2508.00190

## On the u(lity of toy models for theories of consciousness Larissa Albantakis 1,* 1 Department of Psychiatry, University of Wisconsin, Madison, WI, USA * albantakis@wisc.edu ## Abstract Toy models are highly idealized and deliberately simplified models that retain only the essenGal features of a system in order to explore specific theoreGcal quesGons. Long used in physics and other sciences, they have recently begun to play a more visible role in consciousness research. This chapter examines the potenGal uGlity of toy models for developing and evaluaGng scienGfic theories of consciousness in terms of their ability to clarify theoreGcal frameworks, test assumpGons, and illuminate philosophical challenges. Drawing primarily on examples from Integrated InformaGon Theory (IIT) and Global Workspace Theory (GWT), I show how these simplified systems could make abstract concepts more tangible, enabling researchers to probe the coherence, consistency, and implicaGons of compeGng frameworks. In addiGon to supporGng theory development, toy models can also address specific features of experience, as exemplified by the account of spaGal extendedness and temporal flow provided by integrated informaGon theory (IIT) and recent theory-independent structural approaches. Moreover, toy models bring philosophical debates into sharper focus, such as the disGncGon between funcGonal and structural theories of consciousness. By bridging abstract claims and empirical inquiry, toy models provide essenGal insights into the challenges of building comprehensive theories of consciousness. ## Introduc.on Toy models have long been a foundaGonal tool in scienGfic inquiry, especially in fields where full-scale models or direct experimentaGon are either impracGcal or impossible. A toy model is a simplified version of a more complex system that retains only the essenGal elements necessary to explore specific theoreGcal quesGons. These models are deliberately minimalisGc, enabling scienGsts to focus on the core features of an issue without being distracted by extraneous details. In short, toy models are highly idealized and extremely simple models of natural and social phenomena (Reutlinger et al. 2018). Historically, toy models have been widely used in physics. One of the most famous advocates for using simple, conceptual models to gain insights into complex physical systems was Richard Feynman, who also leY us with the memorable words 'what I cannot create, I do not understand.' His work in quantum electrodynamics, for example, introduced simplified representaGons of parGcle interacGons to make highly abstract equaGons more intuiGve and tractable. These 'Feynman diagrams' are graphical tools that depict how parGcles like electrons and photons interact. Although these diagrams are not literal pictures of physical processes, they serve as toy models that help physicists visualize and calculate the probabiliGes of quantum events in a manageable, rule-based way. Another well-known example is the Ising model in staGsGcal mechanics, which is used to study how local interacGons among parGcles can give rise to large-scale phenomena like phase transiGons in magneGsm. Each parGcle is represented as a point on a la]ce that can be in one of two binary states (spin up or spin down) and interacts only with its immediate neighbors. Despite this simplificaGon, the Ising model captures key features of magneGc behavior, such as the emergence of order and the sudden loss of magneGzaGon at criGcal temperatures, offering valuable insights into real-world materials. In economics, toy models such as the 'raGonal actor' model or simplified market simulaGons allow researchers to isolate parGcular economic drivers, avoiding the complexiGes of real-world markets. Similarly, in ecology, simple predator-prey models, described by the Lotka-Volterra equaGons, help biologists understand how the populaGon of two interacGng species such as foxes and rabbits can fluctuate over Gme, without needing to account for the many variables present in a real ecosystem. 1 Toy models can clarify underlying principles, instanGate minimal mechanisms, foster deeper understanding of complex system, and generate novel predicGons about the phenomena under invesGgaGon. Unlike complex mathemaGcal analyses, which can rigorously prove funcGonal relaGonships or implicaGons but oYen remain abstract and difficult to interpret, toy models implement ideas in a tangible way. They offer a way to explore the mechanics of a system while preserving both clarity and interpretability. Although simplificaGon is not always ideal (think of the "spherical cow" joke in physics 2 ), toy models provide an intuiGve grasp of processes that would otherwise be challenging to study in their full complexity. In this sense, toy models occupy a middle ground between highly realisGc models-oYen requiring computaGonal simulaGons that become epistemically opaque black boxes-and purely conceptual thought experiments, which typically lack even minimal mechanisGc structure. AddiGonally, toy models can help idenGfy the minimal condiGons required for certain behaviors or outcomes and lead to novel predicGons that can be empirically tested. In fields like physics, biology, and economics, toy models are thus not just tools for explanaGon but also for discovery. 