The  mention not to initialize all the weights to zero, because:     … if every neuron in the network computes the same output, then they will also all compute the same gradients during backpropagation and undergo the exact same parameter updates. In other words, there is no source of asymmetry between neurons if their weights are initialized to be the same.   I have been trying to understand this, but it is still not clear to me. I have searched on the internet, where some sources have only managed to confuse me further, like  and some other sources claiming that if the weights are initialized to zero, the weights would not update at all during the whole training process (while according to the notes linked above, the weights will update, but the updates to all the weights will be equal)  I tried doing some calculations on my own, which I have attached below.     If I have not made any error then then this derivation is showing that all the weights would undergo updates of equal magnitude, but the weights in the row of the Weight Matrix corresponding to the true class would be updated in the opposite direction compared to the other weights. So if the other weights are increased by delta, the weights in the row corresponding to the true class would be decreased by delta. So when the notes say "(all the neurons would) undergo the exact same parameter updates", they are actually talking about the magnitude – the direction can be different for some weights.  I am no expert in Mathematics, so, if there is any error in the derivation above, or if I am not interpreting it right, your criticism of it would be appreciated. Also, if there is a more intuitive way to see this, that would be helpful
Why is it dangerous to initialize weights with zeros? Is there any simple example that demonstrates it?
How to open a web page from my application? I want to make my WPF application open the default browser and go to a certain web page.  How do I do that? What focal length or range of focal lengths are usually used for portraits?   What is used by professionals? Why would one select a certain focal length? What are the advantages and disadvantages of different choices, and are there certain situations where an unusual choice might be better? I am trying to filter items with a stored procedure using like. The column is a varchar(15). The items I am trying to filter have square brackets in the name.  For example:  WC[R]S123456.  If I do a LIKE 'WC[R]S123456' it will not return anything.  I found some information on using the ESCAPE keyword with LIKE but I do not understand how to use it to treat the square brackets as a regular string. How to fix soft 404 errors in GWT? In GWT I have been receiving soft 404 errors for some URLs of my online shopping website. Ichecked all those URLs and those pages are looking good and there is nothing wrong in that page. Then why I'm receiving that errors?  This is the notification that I received in my GWT:     Dear owner or webmaster,      While crawling your site, we have noticed an increase in the number of   transient soft 404 errors around 2013-06-30 16:00 UTC (London, Dublin,   Edinburgh). Your site may have experienced outages. These issues may   have been resolved. Memory layout of a .NET array What is the memory layout of a .NET array?  Take for instance this array:  Int32[] x = new Int32[10];   I understand that the bulk of the array is like this:  0000111122223333444455556666777788889999   Where each character is one byte, and the digits corresponds to indices into the array.  Additionally, I know that there is a type reference, and a syncblock-index for all objects, so the above can be adjusted to this:  ttttssss0000111122223333444455556666777788889999         ^         +- object reference points here   Additionally, the length of the array needs to be stored, so perhaps this is more correct:  ttttssssllll0000111122223333444455556666777788889999         ^         +- object reference points here   Is this complete? Are there more data in an array?  The reason I'm asking is that we're trying to estimate how much memory a couple of different in-memory representations of a rather large data corpus will take and the size of the arrays varies quite a bit, so the overhead might have a large impact in one solution, but perhaps not so much in the other.  So basically, for an array, how much overhead is there, that is basically my question.  