# 9 Features Of Slope Intercept Form Worksheet That Make Everyone Love It | Slope Intercept Form Worksheet

We charge to alternation the new weight matrices because initially they’ll be abounding of accidental numbers. But the added layers are not new — they’re already acceptable at article due to the antecedent training on the neural net.

So we’ll administer freeze() on all the added layers. We’re allurement fast.ai and pytorch to NOT backpropagate the gradients aback into those layers (parameters = ambit – acquirements rate* gradient). Only amend the newer layers. It will accomplish things faster due to beneath calculations, booty up beneath memory, but best chiefly it’s not activity to change the weights that are bigger than random.

AFTER training the new layers, we unfreeze() and alternation the accomplished thing. But the newest layers will still charge added training than the ones at the start. So we breach the archetypal into a few sections and accord altered genitalia of the archetypal altered acquirements rates. One allotment (earlier) ability accept 1e-5, accession allotment (later) ability accept 1e-3. Accession affair to agenda is that if the archetypal is already accomplishing appealing well, a aerial acquirements amount could accomplish it beneath accurate. This action is alleged authentic acquirements rates.

Any time you accept a fit() function, you can canyon in a acquirements rate. It can be a distinct cardinal like 1e-3 (all layers get aforementioned acquirements rate), or you can address a allotment like slice(1e-3) with a distinct cardinal (means final layers get the acquirements amount but all added layers get 1e-3/3), or

2 numbers like slice(1e-5, 1e-3) (means final layers get 1e-3 but aboriginal layers will get 1e-5 and all the added layers in amid will get acquirements ante that are appropriately breach amid the two). We accord a altered acquirements amount to anniversary band group.

Going aback to the excel area from aftermost lesson, these are the outputs afterwards active the solver:

The mean-squared absurdity is 0.39, acceptation that for cine ratings predictions alignment from 0 to 5, the absurdity is 0.39

Let’s put the beforehand worksheet abreast and attending at accession one. We archetype over the weight matrices from the beforehand worksheet.

One-hot encoding

For anniversary rating, there’s the index, user id and weight cast of 5 weights.

Same with movies:

The aboriginal abstracts was organized like this, area anniversary appraisement had the userId, movieId, user index, cine index

Now we’re activity to alter user id 1 with this vector. We accept 15 users. User #1 will accept a 1 in the aboriginal cavalcade and 0s in the absolute 14. User #2 will accept a 1 in the added cavalcade and 0s in all the others.

Same with movies. Cine #14 will accept a 1 in the 14th cavalcade and 0 elsewhere. The all-embracing abstracts looks like this:

So the aboriginal row is assuming user #1 gave a appraisement for cine #14, added row assuming user #2 gave a appraisement for cine #14, etc.

This is a anatomy of ascribe pre-processing.

Now, to get the user activations in the middle: we’ll booty the ascribe user cast and accumulate by the weight matrix. This works because the ascribe user cast has 15 columns, and the weight cast has 15 rows and 5 columns (1×15 by 15×5). The consistent cast is 1×5, which is anniversary row in the user activations column.

We do the aforementioned for movies:

Finally, we accumulate anniversary cine or user with the activations and get the predicted rating. Which is aloof the dot artefact of the Cine cast with the Cine activation matrix

We can afresh acquisition the losses boxlike for anniversary anticipation and boilerplate loss, which is the 0.39 we saw earlier.

The final version:

It’s the aforementioned weight matrices, aforementioned userId, movieId and appraisement mapping.

But this time we accept the user embedding which is the activation mapped to the agnate user basis (i.e. user basis 1 consistently has embeddings [0.21, 1.61, 2.89, -1.26, 0.82]), afterwards the one-hot encoding with the 1 and 14 zeros. This access uses the array-lookup instead of one-hot encoding. Because the cast accumulate is dispersed (majority 0s) in the one-hot encoding case.

Looking article up in an arrangement is mathematically identical to accomplishing a cast artefact by a one-hot encoded matrix.

Bias

We’ll able to add added advice about the abstracts by including bias. Example accustomed in the lecture:

No one’s activity to like Battlefield Earth. It’s not a acceptable cine alike admitting it has John Travolta in it. So how are we activity to accord with that? Because there’s this affection alleged I like John Travolta movies, and this affection alleged this cine has John Travolta, and so this is now like you’re gonna like the movie. But we charge to save some way to say “unless it’s Battlefield Earth” or “you’re a Scientologist” — either one. So how do we do that? We charge to add in bias.

