16 The results show that the difference in cosine similarity persists from the start up until around 750 ideas when the difference becomes negligible. It is strongest between 100 - 500 ideas. After around 750-800 ideas the significant advantage of CoT can no longer be observed as the strategy starts to deplete the pool of ideas it can generate from. In other words, there are fewer and fewer fish in the pond and the strategy does not matter anymore. This is illustrated in Figure 3. On the x-axis, the Figure displays how many ideas already have been generated. On the y-axis, we show the cosine similarity of a new idea in comparison to the existing ones. Figure 3 suggests diminishing returns, i.e., we are removing more and more “fish” from the pond. The higher initial similarity might be caused by lower entropy at the start which increases after a number of ideas have been generated. To account for minor differences in overall idea count, the graph below only shows the first 1000 per strategy. The graph is smoothed by using exponential smoothing with an alpha of 0.5. Figure 3: Cosine similarity between base prompt and Chain of Thought over 1000 ideas