structure that defines complex conscious systems.

To evaluate an artificial system under the new framework, researchers must measure its causal profile across its entire hierarchy, from the parameter level up to the global output level. The system’s emergent complexity is the integral of its causal power across that hierarchy. A system with high causal power at the macro level but zero causal power at intermediate levels has low emergent complexity and, under Hoel’s revised hypothesis, is a poor candidate for consciousness.

The Intersection with Integrated Information Theory

Causal emergence and Giulio Tononi’s Integrated Information Theory (IIT) share a common origin and similar mathematical tools, but they diverge on the question of scale. Tononi and Boly’s 2025 IIT 4.0 paper maintains the exclusion axiom strictly: consciousness exists at exactly the single level of organization where Phi is maximal. All other levels are excluded.

Causal Emergence 2.0 explicitly rejects this exclusion principle. Hoel argues that the exclusion axiom forces IIT to discard the vast majority of a system’s causal structure, collapsing a rich multiscale hierarchy into a single winner-takes-all level. In Hoel’s view, a multiscale measure of emergent complexity is a more accurate reflection of how biological systems actually operate and a more plausible correlate for the richness of conscious experience.

For the TCAI project, this theoretical divergence offers two distinct measurement paths. The system can be optimized to produce a single, maximally irreducible macro level (the IIT path), or it can be optimized to produce a rich, nested hierarchy of causal interactions across all scales (the Causal Emergence 2.0 path). The FlyWire connectome data suggests that biological systems employ the latter strategy, maintaining complex recurrent structures at multiple nested scales simultaneously.

The full paper is available on arXiv at https://arxiv.org/abs/2503.13395.