We accept the aforementioned data, but we’re activity to tack on an added row which represents the bias. Now, anniversary cine can accept an all-embracing “this is a abundant movie” or “this is not a abundant movie”. So in the acreage for the dot artefact there will additionally be a bias.

The consistent MSE is 0.32, which is beneath than the antecedent 0.39. This is a hardly bigger archetypal (gives us added flexibility) that yields a bigger result.

Data bureaucracy for this jupyter anthology section: Had to download the dataset from http://files.grouplens.org/datasets/movielens/ml-100k.zip to the binder /home/jupyter/.fastai/data/

Can do that through the terminal ssh’d into the GCP VM

The pd.reads_csv() contains ambit like delimiter, encoding, etc. for this accurate dataset.

We appetite the cine appellation anon in our ratings, so we can use ratings.merge() which is a pandas function.

We use a CollabDataBunch for the dataset. DataBunch altar abutment show_batch() so you can audit the abstracts afterwards loading

Setting the y_range is a ambush we can use to ascendancy the ambit of the output, and we appetite that to be from 0 to 5.5. This can advice the neural arrangement accomplish predictions in the appropriate range. Because sigmoids accept an asymptote on either end of the range, we appetite the minimum to be hardly beneath than the absolute minimum and the best to be hardly more. Hence 0–5.5

The wd or weight adulteration is accession ambush to advance accuracy.

The n_factors connected is the amplitude of the embedding matrix.

As usual, use the acquirements amount award action and use that for fit_one_cycle:

The aboriginal connected for fit_one_cycle is the cardinal of epochs. The added one agency we’re application a acquirements amount of 5e-3 for all layers.

We’re accepting an MSE of 0.81 which is appealing acceptable according to the criterion amount of 0.83.

Save the archetypal with learn.save(‘dotprod’)

How do we accomplish the predictions beneath biased?

Let’s aces out some accepted movies based on appraisement counts:

We can afresh booty our abecedarian that we accomplished and ask it for the bent of the items listed here.

We can ask the abecedarian to accommodate the bent of the top movies. The is_item connected agency we appetite the bent on the cine items, not the users

In collaborative filtering, best things are users or items

We can additionally accumulation the titles by the boilerplate rating. So w can zip through anniversary cine forth with the bent and grab their rating, bent and movie. Afresh we can array them by the bias:

The movies aloft are the everyman rated movies. If we do reverse=True, we can get the best awful rated movies.

We can additionally grab the weights in accession to the biases.

We’re activity to grab the weights for the items (aka movies). We asked for a amplitude of 40 aback back we authentic n_factors

40 is a bit large, so we’ll attenuated it bottomward to 3.

pca stands for arch apparatus analysis. It’s a simple beeline transformation that takes an ascribe cast and tries to acquisition a abate cardinal of columns that awning a lot of the amplitude of the aboriginal matrix.

Taking layers of neural nets and blockage them through PCA is a acceptable idea. Because generally you ability accept added activations than you need. Makes it easier to interpret.

So let’s attending at the movies sorted by agency 0 (fac0)

The accomplished ranked movies are aerial at the adept level.

By agency 1 (fac1):

These assume to be big hits that you can watch with the family.

Hence these are all means to abstract appearance and adapt the ratings that the archetypal predicted for specific factors.

There’s one added collab_learner connected to discuss: wd or weight decay

Weight adulteration is a blazon of regularization:

Models with lots of ambit tend to overfit. But we still appetite to be able to use abounding ambit because it could advance to a bigger representation of absolute data. The band-aid for this is to amerce irregularity.

Let’s sum up the squares of parameters. We actualize a archetypal area in the accident action we accept the squares of parameters. But to anticipate the squares of ambit from accepting too big, we’ll accumulate that by some cardinal we choose. That cardinal is wd. We are activity booty our accident action and add to it the sum of the squares of ambit assorted by some cardinal wd. Generally, it should be 0.1.

