From 39fd04bdceefcd8a39ceea4be8d8393596609a48 Mon Sep 17 00:00:00 2001 From: NewAlexandria Date: Wed, 25 Dec 2019 23:36:58 -0500 Subject: [PATCH] Math papers from original `isomorphisms` PR (#587) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Add gitter for community. * Update CODE_OF_CONDUCT.md * Add statecharts paper in a new systems modeling category (#565) * Rename "paradigm" and "plt" folders for findability (#561) * rename "language-paradigm" folder for findability lang para pluralize * rename PLT => languages-theory * fixed formatting * group pattern-* related papers (#564) * combine clustering algo into pattern matching * rename stringology with the pattern_ prefix * improved the README header info for paper related to patterns * consolidate org-sim and sw-eng dirs (#567) * consolidate org-sim and sw-eng dirs * typo and links * Fixed link (#568) * Update README.md * Fixed A Unified Theory of Garbage Collection link * Verification faults dirs (#566) * consolidate program verificaiton and program fault detection listings. * faults and validation gets header info * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * added new papers in Machine Learning dir. fixed-up references Truncation of Wavelet Matrices Understanding Deep Convolutional Networks General self-similarity: an overview cleanup url files (wrong repo format) * what has sphere packing to do with compression? • role of E8 & Leech lattice in optimal codes • mathematically best compression was never used • ikosahedron * surfaces ∑ I show this paper to college freshmen because • it’s pictorial • it’s about an object you mightn’t have considered mathematical • no calculus, crypto, ML, or pretentious notation • it’s short • it’s a classification proof: “How can it be that you know something about _all possible_ X, even the xϵX you haven’t seen yet?’ * good combinatorics Programmers are used to counting boring things. Why not count something more interesting for a change? * added comentaries from commit messages. more consistent formatting. * graphs Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem" (who cares) ). But have you ever tried to construct a simpler building-block (basis) with which graphs could be built? Or at least a different building block to build the same old things. This <10-page paper also uses 𝔰𝔩₂(ℂ), a simple mathematical object you haven’t heard of, but which is a nice lead-in to an area of real mathematics—rep theory—that (1) contains actual insights (1a) that you aren’t using (2) is simple (3) isn’t pretentious. * from dominoes to hexagons why is this super-smart guy interested in such simple drawings? * sorting You do sorting all the time. Are there smart ways to organise sub-sorts? * distributed robots!! Robots! And varying your dimensionality across a space. But also — distributed robots! * knitting Get into knitting. Learn a data structure that needs to be embedded in 3D to do its thing. Break your mind a bit. * female genius * On “On Invariants of Manifolds” 2 pages about how notation and algorithms are inferior to clarity and simplicity. * pretty robots You’ll understand calculus better after looking at these pretty 75 pages. * Farey Have another look at ye olde Int class. * renormalisation Stéphane Mallat thinks renormalisation has something to do with why deep nets work. * the torus trick, applied In Simons Foundation’s interview by Michael Hartley Freedman of Robion Kirby, Freedman mentions this paper in which MHF applied RK’s “torus trick” to compression via wavelets. * renormalisation Here is a video of a master (https://press.princeton.edu/titles/5669.html) talking about renormalisation. Which S Mallat has suggested is key to why deep learning works. * Cartan triality + Milnor fibre This is a higher-level paper, but still a survey (so more readable). It ties together disparate areas like Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra. It has pictures and you’ll get a better sense of what mathematics is like from skimming it. * Create see.machine.learning * tropical geometry Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction. * self-similarity by Tom Leinster Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity. * rename papers accordingly, and add descriptive info remove dup maths papers * fixed crappy explanations * improved the annotations for papers in the Machine Learning readme * remediated descriptive wording for papers in the mathematics section * removed local copy and added link to Conway Zip Proof * removed local copy and added link to Packing of Spheres - Sloane * removed local copy and added link to Algebraic Topo - Hatcher * removed local copy and added link to Topo of Numbers - Hatcher * removed local copy and added link to Young Tableax - Yong * removed local copy and added link to Elements of A Topo * removed local copy and added link to Truncation of Wavlet Matrices Co-authored-by: Zeeshan Lakhani <202820+zeeshanlakhani@users.noreply.github.com> Co-authored-by: Wiktor Czajkowski Co-authored-by: keddad Co-authored-by: i --- data_compression/README.md | 3 +- .../General-self-similarity--an-overview.pdf | Bin 0 -> 267286 bytes machine_learning/README.md | 57 ++++++++++++++---- ...erstanding-Deep-Convolutional-Networks.pdf | Bin 0 -> 1534375 bytes mathematics/README.md | 42 ++++++++++++- mathematics/from-dominoes-to-hexagons.pdf | Bin 0 -> 367623 bytes ...