39fd04bdce
* 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 <wiktor.czajkowski@gmail.com> Co-authored-by: keddad <keddad@yandex.ru> Co-authored-by: i <isomorphisms@sdf.org> |
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Understanding-Deep-Convolutional-Networks.pdf |
Machine Learning
External Papers
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Top 10 algorithms in data mining
While it is difficult to identify the top 10, this paper contains 10 very important data mining/machine learning algorithms
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A Few Useful Things to Know about Machine Learning
Just like the title says, it contains many useful tips and gotchas for machine learning
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The initial paper on random forests
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Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data
The paper introducing conditional random fields as a framework for building probabilistic models.
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The initial paper on support-vector networks for classification.
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The Fast Johnson-Lindenstrauss Transforms
The Johnson-Lindenstrauss transform (JLT) prescribes that there exists a matrix of size
k x d
, wherek = 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 thatO(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
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Applications of Machine Learning to Location Data
Using machine learning to design and analyze novel algorithms that leverage location data.
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"Why Should I Trust You?" Explaining the Predictions of Any Classifier
This paper introduces an explanation technique for any classifier in a interpretable manner.
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Multiple Narrative Disentanglement: Unraveling Infinite Jest
Uses an unsupervised approach to natural language processing that classifies narrators in David Foster Wallace's 1,000-page novel.
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ImageNet Classification with Deep Convolutional Neural Networks
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.
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Interpretable machine learning: definitions, methods, and applications
This paper introduces the foundations of the rapidly emerging field of interpretable machine learning.
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Distilling the Knowledge in a Neural Network
This seminal paper introduces a method to distill information from an ensemble of neural networks into a single model.
Hosted Papers
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📜 A Sparse Johnson-Lindenstrauss Transform
The JLT is still computationally expensive for a lot of applications and one goal would be to minimize the overall operations needed to do the aforementioned matrix multiplication. This paper showed that a goal of a
O(k log d)
algorithm (e.g.(log(d))^2)
may be attainable by showing that very sparse, structured random matrices could provide the JL guarantee on pairwise distances.Dasgupta, Anirban, Ravi Kumar, and Tamás Sarlós. "A sparse johnson: Lindenstrauss transform." Proceedings of the forty-second ACM symposium on Theory of computing. ACM, 2010. Available: arXiv/cs/1004:4240
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📜 Towards a unified theory of sparse dimensionality reduction in Euclidean space
This paper attempts to layout the generic mathematical framework (in terms of convex analysis and functional analysis) for sparse dimensionality reduction. The first author is a Fields Medalist who is interested in taking techniques for Banach Spaces and applying them to this problem. This paper is a very technical paper that attempts to answer the question, "when does a sparse embedding exist deterministically?" (e.g. doesn't require drawing random matrices).
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
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📜 Truncation of Wavelet Matrices: Edge Effects and the Reduction of Topological Control by Freedman
In this paper by Michael Hartley Freedman, he applies Robion Kirby “torus trick”, via wavelets, to the problem of compression.
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📜 Understanding Deep Convolutional Networks 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 can help with more context.
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📜 General self-similarity: an overview by Leinster
Dr Leinster's paper provides a concise, straightforward, picture of self-similarity, and its role in renormalization.