What are some of your favorite simplices?
March 1, 2026 at 3:34 AM
What are some of your favorite simplices?
If you liked my breakfast simplices, you also might enjoy this set of simplices, which would now allow you to locality sensitive hash your breakfasts. moultano.wordpress.com/2018/11/08/m...
February 27, 2026 at 9:42 PM
If you liked my breakfast simplices, you also might enjoy this set of simplices, which would now allow you to locality sensitive hash your breakfasts. moultano.wordpress.com/2018/11/08/m...
But not Jean Leray who invented sheaves to avoid thinking about those god damn simplices
June 16, 2026 at 7:59 PM
But not Jean Leray who invented sheaves to avoid thinking about those god damn simplices
trying to figure out how to find out which parts of a neural network are geometric simplices and which are doing something more complicated. something like "compare the Frobenius norm of attention layers to, e.g., feed-forward layers?"
May 16, 2025 at 9:51 PM
trying to figure out how to find out which parts of a neural network are geometric simplices and which are doing something more complicated. something like "compare the Frobenius norm of attention layers to, e.g., feed-forward layers?"
considering that pretrained models naturally create weight-space simplices, doesn't this imply that there should be natural harmonics where the rank of a low-rank adapter significantly improves the quality of the adaptation?
September 28, 2025 at 4:31 AM
considering that pretrained models naturally create weight-space simplices, doesn't this imply that there should be natural harmonics where the rank of a low-rank adapter significantly improves the quality of the adaptation?
Pluralizations:
matrix → matrices ✅
vertex → vertices ✅
index → indices ✅
appendix → appendices ✅
helix → helices ✅
simplex → simplices ✅
complex → complices ❌
Why does complex get the Kleenex treatment while everything else is so nice and Latinate?
matrix → matrices ✅
vertex → vertices ✅
index → indices ✅
appendix → appendices ✅
helix → helices ✅
simplex → simplices ✅
complex → complices ❌
Why does complex get the Kleenex treatment while everything else is so nice and Latinate?
April 9, 2026 at 3:01 PM
Pluralizations:
matrix → matrices ✅
vertex → vertices ✅
index → indices ✅
appendix → appendices ✅
helix → helices ✅
simplex → simplices ✅
complex → complices ❌
Why does complex get the Kleenex treatment while everything else is so nice and Latinate?
matrix → matrices ✅
vertex → vertices ✅
index → indices ✅
appendix → appendices ✅
helix → helices ✅
simplex → simplices ✅
complex → complices ❌
Why does complex get the Kleenex treatment while everything else is so nice and Latinate?
the reason quantization does not work perfectly is that there is always some leakage from neurons which are near-simplices, and that leakage requires high precision, and that the signal processing necessary to feed further simplices actually does use the full 32 bits.
May 16, 2025 at 10:42 PM
the reason quantization does not work perfectly is that there is always some leakage from neurons which are near-simplices, and that leakage requires high precision, and that the signal processing necessary to feed further simplices actually does use the full 32 bits.
like, the formation of these simplices implies that there are natural basis directions in the weight matrices and that you could do singular value decomposition on the gradient updates to find the natural rank.
considering that pretrained models naturally create weight-space simplices, doesn't this imply that there should be natural harmonics where the rank of a low-rank adapter significantly improves the quality of the adaptation?
September 28, 2025 at 4:38 AM
like, the formation of these simplices implies that there are natural basis directions in the weight matrices and that you could do singular value decomposition on the gradient updates to find the natural rank.
naively, i would expect to see a lot of simplices in the attention blocks -- they are fundamentally implementing discrete operations -- which are first projected into a high-dimensional space and then compacted by the feedforward blocks.
May 16, 2025 at 9:57 PM
naively, i would expect to see a lot of simplices in the attention blocks -- they are fundamentally implementing discrete operations -- which are first projected into a high-dimensional space and then compacted by the feedforward blocks.
St Francis today, From his letter to all the faithful.
Non debémus secúndum carnem esse sapiéntes atque prudéntes, sed magis debémus esse símplices, húmiles et puri.*
We must not be wise and prudent according to the flesh. Rather we must be simple, humble and pure.
Non debémus secúndum carnem esse sapiéntes atque prudéntes, sed magis debémus esse símplices, húmiles et puri.*
We must not be wise and prudent according to the flesh. Rather we must be simple, humble and pure.
October 4, 2025 at 11:25 AM
St Francis today, From his letter to all the faithful.
Non debémus secúndum carnem esse sapiéntes atque prudéntes, sed magis debémus esse símplices, húmiles et puri.*
We must not be wise and prudent according to the flesh. Rather we must be simple, humble and pure.
Non debémus secúndum carnem esse sapiéntes atque prudéntes, sed magis debémus esse símplices, húmiles et puri.*
We must not be wise and prudent according to the flesh. Rather we must be simple, humble and pure.