-isomorphism-and-representation-theory.pdf | Bin 0 -> 220275 bytes .../intro-to-tropical-algebraic-geometry.pdf | Bin 0 -> 247962 bytes mathematics/tilings.pdf | Bin 0 -> 781692 bytes 9 files changed, 89 insertions(+), 13 deletions(-) create mode 100644 machine_learning/General-self-similarity--an-overview.pdf create mode 100644 machine_learning/Understanding-Deep-Convolutional-Networks.pdf create mode 100644 mathematics/from-dominoes-to-hexagons.pdf create mode 100644 mathematics/graph-isomorphism-and-representation-theory.pdf create mode 100644 mathematics/intro-to-tropical-algebraic-geometry.pdf create mode 100644 mathematics/tilings.pdf diff --git a/data_compression/README.md b/data_compression/README.md index a083cf9..a3686cf 100644 --- a/data_compression/README.md +++ b/data_compression/README.md @@ -1,4 +1,5 @@ # Data Compression -* :scroll: [Data Compression](data-compression.pdf) +* :scroll: [Data Compression](https://github.com/papers-we-love/papers-we-love/blob/master/data-compression/data-compression.pdf) + > This paper surveys a variety of data compression methods spanning almost 40 years of research, from the work of Shannon, Fano and Huffman in the 40's, to a technique developed in 1986. \ No newline at end of file diff --git a/machine_learning/General-self-similarity--an-overview.pdf b/machine_learning/General-self-similarity--an-overview.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2c113326bf5d112621a945377273cc32c398b40a GIT binary patch literal 267286 zcma%iQ;;T2v~AnAZQHi(?&)dUw(b7fw(V)#wryL}I`hXp_vyaehpM$>t=w6eQM)QK zR#uTKiAm5iGqAysk6y(W!mtxD5!oAA!SL}h%9+}kyI2r${9{xYB`j@ROr3}rC2R~` zOvOx%?M+Mt1Yn$9oJj9SYsb=gXmfD5Y2L3)XnrXGF+skC+)&-DpUKd^$Rn9%m=kK1B6z!;Qn%@HcUq{is 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a/machine_learning/README.md +++ b/machine_learning/README.md @@ -2,28 +2,52 @@ ## External Papers -* [Top 10 algorithms in data mining](http://www.cs.uvm.edu/~icdm/algorithms/10Algorithms-08.pdf) - While it is difficult to identify the top 10, this paper contains 10 very important data mining/machine learning algorithms -* [A Few Useful Things to Know about Machine Learning](http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf) - Just like the title says, it contains many useful tips and gotchas for machine learning -* [Random Forests](https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf) - The initial paper on random forests -* [Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data](http://repository.upenn.edu/cgi/viewcontent.cgi?article=1162&context=cis_papers) - The paper introducing conditional random fields as a framework for building probabilistic models. -* [Support-Vector Networks](http://rd.springer.com/content/pdf/10.1007%2FBF00994018.pdf) - The initial paper on support-vector networks for classification. +* [Top 10 algorithms in data mining](http://www.cs.uvm.edu/~icdm/algorithms/10Algorithms-08.pdf) + + While it is difficult to identify the top 10, this paper contains 10 very important data mining/machine learning algorithms + +* [A Few Useful Things to Know about Machine Learning](http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf) + + Just like the title says, it contains many useful tips and gotchas for machine learning +* [Random Forests](https://www.stat.berkeley.edu/~breiman/randomforest2001.pdf) + + The initial paper on random forests +* [Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data](http://repository.upenn.edu/cgi/viewcontent.cgi?article=1162&context=cis_papers) + + The paper introducing conditional random fields as a framework for building probabilistic models. +* [Support-Vector Networks](http://rd.springer.com/content/pdf/10.1007%2FBF00994018.pdf) + + The initial paper on support-vector networks for classification. + * [The Fast Johnson-Lindenstrauss Transforms](https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf) The Johnson-Lindenstrauss transform (JLT) prescribes that there exists a matrix of size `k x d`, where `k = O(1/eps^2 log d)` such that