3 Despite their success in the natural and social sciences, toy models are oYen viewed with skepGcism in consciousness science. One common concern is that consciousness appears to be Gghtly linked to complexity (Sarasso et al. 2021). Toy models are simple by design and thus lack As these examples illustrate, toy models can take many forms. Reutlinger et al. (2018) dis@nguish two broad classes: embedded and autonomous toy models. Embedded toy models are simple and idealized models of phenomena developed within an established framework theory. In contrast, autonomous toy models are largely independent of any par@cular theory. For example, the Ising model is an embedded toy model in sta@s@cal mechanics, used to demonstrate how local interac@ons can give rise to phase transi@ons. By contrast, the Lotka- Volterra predator-prey model is an autonomous toy model: it helps to elucidate plausible popula@on dynamics without presupposing a comprehensive theory of ecology. The focus of this chapter is largely on toy models embedded within theories of consciousness, developed to illustrate, refine, or evaluate theore@cal claims. Nevertheless, autonomous toy models are also beginning to emerge in the study of consciousness, aiming to explore the structural features of subjec@ve experience itself (e.g., Prentner 2019). The spherical cow is a humorous metaphor for overly simplified models of complex phenomena that allow for mathema@cal expression but no longer reflect reality in the relevant sense. Throughout, I reserve the term model -and specifically toy model -to refer to tools for exploring theore@cal claims (e.g., simplified simula@ons, concrete idealized examples, or instan@a@ons). I use theory for explanatory frameworks, even though it has been argued that many so-called theories of consciousness might more accurately be described as models themselves (Signorelli et al. 2025). the very complexity that many believe is necessary for consciousness to emerge (e.g., Aaronson 2014). Another concerns relates to the dynamical role of consciousness: if a system's behavior can be fully understood and predicted from its physical dynamics, there may seem to be no explanatory role leY for consciousness (Leibniz 1714; Kleiner and Ludwig 2023). If one takes dynamical relevance to be a necessary condiGon for consciousness, then a fully specified toy model would be excluded as a plausible substrate. Nevertheless, when reduced to their essenGal features, the mechanisms proposed by various neuroscienGfic theories to underlie conscious experience can oYen be implemented using only a small number of interacGng neurons. This has been referred to as the 'small network argument' (M. H. Herzog et al. 2007; Doerig et al. 2020), and highlights another challenge: due to the inherently subjecGve nature of consciousness, we cannot assess whether a toy model that meets the essenGal criteria of a given theory is genuinely conscious in the same way we might validate predicGons in other scienGfic domains. Theories of consciousness can only be validated through our own experience (Albantakis 2020; Tononi et al. 2025; Tononi 2014), in healthy adult humans who can report on their experiences. Given these limitaGons, what purpose can toy models serve in consciousness science? In the following, I advocate for the uGlity of toy models in consciousness science, parGcularly in the development of principled theories of consciousness. First, toy models can be used to evaluate the coherence and explanatory power of theories of consciousness, ensuring they are more than abstract ideas removed from physical implementaGon. Second, toy models can clarify the predicGons and implicaGons of theories of consciousness. By providing concrete examples, toy models can bridge the gap between abstract theoreGcal claims and empirical tests, guiding experimental research and helping refine theories based on internal and empirical consistency. Finally, toy models can help bring philosophical challenges to light, exposing methodological limitaGons of prevailing approaches and points of contenGon in the field. ## Theory-driven approaches to consciousness and 'good' explana.ons The contemporary science of consciousness iniGally focused on idenGfying the neural correlates of consciousness (NCCs), a deliberately 'theory-neutral' approach aimed at characterizing the presence or absence of consciousness, as well as specific contents of consciousness, in human subjects. NCCs are typically defined as the minimal neural mechanisms jointly sufficient for a specific conscious experience. However, as consciousness science has progressed, the limitaGons of this approach have become clear, parGcularly in its inability to generalize beyond human-like neural systems and its failure to provide a principled account of what consciousness is in physical terms (understood here as a systemaGc correspondence between conscious states and physical systems, without metaphysical assumpGons). While some set of neural mechanisms may be sufficient to reliably infer conscious experience in healthy adult humans, this does not help us assess consciousness in structurally or funcGonally different systems, such as infants, non-human animals, or intelligent machines, which may lack the same mechanisms but could sGll support a similar experience in different ways. These limitaGons, along with the rapid rise of arGficial intelligence, have prompted a shiY in focus toward theories that aim to account for the nature of consciousness and offer principled frameworks that are generalizable beyond biological brains. While 'theory-neutral' or 'theorylight' approaches (Birch 2022) may have some merit when extrapolaGng from humans to animals, where we can rely on evoluGonary relatedness and similariGes in cogniGve funcGon, drawing on principled theories becomes essenGal when evaluaGng consciousness in arGficial intelligence (Butlin et al. 2023; Findlay et al. 2024). This growing emphasis on theory-driven approaches has led to a proliferaGon of candidate 'theories.' IllustraGve of this trend is Kuhn's (2024) recent aoempt at an extensive taxonomy of the 'landscape of consciousness,' surveying proposed explanaGons spanning from philosophical accounts to quantum physics. A more focused overview is offered by Signorelli