Junyu Ren

PhD @UChicago. From the geometry of neural representations to reliable, multi-agent AI reasoning.

[Junyu Ren @junyu_r]

In 2014, Chris Olah's 'Neural Networks, Manifolds, and Topology' drew a disk inside a ring narrow nets can't separate: layers stretch and squash but never fold. We theorize and generalize this observation, noting skip connections learn the fold. #ICML2026 https://t.co/V7cGJFWgja

[Junyu Ren @junyu_r]

@babyadoresyou This is actually from the same group led Lek-Heng Lim! In that earlier paper homological classes were empirically observed to be destroyed across layers in classification task. Now we have a tentative explanation: they were destroyed to unlink the links.

[Junyu Ren @junyu_r]

In 2014, Chris Olah's 'Neural Networks, Manifolds, and Topology' drew a disk inside a ring narrow nets can't separate: layers stretch and squash but never fold. We theorize and generalize this observation, noting skip connections learn the fold. #ICML2026 https://t.co/V7cGJFWgja

[Junyu Ren @junyu_r]

Takeaway: the linking and knotting of manifolds matter as much as their intrinsic shape does, and networks' ability to manipulate them is a lens to compare architectures. Paper & code: https://t.co/V7cGJFWgja. · w/ Lek-Heng Lim. At ICML, Hall A poster session 1 #4609.

[Junyu Ren @junyu_r]

Then we ran it. On thickened Hopf links (30 seeds), ReLU nets cap near 93% while GELU nets and ResNets hit 100%, and a ResNet recovers the |x| fold. On 3D PCA of CIFAR-10, we detect links and use them to predict class-pair confusion (Spearman |r| = 0.48).