We thank the referees for their comments

Neural Information Processing Systems 

We thank the referees for their comments. Following the suggestions of R1 and R2, we will add a conclusion to the paper and modify the broader impact statement. This will clarify our contribution, its practical impact, but also the results described in Section 5. We will, of course, Our "trap-avoidance" result suggests that, at high precision, artificial critical points are not met in practice. On the other hand, at low precision, "genericity results" may partly collapse. Y et the theory says uniqueness is generic.

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