et al. (2021), who provide a systemaGc classificaGon of the explanatory profiles of different theories of consciousness. Focusing solely on neurobiological theories of consciousness, Seth and Bayne (2022) counted 22 current proposals, noGng that, rather than being progressively ruled out as empirical data accumulate, proposed hypotheses about consciousness seem to be mulGplying. One challenge with many of these ideas is that they are formulated either in abstract (i.e., mechanisGcally vague) terms, or have limited scope, primarily focusing on neural mechanisms related to consciousness in humans and closely related species. While many approaches propose-or can be interpreted to propose (Shevlin 2021)-general principles that should, in theory, be applicable to any physical system, the mechanisGc details provided are usually insufficient for construcGng a formal framework that would allow evaluaGng whether a given physical system is conscious and in what way (Kanai and Fujisawa 2024). This lack of specificity can make it difficult to assess whether a theory proposal is coherent and has merit as a 'good' 4 explanaGon for consciousness-one that can account for a broad set of facts ( scope ), does so in a unified manner ( synthesis ), explains facts precisely ( specificity ), is internally coherent ( selfconsistency ), aligns with our broader understanding ( system consistency ), is simpler than alternaGves ( simplicity ), and can make testable predicGons ( scien1fic valida1on ) (Albantakis, Barbosa, et al. 2023). Toy models in this context may facilitate a deeper understanding of the theories that aim to explain it, benefi]ng both skepGcs and proponents alike. Moreover, differences in predicGons among current accounts of consciousness suggest inconsistencies that may arise not solely from the diversity of proposals, but from more fundamental issues, such as mechanisGc incoherence or incompaGbility with physical principles (Kleiner and Hartmann 2023). Even in the absence of decisive new evidence from human subjects, toy models offer a way to instanGate abstract concepts in simplified systems, providing a plaporm to clarify and scruGnize the theoreGcal assumpGons and condiGons each theory claims are essenGal for conscious experience. For example, how does a global workspace posited by Global Workspace Theory (GWT) actually look like when we try to construct one? Which types of neural architectures genuinely support a high degree of integrated informaGon as required by Integrated InformaGon Theory (IIT)? Is there really a qualitaGve difference between top-down predicGons and booom-up predicGonerror signals, given their disGnct phenomenal roles in predicGve processing accounts of consciousness? And, most criGcally, is a given theory coherent in the first place? In this sense, toy models may serve as tesGng grounds for assessing the explanatory power, mechanisGc plausibility, and coherence of theories of consciousness. The quota@on marks around 'good' are meant to indicate a modest and pragma@c use of the term, adap@ng the common no@on of inferences to the explana@on, as in (Albantakis, Barbosa, et al. 2023). best Furthermore, toy models provide a framework to relate different theories of consciousness to each other. An iniGal aoempt can be found in (Lundbak Olesen et al. 2023), which applied both a measure of integrated informaGon and surprisal (a basic informaGon theoreGc measure from the free energy principle formalism) to small, arGficial agents evolving in a simulated environment. ## Two case studies-IIT and GWT Despite a proliferaGon of proposed hypotheses, consciousness science has coalesced around a few prominent theoreGcal frameworks, each with disGnct explanatory goals and methodologies (Yaron et al. 2021). Among these, global workspace theory (GWT) and integrated informaGon theory (IIT) are two of the most influenGal, along with higher-order theories (HOTs), re-entry theories, and predicGve processing theories (Seth and Bayne 2022). Not only do these frameworks propose different explanaGons for consciousness, but they also target different aspects of conscious experience (Signorelli, Szczotka, et al. 2021). While IIT centers on phenomenal features of consciousness, aiming to explain the subjecGve quality of experience, others, such as GWT, emphasize funcGonal, behavioral aspects. In the following, I will focus specifically on IIT and GWT, as they represent two contrasGng approaches to consciousnessone grounded in phenomenology 5 , the other in funcGonal cogniGve architecture-and examine the role of toy models in evaluaGng these frameworks. ## Integrated Informa4on theory (IIT) Most neurobiological theories of consciousness start from experimental observaGons, aiming to explain specific phenomena and eventually derive general principles. In contrast, IIT has strived from the outset to provide a principled and comprehensive account of consciousness. To that end, IIT starts from consciousness itself (as opposed to potenGal physical correlates), aiming to idenGfy the essenGal properGes of conscious experience through introspecGon and reasoning, and to translate them into postulates about its physical substrate. The resulGng framework can then be evaluated against experimental data, with the ulGmate goal of creaGng an objecGve account of the presence and properGes of experience (Albantakis, Barbosa, et al. 2023). IIT concludes that a substrate of consciousness, consGtuted of interacGng units, must be a maximum of irreducible cause-effect power. Furthermore, IIT proposes an explanatory idenGty between the cause-effect structure supported by such a 'complex' in its current state and the quality of its experience (see IIT Wiki (2024) for more informaGon and Bayne (2018) and McQueen (McQueen 2019) for a criGcal perspecGve on IIT's