with high probability, a matrix A drawn from this distribution preserves pairwise distances up to epsilon (e.g. `(1-eps) * ||x-y|| < ||Ax - Ay|| < (1+eps) ||x-y||`). This paper was the first paper to show that you can actually compute the JLT in less that `O(kd)` operations (e.g. you don't need to do the full matrix multiplication). They used their faster algorithm to construct one of the fastest known approximate nearest neighbor algorithms. *Ailon, Nir, and Bernard Chazelle. "The fast Johnson-Lindenstrauss transform and approximate nearest neighbors." SIAM Journal on Computing 39.1 (2009): 302-322. Available: https://www.cs.princeton.edu/~chazelle/pubs/FJLT-sicomp09.pdf* -* [Applications of Machine Learning to Location Data](http://www.berkkapicioglu.com/wp-content/uploads/2013/11/thesis_final.pdf) - Using machine learning to design and analyze novel algorithms that leverage location data. +* [Applications of Machine Learning to Location Data](http://www.berkkapicioglu.com/wp-content/uploads/2013/11/thesis_final.pdf) + + Using machine learning to design and analyze novel algorithms that leverage location data. -* ["Why Should I Trust You?" Explaining the Predictions of Any Classifier](http://www.kdd.org/kdd2016/papers/files/rfp0573-ribeiroA.pdf) - This paper introduces an explanation technique for any classifier in a interpretable manner. +* ["Why Should I Trust You?" Explaining the Predictions of Any Classifier](http://www.kdd.org/kdd2016/papers/files/rfp0573-ribeiroA.pdf) -* [Multiple Narrative Disentanglement: Unraveling *Infinite Jest*](http://dreammachin.es/p1-wallace.pdf) - uses an unsupervised approach to natural language processing to classify narrators in David Foster Wallace's 1,000-page novel. + This paper introduces an explanation technique for any classifier in a interpretable manner. -* [ImageNet Classification with Deep Convolutional Neural Networks](http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) - This paper introduces AlexNet, a neural network architecture which dramatically improved over the state-of-the-art in image classification algorithms and is widely regarded as a breakthrough moment for deep learning. +* [Multiple Narrative Disentanglement: Unraveling *Infinite Jest*](http://dreammachin.es/p1-wallace.pdf) -* [Interpretable machine learning: definitions, methods, and applications](https://arxiv.org/pdf/1901.04592.pdf) - This paper introduces the foundations of the rapidly emerging field of interpretable machine learning. + Uses an unsupervised approach to natural language processing that classifies narrators in David Foster Wallace's 1,000-page novel. -* [Distilling the Knowledge in a Neural Network](https://arxiv.org/pdf/1503.02531.pdf) - This seminal paper introduces a method to distill information from an ensemble of neural networks into a single model. +* [ImageNet Classification with Deep Convolutional Neural Networks](http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) + + This paper introduces AlexNet, a neural network architecture which dramatically improved over the state-of-the-art in image classification algorithms and is widely regarded as a breakthrough moment for deep learning. + +* [Interpretable machine learning: definitions, methods, and applications](https://arxiv.org/pdf/1901.04592.pdf) + + This paper introduces the foundations of the rapidly emerging field of interpretable machine learning. + +* [Distilling the Knowledge in a Neural Network](https://arxiv.org/pdf/1503.02531.pdf) + + This seminal paper introduces a method to distill information from an ensemble of neural networks into a single model. ## Hosted Papers @@ -39,3 +63,14 @@ *Bourgain, Jean, and Jelani Nelson. "Toward a unified theory of sparse dimensionality reduction in euclidean space." arXiv preprint arXiv:1311.2542; Accepted in an AMS Journal but unpublished at the moment (2013). Available: http://arxiv.org/abs/1311.2542* +* :scroll: **[Truncation of Wavelet Matrices: Edge Effects and the Reduction of Topological Control](https://reader.elsevier.com/reader/sd/pii/0024379594000395?token=EB0AA78D59A9648480596F018EFB72E0A02FD5FA70326B24B9D501E1A6869FE72CC4D97FA9ACC8BAB56060D6C908EC83)** by Freedman + + In this paper by Michael Hartley Freedman, he applies Robion Kirby “torus trick”, via wavelets, to the problem of compression. + +* :scroll: **[Understanding Deep Convolutional Networks](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/Understanding-Deep-Convolutional-Networks.pdf)** by Mallat + + Stéphane Mallat proposes a model by which renormalisation can identify self-similar structures in deep networks. [This video of Curt MacMullen discussing renormalization](https://www.youtube.com/watch?v=_qjPFF5Gv1I) can help with more context. + +* :scroll: **[General self-similarity: an overview](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/General-self-similarity--an-overview.pdf)** by Leinster + +Dr Leinster's paper provides a concise, straightforward, picture of self-similarity, and its role in renormalization. \ No newline at end of file diff --git a/machine_learning/Understanding-Deep-Convolutional-Networks.pdf b/machine_learning/Understanding-Deep-Convolutional-Networks.