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Explanation of Spikes in training loss vs. iterations with Adam Optimizer I am training a neural network using i) SGD and ii) Adam Optimizer. When using normal SGD, I get a smooth training loss vs. iteration curve as seen below (the red one). However, when I used the Adam Optimizer, the training loss curve has some spikes. What's the explanation of these spikes?   Model Details:  14 input nodes -> 2 hidden layers (100 -> 40 units) -> 4 output units  I am using default parameters for Adam beta_1 = 0.9, beta_2 = 0.999, epsilon = 1e-8 and a batch_size = 32.  i) With SGD  ii) With Adam I only occasionally use the Fixed Zoom In/Out buttons on the Tools toolbar of ArcMap and had always assumed that they zoomed in/out by a set scale factor.  However, using ArcGIS for Desktop 10.2, I just set my scale to be 1:10,000,000 and then hit the Fixed Zoom In button 10 times while recording the subsequent scale each time and was surprised to see:  10,000,000 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,500,000 2,000,000 1,500,000 1,250,000 1,000,000   Dividing each scale denominator by its successor shows a sequence of: 1.25, 1.33, 1.2, 1.25, 1.33, 1.2, 1.25, 1.33, 1.2  Curious about what happened in between the scales above I experimented a little to discover that the first issuance of the Fixed Zoom In button simply takes the scale to the first of those listed above and then starts following the same pattern.  Try starting with 1:8,000,001 to see ...  8,000,001 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000   This seems like quite a neat solution, but not one that I had realised was in place - does anyone know if it has been documented anywhere?    I've looked in the Online Help without success.  In answer to @DevdataTengshe, the scales currently in my available list (see below) seem to bear no relation to those used by Fixed Zoom In/Out.    However, when I add 1:7,500,000 into my available list it does seem to insert that as an additional scale step ...  10,000,000 8,000,000 7,500,000 6,000,000 5,000,000 4,000,000   This makes the algorithm being used even more mysterious to me. Intuition for why the sum of Bernoulli trials is a sufficient statistic via cancellations on numerator and denominator? Suppose that $X_1, \ldots, X_n$ are iid Bernoulli trials with parameter $p$, and that $Y = \sum_{i=1}^nX_i$. Then, we have that $Y$ is a sufficient statistic by the following condensed proof:  $$ P(X_1 = x_1,  ... , X_n = x_n |Y = y) = \frac{p^y(1-p)^{n-y}}{\binom{n}{y}  p^y(1-p)^{n-y}} =\frac{1}{\binom{n}{y}}   \text{ if } \sum_{i=1}^{n}x_i = y $$  I am trying to see why this is the case. My reasoning is that there is some cancellation property on top and bottom that "kills" off the parameter $p$. In that whatever is on top through $p$ is perfectly matched by whatever is on the bottom minus scaling factors (in this case $\binom{n}{y}^{-1}$).   However, I am wondering what the deeper meaning behind this is, that the numerator of the joint distribution of the data and the sufficient statistic has its EXACT form on the bottom, except for constants which are only multiplicative (to facilitate cancellations). Am I onto something bigger and deeper here? I am running centos 5.8 with cpanel. Lately I am getting reports that my swap is full , but there is a lot of free memory  to use.  top - 10:33:43 up 133 days, 17:00,  1 user,  load average: 0.05, 0.03, 0.05   Tasks: 170 total,   1 running, 169 sleeping,   0 stopped,   0 zombie   Cpu(s):  2.1%us,  0.5%sy,  0.0%ni, 97.2%id,  0.0%wa,  0.0%hi,  0.2%si,  0.0%st   Mem:  24726100k total,  8255368k used, 16470732k free,   599560k buffers   Swap:  1046520k total,   984740k used,    61780k free,  3641828k cached     How do I solve this? The unused ram memory should be used instead of the swap. Or should I increase the swap ( and how do I do that ? ).  Thanks Mouse rotated 90 degrees Is there a pattern to which Star Trek ships get the definite article? Some ships in Star Trek are referred to with definite articles. "The Enterprise", "The Defiant". Other ships are referred to without them. "Voyager", "Enterprise". Is there a pattern to or explanation for this behavior? arcpy.env.overwriteOutput = True not working for one dataset MySQL Date Between What are reserved filenames for various platforms? Where are the proprietary NVIDIA drivers in 16.04? The proprietary NVIDIA drivers "disappeared" with my latest update:    The option of "Proprietary drivers for devices" is correctly set under the "Ubuntu Software" tab. I have the graphics-driver PPA (ppa:graphics-drivers/ppa) correctly added to my sources.  Any ideas on how to bring the proprietary drivers back?  PS1: I need them because some of the games I play under wine don't work without them, for whatever reason.  PS2: Also, this feels like it should have a straightforward answer, but I've been looking online for a while without luck. Would a very small creature inside a sealed container carried by a character take damage from AOE spells? Assume character A is in the AOE of a damaging spell.  