axiomaGc approach). From its incepGon, IIT's conceptual claims have been accompanied by a developing mathemaGcal framework. Each successive refinement and publicaGon has featured toy models that clarify and illustrate the proposed formalism and its implicaGons (Tononi et al. 1994; Tononi and Sporns 2003; Balduzzi and Tononi 2008; Oizumi et al. 2014; Albantakis, Barbosa, et al. 2023). A typical IIT toy model consists of a small network consGtuted of 3 to 6 binary units ('toy neurons') that interact according to predefined update rules. These units may be implemented 5 Here and throughout, 'phenomenology' refers to the structure and character of subjec@ve experience itself, not the philosophical tradi@on of Phenomenology associated with Husserl. as simple logic gates (e.g., AND, OR, XOR) or as probabilisGc elements governed by statetransiGon probability funcGons. Such simple systems allow for a rigorous evaluaGon of the causal and informaGonal quanGGes specified by the IIT formalism, which makes it possible to explore how architectural and funcGonal features influence the quanGty and quality of experience according to the theory. These toy models have not only been used to elucidate IIT's theoreGcal framework in publicaGons but have also served as test cases for assessing its internal coherence. They have driven advancements such as a novel measure of intrinsic informaGon (Barbosa et al. 2020), an account of causal emergence and macroscopic intrinsic units, with toy models providing proofof-principle examples (Hoel et al. 2013; 2016; Marshall et al. 2018; 2024), and formal extensions to quantum computaGonal systems (Zanardi et al. 2018; Albantakis, Prentner, et al. 2023). While, on the one hand, the use of toy models has made the IIT framework sufficiently specific and accessible to invite criGcism and opposing views (e.g., (Aaronson 2014; Hanson and Walker 2019; Doerig et al. 2019; Merker et al. 2021), on the other hand, it served to illustrate its explanatory and predicGve power. For example, IIT explains why the cerebellum, despite having more neurons than the cortex and being connected to the rest of the brain, does not contribute to experience due to its modular and primarily feedforward anatomy. It also accounts for why consciousness is lost when the causal interacGons among corGcal neurons break down, such as during deep sleep (when neurons become bistable) or seizures (when neural acGvity becomes saturated and unresponsive). Simple examples also suffice to demonstrate that, according to IIT, silent neurons with funcGonal connecGons may contribute to experience (Albantakis, Barbosa, et al. 2023)-a predicGon currently under evaluaGon (Olcese et al. 2024, Experiment 1). Similarly, the predicGon that changes in connecGvity within the main complex should lead to changes in experience even without changes in acGvity can be captured by simple toy examples and tested in human subjects (Tononi et al. 2016; Song et al. 2017). In part, the prominent role of toy models in IIT arises from necessity: rigorous applicaGon of the mathemaGcal framework is feasible only in systems with small numbers of discrete units. This is because the state space, the number of subsystems, and the system parGGons that must be evaluated all grow exponenGally with system size, rendering the computaGons intractable for anything but very small networks. Consequently, some aspects of IIT are more readily testable than others, which has prompted a disGncGon in the secondary literature between 'weak' IIT, focused on empirical correlates of integrated informaGon, and 'strong' IIT, which aims to provide a universal account of consciousness that idenGfies experiences with the cause-effect structures of maximally irreducible substrates (Mediano et al. 2022; Leung and Tsuchiya 2023). While the empirical testability of 'strong' IIT has been challenged (Michel and Lau 2020; Klincewicz et al. 2025; but see (Tononi et al. 2025), toy models offer a way to connect more specific theoreGcal implicaGons of the theory in the strong sense with empirically accessible observables. As in other disciplines, insights drawn from simple examples represenGng different types of neuronal architectures (e.g., modular, grid-like, random, or all-to-all) or mechanisms (e.g., linear, nonlinear, excitatory, or inhibitory) can be generalized to larger systems. These generalizaGons enable IIT to provide explanaGons and predicGons that can be validated in human subjects. Toy models in IIT have also been used to elucidate specific phenomenal experiences, going beyond their use-case of illustraGng the theoreGcal framework itself. For instance, IIT explains the experience of spaGal extendedness using non-directed grids, whose cause-effect structures are composed of relaGons arranged according to reflexivity, inclusion, connecGon, and fusionmirroring spaGal phenomenology (Haun and Tononi 2019). Similarly, the feeling of temporal flow can be accounted for by the cause-effect sub-structures specified by arrays of directed grids (Comola] et al. 2024). These highly specific predicGons address core principles of IIT and demonstrate its capacity to link theoreGcal postulates with concrete phenomenological accounts. Notably, the structural features of consciousness have recently gained renewed aoenGon beyond the context of IIT (Kleiner 2024). Within the emerging framework of mathemaGcal consciousness science (Kleiner and Ludwig 2024; Signorelli et al. 2025; Prentner 2024), several studies have introduced toy models that are not embedded within a specific theory of consciousness but instead aim to directly characterize or explain parGcular aspects of experience such as its unity, its composiGonal character, and its subjecGvity (Prentner 2019; Signorelli, Wang, and Khan 2021; Signorelli, Wang, and