Renormalising Generative Models for Active Inference: Foundations, Derivations, and Verification

Active inference offers a unified framework for perception, learning, and action, but scaling discrete active-inference models to rich spatial and temporal domains remains difficult. Renormalising generative models (RGMs) address this challenge by composing discrete generative models across spatial and temporal scales, coarse-graining lower-level states and paths into higher-level causes for objects, events, and action. However, fully reproducing and adapting the framework remains difficult: the mathematical exposition is compact, and the reference implementations are deeply integrated within specialized software environments, leaving many algorithmic details implicit. This paper addresses these challenges by providing a self-contained, derivation-oriented account of RGMs together with an open, verified implementation. We explain how the hierarchy is built, how beliefs and actions are updated within it, and how information is passed between levels. Where the published equations and implementation differ in emphasis, we make those choices explicit and explain their modelling consequences. By clarifying the theory and separating it from its original implementation context, this work lowers practical barriers to entry and makes RGMs more transparent, auditable, and reproducible, providing a foundation for future quantitative evaluation and development on machine-learning benchmarks.

The Discovery Engine: A Framework for AI-Driven Synthesis and Navigation of Scientific Knowledge Landscapes

The prevailing model for disseminating scientific knowledge relies on individual publications dispersed across numerous journals and archives. This legacy system is ill suited to the recent exponential proliferation of publications, contributing to insurmountable information overload, issues surrounding reproducibility and retractions. We introduce the Discovery Engine, a framework to address these challenges by transforming an array of disconnected literature into a unified, computationally tractable representation of a scientific domain. Central to our approach is the LLM-driven distillation of publications into structured "knowledge artifacts," instances of a universal conceptual schema, complete with verifiable links to source evidence. These artifacts are then encoded into a high-dimensional Conceptual Tensor. This tensor serves as the primary, compressed representation of the synthesized field, where its labeled modes index scientific components (concepts, methods, parameters, relations) and its entries quantify their interdependencies. The Discovery Engine allows dynamic "unrolling" of this tensor into human-interpretable views, such as explicit knowledge graphs (the CNM graph) or semantic vector spaces, for targeted exploration. Crucially, AI agents operate directly on the graph using abstract mathematical and learned operations to navigate the knowledge landscape, identify non-obvious connections, pinpoint gaps, and assist researchers in generating novel knowledge artifacts (hypotheses, designs). By converting literature into a structured tensor and enabling agent-based interaction with this compact representation, the Discovery Engine offers a new paradigm for AI-augmented scientific inquiry and accelerated discovery.