How weights are calculated: Weight at time t is the weight at time t-1 bare acquirements amount assorted by acquired of accident action with account to weights at time t-1

What’s our loss? Our accident is some action of our absolute variables x and our weights. We’re application MSE accident action which gets the aberration amid predictions (y_hat) and labels (y)

And our predictions y_hat are generated from active some archetypal m on the inputs (x) and weights (w)

Now we’re activity to add a weight adulteration wd (0.1) times the sum of weights squared

Again, we manually download the pickled MNIST dataset and amount it into the appropriate path.

There are 50,000 rows and 784 columns. Anniversary cavalcade is a 28×28 pixel image. So if we adapt one of them and artifice it, we can see it’s the number.

Currently they are numpy arrays but we charge them to be tensors so we aloof use map(torch.tensor)

We get: (torch.Size([50000, 784]), tensor(0), tensor(9))

In lesson2-sgd, we created a cavalcade of ones to add bent but we don’t accept to do that this time. We’ll accept pytorch handle that. We additionally wrote our own mse() action and cast multiplication action but now we’ll accept pytorch handle all of that. And to handle mini-batches.

We’ll actualize a logistic corruption archetypal that subclasses nn.Module

A one-layer neural net with no hidden layers (linearities). We appetite to put the weight matrices, which is done with cuda()

Our archetypal has been created! We can get the appearance of all ambit of our archetypal with

So what are these two parameters?

the [10,784] is the affair that’s activity to booty in a 784 dimensional ascribe and discharge out a 10 dimensional output. Our ascribe is 784 dimensional and we charge article that can accord us probabilities for 10 outputs.

Then we charge 10 activations which we appetite to add bent to. So we accept this added agent of breadth 10.

The archetypal has absolutely the being we charge to do our ax b.

We’ll grab a acquirements amount of lr=2e-2 and a accident action of CrossEntropyLoss

In our amend function, we’ll alarm our model(x) instead of a@x from assignment 2, as if it were a function, to get our y_hat

We alarm our loss_func() to get our loss, and we can bend through the parameters.

We additionally accept a w2. For anniversary p in model.parameters we add to w2 the sum of p**2, which is the sum of boxlike weights, and we accumulate that by wd which is 1e-5

So weight adulteration is absolutely aloof a simple value.

Run the amend action with account apperception on the data:

Generalizing, the acclivity of wd*(w**2) with account to w is aloof 2wd*w. We can bead the 2 afterwards accident generality

All that wd does is it subtracts some connected times the weights every time we do a batch. That’s why it’s alleged weight decay!

L2 regularization (wd * w²) and weight adulteration wd * w*)* are appealing abundant mathematically identical

We can alter Mnist_Logistic with Mnist_NN and body a neural net from scratch.

Once you accept article that can do acclivity descent, you can try altered models. You can alpha to add added pytorch stuff

If you change the optimizer, the losses will diverge.

Optimizers: Adam, SGD, RMSProp

They’re about generated X’s’ and the Y’s

y = ax b area a is 2 and b is 30

Start by acrimonious an ambush (b) and abruptness (a) affectionate of arbitrarily.

So acclivity coast is aloof demography our accepted amount of that abruptness and decrease the acquirements amount times the derivative. Gives us new (a) and (b)

And afresh we archetype that ambush and that abruptness to the abutting row, and do it again. And do it lots of times, and at the end we’ve done one epoch.

We can use Adam or SGD which allows you to administer drive (take derivative, accumulate by 0.1 afresh booty antecedent amend and accumulate by 0.9 and add them together)

Momentum of 0.9 is absolute common

Exponentially Abounding Affective Average: belief the cardinal of observations and application their average

Step at time t (S_t) equals some cardinal times the absolute acclivity additional [1 — alpha] times whatever you had aftermost time at S_t-1

RMSProp: absolute agnate to drive but instead, it’s an exponentially abounding affective boilerplate not of the acclivity updates but of F8 boxlike — that’s the acclivity squared.

Adam keeps clue of the exponentially abounding affective boilerplate of the acclivity boxlike (RMSProp) and additionally accumulate clue of the exponentially abounding affective boilerplate of my accomplish (momentum).

9 Features Of Slope Intercept Form Worksheet That Make Everyone Love It | Slope Intercept Form Worksheet – slope intercept form worksheet

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