Coecke 2021; Mason 2021; Díaz-Boils et al. 2025). These autonomous toy models prioriGze the internal structure of consciousness itself and exemplify an alternaGve use case: exploring experience from a structural standpoint rather than deriving it from a broader mechanisGc theory. Returning to IIT, toy networks have also been used to explore broader quesGons about the evoluGon of consciousness and the possibility of consciousness in arGficial systems. Simulated evoluGon experiments with simple agents equipped with evolvable neural networks have shown that integrated informaGon increases over generaGons when agents face selecGve pressures under biological constraints in sufficiently complex environments (Edlund et al. 2011; Albantakis et al. 2014; Fischer et al. 2020). These findings provide a possible explanaGon, grounded in IIT, for why complex conscious systems evolved and why consciousness and intelligence correlate in biological systems, even though they can be dissociated in principle, meaning that a system may exhibit intelligent behavior without being conscious. This dissociaGon has been demonstrated using a toy-model implementaGon of a standard computer (Findlay et al. 2024), which exposed that computers do not typically specify cause-effect structures that resemble those of the systems they simulate. According to IIT, this means that funcGonal equivalence does not imply phenomenal equivalence, which challenges widely held computaGonal-funcGonalist assumpGons (Butlin et al. 2023). ## Global workspace theory (GWT) In contrast to IIT's 'phenomenology-first' approach, GWT originated in cogniGve science, drawing inspiraGon from arGficial intelligence research on cogniGve architectures (Baars 1988). It was subsequently developed into a neurobiological model known as the Global Neuronal Workspace Theory (GNWT) (Dehaene et al. 1998; 2003; Dehaene and Changeux 2011). GNWT posits that (sensory) informaGon becomes conscious when it enters and is 'broadcast' within an anatomically widespread neural workspace, primarily involving higher-order corGcal associaGon areas, with a parGcular (though not exclusive) emphasis on the prefrontal cortex (Mashour et al. 2020; Seth and Bayne 2022). ComputaGonal models have been central to GWT and GNWT, but they funcGon primarily as simplified models of neurobiological processes rather than as toy models aimed at evaluaGng GWT as a theory of consciousness. Early conceptual sketches of cogniGve architectures outlined the minimal components thought to be required for consciousness-distributed specialized processors and a reciprocally connected global workspace or 'blackboard'-in abstract terms, without mechanisGc detail (Baars 1988). In contrast, mechanisGc models have been used to target specific neural phenomena, such as an amplificaGon of perceptual acGvity ('igniGon'), long-distance correlaGons, or the P300 waveform, while explicitly denying that these are exhausGve models of conscious substrates (Dehaene et al. 1998; Dehaene and Naccache 2001). aoenGonal blink and inaoenGonal blindness (Dehaene et al. 2003; Dehaene and Changeux 2005), they are not aimed at exploring minimally sufficient mechanisms or clarifying the core principles of GWT/GNWT as a theory of consciousness. Although these models provide testable hypothesis about psychological phenomena such as the As with other neurobiological theories of consciousness, but in contrast to IIT, the scope and generality of GWT/GNWT remain, to some extent, open to interpretaGon (Birch 2022; Shevlin 2021). Specifically, it is unclear whether the computaGonal principles underlying GWT are generally sufficient for conscious experience, or if the specific neural mechanisms proposed by GNWT in healthy, adult humans are required to make meaningful predicGons about the presence or absence of consciousness in a given system. As suggested in (Doerig et al. 2020), a network consisGng of two peripheral neurons connected to a small recurrent global workspace meets the funcGonal criteria for consciousness outlined by GWT. Yet, according to (Dehaene et al. 1998) even their simple neural model of a global workspace was explicitly not intended to provide 'an exhausGve descripGon of a 'conscious workspace.'' This leaves open the quesGon of what addiGonal features, if any, might be required to construct a conscious system under this framework, an issue discussed further below. A 'cauGous' interpretaGon of GWT merely implies that the presence of a global broadcast network in healthy adults is sufficient for consciousness (Birch 2022). While this avoids potenGal overgeneralizaGon, it has no bearing on the presence or absence of consciousness in systems different from us and does not provide an account of the nature of consciousness. By contrast, an 'ambiGous' interpretaGon of GWT would imply that the presence of specialized modules compeGng for access to a global workspace, combined with the capacity for global broadcast, could be taken as evidence for consciousness (Birch 2022). For instance, Dehaene, Lau, and Kouider (2017) proposed a funcGonal definiGon of consciousness that could, in principle, extend to machines, while leaving open the quesGon of phenomenal consciousness. However, the lack of a principled formal framework to rigorously determine whether an arbitrary system possesses a global workspace-or to precisely define what consGtutes broadcasGng-limits the applicability of this interpretaGon (Seth and Bayne 2022; Birch 2022; Kanai and Fujisawa 2024). Since GWT is generally presented as a computaGonal funcGonalist theory of consciousness, various aoempts have been made to formalize its principles in computaGonal terms (Franklin and Graesser 1999; VanRullen and Kanai 2021; Goyal et al. 2022). In the spirit of a true toy model, Blum and Blum (2021) introduce