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Neural Networks, Manifolds, and Topology

colah.github.io Essays & writing Essays & articles AI & data Candidate
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Resurfaced independently across 5 calendar years, with breakout response in 2 of them.

submissions
6
submitters
6
observed span
2014–2025
peak thread · 29 comments
263 pts
latest 20+ return · 2019-02-11
129 pts

Submission timeline

2007–2026

One slot for every year since HN launched. Height is that year's peak points; orange marks a 100+ point or 50+ comment breakout. Select a bar to open its strongest thread.

First comments on top threads

HN comment order

This is a very interesting perspective on neural networks, is it novel? I've never seen a geometric interpretation of NNs. In particular this: > (Apparently determining if knots are trivial is NP. This doesn’t bode well for neural networks.) Is there any theoretical research on obstructions to NN learning? Not that it would change much the practice (for instance, MLE learning of gaussian mixtures is NP-hard, but everybody does it anyway), but it could shed some light on the geometry…

ot·263-point thread·

> (Apparently determining if knots are trivial is NP. This doesn’t bode well for neural networks.) Yes it doesn't, but what do I know (not much). Another annoying property of NN is knowing when they are fully baked. Edit: Yet they have clearly grown in popularity over the past year. Does that imply anything about the "determining if knots are trivial is NP" criticism? Or does it just mean they are popular for other reasons such as their appeal to…

The first top-level comment from each of the four biggest threads, in HN’s own order. Excerpts are shortened; open a comment for full context.

Breakout years
2

100+ points or 50+ comments

Total points
504

reference only — not used in Hall rules or ranking

Total comments
61

reference only — not used in Hall rules or ranking

Every submission

DateTitle as submittedByPointsComments
2014-04-09Neural Networks, Manifolds, and TopologyFirst breakout · Best threadcf26329
2014-04-11Neural Networks, Manifolds, and Topologymilliams80
2015-07-01Neural Networks, Manifolds, and Topology (2014)signa11987
2016-12-03Neural Networks, Manifolds, and Topologyespeed30
2019-02-11Neural Networks, Manifolds, and Topology (2014)Latest 20+ point returnflancian12925
2025-05-20Neural Networks, Manifolds, and Topologyskadamat30