In most Variational Autoencoder architectures I have seen the following forward path: x = torch.nn.Linear(in_features,hidden_features)(input) x = nn.ReLU()(x) x_mean = torch.nn.Linear(hidden_features,code_features)(x) x_logvar = torch.nn.Linear(hidden_features,code_features)(x)  where in the last part we get log variance. So my question is: Why do we get log variance from the encoder? My understanding is, that we might get negative numbers after torch.nn.Linear(hidden_features,code_features)(x) and for numerical stability we need positive numbers. Am I correct? If you have more complete answer, you are welcome to add/correct me.
In theory the encoder in VAE (assuming that variational family is Gaussian) generates the $\mu$ and $\sigma$ (or $\sigma^2$). But, in practice, I have seen people assuming the output is $\log\sigma^2$. Why this is necessary or useful?
Is it possible to browse the internet from a laptop so that the web sites you visit think you are browsing from a mobile device?  Say I need to connect via a very low bandwidth connection and just using the mobile version of the site is sufficient?  Currently I'm using Vista and Firefox 3.5 I'm looking for a phrase that describes trying to fix problems caused by underlying issues, with the result of compounding the issue. I usually call this "targeting surface problems rather than root problems", but my terminology is verbose.  Example 1: A government bans buying and selling bananas in the state. Later, it passes a clause allowing citizens to purchase imported bananas.  Example 2: A divided highway is erected with two lanes going in each direction but, since it gets lots of traffic, the shoulders are widened into new lanes. This leaves no shoulder room.  What would be a more concise phrase? Why not use tables for layout in HTML? It seems to be the  that tables should not be used for layout in HTML.   Why?  I have never (or rarely to be honest) seen good arguments for this. The usual answers are:   It's good to But this is a fallacious argument; . I guess it's true that using the table element for layout has little to do with tabular data. So what? Does my boss care? Do my users care?Perhaps me or my fellow developers who have to maintain a web page care... Is a table less maintainable? I think using a table is  than using divs and CSS.By the way... why is using a div or a span good separation of content from layout and a table not? Getting a good layout with only divs often requires a lot of nested divs. Readability of the codeI think it's the other way around. Most people understand HTML, few understand CSS. It's better for SEO not to use tablesWhy? Can anybody show some evidence that it is? Or a statement from Google that tables are discouraged from an SEO perspective? Tables are slower.An extra tbody element has to be inserted. This is peanuts for modern web browsers. Show me some benchmarks where the use of a table significantly slows down a page. A layout overhaul is easier without tables, see .Most web sites that need an upgrade need new content (HTML) as well. Scenarios where a new version of a web site only needs a new CSS file are not very likely. Zen Garden is a nice web site, but a bit theoretical. Not to mention its  of CSS.   I am really interested in good arguments to use divs + CSS instead of tables. Prove that there is no continuous functions $f:[0,1]\to R$, such that   $$ f(x)+f(x^2)=x. $$   My try. Assume that there is a continuous function with this property. Thus, for any $n\ge 1$ and all $x\in [0,1]$, \begin{align*} f(x)&amp;=x-f(x^2)=x-\big(x^2-f(x^4)\big)=x-x^2+\big(x^4-f(x^8)\big)=\cdots\\ &amp;=x-x^2+x^4-\cdots+(-1)^n\left(x^{2^n}-f\big(x^{2^{n+1}}\big)\right) \end{align*}  since $f(0)=0$ and $\displaystyle\lim_{n\to \infty}x^{2^{n+1}}=0$ for any $x\in(0,1)$,it follows by the continuity of $f$ that $\displaystyle\lim_{n\to \infty}f\big(x^{2^{n+1}}\big)=0$, hence $$f(x)=x-x^2+x^4-x^8+\cdots+(-1)^nx^{2^n}+\cdots$$ for any $x\in (0,1)$  Why do I have prove that there is exists such a continuous functions $f$? Maybe  my example is wrong? Why?  if my   method is wrong,then How prove this problem ? Thank you. Here is the proof I tried to weave while trying to prove this theorem:     Theorem. Every infinite subset of a countable set is countable.      Proof. Let $A$ be a countable set and $E\subset A$ be infinite. Then $A\thicksim\mathbb{N}$. This implies that there is a sequence $\left\{x_{n}\right\}_{n\in\mathbb{N}}$ where $x_{n}\in A$. Construct a sequence $\left\{n_{k}\right\}_{k\in\mathbb{N}}$ where $x_{n_{k}}\in A$, $n_{1}$ is the smallest positive integer such that $x_{n_{1}}\in A$, and $n_{k+1}&gt;n_{k}$. Then      $$ E=\bigcup_{k=1}^{\infty}x_{n_{k}}, $$      and $E$ is countable, because $E\thicksim\mathbb{N}$. $\blacksquare$   Is it convincing? Difference between UART and RS-232? Most of the time  and UART come together in serial communication theories. Are they both the same? From my readings I concluded UART is a hardware form of the RS-232 protocol. Am I correct? How do I check if a file exists in Java? How are the age restrictions followed by ICC for under 19 cricket tournaments? I have some doubts under this topic,   Can a player aged 19 play under 19 international cricket match? (Since 19 is not under 19) Consider a player having birthday during the series/tournament. How the age will be calculated for him? Prove $f(S \cup T) = f(S) \cup f(T)$ I would like to search my table having a column of first names and a column of last names.  I currently accept a search term from a field and compare it against both columns, one at a time with       select * from table where first_name like '%$search_term%' or      last_name like '%$search_term%';   This works fine with single word search terms but the result set includes everyone with the name "Larry". But if someone enters a first name then a space, then a last name, I want a narrower search result. I've tried the following without success.         select * from table where first_name like '%$search_term%' or last_name      like '%$search_term%' or concat_ws(' ',first_name,last_name)      like '%$search_term%';   Any advice?  EDIT:  The name I'm testing with is "Larry Smith".  The db stores "Larry" in the "first_name" column, and "Smith" in the "last_name" column.  The data is clean, no extra spaces and the search term is trimmed left and right.  EDIT 2:  I tried Robert Gamble's answer out this morning.  