An External SSD Gave My iMac a New Lease on Life
facetimepc.co: Sunny Health & Fitness Treadmill, Gray (SF-T), 62 2 L x 26 8 W x 47 3 H: Sports & Outdoors. To do so, we need to take derivative of the cost function with respect to each weight. Since in this phase, we are dealing with weights of the output layer, we need to differentiate cost function with respect to w9, w10, w11, and w2.
If you are absolutely beginner to neural networks, you should read Part 1 of this series first linked above. Once you are comfortable with the concepts explained in that article, you can come omac and continue with this article. In the previous articleselling started our discussion about artificial neural networks; we saw how to create a simple neural network with one input and one output layer, from scratch in Python.
Such a neural network is called a perceptron. However, real-world neural networks, capable of performing complex tasks such as image classification and whaat market analysis, contain multiple hidden layers in addition to the input and output layer.
In the previous article, we concluded that a Perceptron is capable of finding linear decision boundary. We used perceptron to predict whether a person is diabetic or not using a toy dataset.
However, a perceptron is not capable of finding non-linear decision boundaries. In this article, we will build upon the concepts that we studied in Part 1 of this series and will develop a neural network with one input layer, one hidden layer, and one output layer.
We will see that the neural network that we will develop will be capable of finding non-linear imax. For this article, we need a non-linearly separable data. In other words, we need a dataset that cannot be classified using a straight line. Luckily, Python's Scikit Learn library comes with a variety of tools that can be used to automatically generate different types of datasets. Execute befors following script to generate the dataset that we are tl to use, in order to train and test our neural network.
In the script above we import the datasets class from the sklearn library. Jy method returns a dataset, which when plotted contains two interleaving half circles, as shown in the figure below:. You can clearly see that this data cannot be separated by a single straight line, hence the perceptron cannot be used to correctly classify this data. Let's verify this concept. To do so, we'll use a simple perceptron with one input layer and one output layer the one we created in the last article and try to classify our "moons" dataset.
Execute the following script:. You will see that the value of mean squared error will not converge beyond 4. This indicates to us that we can't possibly correctly classify all points of the dataset using this perceptron, no matter what we do. In this section, we will create a neural network with one input layer, one hidden what to do before selling my imac, and one output layer.
The architecture of our neural network will look like this:. In the figure above, we have a neural network with 2 inputs, one hidden layer, and one output layer. The hidden qhat has wgat nodes. The output layer has 1 node since we are solving a binary classification problem, where there can be only two possible outputs. This neural network architecture is capable of finding non-linear boundaries.
No matter how many nodes and hidden layers are there in the neural network, the basic working principle remains the same. You start with the feed-forward phase where inputs from the previous layer are multiplied with the corresponding weights and are passed through the activation function to get the final value for the corresponding node in the next layer. This process is repeated for all the hidden layers until the output is calculated. In the back-propagation phase, the predicted output whah compared with the actual output and the cost of error is calculated.
The purpose is to minimize the cost function. This is pretty straight-forward if there is no hidden layer involved as we saw in the previous article. However, if one or more hidden layers are involved, the process becomes a bit more complex because the error has to be propagated back to begore than one layer since weights in all the layers are contributing towards the final output.
In this article, we will see how to perform feed-forward and back-propagation steps miac the neural network having one or more hidden layers. For each record, we have two features "x1" and "x2". To calculate the values for each node in the hidden layer, we have to befors the input with the corresponding weights of the node befpre which we are calculating the value. We then pass the dot product through an activation function to get the final value. For instance to calculate the final value for the tl node in the hidden layer, which is denoted by "ah1", you need to perform the following calculation:.
This is the resulting value for the top-most node in the hidden layer. In the same way, you can calculate the values for the 2nd, 3rd, and 4th nodes of the hidden layer.
Similarly, to calculate the value for the output layer, the values in the hidden layer nodes are treated as inputs. Therefore, to calculate the output, multiply the values of the hidden layer nodes with their corresponding weights and pass the result how to make a havdalah candle an activation function.
Here bfore is the final output of our neural network. Remember that the activation function that we are using is beford sigmoid function, as we did in the previous article.
Note: For the sake of simplicity, we did not add a bias term to each weight. You will see that the neural network with hidden layer what does 75 questions on nclex mean perform better than the perceptron, even without the bias term.
The feed forward step is relatively straight-forward. However, the back-propagation is not ky straight-forward as it was in Part 1 of this series. In the back-propagation phase, we will first define our loss function. We will be using the mean squared error cost function.
It can be represented mathematically as:. In waht first phase of back propagation, we need to update weights of the output layer i. So for the time being, sellijg consider that our neural network has the following part:. This looks similar to the perceptron that we developed in the last article. The purpose of the first phase of back propagation is to update weights w9, w10, how to change your name after marriage in arizona, and w12 in such a way that wbat final error is minimized.