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0f4cbd8937f50017acdf9ebb0854e58d2cc630e1 GIT binary patch literal 1534375 zcma&tQ*$l~uqNO*S+Q-~Ua@W4ww*7wZ96NrZQHhO%$};bIW;%us{0pocRlqsnSzKI z9TPnpG+7)pCmSInp}mn6G!G9UgP5g_i>cFp)yB}pRK(QS-o%uULB`b1+{J>Bm5Ggo zkdF`A*~Q7!&=%Tbqgz|D@vsG{XSQ}Oq1H+S1+1-v8j?b9f=WH{K}Hq61;K~7WRyvC 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pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer +* :scroll: [The Transcendence of Pi](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/transcendence-of-pi.pdf) by Steve Mayer +* :scroll: [Tilings](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/tilings.pdf) by Ardila + The paper covers a broad swath of the topic on analysis of tiling, and related strategies. + +* :scroll: [From Dominoes to Hexagons](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/from-dominoes-to-hexagons.pdf) by Thurston + + A paper on the generalization of tilings across different base planes. + +* :scroll: [Graph Isomorphism and Representation Theory](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/graph-isomorphism-and-representation-theory.pdf) by Daniel Litt + + The *graph isomorphism problem* shows how to construct graphs using a simple building-block ("basis"). The same method applies to finding different building blocks to construct the same things. This technique can be applied to file systems, greplin, trees, virtual DOM, etc. + + A short paper, it also shows how to use `𝔰𝔩₂(ℂ)` as a simple mathematical object that leads into the area of real mathematics—represention theory. + +* :scroll: [Conway's ZIP proof](https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf) by George Francis and Jeffrey Weeks + + This paper presents a classification proof: "How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?" The well-diagramed discussion requires no calculus, crypto, ML, or dense notation, making it good for most knowledge levels. + +* :scroll: [Packing of Spheres](http://neilsloane.com/doc/Me109.pdf) by N. Sloane + Discusses the role of E8 & Leech lattices in optimal codes for mathematically-ideal compression. Ikosahedrons, a tool in this investigation, are also presented. + +* :scroll: [Some Underlying Geometric Notions](https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) by Hatcher + + High-Level survey which relates disparate topics, e.g. Platonic solids (A-D-E), Milnor’s exceptional fibre, and algebra. + +* :scroll: [What is a Young Tableaux?](https://www.ams.org/notices/200702/whatis-yong.pdf) by Alexander Yong + + Young Tableau appear in combinatoric problems, representation theory, and the calculus of Grassmannians. Another common topic is sorting, and smarter ways to organise sub-sorts. + + + +### Topology +* :scroll: [Topology of Numbers](https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf) by hatcher +* [Applied Algebraic Topology and Sensor Networks](https://www.math.upenn.edu/~ghrist/preprints/ATSN.pdf) by Robert Ghrist +* :scroll: [Intro to Tropical Algebra Geometry](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/intro-to-tropical-algebraic-geometry.pdf) + + Recently there have been some papers posted about tropical geometry of neural nets. Tropical is also said to be derived from CS. This is a good introduction. + +* :scroll: [Elements of Algebraic Topology: Sheaves](https://www.math.upenn.edu/~ghrist/EAT/EATchapter9.pdf) by Ghrist + + Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology' \ No newline at end of file diff --git a/mathematics/from-dominoes-to-hexagons.pdf b/mathematics/from-dominoes-to-hexagons.pdf new file mode 100644 index 0000000000000000000000000000000000000000..93211f16a10f2624e7e31562d768e74ad8fe7f47 GIT binary patch literal 367623 zcma&NLy$0B(4^b8ZQHhO+qUg~+qP}nwr$(CeZRReiAz}Y=wd2jYHV*}N|ZLBPt%&O*S) z2j%SIWNK&&<*|9ABiTgU;n>@!Kj3iQAAzxIpzo4o5@#d24rQrTFk}I@;*;(793MxU zC|}d?*WD*W1Bw#W6D|CRJsHOM4?VNvKs-?rv4f z28B{AgYtWVNg|`6pZAJxHS)6cK#S$q!|fl@H(R~uTQKOArq{cL4_7gCFsxCAzj)*! z3t{ZVa|d_i`j(DI_jNVpv6Gj}Jm8D>w6o;*1!}=#iuM}z^OPm+=#GJ;jVh-NCigT=DRw&tKhpQX7dN{!Pw3VQ>iAx{1;tfmAJTgemAz zl%m=9AyoV3PiW>g2g$UE-{a?l2@iSi*4NWZ;`5^ztw?Tm{lYuiE0g>-7hyq60fZi+ 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