What concept did generative models, dominant in the 2000s, allow the system to explicitly represent using a distribution over states?

Answer

Its own uncertainty.

Generative models marked a shift toward probabilistic reasoning to address the inherent uncertainty in dialogue. Specifically, generative POMDP-based trackers utilized Bayes' rule to calculate $b(s_t)$, which is a distribution over all potential dialog states given the preceding state distribution and the current observation ($ ilde{u}_t$). This mathematical framework represented a significant intellectual advancement because it allowed the system to explicitly maintain and reason about its level of certainty regarding the true state of the conversation. Instead of committing to a single, potentially flawed hypothesized state, the system carried a probabilistic belief distribution.

What concept did generative models, dominant in the 2000s, allow the system to explicitly represent using a distribution over states?
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