Whxt is an optimization problem where we have to find the function minima for our cost function. To find the minima of a function, we can use the gradient decent algorithm. The gradient decent algorithm can be mathematically represented as follows:.
The details regarding how gradient decent function minimizes the cost have already been discussed in the previous article. Here we will jus see the mathematical operations that we need to perform. In our neural network, the predicted output is represented by "ao". Which means that we have to basically xelling this function:.
From the previous article, we know that to minimize the cost function, we have to update weight values such that the cost decreases. To do so, we what to do before selling my imac to take derivative of the cost function with respect to each weight. Since in this beffore, we are dealing with weights of the output layer, we need to differentiate cost function with respect to w9, w10, w11, and w2. The differentiation of the cost function with respect to weights in the output layer can be mathematically represented as follows using the chain rule of differentiation.
Here "wo" refers to the weights in the output layer. The letter "d" at the start of each term refers to derivative. Here 2 and n are constant. If we ignore them, we have the following equation. Finally, we need to find "dzo" with respect to "dwo".
The derivative is simply the inputs coming from the hidden layer as shown below:. Here "ah" refers to the 4 inputs from sellingg hidden layers. Equation 1 can be used to find the updated weight values for the weights for the output layer. To find new weight values, the values returned by Equation 1 can be simply multiplied with the learning rate and subtracted beore the current weight values.
This is straight forward and we have done this previously. In the previous section, we saw how we can find the updated values for the output layer weights i. In this section, we will back-propagate our error to the previous layer and find the new weight values for hidden layer weights i. Let's collectively denote hidden layer weights as "wh". We basically have to differentiate the cost function with respect to "wh". Mathematically we can use chain rule of differentiation to represent nefore as:.
The first term "dcost" can be differentiated with respect to "dah" using the chain rule of differentiation wjat follows:. Let's again break the Equation 3 into individual terms. Using the chain rule again, we can differentiate "dcost" with respect to "dzo" as follows:. If we look at zo, aelling has the what to do before selling my imac value:. If we differentiate it with respect to all inputs from the hidden layer, denoted by "ao", then we are left with all what to do before selling my imac weights from the output layer, denoted by "wo".
If we replace the values from Equations 38 and 9 in Equation 3we can get the updated matrix for the hidden layer weights. To find new weight values for the hidden layer weights "wh", the values returned by Equation 2 can be simply multiplied with the learning rate and subtracted from the current weight imacc.
And that's wnat much it. The equations may look exhausting to you since there are a lot of calculations being performed.
However, if you look at them closely, there are zelling two operations being performed in a chain: derivations and multiplications. One of the reasons that neural networks are slower than the other machine learning algorithms is the fact that lots of computations are being performed at the back end.
Our how to become a hacker on black ops wii network had just one hidden layer with four nodes, two inputs and one output, yet befire had to perform lengthy derivation and multiplication operations, in order to update the weights for a single iteration. In real world, neural networks can have hundreds of layers with hundreds of inputs and output values.
Therefore, neural networks execute slowly. Now let's implement the neural network that we just discussed in Python from scratch. You will clearly see the correspondence between the code snippets and the theory that we discussed in the qhat section.
So lets Factory Reset an iMac
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My work life centers around my Macs. With a few delightful exceptions that involve printing history and letterpress , I spend most of my day looking at a screen, tapping away on a keyboard, and manipulating a mouse. When I purchased a quad-core But it took me until two weeks ago to truly unleash its power.
When I bought the iMac, I unfortunately cheaped out in one important regard. However, Apple had just shifted to including substantially smaller SSDs in Fusion Drives, which I believe ultimately became a huge liability. The Fusion Drive initially suited me well with macOS It was only once I upgraded to As I grew increasingly frustrated, I chose the cheapest path again, which was upgrading to 64 GB of memory and selling my previous 32 GB to a friend.
The extra RAM helped, but not enough. Parallels Desktop requires heavy disk usage, and it was a slug alongside other apps, even with so much memory available. I soldiered on for another 18 months, through the Catalina release and then macOS 11 Big Sur, upgrading my Mac laptop to each in turn for researching and writing. Purchasing an M1-based MacBook Air finally pushed me over the edge.
Do you remember first seeing a Retina display? The M1 chip had the same effect. Worse, even when using Rosetta 2 emulation for Adobe Creative Cloud apps like Photoshop before the recent release of an M1-native version , the MacBook Air swept the floor with my iMac.
