# Full Text: Generalized Notation Notation for Active Inference Models > Extracted from `2023_GNN.pdf` --- ## Page 1 Generalized Notation Notation for Active Inference Models Jakub Sm´ekal1[0000−0003−4989−4968] and Daniel Ari Friedman1[0000−0001−6232−9096] Active Inference Institute, USA https://www.activeinference.institute/ blanket@ActiveInference.institute Abstract. This paper introduces Generalized Notation Notation (GNN), a novel approach to generative model representation that facilitates com- munication, understanding, and application of Active Inference across various domains. GNN complements the Active Inference Ontology as a flexible and expressive language for education and modeling, by provid- ing a standardized method for describing cognitive models. In this paper we introduce GNN, and provide a Step-by-Step example of what GNN looks like in practice. We then explore ”the Triple Play”, a pragmatic approach to expressing GNN in linguistic, visual, and executable cogni- tive models. By situating GNN within the broader context of cognitive modeling and Active Inference, this work aims to bridge and respect the gaps among different modeling settings. The goal of this work is to fa- cilitate interdisciplinary research and application, ultimately promoting the advancement of the field. Keywords: Active Inference · cognitive models · model representation · hierarchical cognitive models · Bayesian statistics · generative models. 1 Introduction 1.1 Communicating Active Inference: Challenges and opportunities In recent years, the cognitive sciences have made significant strides towards un- derstanding the complex nature of human cognition and behavior. One promis- ing approach is Active Inference, a unifying theoretical framework that combines perception, action, and learning in a coherent manner [1] [2]. Despite the poten- tial value of models within this framework, the widespread adoption of Active Inference has been hindered by the lack of a standardized method for effectively representing and communicating them. In this paper, we address this challenge by introducing a novel approach to cognitive model representation called Gen- eralized Notation Notation (GNN), which aims to facilitate communication and understanding of Active Inference models across various domains and settings. 1.2 Comprehensively described cognitive models are key Developing comprehensive, accessible, reproducible, interoperable cognitive mod- els is crucial for the advancement of the Active Inference field. Without a stan- ## Page 2 2 J. Sm´ekal and D. Friedman dardized language for describing cognitive models, researchers experience fric- tion when collaborating, sharing, and building upon existing work. In Active Inference research, models are often conveyed through assemblages of natural language, pseudocode, programming languages, analytical formulas, and picto- rial representations. In this paper, we present GNN as a flexible and expressive language tailored for expressing Active Inference models, and encompassing var- ious relevant aspects of languages, including ontology, morphology, grammar, and pragmatics. By leveraging GNN as an Active Inferlingua (or Interlingua, In- fralingua, or Supralingua), we aim to bridge and respect the gaps among different modeling approaches in order to facilitate interdisciplinary research. 1.3 Goals and structure of the paper In this paper, first we present the current specification of the GNN language and method (Section 2). To provide an example of GNN in action, we pro- vide the GNN representation of a recent step-by-step Active Inference tutorial [3] [4] (Section 3). We point towards the practical utility of GNN by exploring ”the Triple Play” – a pragmatic approach to expressing GNN in three distinct modalities: text-based models, statistical graphical models, and executable cog- nitive models (Section 4). Lastly, we discuss the implications of our findings, in terms of philosophical and taxonomic perspectives on the diversity of Active Inference generative models, and suggest future research directions (Section 5). By situating GNN within the broader context of hierarchical cognitive models and Active Inference, we hope to inspire further exploration and development of this promising approach to understanding and communicating complex cognitive processes. ## Page 3 Generalized Notation Notation 3 2 Active Inference Linguistics: Ontology, Morphology, and Grammar 2.1 Generalized Notation Notation (GNN) overview GNN describes Active Inference models with ASCII letters and punctuation, structured in a source file that accords with the principles of Markdown. In this section we provide a snapshot of the current specification of GNN. Updated information on GNN can be found at Github [10] or in Coda [11]. 