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/README.md b/machine_learning/README.md index 7892bb7..0cf3550 100644 --- a/machine_learning/README.md +++ b/machine_learning/README.md @@ -24,10 +24,6 @@ *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* -* [Renormalization](https://www.youtube.com/watch?v=_qjPFF5Gv1I) by Curt MacMullen - - 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. - * [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. @@ -38,7 +34,7 @@ * [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. + Uses an unsupervised approach to natural language processing that classifies narrators in David Foster Wallace's 1,000-page novel. * [ImageNet Classification with Deep Convolutional Neural Networks](http://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) @@ -67,13 +63,13 @@ *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 arXiv preprint arXiv:1311.2542; Accepted in an AMS Journal but unpublished at the moment (2013).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://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/Truncation-of-Wavelet-Matrices--Edge-Effects-and-Reduction-of-Topological-Control.pdf)** by Freedman + + In this paper by Michael Hartley Freedman, he applies Robion Kirby “torus trick”, via wavelets, to the problem of compression. - 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. +* :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 -* :scroll: **[Understanding Deep Convolutional Networks](https://github.com/papers-we-love/papers-we-love/blob/master/machine_learning/Understanding-Deep-Convolutional-Networks.pdf)** by Mallet - - Stéphane Mallat thinks renormalisation has something to do with why deep nets work. + 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 - Again on the topic of renormalisation. Dr Leinster has a nice, simple picture of self-similarity \ No newline at end of file +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/mathematics/README.md b/mathematics/README.md index a2c11ef..725b41a 100644 --- a/mathematics/README.md +++ b/mathematics/README.md @@ -1,21 +1,21 @@ ## Mathematics -* [:scroll:](transcendence-of-pi.pdf) [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 +* :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 This paper takes programmers out of the domain of what they are familair with counting, and into new terrain. The paper covers a broad swath of the topic of 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 +* :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 +* :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 Programmers work with graphs often (file system, greplin, trees, "graph isomorphism problem"). 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)` that will be seen to be a simple mathematical object, which leads into an area of real mathematics—rep theory. -* [:scroll:] [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/conways-zip-proof.pdf) by George Francis and Jeffrey Weeks +* :scroll: [Conway's ZIP proof](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/conways-zip-proof.pdf) by George Francis and Jeffrey Weeks This paper is good for most knowledge levels because * it is pictorial @@ -24,16 +24,16 @@ * it is short * it is a classification proof: “How can it be that you know something about _all possible_ `X`, even the `xϵX` you haven’t seen yet?” -* [:scroll:] [packing of spheres](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/packing-of-spheres.pdf) by N. Sloane +* :scroll: [packing of spheres](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/packing-of-spheres.pdf) by N. Sloane * The role of E8 & Leech lattice in optimal codes * An understanding of how mathematically-best compression was never used * Ikosahedrons -* [:scroll:] [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf) +* :scroll: [some underlying geometric notions](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/some-underlying-geometric-notions.pdf) 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. -* [:scroll:] [what is a young tableaux?](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/what-is-a-young-tableau.pdf) by Alexander Yong +* :scroll: [what is a young tableaux?](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/what-is-a-young-tableau.pdf) by Alexander Yong Young Tableau appear in many areas of mathematics. Beyond combinatoric problems, we also see them in representation theory, and the calculus of Grassmannians. @@ -42,12 +42,12 @@ ### Topology -* [:scroll:] [Topology of Numbers](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/topology-of-numbers--hatcher.pdf) by hatcher +* :scroll: [Topology of Numbers](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/topology-of-numbers--hatcher.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) +* :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://github.com/papers-we-love/papers-we-love/blob/master/mathematics/elements-of-algebraic-topology-ch9-sheaves.pdf) +* :scroll: [Elements of Algebraic Topology: Sheaves](https://github.com/papers-we-love/papers-we-love/blob/master/mathematics/elements-of-algebraic-topology-ch9-sheaves.pdf) Seminal writing on topological structures, from one most lauded books 'Elements of Algebraic Topology' \ No newline at end of file