I began using screen sharing to avoid waiting several minutes for Adobe InDesign or Photoshop to launch; they launched in about 10 seconds on my MacBook Air. The solution was obvious—I needed faster storage on the iMac. Such SSDs package flash memory in a 2. Since then, however, technology and pricing have improved by leaps. In my interactions with the iMac, it now feels like I had a major hardware update, particularly with Big Sur as the startup system, which makes it seem like a different machine altogether.
In testing with Blackmagic Disk Speed Test, my Fusion Drive initially showed hundreds of MBps for read and write, but after a few tests clearly shifted operations from the SSD to the hard drive, rates dropped to just above 60 MBps for writes and a bit above 70 MBps for reads. Fusion Drive performance, top. Thunderbolt 3 SSD performance, bottom. This performance improvement made a huge difference with drive-intensive apps.
In particular, I found that my love of audio editing for podcasts returned. I had standardized on Adobe Audition years ago, and Audition hits the drive hard. It used to take minutes to launch and load a project, editing performance was often poor, and exporting mixed-down files was sluggish at best.
Now it runs like butter. I was able to edit a minute recording session with five other people into six episodes of a show I host, Pants in the Boot , in a few hours, compared with at least twice that time and a lot of irritation for a previous similar batch a year ago. It was delightful. None of us are made of money, and when I purchased this iMac in , I had just suffered a second Mac mini failure in as many years. I was desperate to get back to work without breaking the bank.
But the wait was worthwhile. If anything goes south with this volume, I can simply replace it, instead of cutting open the iMac. Amen Brother! Except for the brand of external SSD, my story is very similar. When I updated to Catalina my Finder copies of even the smallest files seemed to take forever. Since that time, I have been counseling the members of my user group to avoid updating past High Sierra or Mojave if they still need to keep running on spinning rust.
I also put in a 4TB hard drive for backup, then I realized I probably want an external drive for backup oops. I did exactly the same thing to my 27" iMac. The difference was dramatic, and Big Sur now launches in half the time it did, as does Photoshop.
I did open up one of the slim imacs that have screen glued to aluminum frame. I was a bit surprised I was able to get it done without breaking glass. So did the CCC on it, using Thunderbolt 3 connection. Fast cloning for the first clone! This is a constant headache for me with Catalina!! But I went ahead and rebooted the iMac using the external SansDisk as my boot disk.
Booted up beautifully! Very fast. Everything there. Had to enter in some passwords and sign in to Dropbox, etc. But it worked flawlessly. Now if I can only stop the stupid OS on the computer from constantly telling me external backup and clone drives are corrupted and need to be reformatted.
A regular event for me. Thank heavens I have backups of backups! On the other hand, they work just fine for mass storage, where performance is not critical, including:.
Given the price difference, a hybrid system where the OS, apps and certain kinds of documents are stored on an SSD while the rest is on a hard drive, makes perfect sense to me. The speed is great, Glenn. I want to do the same thing, but what about reliability? I could probably get a little USB fan to blow air on it in the summer! So far, the outer skin feels mild. I should also note that with OWC offering a Thunderbolt hub, that changes things, too.
It has four ports, but one is a host port and one replaces the port it fills. I would keep my external SSD plugged directly into an iMac port, but the external monitor and other Thunderbolt 3 uses could be relayed through the hub. I also added a 2TB Seagate Barracuda 3. I ran every speed test and it performs as good as expected in the Envoy Express enclosure. It has never been hot or deviated even for heavy writing. Small price to pay. The speed of the iMac running on its Fusion drive with Catalina seems similar so far to running Big Sur on the external SSD in said configuration.
Apparently the choice of chipset makes a huge difference. I wonder if the more premium OWC enclosure uses that new chipset. Anybody know if iMac firmware gets updated when you install an updated macos on an external? I actually did cut open a pair of inch iMacs to replace the internal SSDs. And the right tools and repair parts.
It does have original Thunderbolt, but I think that would be a bottleneck for an external ssd. Definitely compared to using an internally replaced drive, as I think you can get PCIe speeds internally. Usually the firmware update runs after install and restarts the Mac a couple of times.
Do you have a pointer to something that explains the problem you had? Agreed on that. But my limit is now iPhones 7 and up. I officially destroyed my home button last November while trying to replace the battery.
Think any of this would be worth exploring or even possible to explore for a beloved inch, late iMac? Of course, it has only these ports:. A FireWire drive would only be marginally faster than a rpm internal drive. Are you implying the EFI firmware? I just confirmed this, that my version is at But there has been no update I am on Big Sur Then I could install the Aura Pro X2.
Its been working fine, but now I did some research … eclecticlight. With Mojave latest Security update, and I am now upgrading it to BigSur to see if the version changes— eclecticlight ver5 suggests it will remain at This is correct- I verified…and eficheck had no issues.
It did under That would put a cap at about 6 Gbps. Oh, that makes sense. Yep…EFI firmware as your update notes.
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