The algebra of cognition
In recent years, my lab and others have demonstrated the value of vector symbolic algebras (VSAs) for capturing a wide variety of neural and behavioural results. In this talk I discuss the surprising and compelling variety of tasks and styles of reasoning that are well-suited to descriptions using a specific VSA. These tasks include path integration, navigation, Bayesian reasoning, sampling, memorization, and logical inference. The resulting spiking neural network models capture various hippocampal cell types (grid, place, border, etc.), behavioural errors, and a variety of observed neural dynamics. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2024-11-20. Recording duration: 00:47:23.
Logical Neural Networks
The work to be presented in this talk proposes a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly interpretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.