A new disproof shows local goodness does not imply a good global inverse
_arohan_ · x · 2026-07-21
A local inverse can look good and still fail globally
The post points out a math lesson relevant to neural network training: being locally good is not enough to guarantee a good global inverse.
- The author says mathematicians had not disproved the claim until now.
- They connect this to the spirit of the Jacobian conjecture and to neural network optimization.
- The suggested intuition is to initialize a network so it preserves distances and keeps the residual stream globally unfolded.
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