\[\hat{s}= \sum_{k \in \mathcal{D}} k\,p(k).\]This produces a smooth score such as (5.4), rather than forcing the model to commit to a single sampled integer. In practice, this is substantially more stable than naive score sampling and better reflects the model’s uncertainty. It also handles cases where the judge distribution is broad or multimodal. For example, two candidates may both have mean score (5.4), while one has most of its mass tightly concentrated around (5) and (6), and the other splits mass between much lower and much higher ratings. The mean alone is the same, but the underlying judgement is very different.
\n“Exteroception is basically how we perceive the outside,” Thaiss said. “We have a lot of detailed knowledge about how this works. But we know much less about how the brain senses what is going on inside the body. We don’t know how many internal senses there are, or even all of what they are sensing. It’s clear that our exteroception capabilities decline with age — we grow to need eyeglasses and hearing aids, for example. And this study shows that aging also affects interoception.”
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