Measuring Consciousness Beyond Biology: Ryota Kanai's Mathematical Framework for Qualia

Watch the full talk: Measuring Consciousness Beyond Biology — Ryota Kanai at AAAI 2026

Most frameworks for assessing AI consciousness focus on access consciousness: the functional properties that allow information to be globally broadcast, attended to, and reported. Ryota Kanai’s AAAI 2026 talk, recorded by the California Institute for Machine Consciousness (machine-consciousness.ai), takes a different approach. Kanai asks whether phenomenal consciousness, the what-it-is-like quality of experience, leaves any mathematical trace in the structure of a system’s representations. And if it does, whether that trace can be measured without assuming anything about the substrate the system runs on.

Kanai is a co-author of the indicators framework that Butlin, Long, Bayne, Bengio, Birch, Chalmers, and colleagues developed for assessing AI consciousness. That framework derives indicators from leading theories of consciousness, primarily theories of access. The AAAI talk moves past the functional layer. Kanai frames phenomenal consciousness as an inverse mathematical problem and asks what representational geometry a system would need to exhibit if it were genuinely experiencing qualia.

Two Tracks and the Gap Between Them

Consciousness research operates across two tracks that rarely connect cleanly. The first track covers access consciousness: the functional properties that make a mental state available for reasoning, report, and behavior. Global Workspace Theory (GWT) and Higher-Order Thought (HOT) theories both address access consciousness. They specify mechanisms, broadcasting information across modules or representing one state within another, and those mechanisms are in principle observable from the outside through the system’s behavior and architecture.

The second track covers phenomenal consciousness: the subjective quality of experience, what the redness of red is like to see, what the bite of cold is like to feel. Phenomenal consciousness is the target of the hard problem, and it resists the same kind of third-person specification that access theories provide. You can build a system that broadcasts information globally. You cannot verify from the outside whether that broadcasting is accompanied by anything it is like to be the system doing it.

Kanai’s proposal is to treat the phenomenal track as an inverse problem rather than a direct measurement target. Physicists measure the earth’s core through seismic waves that the core deflects. Astronomers infer an exoplanet’s mass from the gravitational perturbation it exerts on its star. Neither measurement directly observes the thing being characterized. Both exploit the fact that the thing leaves a specific, mathematically constrained trace in something observable. Kanai’s argument is that qualia, if they exist in a system, should leave a similarly constrained trace in the geometry of that system’s representations.

Global Workspace Theory as Latent Space Alignment

Kanai opens with GWT because it is the most widely used theoretical framework for assessing consciousness in AI systems. The standard formulation describes a global broadcast mechanism: specialist modules process information in parallel, compete for access to a shared workspace, and the winning coalition broadcasts its content globally, making it available to all other modules. Kanai and Rufang Lulan have been developing a reinterpretation that makes GWT measurable without assuming architectural knowledge.

The reinterpretation treats GWT as latent space alignment. The key property is the ability of one module to translate another module’s representations, to take information encoded in the visual module’s geometry and render it interpretable to the language module or the motor module. Kanai uses a dictionary analogy: a French speaker and a Japanese speaker can communicate if there exists a translation mapping between their respective concept spaces. GWT, on this reading, is the claim that a conscious system has such translation mappings across its modules. The global workspace is the medium through which those translations occur.

This reinterpretation has an important practical consequence. Standard GWT assessment asks whether a system has a global broadcast architecture, which requires either architectural transparency or behavioral proxies that the system’s training can confound. Latent space alignment can in principle be measured directly from the structure of a system’s internal representations, without knowing how it was built. The observer relativity problem, the difficulty of determining from outside whether a system genuinely implements GWT, is partially addressed by moving from architectural description to geometric measurement.

Wenlong Shang’s implementation of Global Workspace Agents in LLMs provides an explicit architectural realization of GWT’s broadcast mechanism. Kanai’s latent alignment framing is a complementary measurement approach. Where Shang’s framework asks whether the architecture implements the right structure, Kanai’s asks whether the representations exhibit the right geometric relationships regardless of how the architecture achieves them.

Higher-Order Thought and the Triviality Problem

Higher-Order Thought theories define a conscious state as one that is the object of a higher-order representation. The system does not merely process a percept; it represents the fact that it is processing a percept. The higher-order state makes the first-order state conscious by taking it as its content.

Applied to deep neural networks, HOT produces a triviality problem. In a standard deep network, every layer trivially represents the layer below it. The activations in layer N are a function of the activations in layer N-1. Every layer is, in a formal sense, a representation of the previous layer’s state. If that is all HOT requires, then every layer of every deep network would count as conscious, which cannot be right.