the Conscious Turing Machine (CTM) as a formalizaGon of GWT, prioriGzing simplicity over complexity to provide a minimal model of a conscious system rather than a detailed simulaGon of the brain. The CTM was proposed for the express purpose of understanding Baars' Theater Model and for providing a theoreGcal computer science framework to understand consciousness. Central to the CTM is an expressive "inner language" called Brainish, which facilitates global broadcast and enables inner speech, vision, and sensaGons. This inner language is considered a key component of the feeling of consciousness, though its arGculaGon remains to be developed. Blum and Blum's proposal is notable in its explicit aim to address the minimal requirements for phenomenal experience, disGnguishing these from mere simulaGons of such experiences. However, the precise nature of the 'feeling of consciousness' remains unspecified, and the authors point to IIT as a potenGal framework for addressing this challenge. In sum, exisGng simple models of GWT provide basic instances of funcGonal workspaces and serve to elucidate the architectures and dynamics of global workspaces. However, they also reveal an open challenge for GWT/GNWT: the absence of a clearly arGculated set of necessary and sufficient condiGons for a system to be conscious within the current framework. This vagueness is not necessarily problemaGc within a funcGonalist framework of consciousness, where the focus is on uGlity and behavioral outcomes. Indeed, general systems can be assessed against broad criteria like those proposed by Butlin et al., (2023) who compiled a list of indicators of phenomenal consciousness for assessing AI consciousness based on an assumpGon of computaGonal funcGonalism. Nevertheless, many systems ranging from the minimal examples above to real-world cases like infants or paGents with severe brain would occupy a gray zone in which exisGng criteria are insufficient to establish the presence or absence of experience. While the richness of experience of such systems could vary widely, subjecGvely, it either feels like something to be that system or it does not. As Kanai and Fujisawa (2024) put it: 'Concepts such as 'global workspace' (…) are understood by human neuroscienGsts. However, deciding whether they are present in an arbitrary physical system requires more precise mathemaGcal definiGons to allow their idenGficaGon.' ## Philosophical challenges brought to light Beyond their role as tools for elucidaGng theoreGcal frameworks, toy models have been instrumental in clarifying and addressing key philosophical challenges in consciousness science. By providing simplified yet tangible instanGaGons of theoreGcal claims, they expose methodological limitaGons and sharpen debates on foundaGonal issues. For instance, toy models have focused discussions about the minimal condiGons for consciousness, baring the choice between postulaGng addiGonal, oYen arbitrary requirements to exclude simple systems or accepGng that many theories imply consciousness in very basic systems. Similarly, toy models have underscored the tensions between computaGonal funcGonalist and structural theories of consciousness, exposing key differences and shedding light on the assumpGons underlying these compeGng perspecGves. ## Minimal conscious systems UlGmately, any scienGfic theory of consciousness that aims to be comprehensive should provide a principled account of what consciousness is in physical terms, necessary and sufficient condiGons for the presence or absence of consciousness that can be evaluated in a wide range of physical systems, and an account of why an experience feels the way it feels (Ellia et al. 2021). Notably, a principled account necessarily implies that there is a minimal system consistent with the theory that should be granted consciousness-if minimally so 6 . 6 With 'minimal system' I refer to the simplest (type of) physical system that sa@sfies a theory's condi@ons for consciousness. Such a system can be instan@ated as a concrete, mechanis@cally interpretable toy model to explore These minimal systems challenge our intuiGons about consciousness, which oYen link it to intelligence, likely because in biological systems, the two seem closely connected. As a result, toy model instanGaGons of such minimal systems provoke discomfort, prompGng asserGons that the proposed features may be necessary but cannot be sufficient for consciousness. For example, proponents of GWT generally resist aoribuGng consciousness to toy models of global workspaces, implying that addiGonal criteria are needed to explain why these systems are not conscious (Doerig et al. 2020). However, adding arbitrary requirements, such as a minimal size, complexity threshold, or restricGon to biological substrates, without offering addiGonal explanatory power, is unscienGfic if done merely to avoid an uncomfortable implicaGon. AlternaGvely, one could accept that any system implemenGng all the essenGal features postulated by a theory of consciousness would indeed be (minimally) conscious (Lamme 2006; Albantakis, Barbosa, et al. 2023). This, however, raises concerns among criGcs who worry that such implicaGons could lead down a slippery slope toward panpsychism- a philosophical posiGon oYen criGcized for its lack of empirical testability and its perceived risk of undermining the scienGfic uGlity of the concept of consciousness (Doerig et al. 2020; Merker et al. 2021; Seth 2021; Klincewicz et al. 2025). Panpsychism holds that consciousness is a fundamental and ubiquitous feature of reality, which, if taken literally, suggests that some form of consciousness is present in all things. The concern is that if a theory allows for simple systems to be conscious, it risks failing to address the rich and complex features of human