This paper introduces the Graph Continuous Thought Machine (Graph CTM), a novel neuro-inspired compu- tational architecture that emulates biological cognition through dynamic graph-based representations and dispositional neural connectivity. Unlike conventional neural networks with static topologies, Graph CTM employs a three-dimensional disposi- tional neural tensor from which context-specific subgraphs are instantiated at each processing step (or ”tick”). Each node within this architecture maintains a learnable property vector that encodes both accumulated knowledge and dispositional weights that determine activation probabilities for downstream nodes. Importantly the nodes of the GNN ARE a subset of the neurons in the dispositional neural tensor, instantiating just those that are currently firing. Since the GNN outputs graphs it means that currently firing nodes cause the next nodes by the effect they have on the graph neural network’s (GNN’s) output and so may be seen to be connected to them in some sense. A neural synchronization mechanism dynamically forms and dissolves these connections in this dispositional model, based on activation covariance, effectively implementing Hebbian-like plasticity to minimize prediction loss and building brain like connectivity. The architecture incorporates a simulated prefrontal cortex module that regulates information flow through reinforcement learning and employs harmonic constraints derived from musical conso- nance in the cyclic group Z12 to determine solution convergence. We formalize the mathematical foundations of Graph CTM, in- cluding the synchronization dynamics, dispositional connectivity, and prefrontal regulation mechanisms. Experimental evaluation on the Abstraction and Reasoning Corpus for Artificial Gen- eral Intelligence (ARC-AGI 2) demonstrates the architecture’s capacity for adaptive problem-solving, albeit with limited success compared to human performance. This limitation is theoretically expected given the vast scale disparity: the human brain employs approximately 80 billion neurons, while our implementation uti- lizes merely 10,000 nodes. Nevertheless, Graph CTM represents a significant step toward biologically plausible AI by modeling how neural synchronization dynamically creates and breaks dispositional connections to optimize information processing, mirroring fundamental mechanisms observed in biological neural systems.

We have presented Graph Continuous Thought Machine (Graph CTM), a novel neuro-inspired architecture that mod- els cognition as dynamic traversal through a dispositional graph space. By integrating neural synchronization, reinforce- ment learning, and harmonic constraints within a graph-based framework, Graph CTM captures essential aspects of biologi- cal neural computation while maintaining mathematical rigor and computational tractability. Experimental evaluation on ARC-AGI 2 was poor though this was expected given the large disparity of the human brain and this system in neuron counts. Future work will pursue key enhancements to improve biological plausibility and performance: multi-task training with language modeling objectives,leading to the integration of neuro scientifically-grounded architectural constraints, through specialized prompting to guide the formation of brain-like topological organizations within the dispositional connectivity patterns.This would be optimised by including neuroscience research with the language modeling objectives. References

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