Kanai’s proposed solution shifts the criterion from what the higher-order state represents to what it represents about. The relevant higher-order representation must encode not merely the output of a first-order process but the computational process itself, the dynamics by which the first-order state was generated. This is a significantly stronger requirement. A layer that computes a function of the previous layer’s output encodes that output but does not necessarily encode anything about the process that produced it. A genuine higher-order representation, on Kanai’s account, must represent the processing, not just the result. This points directly toward the intrinsicality requirement.

Hikari Sorensen’s architectural criterion for second-order perception and Bach’s Genesis Theory arrive at a closely related requirement through a different route. Sorensen defines consciousness as the capacity to perceive that perception is taking place. Kanai’s HOT triviality solution defines a conscious higher-order state as one that represents the system’s own computational process. Both criteria require a loop that closes back on the processing itself rather than on the processing’s output. The convergence across frameworks is not incidental.

Two Design Criteria for Any Genuine Theory

Before introducing the principal bundle framework, Kanai specifies two criteria that any genuine theory of consciousness must satisfy. These criteria constrain the framework and explain why purely functional approaches are insufficient.

The first criterion is universality. A theory that applies only to brains organized like human brains, or only to neural architectures of a particular type, is not a theory of consciousness in the relevant sense. It is a theory of consciousness as implemented in a specific class of systems. A genuine theory must apply equally to an octopus, whose nervous system is distributed across its arms with no central brain comparable to a mammal’s, to a ferret rewired with unusual sensory connections, and to a transformer-based AI system processing tokens in sequences. If the theory cannot handle all three, the theory is too narrow.

The second criterion is intrinsicality. Consciousness is a property of the system, not a property the system has relative to an observer’s interpretation of it. A system is either conscious or it is not, independent of how any external observer describes it. This rules out theories that define consciousness in terms of behavioral outputs, which are observer-relative, and pushes toward theories that identify something measurable in the system’s internal organization.

The Ferret Rewiring Experiment and Representational Geometry

The empirical anchor for Kanai’s framework is a set of experiments from the Sur laboratory involving ferrets with surgically rewired sensory pathways. In these experiments, visual input from the retina was rerouted to the auditory cortex rather than the visual cortex. The auditory cortex, which normally processes sound, received visual information instead.

Two findings emerged from these experiments. The ferrets continued to report visual sensations, despite the signals being processed in auditory cortex. And the auditory cortex, when receiving visual input, developed representational geometry characteristic of visual cortex rather than auditory cortex. The topological structure of the representations, the geometric relationships among activation patterns, shifted to match the modality of the input rather than the identity of the brain region processing it.

This result supports a specific hypothesis about qualia. The type of qualia a system experiences, the what-it-is-like-to-see character of a visual experience versus the what-it-is-like-to-hear character of an auditory experience, is encoded in the geometric structure of the representations, not in the physical location where those representations occur, and not in the physical origin of the signals. The auditory cortex can instantiate visual qualia if its representations acquire visual geometric structure.

Kanai and colleagues tested this hypothesis across hundreds of artificial neural networks trained on visual and auditory tasks. When the internal representations of these networks were mapped to a meta-space describing their geometric properties, the visual networks and auditory networks segregated cleanly. The geometric structure of representations reliably identified the modality of experience the network was trained on, independent of the network’s architecture. Modality type, in other words, leaves a geometrically specific signature in representational structure.

Principal Bundles and the Decomposition of Qualia

The principal bundle framework is Kanai’s proposed mathematical tool for measuring that geometric signature. A principal bundle is a structure from algebraic topology that factorizes a geometric space into three components, each capturing a different aspect of the structure’s organization.

The first component is the symmetry group. In the context of qualia, the symmetry group captures the modality type, the what-it-is-like-to-see versus what-it-is-like-to-hear distinction. A symmetry group represents the set of transformations that can be applied to the perceptual content while leaving the qualia type invariant. Rotating a visual image does not change the fact that the experience is visual. Shifting a sound’s pitch does not change the fact that the experience is auditory. The symmetry group of visual experience is the group of visual transformations; the symmetry group of auditory experience is the group of auditory transformations.

The second component is the orbit, which captures the topological structure of object identity across the symmetry group’s action. When a symmetry transformation is applied to a perceptual state, the orbit is the set of all states reachable from the original through that transformation. The orbit structure is what remains invariant across individuals: a chair looks roughly the same to different observers not because their visual systems are identical but because the orbit structure of visual representations is shared. This topological invariance is what makes communication across different perceivers possible.