conscious experience. This concern is parGcularly relevant for theories like GWT, which offer broad funcGonal explanaGons but do not address the qualitaGve aspects of experience. Such theories inherently struggle to differenGate between minimal and complex systems. If consciousness arises from the global broadcast of informaGon, what disGnguishes a small global workspace from a larger one? Moreover, without a principle to arbitrate between nested or overlapping workspaces, GWT cannot resolve the ambiguity of whether subsets (or supersets) of a larger workspace that meet its funcGonal criteria might also independently qualify as conscious. Without a framework to explain how the scale, structure, or extent of the global workspace shapes the quality and content of experience, these theories leave unanswered the fundamental quesGons of why and how the rich and complex conscious experiences of humans differ from the simpler, potenGally conscious states of minimal systems operaGng under equivalent funcGonal principles. These unresolved issues highlight the great challenge faced by any comprehensive theory of consciousness: it must account for every aspect of experience, from its essenGal properGes, such as the unity of consciousness, to its accidental properGes, like the fleeGng feeling of familiarity evoked by a faintly remembered tune. While most proposed theories of consciousness are narrower in scope, IIT stands out in its aim to provide a comprehensive account. According to IIT, a substrate of consciousness must specify a maximum of system integrated informaGon, a quanGty defined to reflect the essenGal properGes of experience idenGfied by IIT in physical terms. In addiGon, every accidental property of experience-the feeling of spaGal extendedness, of temporal flow, of objects, of colors, and so on-must be fully accounted for by the properGes of the substrate's cause-effect structure, with no addiGonal ingredients. While IIT is oYen associated with panpsychism (Merker et al. 2021; Tononi and Koch a theory's implica@ons. I do not mean minimal models of explana@on in the sense of autonomous, idealized representa@ons that aim to capture generalizable abstract features of consciousness. 2015; Klincewicz et al. 2025), it is far from aoribuGng consciousness indiscriminately to all things (Kanai and Fujisawa 2024; Tononi et al. 2025). Whether its exacGng predicGons can be empirically validated remains an open quesGon. Crucially, though, the universality of IIT does not prevent it from making precise, testable predicGons about the causal structure underlying complex human experiences. Toy models are instrumental in formulaGng these predicGons, as they enable a full evaluaGon of cause-effect structures in systems that are explicitly defined and analyGcally tractable. Whether IIT proves to be correct or misguided, any complete theory of consciousness will eventually require us to acknowledge that its proposed criteria are sufficient condiGons for aoribuGng consciousness to any system that saGsfies them, no maoer how simple or counterintuiGve that system might seem. As Kuhn aptly stated, 'any theory of consciousness, to be complete and sufficient, must make an idenGty claim. (…) Something happening or exisGng in every senGent creature just is consciousness.' A comprehensive scienGfic theory of consciousness must, in some way, connect subjecGve experience to the natural world and should thus offer fundamental principles that account for conscious experience in any system. Toy models provide a clear and principled way to explore the coherence of these principles, bridging the gap between abstract theory and empirical validaGon. A theory that merely predicts which regions of the primate brain correlate with consciousness will fall short of addressing 'why,' 'how,' and under which condiGons consciousness arises from a physical enGty (Kanai and Fujisawa 2024). ## The structural-func4onal divide As demonstrated by a series of simple example systems, IIT allows for funcGonal equivalence without phenomenal equivalence (Albantakis and Tononi 2019; Albantakis, Barbosa, et al. 2023; Hanson and Walker 2019; 2020). Specifically, two systems may exhibit idenGcal input-output funcGons (probing a subset of possible system states), or even share the same internal global dynamics (whole-system state transiGons), yet differ in their amount of system integrated informaGon and intrinsic cause-effect structures. This is because idenGcal global dynamics and input-output behavior can arise from different physical systems with disGnct internal causal structures, meaning that their components interact in very different ways. For IIT, the quality of experience corresponds to the unfolded cause-effect structure of a substrate, which captures the irreducible cause-effect informaGon of every subset of the substrate, not just the system as a whole. In other words, whether and how a system is conscious depends on what the system is, in causal terms, rather than what it does. This implicaGon challenges the dominant computaGonal-funcGonalist paradigm, which holds that performing computaGons of the right kind is both necessary and sufficient for consciousness (Butlin et al. 2023). Since these implicaGons were made explicit through a set of toy examples, they have sparked an ongoing philosophical debate-primarily targeGng IIT-about the testability of theories that put constraints on the types of physical systems that could serve as substrates of consciousness, which also include Recurrent Processing Theory (RPT) and others (Doerig et al. 2020). Introduced as the 'unfolding argument'(Doerig et al. 2019) and generalized to the 'subsGtuGon argument' (Kleiner and Hoel 2020), the central claim is that if it is possible, even in principle, to replace the mechanisms of a conscious