Character A is carrying a closed container inside his backpack, alongside several sheets of parchment.  Damaging spell description specifically states that items carried by a creature are not damaged even on a failed save. Unattended objects are damaged, though.  Inside said container there is a small creature. Creature has no problem living inside container for a long amount of time.  Does this creature take damage from the spell? If it does not, what mechanic prevents damage? Can you intentionally fail a skill check? This comes up to me in the context of the 3.x/PF/d20 Fly skill, even when I simply read about it: Can you intentionally fail a Fly skill check, or any other skill check for that matter, if you, or your character for that matter, decides that the effects of failing the check are what is desired in the situation?  Example:  Take a a shapeshifted Draconian cruising at high altitude, with a few friends on his back who have some means of breathing air supply, whether it be mundane or magical.  Now lets say that the air supply goes kablooie, similar to a decompression or all-packs-trip in an airliner.  For the sake of the folks on his back -- if not himself, depending on if dragon forms need supplemental air to fly at such high altitudes, the Draconian has to lose altitude, and fast.  Considering that by RAW, a Fly check failure leaves yourself falling, would saying "I initiate a rapid descent" be enough to treat the next Fly check as an intentional failure, or would you have to roll a 'reverse' Fly check, where failing the check gives you the desired outcome of a rapid descent, and succeeding leaves you stuck at altitude?  P.S. I added the rules-as-written tag because a RAW answer is highly desired here, albeit not mandatory.  I can already mostly figure it out from a simulationist standpoint, but that answer involves going in-depth into airline flying and non-normal procedures. Spurious whitespace with algpseudocode and noend I'm currently typesetting some pseudocode and was up to now pretty happy with the algorithmicx package and the algpseudocode command set. However, I would now like to use the noend option to omit end lines. That works, but unfortunately introduces additional whitespace (see lines 6 and 7 in the example below). I fiddled around with negative \vspaces but could not come up with a consistent value that works in all cases.    \documentclass{article} \usepackage[noend]{algpseudocode}  \begin{document}  \begin{algorithmic}[1]   \Function{lsolve}{$L$, $b$}     \State $x \gets b$     \For{$j \gets 0$ to $n - 1$}       \State $x_j \gets x_j / l_{jj}$       \ForAll{$i &gt; j$ where $l_{ij} \neq 0$}         \State $x_i \gets x_i - l_{ij} x_j$       \EndFor     \EndFor     \State \Return $x$   \EndFunction \end{algorithmic}  \end{document}   Is there any way to patch algorithmicx or do I have to finetune the pseudocode on a case by case basis? Script to remove certain span elements from an HTML file What happens if you use a drone to build a building while he's carrying minerals? Kind of a basic question, but what happens? Do you lose it? Does it count as harvested?  In a similar fashion, what happens when a drone/scv/probe goes harvesting gas when he's holding a mineral? Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$.   This is my proof to show that a ring is commutative if it has the property that ab = ca implies b = c.  We need to show that if x, y ∈ R then xy = yx. Let a = x, b = yx and c = xy. Then ab = x(yx) = (xy)x = ca. Thus, by the hypothesis, b = c, or xy = yx. Thus, for x, y ∈ R we have xy = yx.   How would I show when $a\neq 0$? Background  Would like to center all tables within floats, without having to add \centering to each table.  Ideas  Tried the following:  \let\originaltabular\tabular \renewcommand\tabular{\centering\originaltabular}   It compiles, but the tables remain left-justified.  Question  How would you edit the Preamble of a LyX document to make all the floating tables be centred? Badge symbol in notification is of the site you're on, not where badge was earned It's so cool that the notification reminds you of the colour of badge you've earned. But I am a little puzzled by the symbols:      Is it feasible to use the symbol from the earned site? At the moment it uses the symbol from the site I happen to be on (as you can see by looking to the left of the dropdown in each case.) Activate Rigid Body Physics at certain time? I've been trying to make a wrecking ball smash through a figure of sorts, not really sure what exactly but I made an example. The problem I'm having is that the figure does indeed fall apart, but I would like it to stay put together until the ball hits it. I achieved this by using Cell Fracture on the figure and just using Rigid Body. Again, I just need a way for the figure to stay still until hit by the ball, and then have all of its pieces come apart. How do you Set Custom Time in Ubuntu?