The clipping bug has lived in every 3D simulation pipeline for three decades. Here is exactly why it happens, how the math breaks, and how swapping one equation fixes it; as well as the python code to see it for yourself!
Summary generated by The Flow from the publisher's feed. The full article lives at Towards Data Science.
arXiv:2506. 21306v2 Announce Type: replace-cross Abstract: Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains.
arXiv:2605. 02701v2 Announce Type: replace-cross Abstract: We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically.
The full conjecture is stated over abstract fields, but the counterexample is a concrete 3D function that we can explain and visualize using familiar geometric ideas and a little algebra. The post A Simplified View of the Jacobian Conjecture appeared first on Towards Data Science .
arXiv:2607. 28733v1 Announce Type: cross Abstract: This proceedings contribution elaborates on the findings of arXiv:2605.
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.