system in a way that renders it unconscious without changing its outward responses, then those mechanisms cannot be necessary to explain empirical data about consciousness. The premises underlying the unfolding argument and its conclusions have since been challenged on mulGple fronts, including pracGcal, methodological, and philosophical concerns (Usher 2021; Tsuchiya et al. 2019; Negro 2020). One parGcularly relevant issue is the argument's refusal to recognize first-person experience as a means to validate reports in healthy adult humans-validaGon that would be absent in the subsGtuted system (Albantakis 2020). While IIT is unapologeGcally structural in its approach, whether other neurobiological theories imply specific causal implementaGons is a maoer of interpretaGon. For instance, Butlin et al. (2023), include RPT in their list of theories compaGble with computaGonal funcGonalism, provided the requirement for recurrent processing is interpreted algorithmically rather than as necessitaGng a specific causal implementaGon. Similarly, a global workspace architecture can be understood as either a purely funcGonal construct-implementable by something as abstract as a giant input-output lookup table (e.g. Herzog et al. 2021), or as implying a more constrained implementaGon (Blum and Blum 2021). However, a purely funcGonalist interpretaGon would demand principled methods to determine which input-output funcGons genuinely imply global workspaces-methods that have yet to be developed. For instance, what specific behaviors would demonstrate that a lookup table truly implements a global workspace? The quesGon of whether funcGonal equivalence necessarily implies phenomenal equivalence has gained new urgency in the era of advanced arGficial intelligence. In this context, IIT demonstrates through a toy model of a standard computer simulaGng a simple integrated system that the cause-effect structure of the computer diverges fundamentally from that of the system it simulates (Findlay et al. 2024). In contrast, computaGonal funcGonalism asserts that phenomenological and funcGonal equivalence are inherently linked. However, the resoluGon of this debate will not depend on the increasing sophisGcaGon of arGficial systems but instead on the explanatory power of each theoreGcal framework when applied to human consciousness. As argued earlier, a comprehensive theory of consciousness must account for an astonishing breadth of evidence, without resorGng to addiGonal (arbitrary) ingredients. As well as predicGng the presence or absence of consciousness, such a theory can be tested on its predicGons about the essenGal and accidental properGes of experience in healthy adult humans, under circumstances where there should be liole doubt about what the subject is experiencing. While the "small-network" and "unfolding argument" remain debated, toy models have played a pivotal role in sharpening these discussions. They have highlighted the need for future work to focus on how various theories link experience to report, clarified the kinds of experiments that are admissible as test cases, and advanced our understanding of how a science of consciousness might develop when grounded in more nuanced noGons of philosophy of science. ## Conclusion As reviewed above, toy models may reveal much about the limits and possibiliGes of our theories of consciousness. In this context, Feynman's dictum-'What I cannot create, I do not understand'-serves as a guiding principle, not for building consciousness itself but for construcGng and evaluaGng theories about it. By making abstract concepts tangible and accessible, toy models allow researchers to probe the coherence and consistency of theoreGcal frameworks. They disGll complex phenomena into simplified systems, fostering a deeper understanding of proposed mechanisms and their implicaGons. In this way, toy models offer intuiGve insights that are oYen obscured in larger, more intricate systems or abstract formulaGons. At the same Gme, they serve as quanGtaGve implementaGons of thought experiments, enabling researchers to rigorously test theoreGcal assumpGons. CriGcally, toy models also help assess the scope of theories, determining whether their predicGons are universal or constrained by their premises. For example, toy models have been pivotal in refining IIT's mathemaGcal framework and illustraGng its predicGons, while also inviGng criGcism and exposing philosophical challenges. AddiGonally, toy models have highlighted the funcGonal principles of GWT, while also drawing aoenGon to the open quesGon of what, within the theory, consGtute necessary and sufficient condiGons for consciousness. While the primary focus of toy models has been to illuminate theoreGcal frameworks, they have also shown promise in addressing specific features of experience. For example, IIT's toy model of spaGal extendedness provides a mechanisGc account of a phenomenal property, linking it to the underlying cause-effect structure of a system. Moreover, toy models bring philosophical challenges into sharper focus. Debates surrounding the "small network" and "unfolding" arguments, for example, have underscored the broader challenges of relaGng conscious experience to physical systems. Toy models have also been used to argue that funcGonal equivalence does not necessarily imply phenomenal equivalence, sharpening disGncGons between structural and funcGonal theories of consciousness. UlGmately, toy models act as bridges between abstract theoreGcal claims and empirical science, providing invaluable tools for navigaGng the complexiGes of consciousness science. They elucidate not only the theories themselves but also the broader challenges that a comprehensive theory of consciousness must address. 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