And before the arrays are bad squad wakes up, this part of the solution is a static build-once-reference-often type of thing so using growable lists is not necessary here. I'm searching how to remove the chapter+section number on the theorem numbering with a section counter.  With no section counter it's like:  \newtheorem{thm}{Title} Chapter1 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 3 --------thm 4 Chapter2 ----Section 1 --------thm 5 --------thm 6 ----Section 2 --------thm 7 --------thm 8   And with the section counter:  \newtheorem{thm}{Title}[section] Chapter 1 ----Section 1 --------thm 1.1.1 --------thm 1.1.2 ----Section 2 --------thm 1.2.1 --------thm 1.2.2 Chapter 2 ----Section 1 --------thm 2.1.1 --------thm 2.1.2 ----Section 2 --------thm 2.2.1 --------thm 2.2.2   And I want numbering my theorems like this:  \newtheorem???????? Chapter 1 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 1 --------thm 2 Chapter 2 ----Section 1 --------thm 1 --------thm 2 ----Section 2 --------thm 1 --------thm 2   I know it's always a pain to remove such things, thanks for whoever will help me ^^ Let's say I am building a logistic regression model where the dependent variable is binary and can take the values $0$ or $1$. Let the independent variables be $x_1, x_2, ..., x_m$ - there are $m$ independent variables. Let's say for the $k$th independent variable, the bivariate analysis shows a U-shaped trend - i.e., if I group $x_k$ into $20$ bins each containing roughly equal number of observations and calculate the 'bad rate' for each bin - # observations where y = 0 / total observations in each bin - then I get a U shaped curve.  My questions are:   Can I directly use $x_k$ as input while estimating the beta parameters? Are any statistical assumptions violated which might cause significant error in estimating the parameters? Is it necessary to 'linearize' this variable through a transformation (log, square, product with itself, etc.)? Ohm's law states that  electric current is directly proportional to voltage provided that physical conditions like temperature remain constant i.e. $$V = IR$$  On the other hand,  $$\text{Power = Voltage} \times \text{Current}$$  So here it seems that the higher the voltage, the lower the current, provided that the power remains constant (i.e. current is inversely proportional to the voltage here which is against Ohm's Law.).   Now my question is how do physicists explain this apparent contradiction? Or maybe this not a contradiction because I am analysing things incorrectly?   P.S.: I am a tenth grade student so please refrain from the usage of highly complicated terminologies in your answers. Why can't I install iOS 9.3? I saw an update for my iOS 9.2.1 device to iOS 9.3.  However, it said that the update cannot be verified, although it was downloaded.  I even deleted all data and applications from the device, but I still cannot update the device to 9.3; it just says "Your software is up to date" on iOS 9.2.1.  Can you force an update to 9.3? Problem with literate and breaklines=true in listings package As the title says, the option breaklines=true seems to have an undesired interaction when using literate; in the following example the closing parenthesis doesn't get colorized   \documentclass{article} \usepackage{xcolor} \usepackage{listings}  \lstset{   literate=     {)}{{\textcolor{red}{)}}}{1}     {(}{{\textcolor{red}{(}}}{1},   breaklines=true, }  \begin{document}  \begin{lstlisting} () \end{lstlisting}  \end{document}     Commenting out the breaklines=true option produces the desired result. What is producing this odd behaviour and how can it be prevented? Children’s books, one in space setting, the other in a jungle How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$? How to find the sum of the following series? $$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{n}$$ This is a harmonic progression. So, is the following formula correct? $\frac{(number ~of ~terms)^2}{sum~ of~ all ~the~ denominators}$ $\Rightarrow $ if $\frac{1}{A} + \frac{1}{B} +\frac{1}{C}$ are in H.P. Therefore the sum of the series can be written as : $\Rightarrow \frac{(3)^3}{(A+B+C)}$ Is this correct? Please suggest. Beamer: how to justify the whole text? How can I justify the text in the whole document in beamer without using \usepackage{ragged2e} and \justifying at the beginning of each frame?  \documentclass[8pt,handout,t]{beamer} \usepackage{pifont} %used inside itemize environment \item[\ding{226}] \usepackage{lipsum} \begin{document}  \begin{frame} \begin{columns}[T]  \begin{column}{0.3\textwidth} \includegraphics[width=\columnwidth]{example-image-1x1} \end{column} \begin{column}{0.65\textwidth} \begin{itemize} \item[\ding{226}] \lipsum[2] \item[\ding{226}] \lipsum[3] \end{itemize} \end{column}  \end{columns} \end{frame}  \begin{frame}  \lipsum[3]  \begin{itemize}    \item[\ding{226}] \lipsum[4]  \end{itemize} \end{frame} \begin{frame}   \begin{columns}[t] \begin{column}{0.4\textwidth} \lipsum[3] \end{column} \begin{column}{0.4\textwidth} \lipsum[5] \end{column} \end{columns} \end{frame} \end{document}     Edit: I had already checked  out but it does not work for both the columns and the itemize environment. My OpenID provider is shutting down; how do I change my Stack Exchange login? Do I need the original discs to install WoW on a new computer? My boyfriend bought the World of Warcraft Battle Chest, Wrath of the Lich King, &amp; Cataclysm. He downloaded them to our previous computer, but now we have a new one and when he took out the first disk from the battle chest he severely scratched it. Anyway, I tried putting in disk #2, and it said I couldn't do it without disk 1 (which is scratched!).  I've recently put in Wrath of the Lich King (it came with 2 CDs), and it said that I haven't downloaded the original and asked me if I wanted to downloaded. I clicked "yes" -- does that mean its downloading WoW &amp; The Burning Crusade? Or do we need to buy it all again?  We just bought the whole set on June of this year... How does the British-Irish Visa Scheme (BIVS) work? I am an Indian citizen and have applied for the Standard Visitor visa to the UK, and wish to travel to Ireland by using the BIVS scheme.    Do I need to fill up a separate application for BIVS endorsement or is it handed out automatically?  Also, If I enter the UK, and then travel to Ireland, can I re-enter the UK again? Two different solutions to integral Given the very simple integral  \begin{equation} \int -\frac{1}{2x} dx \end{equation}  The obvious solution is  \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2} \int \frac{1}{x} dx = -\frac{1}{2} \ln{|x|} + C \end{equation}  However, by the following integration rule \begin{equation} \int \frac{1}{ax + b} dx = \frac{1}{a} \ln{|ax + b|} + C \end{equation}  the following solution is obtained \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2}\ln{|-2x|} + C \end{equation}  Why are these solutions different? Which is correct?   The second solution can be simplified \begin{equation} -\frac{1}{2}\ln{|-2x|} + C = -\frac{1}{2}\ln{|-2|} -\frac{1}{2}\ln{|x|} + C= -\ln{\frac{1}{\sqrt{2}}} - \frac{1}{2}\ln{|x|} + C \end{equation} but they still differ. Effect of linear terms on a QFT I was told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model, \begin{equation}  {\cal L} = \frac{1}{2} \partial _\mu \phi _i \partial ^\mu \phi _i - \frac{m ^2 }{2} \phi _i \phi _i  - \frac{ \lambda }{ 4} ( \phi _i \phi _i ) ^2  \end{equation}  with $m ^2 =-\mu^2 &gt; 0$, adding a linear term in one of the fields $\phi_N$, does change the final results as you no longer have Goldstone bosons (since the $O(N)$ symmetry is broken to begin with).   Are there any other effects of linear terms that we should keep in mind or is this the only exception of the "forget about linear terms" rule? Is it poor form to switch accepted answers? I had a question of the form "does something like X exist?" Someone wrote a response to say that, No, X does not exist, but I could write it if I liked. I had suspected as much, so I marked his answer as the accepted answer. Today someone actually posted the code to do X for me, and I feel that the new poster deserves the "Accepted Answer" checkmark.  Is it poor form for me to pick a new Accepted answer? Does the original answerer get penalized in terms of reputation?  While the original responder's answer was accepted at the time, I feel this new answer is really more helpful.  Edit: Which of these responses should I accept? What does the notion of a single accepted answer mean with a question that is subjective that could have multiple "right" answers? We are familiar with the nifty fact that given the Fibonacci series $F_n = 0, 1, 1, 2, 3, 5, 8,\dots$ then $0.0112358\dots\approx 1/89$. In fact,  $$\sum_{n=0}^{\infty}\frac{F_n}{10^n} = \frac{10}{89}$$  How do we prove that, more generally, for $p &gt; 1$ then,  $$\sum_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$$  (The above simply was the case $p = 10$.)