2.2 GNN punctuation ## Page 4 4 J. Sm´ekal and D. Friedman 2.3 GNN source file structure 3 Step-by-Step GNN 3.1 A Step-by-Step example of GNN applied to Smith et al. 2022 Here we provide several examples of increasing expressiveness of GNN, as defined in the prior section. The examples are directly drawn from ”A step-by-step tutorial on active inference and its application to empirical data” by Smith, Friston, and Whyte 2022 [3] [4]. Just as the goal of the initial step-by-step paper was to start simple and progressively add model features till one has arrived at a full Active Inference generative model, here we use that exact same progression to demonstrate the flexibility of GNN. ## Page 5 Generalized Notation Notation 5 ## Page 6 6 J. Sm´ekal and D. Friedman 4 Expressing GNN: The Triple Play 4.1 Every GNN expression has a pragmatic and epistemic context As with communication more broadly, it is key to consider the pragmatic and epistemic context associated with the use of any given Generalized Notation Notation (GNN) expressions. Here, the pragmatic context refers to the practi- cal aspects of communication, such as the preferences and behavioral policies of the communicators, while the epistemic context pertains to the beliefs of those involved in the ”ecosystem of shared intelligence” [5]. By taking agent-scale prag- matic and epistemic contexts into account, GNN expressions can be tailored to effectively convey complex concepts using a linguistics that translates seamlessly across different modalities. Various strategies and tactics may be helpful when employing GNN expres- sions in different settings and using a spectrum of model precisions (e.g. from informal conversation, to a beautiful presentation, to a fully-documented repro- ducible research product). Model precision should be balanced against the need for comprehensibility and ease of communication. Broadly, strategic considerations for expressing GNN include the overall ap- proach to communication, such as the choice of modality and level of technical rigor applied for a given audience. Tactical considerations for expressing GNN in- clude specific techniques for enhancing clarity and understanding, such as using visual aids, examples, and analogies. Below we highlight the “Triple Play”, gesturing towards the high-fidelity rendering of a GNN expression (of a small motif or complete ecosystem-scale generative model) across plain-text, graphical, and executable (computational) forms. 4.2 Text-based models At its core, GNN is a text-based model that can be rendered into different for- mats, including mathematical notation, visualized figures, natural language de- scriptions, algorithmic pseudocode, and executable simulations. The plain-text basis of GNN provides a flexible framework for communicating these computa- tional models, allowing for the integration of different representations to better convey the underlying concepts and relationships of active inference linguistics. Additionally the plain-text basis of GNN enables the use of tools such as Regular Expressions and Large Language Models. 4.3 Graphical models Graphical models can be visualized using GNN. In the context of Bayesian statis- tics, graphical models offer a powerful way to represent complex relationships and dependencies. GNN enables the detailing and rendering of clear and informa- tive visual representations that can be easily understood by different audiences. Here GNN can be applied as post hoc documentation, by deriving plain-text of ## Page 7 Generalized Notation Notation 7 Figures drawn in papers. Additionally GNN can be used pre hoc or in medias res during the process of designing and implementing Active Inference models. By incorporating graphical models into GNN expressions, we can on one hand utilize the power of Bayesian statistics, and on the other hand benefit from improved visual communication of intricate cognitive models and concepts. 4.4 Executable Cognitive models Lastly, cognitive models can be executed using GNN. Cognitive models represent the mental processes and structures described by Active Inference. GNN provides a means to specify these models in a formal and precise manner, allowing for their implementation and testing in computational simulations. Critically, GNN as a pseudocode does not restrict which programming language or package ultimately implements the particular generative model in question. As already multiple software implementations of Active Inference exist with only more on the horizon [6], GNN will aid the backwards- and forwards-compatibility of the field. This flexible capability of GNN will enable researchers to explore the implications of various cognitive models, advancing understanding of active inference and catalyzing applications across diverse domains. 5 Discussion 5.1 Summary of key findings and developments In recent years, the field of cognitive science has experienced significant epistemic advancements and pragmatic developments, especially in the context of Active Inference generative models [2]. These models, which encompass wide ranges of statistical and symbolic model types [7], have been instrumental in shaping our understanding of cognitive processes. 