Claims of novel abrupt transitions with hypergraphs (e.g. synchronization, contagion, cooperation, etc) rest on mean-field approximations that discard hypergraph structure entirely and are exactly reproduced by *tree-like* graphs, making cliques, let alone hyperedges or simplices, superfluous. 9/N
February 20, 2026 at 8:04 AM
Claims of novel abrupt transitions with hypergraphs (e.g. synchronization, contagion, cooperation, etc) rest on mean-field approximations that discard hypergraph structure entirely and are exactly reproduced by *tree-like* graphs, making cliques, let alone hyperedges or simplices, superfluous. 9/N
This makes me wonder if people have done space filling curves on triangles (or simplices in general!)
November 15, 2025 at 4:21 PM
This makes me wonder if people have done space filling curves on triangles (or simplices in general!)
@vikramsaraph.com simplices mentioned
February 28, 2026 at 12:11 AM
@vikramsaraph.com simplices mentioned
I recently discussed in my class, how many standard simplices fit, volume-wise, inside a standard cube: bsky.app/profile/chri...
This resulted in me buying a 3d printer for visualization.
#MathSky #iTeachMath
This resulted in me buying a 3d printer for visualization.
#MathSky #iTeachMath
December 12, 2023 at 5:05 PM
I recently discussed in my class, how many standard simplices fit, volume-wise, inside a standard cube: bsky.app/profile/chri...
This resulted in me buying a 3d printer for visualization.
#MathSky #iTeachMath
This resulted in me buying a 3d printer for visualization.
#MathSky #iTeachMath
🎥 Shapes, Spaces, Simplices, and Structure: Geometry, Topology & Machine Learning
"What if the answer to some problems in graph learning is not more, but better structure?"
This is the central premise of my talk @logml.bsky.social and @unireps.bsky.social.
🧵1/5
"What if the answer to some problems in graph learning is not more, but better structure?"
This is the central premise of my talk @logml.bsky.social and @unireps.bsky.social.
🧵1/5
August 7, 2025 at 3:56 PM
🎥 Shapes, Spaces, Simplices, and Structure: Geometry, Topology & Machine Learning
"What if the answer to some problems in graph learning is not more, but better structure?"
This is the central premise of my talk @logml.bsky.social and @unireps.bsky.social.
🧵1/5
"What if the answer to some problems in graph learning is not more, but better structure?"
This is the central premise of my talk @logml.bsky.social and @unireps.bsky.social.
🧵1/5
so the thing is that, re: LLMs, attention is closer to being an abstract Turing machine than an actual physical computer, and -- in high dimensions -- the fact that everything is almost orthogonal means that, geometrically, most neurons are simplices implementing very simple decisions.
August 14, 2025 at 1:04 AM
so the thing is that, re: LLMs, attention is closer to being an abstract Turing machine than an actual physical computer, and -- in high dimensions -- the fact that everything is almost orthogonal means that, geometrically, most neurons are simplices implementing very simple decisions.
The grand antiprism is neat because it’s not whytoffian.
But I like fully truncated (that is, truncated to the midpoint) simplices (I guess Wikipedia calls them “rectified”). Their connection groups are especially nice.
en.wikipedia.org/wiki/Rectifi...
en.wikipedia.org/wiki/Uniform...
But I like fully truncated (that is, truncated to the midpoint) simplices (I guess Wikipedia calls them “rectified”). Their connection groups are especially nice.
en.wikipedia.org/wiki/Rectifi...
en.wikipedia.org/wiki/Uniform...
Uniform 4-polytope - Wikipedia
en.wikipedia.org
May 27, 2026 at 1:16 AM
The grand antiprism is neat because it’s not whytoffian.
But I like fully truncated (that is, truncated to the midpoint) simplices (I guess Wikipedia calls them “rectified”). Their connection groups are especially nice.
en.wikipedia.org/wiki/Rectifi...
en.wikipedia.org/wiki/Uniform...
But I like fully truncated (that is, truncated to the midpoint) simplices (I guess Wikipedia calls them “rectified”). Their connection groups are especially nice.
en.wikipedia.org/wiki/Rectifi...
en.wikipedia.org/wiki/Uniform...
So it was stressful at first but I’m finding myself enjoying drawing simplices
March 15, 2024 at 2:14 AM
So it was stressful at first but I’m finding myself enjoying drawing simplices
Felix Christian Clemen, Dingyuan Liu: On the number of regular simplices in odd dimensions https://arxiv.org/abs/2609.26801 https://arxiv.org/pdf/2609.26801 https://arxiv.org/html/2609.26801
September 24, 2026 at 6:46 AM
Felix Christian Clemen, Dingyuan Liu: On the number of regular simplices in odd dimensions https://arxiv.org/abs/2609.26801 https://arxiv.org/pdf/2609.26801 https://arxiv.org/html/2609.26801
Do the 5-simplices consist of 45-tuples? (⚠️ Guess derived by pure numerology.)
March 4, 2024 at 4:18 PM
Do the 5-simplices consist of 45-tuples? (⚠️ Guess derived by pure numerology.)
More barycentric subdivisions of the 3-simplex. Feel like I might redraw them tomorrow because these are a little messy
March 15, 2024 at 3:40 AM
More barycentric subdivisions of the 3-simplex. Feel like I might redraw them tomorrow because these are a little messy