I do not think that it is “linear” progression. ANN by definition is nonlinear. Neither I think anything is “mathematically proven”. If I am wrong, please provide a link.
Thank you. This paper though does not state that there are no emergent abilities. It only states that one can introduce a metric with respect to which the emergent ability behaves smoothly and not threshold-like. While interesting, it only suggests that things like intelligence are smooth functions, but so what? Some other metrics show exponential or threshold dependence and whether the metric is right depends only how one will use it. And there is no law that emerging properties have to be threshold like. Quite the opposite - nearly all examples in physics that I know, the emergence appears gradually.
I do not think that it is “linear” progression. ANN by definition is nonlinear. Neither I think anything is “mathematically proven”. If I am wrong, please provide a link.
Sure thing: here’s a white paper explicitly proving:
https://arxiv.org/abs/2304.15004
Thank you. This paper though does not state that there are no emergent abilities. It only states that one can introduce a metric with respect to which the emergent ability behaves smoothly and not threshold-like. While interesting, it only suggests that things like intelligence are smooth functions, but so what? Some other metrics show exponential or threshold dependence and whether the metric is right depends only how one will use it. And there is no law that emerging properties have to be threshold like. Quite the opposite - nearly all examples in physics that I know, the emergence appears gradually.