\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \newcommand{\groupMul}[1] { \cdot_{\small{#1}}} \newcommand{\groupAdd}[1] { +_{\small{#1}}} \newcommand{\inv}[1] {#1^{-1} } \newcommand{\bm}[1] { \boldsymbol{#1} } \require{physics} \require{ams} \require{mathtools} \) Math and science::Theory of Computation Examples of decidable and undecidable languages Consider the decidability and recognizability of some specific languages. All the below languages represent answers to certain questions. If one of the languages is decidable, then the corresponding question can be answered definitively in finite time by a Turing machine. Read more...

Math and science::Theory of Computation Language and Turing machine visualization Can you remember a visualisation that connects languages and Turing machines? It also includes the language representing the question of whether an arbitrary Turing machine accepts some input.

Math and science::Theory of Computation Language and Turing machine visualization Can you remember a visualisation that connects languages and Turing machines? It also includes the language representing the question of whether an arbitrary Turing machine accepts some input.

\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \newcommand{\groupMul}[1] { \cdot_{\small{#1}}} \newcommand{\groupAdd}[1] { +_{\small{#1}}} \newcommand{\inv}[1] {#1^{-1} } \newcommand{\bm}[1] { \boldsymbol{#1} } \require{physics} \require{ams} \require{mathtools} \) Math and science::Theory of Computation Number theory is undecidable  Mathematical model An alphabet \( \land, \lor, \lnot, (,), \forall, \exists, x_1, x_2, ..., R_1, ... R_k \) has a model which is a tuple \( (U, P_1, . Read more...

\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \newcommand{\groupMul}[1] { \cdot_{\small{#1}}} \newcommand{\groupAdd}[1] { +_{\small{#1}}} \newcommand{\inv}[1] {#1^{-1} } \newcommand{\bm}[1] { \boldsymbol{#1} } \require{physics} \require{ams} \require{mathtools} \) Math and science::Theory of Computation Number theory is undecidable  Mathematical model An alphabet \( \land, \lor, \lnot, (,), \forall, \exists, x_1, x_2, ..., R_1, ... R_k \) has a model which is a tuple \( (U, P_1, . Read more...

A lot of machine learning techniques can be viewed as an attempt to represent high-dimensional data in fewer dimensions without losing any important information. In a sense, it is lossy compression—compressing the data to be small and amenable before being passed to some next stage of data processing. If our data consists of elements of \( \mathbb{R}^D \), we are trying to find interesting functions of the form: \[ f : \mathbb{R}^D \to \mathbb{R}^d \] where \( D \) is fixed, but \( d \) can be chosen freely. Read more...

Color dot dataset.

Machine learning Neural network playground Interact with a small neural network for classification or regression. Kernel methods and SVM Andrew Ng's class notes on kernel methods and support vector machines. Computer vision groups list This page has an outdated (2005) but extensive list of computer vision related labs. Tom Leinster's book on entropy A non-standard approach to entropy that motivates the topic from deeper concepts compared to other treatments. What are the desired properties that led entropy to be used? Read more...

Looking for ImageNet classes that differ only in color.

スーパーに買い物に行ったとき、お菓子ばかりをカゴに入れたけれど、 店員さんにお菓子ばかり買うところを見られたくないので、家にもうあるけど、 この安い納豆も買った。