His is very similar to what I was running last night.  I can't explain it, but this morning it works.  The only difference I can think of is that last night I ran the concat function as the third "or" segment of my search query (after looking through first_name and last_name). This morning I ran it as the last segment after looking through the above as well as addresses and business names.    Does running a mysql function at the end of a query work better than in the middle? How many integers between $1$ and $10^4$ contain exactly one $8$ and one $9$? I have this problem: How many integers between $1$ and $10^4$ contain exactly one $8$ and one $9$?, but i dont know if $18, 19, 28, 29...$ serve, else it could be $8$ y $9 = 2$ numbers, help please. Should flawed questions be closed immediately? Possible Duplicate:          Given a question that is not clear at first, which satisfies the criterion for being "not a real question":      "It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot   be reasonably answered in its current form."   should that question be closed immediately, or should the OP get a chance to improve the quality of his question.  My modus operandi is this: When I encounter a question which is "not a real question", I respond via a comment - I might ask one or more counter-questions (about the issue), I might comment that I don't understand the question. So, I let the OP know that his question should be improved. I then give the OP say 15 minutes to respond (and in most cases the OP does respond). However, if the OP doesn't respond, then I consider voting for "not a real question".  Is this how SO should work?   I have witnessed in the past several questions for which I saw potential, being closed immediately, and I wonder if that is appropriate.   Edit: Of course, questions that are duplicates should be closed immediately, and off-topic questions should also be moved / closed immediately. In this question I am specifically referring to those questions which "have potential" (which could be corrected / improved).. facl ignoring the "x" permission but only on files When I use setfacl to manage on what permissions should the children files / directories have, for some reason the files have all the permissions except the execute ("x") one.  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ getfacl . # file: . # owner: someuser # group: webs # flags: -s- user::rwx group::rwx other::rwx default:user::rwx default:group::rwx default:other::rwx  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ touch file someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ mkdir dir someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ ls -l total 4 drwxrwsrwx+ 2 someuser webs 4096 paź 31 13:35 dir -rw-rw-rw-  1 someuser webs    0 paź 31 13:35 file   I thought it has something to do with umask but changing it in various ways never gives the expected result unless I'm missing something.  How can this be fixed? How does the Mac choose which connection to use when both Wifi and Ethernet are connected? When I'm connected to two networks with separate routers using Wifi and Ethernet, how does my Mac know what connection to use when I visit a website? What is the lowest level of mathematics required in order to understand how encryption algorithms work? After upgrading to 12.10 quantal, the packaged version of fglrx no longer works. I discovered that this is because there is a separate 'legacy' fglrx driver for the HD 2k-4k series cards, but it is incompatible with the xorg server on 12.10.  This is the most current version of the driver for HD 2000 through HD 4000 series cards. You can't use the non-legacy fglrx driver, but you can use the open-source radeon driver if you prefer your WM compositing to be laggy and your YouTube videos to play like they would on a Pentium MMX series:    Usually this driver can be installed in the following way, necessary because apt-get install fglrx would pull in the non-legacy driver:  wget http://www2.ati.com/drivers/legacy/amd-driver-installer-12.6-legacy-x86.x86_64.zip unzip amd-driver-installer-* sudo sh ./amd-driver-installer-*.run --buildpkg Ubuntu/quantal sudo dpkg -i fglrx*.deb sudo aticonfig --initial -f   If you use a different version of fglrx (for example, a newer 12.9 that doesn't support those cards) then the final command will give you an error no supported hardware detected or something similar. However, everything works at this point and you will get a reasonable xorg.conf:  ... other stuff  Section "Device"         Identifier  "aticonfig-Device[0]-0"         Driver      "fglrx"         BusID       "PCI:1:5:0" EndSection  ... other stuff   At this point you're supposed to reboot and everything will be working with the fglrx driver. However, upon rebooting, you'll be treated to the following errors in Xorg.0.log when fglrx attempts to load:  (EE) Failed to load /usr/lib/xorg/modules/drivers/fglrx_drv.so: /usr/lib/xorg/modules/drivers/fglrx_drv.so: undefined symbol: noXFree86DRIExtension   Some searching around will show that this is a problem with the legacy ATI drivers not supporting xserver 1.13 or newer. () ATI has released a fixed driver for its most recent (HD 5000 series or later) cards, but not for the 'legacy' cards yet. The non-legacy ATI drivers can't be used with the old cards.  What should an Ubuntu user, using one of these HD 2000-4000 series cards, do?    Wait for an updated 'legacy' ATI driver that properly works with xserver 1.13?   Downgrade back to 12.04 Precise, which uses xserver 1.11? Try to downgrade xserver on 12.10 Quantal to 1.12, which could possibly break Unity and GNOME? Forced upgrade to HD 5000 series or later card? (Not possible with integrated graphics...) Some other 1337 action that fixes this problem painlessly? Using different delimiters in sed commands and range addresses I am working on a game and would like to include a few jump scares. So here is a rather simple question — What makes a good jump scare and when and how should they happen? Surjectivity of Composition of Surjective Functions Suppose we have two functions, $f:X\rightarrow Y$ and $g:Y\rightarrow Z$. If both of these functions are onto, how can we show that $g\circ f:X\rightarrow Z$ is also onto? What is the difference between the Bash operators [[ vs [ vs ( vs ((? I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition)