Modular, Hierarchical Cognitive Map Learners with Hyperdimensional Computing for Solving the Tower of Hanoi Puzzle

Core Concepts

Cognitive map learners (CMLs) can be assembled into modular, hierarchical systems using hyperdimensional computing (HDC) to solve complex problems like the Tower of Hanoi puzzle without retraining the individual CMLs or explicit knowledge of their graph topologies.

Abstract

The content describes a method for assembling modular, hierarchical cognitive map learners (CMLs) using hyperdimensional computing (HDC) to solve the Tower of Hanoi (ToH) puzzle.
Key highlights:

CMLs are a collection of single-layer neural networks that learn internal representations of node states, edge actions, and edge action availabilities in an abstract graph.
CMLs can perform near-optimal path planning between any two graph node states, but do not learn when or why to transition from one node to another.
This work integrates CMLs with HDC, a form of symbolic machine learning, to create semantically meaningful node state representations that can be shared and orchestrated across multiple CMLs.
Several CML modules were prepared independently and then repurposed to solve the ToH puzzle without retraining the CMLs and without explicit reference to their respective graph topologies.
Four methods were demonstrated for orchestrating the ring CMLs to solve the ToH puzzle: 1) an external, monolithic policy; 2) local, partial policies; 3) mapping ToH states to ring states; and 4) a composite ToH CML constructed from the ring CML states.
This work suggests a template for building levels of biologically plausible cognitive abstraction and orchestration using modular, hierarchical CML-HDC systems.

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Key Insights Distilled From

Assembling Modular, Hierarchical Cognitive Map Learners with Hyperdimensional Computing

by Nathan McDon... at arxiv.org 05-01-2024

https://arxiv.org/pdf/2404.19051.pdf

Deeper Inquiries

How could the modular, hierarchical CML-HDC framework be extended to solve more complex, real-world problems beyond the Tower of Hanoi puzzle

The modular, hierarchical CML-HDC framework can be extended to solve more complex, real-world problems by incorporating additional layers of abstraction and orchestration. For instance, in a robotics scenario, the framework could be used to plan and execute complex sequences of actions involving multiple robotic arms or agents. Each component CML could represent a specific task or sub-goal, while the overarching CML orchestrates the overall plan by coordinating the actions of the individual components. By integrating more CML modules and designing a hierarchical structure that allows for the delegation of tasks at different levels of abstraction, the system can tackle intricate problems that require sophisticated planning and decision-making.

What are the potential limitations or challenges in scaling this approach to larger, more complex problem domains

Scaling the CML-HDC approach to larger, more complex problem domains may pose several challenges. One limitation could be the computational complexity associated with managing a large number of CML modules and their interactions. As the system grows in size and complexity, the training and optimization of the individual modules may become more challenging, requiring efficient algorithms and computational resources. Additionally, ensuring the seamless integration and communication between different modules while maintaining modularity and flexibility could be a challenge. Furthermore, as the problem domain expands, the need for robust error handling, adaptive learning mechanisms, and dynamic reconfiguration of the system to accommodate changing requirements may increase, adding complexity to the overall system design.

How might the biological plausibility of the CML-HDC system be further explored and validated, particularly in the context of cognitive abstraction and orchestration in the brain

Exploring the biological plausibility of the CML-HDC system in the context of cognitive abstraction and orchestration in the brain could involve conducting neuroscientific studies and experiments. One approach could be to compare the behavior and performance of the CML-HDC system with neuroscientific findings on cognitive processes in the brain. This comparative analysis could help validate the system's ability to mimic or simulate cognitive functions observed in biological neural networks. Additionally, conducting brain imaging studies or neural recordings while subjects engage in tasks similar to those addressed by the CML-HDC system could provide insights into the neural mechanisms underlying cognitive abstraction and orchestration. By aligning the system's behavior with known cognitive processes in the brain, researchers can further validate the biological plausibility of the CML-HDC framework.