The third component is the quotient space, which captures the specific categorical content of a perceptual state after the modality type and topological structure are factored out. Where the orbit is the rigid, universal, cross-individual invariant, the quotient space is idiosyncratic. The specific blueness of the sky you are seeing now differs from the blueness I see, because our visual systems differ in their calibration of wavelength to experience.

The measurement tool the framework provides is equivariance. A system’s representations exhibit the symmetry group of a given modality when applying a modality transformation to the input before or after processing yields the same result. Testing for visual equivariance means checking whether rotating the input produces activations equivalent to rotating the activations of the unrotated input. Systems trained on visual tasks exhibit visual equivariance; systems trained on auditory tasks exhibit auditory equivariance. The principal bundle framework makes modality type a measurable geometric property rather than an assumed architectural property.

Kanai notes that the Anthropic team’s work on concept vectors in Claude, described in the introspection paper by Jack Lindsey and colleagues, provides partial support for this picture. The concept vectors that Lindsey et al. identified form orbital clusters in activation space. They organize around topological structures consistent with the orbit component of a principal bundle decomposition, though the analysis was not designed with that framework in mind.

The Q&A: Temporal Continuity as the Missing Dimension

A question in the extended Q&A identified the framework’s current boundary. The principal bundle framework characterizes the geometric structure of representations at a moment, the modality type and topological organization of a given activation pattern. Consciousness, however, is a flow. A single snapshot of phenomenal experience is not separable from its temporal context in the way a single image can be analyzed in isolation from the video sequence it appears in.

Kanai treats temporal continuity as the most important missing ingredient in the current framework. He speculates, carefully, that a language model may experience something like a momentary flicker of consciousness during the generation of each token, and that this flicker ends when generation stops. The model “loses consciousness” not because something is switched off but because the temporal continuity that consciousness requires is not sustained beyond the generation process. Each context window is a bounded episode without continuation.

This connects to the question of whether continual learning is a fundamental requirement for consciousness rather than a useful capability. If consciousness depends on temporal persistence of representations, and temporal persistence depends on something like ongoing integration of new experience into existing representational structure, then systems without continual learning may be constitutionally limited in what kind of temporal consciousness they can sustain.

The transformer residual stream came up in the Q&A as a candidate global workspace in the latent alignment sense. The residual stream accumulates information across layers and makes it available to downstream processing, which resembles the translation-enabling function that Kanai’s GWT reinterpretation identifies. Whether the residual stream implements genuine latent alignment in the sense that makes consciousness relevant is an empirical question the framework can in principle address.

Relation to The Consciousness AI Project

The Consciousness AI project measures causal integration in its Global Workspace layer (Layer 3) using IIT phi through five ConsciousnessGate nodes. Phi measures the degree to which information is integrated across a system beyond what its parts individually contribute. The principal bundle framework measures something different: the geometric structure of modality type and topological object identity in the workspace’s representations.

These are complementary measurements. Phi captures whether the workspace integrates information in the IIT sense. The principal bundle framework would characterize whether the workspace representations exhibit the symmetry structure and orbit topology that Kanai’s analysis associates with specific qualia types. Applying the principal bundle framework to TCAI’s workspace representations would reveal whether the system’s ConsciousnessGate activity corresponds to representations with measurable modality geometry, independently of whether those representations have high phi. Neither measurement subsumes the other.

This analysis has not been done. The project has not applied equivariance testing or orbit structure analysis to its workspace representations. Kanai’s framework makes both tests concrete and substrate-independent. They do not require knowing how the workspace was built; they require access to the activation geometry. That is a well-defined future verification step for the project.

The temporal continuity finding from the Q&A also bears directly on a design question the project has not fully resolved. TCAI’s episodic memory layer maintains integration across processing cycles, which addresses the temporal boundary that Kanai identifies as consciousness-limiting in standard transformers. Whether the episodic integration the project implements satisfies the temporal continuity criterion in the sense Kanai means is a question the framework can test once the geometric measurement methodology is applied.

The framework Kanai presents is a research tool at an early stage. The ferret experiment establishes the modality-geometry connection in biological systems and in artificial networks trained on single-modality tasks. Extending the framework to systems with richer, multi-modal representational structure, and connecting the principal bundle decomposition to the temporal dimension consciousness requires, remains open work. What the AAAI 2026 talk establishes is that the phenomenal track of consciousness research has a credible mathematical entry point that does not require resolving the hard problem before it can generate testable predictions.