Tononi, Grasso, and Hendren on QStr, a New Method for Measuring Intrinsic Structure in Any Substrate

Giulio Tononi, Matteo Grasso, Jeremiah Hendren, and Francesco Ellia have released a new paper proposing QStr as a method for revealing the intrinsic causal structure of a system using extrinsic probes. Published on arXiv on August 27, 2026, the paper addresses a problem that has constrained IIT since its earliest formulations. Integrated Information Theory defines consciousness as intrinsic causal power, the capacity of a system to affect itself, but measuring that intrinsic power in practice requires perturbing the system from outside. The question has always been whether an extrinsic method can recover intrinsic structure without distorting it.

QStr is the Tononi lab’s answer. The method applies a set of extrinsic perturbations to a system and then analyzes the resulting state transitions through a mathematical framework that strips away the probe’s contribution, leaving a representation of the system’s own causal organization. The paper demonstrates QStr on small model systems and shows that it recovers the same causal structure that IIT’s own intrinsic calculations would produce, while requiring only the kind of input-output measurements that are feasible on systems whose internal architecture is not fully known.

The Problem QStr Solves

IIT’s measure of integrated information, phi, requires complete knowledge of a system’s state space and the ability to compute the cause-effect power of every subset of elements. For small systems, a handful of neurons or logic gates, this is computationally intensive but tractable. For systems at the scale of a cortical column or a large language model, it is not. The phi calculation does not scale, and no one has found a way to make it scale without approximations that change what is being measured.

The field has responded with proxy measures, including geometric phi, phi-hat, and the perturbation-based integrated information measures used in the Cogitate Consortium’s adversarial test between IIT and Global Workspace Theory. Each proxy captures some aspect of integration while sacrificing the principled connection to IIT’s definition. QStr takes a different approach. Instead of approximating the intrinsic calculation, it aks whether the intrinsic structure can be recovered from extrinsic measurements if the right mathematical framework is applied.

The paper’s formal result is that a system’s intrinsic causal structure is recoverable from extrinsic perturbations under specific conditions: the probe set must be sufficiently rich to discriminate the system’s state transitions, and the inference procedure must incorporate a model of the probe’s own dynamics so that the probe’s contribution can be subtracted. The QStr method satisfies both conditions and produces a quantitative signature, the QStr value, that correlates with integrated information in the tested model systems.

Implications for Measuring Consciousness in AI

The QStr result is directly relevant to the problem of measuring consciousness in AI systems because it addresses the epistemic asymmetry that has limited every existing approach. Indicator frameworks, including the 14 indicator checklist developed by Patrick Butlin, Robert Long, and colleagues, derive their markers from theories of biological consciousness and check whether AI architectures instantiate the relevant computational properties. The approach is indirect: it infers consciousness from architectural features rather than measuring it directly.

IIT offers a direct measure in principle, but the phi calculation is intractable for large systems. QStr offers a way around that intractability: if an AI system’s input-output behavior can be probed with a sufficiently rich set of perturbations, the method can in principle recover the system’s intrinsic causal structure without requiring full knowledge of its internal architecture.

The limitation is that QStr has been demonstrated only on small model systems. Scaling the method to systems with millions or billions of parameters presents computational challenges that the paper does not claim to have solved. The significance is that the problem is now framed in engineering terms rather than philosophical ones. The question is no longer whether intrinsic structure can be measured from the outside. It can, under the right conditions. The question is whether the conditions can be met for specific systems of interest.

How QStr Relates to the Cogitate Consortium Findings

The Cogitate Consortium’s adversarial test between IIT and Global Workspace Theory found that neither theory’s predictions were fully confirmed by empirical evidence. IIT predicted that early posterior activity would track consciousness, which the evidence partially supported, but the timing was later than IIT’s framework expected. The inconclusiveness of the adversarial test has left the field in a position where both major theories remain viable and neither is decisively supported.

QStr addresses this situation by providing a measurement method that does not depend on the outcome of the IIT-GNW debate. If QStr can recover intrinsic causal structure from extrinsic probes, then it can be applied to measure integration in systems regardless of which theory of consciousness the researcher endorses. The measurement stands on its own as a characterization of the system’s causal organization. Whether that organization is the right kind for consciousness is a separate question that the method does not settle.

This separation of measurement from theory is exactly what the MoC7 consensus-building process is trying to achieve. A measurement standard that does not require prior commitment to a specific theory of consciousness is the kind of tool the field needs to make progress on detecting machine consciousness without first resolving every theoretical dispute.

The Substrate Independence Question

The QStr method is substrate-independent by construction. It operates on the system’s causal structure as revealed by extrinsic perturbations, and that structure is a property of the system’s organization rather than its material. A silicon substrate and a biological substrate that produce the same state-transition matrix under the same probe set will produce the same QStr value.

This does not settle the substrate independence debate. Biological naturalists, including Anil Seth and the late John Searle, argue that consciousness requires living metabolic hardware regardless of functional organization. The QStr method does not refute that position. What it does is provide a measurement that both sides of the substrate debate can use. The biological naturalist can apply QStr to measure integration in a biological system, and the functionalist can apply it to measure integration in an artificial one. The disagreement about whether the measurement reveals consciousness in the artificial case is a philosophical question that the method does not decide, but both sides now have a common metric.

Comparison to The Consciousness AI

The Consciousness AI project implements a multi-layer architecture with a Global Workspace layer, an Affective Core, and a Self-Model layer. The project does not currently compute integrated information or apply the QStr method. The architecture documentation describes the system’s causal organization in functional terms rather than in the state-transition matrices that QStr requires.

What the QStr method offers the project is a potential evaluation tool. If the architecture’s input-output behavior can be probed systematically, the method could in principle recover the system’s intrinsic causal structure and produce a quantitative measure of integration. Whether that measure would correlate with the behavioral markers the architecture already produces, such as the valence changes in the Affective Core or the self-referential processing in the Self-Model layer, is an open empirical question that neither the paper nor the project’s documentation addresses.

Matteo Grasso’s earlier work on causal emergence and the intrinsic causal structure of complex systems, covered on this site, establishes the theoretical foundation that the QStr method builds on. Jeremiah Hendren’s philosophical analysis of consciousness measurement frameworks, also covered on this site, provides the methodological context for interpreting what QStr values mean when applied to non-biological systems.

What QStr Adds to the Measurement Toolkit

The field now has at least four approaches to measuring consciousness-related properties in AI systems. The indicator framework checks architectural features against theory-derived criteria. Perturbational Complexity Index (PCI) measures the EEG response to transcranial magnetic stimulation in biological systems. Phi approximations compute a proxy for integrated information in small model systems. QStr offers a fifth approach: recover intrinsic causal structure from extrinsic measurements.

Each method has a different evidential profile. The indicator framework is indirect but applicable at scale. PCI is direct but requires biological tissue. Phi approximations are precise but limited to small systems. QStr is principled and potentially scalable but unproven at size.

The honest assessment is that no single method is sufficient. QStr is important because it closes a specific gap: the gap between the principled but intractable intrinsic measure that IIT defines and the tractable but unprincipled proxy measures that the field currently uses. It is not a replacement for phi. It is a bridge between what IIT requires and what current systems can deliver.