Source Invariance and Probabilistic Transfer: A Testable Theory of Probabilistic Neural Representations

As animals interact with their environments, they must infer properties of their surroundings. Some animals, including humans, can represent uncertainty about those properties. But when, if ever, do they use probability distributions to represent their uncertainty? It depends on which definition we choose. In this paper, we argue that existing definitions are inadequate because they are untestable. We then propose our own definition. There are two reasons why existing definitions are untestable. First, they do not distinguish between representations of uncertainty and representations of variables merely related to uncertainty ('representational indeterminacy'). Second, they do not distinguish between probabilistic representations of uncertainty and merely "heuristic" representations of uncertainty. We call this 'model indeterminacy' because the underlying problem is that we do not have access to the animal's generative model. We define probabilistic representations by two properties: 1) they encode uncertainty regardless of the source of the uncertainty ('source invariance'), 2) they support the efficient learning of new tasks that would be more difficult to learn given non-probabilistic representations ('probabilistic task transfer'). Source invariance indicates that they are representations of uncertainty rather than variables merely related to uncertainty, thereby solving representational indeterminacy. Probabilistic task transfer indicates that they are probabilistic representations of uncertainty rather than merely heuristic representations, thereby solving model indeterminacy.