5.2 Philosophical and Taxonomic perspectives on Active Inference model diversity Ongoing discussions among various factions (e.g. scientific realism and instru- mentalism) have raised important questions about the nature, function, and purpose of Active Inference models [8]. The realism-instrumentalism distinction plays a crucial role in shaping our understanding of generative models in Active Inference. Scientific realism posits that these models are approximations of universal truths about reality, implying that they provide veridical representations of the cognitive processes they aim to describe. On the other hand, scientific instrumentalism suggests that these models are intellectual structures that facilitate predictions and problem-solving in specific domains, without necessarily corresponding to any underlying reality. This distinction raises the question of how these models might be viewed as tools for representing objective cognitive truths, and/or for subjective understanding and prediction. ## Page 8 8 J. Sm´ekal and D. Friedman There are significant implications of the realism-instrumentalism conversa- tion in the context of Active Inference cognitive models. Both the realist and instrumentalist perspectives can inform the development of more comprehen- sive and accurate models, by emphasizing the need for a balance among factors such as explanatory power and predictive utility. By taking into account the strengths and limitations of specific perspectives as applied to particular gener- ative models, researchers can develop methods that are better suited to capture and respect the complexity of cognitive processes, while also providing useful frameworks for problem-solving and prediction. 5.3 Some future research directions Various future research directions have emerged related to GNN, and will be the subject of ongoing work at the Active Inference Institute and elsewhere. Some salient directions are briefly listed here. In terms of realizing the utility of GNN, improved automatic rendering software and better integration with the Active Inference Ontology [9] will enable the ”Triple Play” outlined above. Complex Systems Engineering frameworks such as cadCAD will be useful for specifying the execution order of GNN expressions [6] as well as for mapping the complete landscape of the particular model in question (parameter sweeps across the state- space/belief configurations), for example in the context of cyberphysical systems. From a linguistics perspective it would be interesting to explore possible gram- matical case systems, morphology, and dialects associated with GNN. Better integration with natural language processing and formal semiotic methods will enable new kinds of analyses on, with, and for the generative models described by GNN. 5.4 Final thoughts on GNN and Beyond By adhering to scientific principles such as rigor, accessibility, and plurality, Active Inference researchers can develop and use versatile methods that point towards the intricacies of cognitive processes while also providing practical so- lutions to real-world problems. As the field continues to evolve, it is crucial to remain open to new ideas, methodologies, action policies, and inferred beliefs, in order to foster a more comprehensive understanding of minds and their workings [1]. References 1. Friston, KJ.: The free-energy principle: a unified brain theory?. Nature Reviews Neuroscience 11, pages 127–138 (2010) https://doi.org/10.1038/nrn2787 2. Parr, T., Pezzulo, G., Friston, KJ.: Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. MIT Press (2022) 9780262045353 3. Smith, R., Friston, KJ, Whyte, CJ: A step-by-step tutorial on active inference and its application to empirical data. Journal of Mathematical Psychology, Volume 107 (2022) https://doi.org/10.1016/j.jmp.2021.102632 ## Page 9 Generalized Notation Notation 9 4. Smith, R., Whyte, CJ., Murphy, M., Friedman, DA: ActInf ModelStream 001.1, 001.2, 001.3, 001.4: ”A Step-by-Step Tutorial on Active Inference”. Active Inference Journal (2022) https://doi.org/10.5281/zenodo.7452789 5. Friston, KJ., Ramstead, MJD, Kiefer, AB, Tschantz, A, Buckley CL, et al.: De- signing Ecosystems of Intelligence from First Principles. arXiv:2212.01354 (2022) https://doi.org/10.48550/arXiv.2212.01354 6. Friedman, DA, Applegate-Swanson, S, Balbuena, JA, Choudhury, A, Cordes, RJ: An Active Inference Ontology for Decentralized Science: from Situated Sensemaking to the Epistemic Commons. Zenodo (2022) https://doi.org/10.5281/zenodo.7484994 7. Cloutier, J-F: Towards a symbolic implementation of Active Inference for Lego robots. Zenodo (2022) https://doi.org/10.5281/zenodo.6862626 8. Andrews, M: The math is not the territory: navigating the free energy principle. Biology Philosophy 36, 30 (2021) https://doi.org/10.1007/s10539-021-09807-0 9. Active Inference Institute: Active Inference Ontology. (2022) https://doi.org/10.5281/zenodo.7430333 10. Active Inference Institute: Generalized Notation Notation (GNN) Github repo: github.com/ActiveInferenceInstitute/GeneralizedNotationNotation https://doi.org/10.5281/zenodo.7803314 11. Active Inference Institute: Generalized Notation Notation (GNN) Coda: https://coda.io/@active-inference-institute/generalized-notation-notation --- *Extraction method: pymupdf*