Luyện nói tiếng Anh bằng Shadowing qua video: The GELU, SiLU and SwiGLU activation functions, clearly explained!!!
Đang tạo bài học...
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Sometimes drop out is all you need.
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Hooray!
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StatQuest.
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Hello, I'm Josh Starmer and welcome to StatQuest.
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Today we're going to talk about the GelU, SilU, and Swiglu activation functions, and they're going to be clearly explained.
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This StatQuest is brought to you by the letters A, B, and C.
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A always, B be, C curious, always be curious.
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Too long, didn't watch.
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If you're already familiar with the REL U activation function, then the GAL U activation function,
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which sounds like it could be some sort of expletive, but is short for Gaussian Error Linear Unit, and the CIL U activation function,
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which is short for Sigmoid Linear Unit and thus sound sort of like an oxymoron, are almost the same.
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One relatively subtle difference is that the RELU outputs zero for all negative input values.
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And the GELU and CELU have this little dip for input values between negative two and zero.
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Another subtle difference is that the RELU has this angular bend at zero.
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And the Gell-U and Sill-U have a softer, differentiable curve at zero.
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Lastly, for all positive input values, the Rell-U just outputs the original input value.
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While the Gell-U and Sill-U have a slight curve
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that makes the output values just a little smaller than the positive input values.
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In contrast, the SWIGLU, which stands for Swish Gated Linear Unit, which sounds like a random jumble of words,
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can look like a smooth version of the RELU, or it can look like pretty much anything else it wants to look like.
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That said, despite the glaring differences in the shapes that the SWIGLU can take on, it's closely related to the GELU and CILU.
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Anyway, as a result of these relatively subtle differences for the Gelu and Siyu,
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and the relatively extreme differences for the Swiglu,
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these activation functions do not tend to overfit training data as much as the Relu.
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In other words, if all these dots were the training data,
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then a large neural network using the Relu activation function would have a strong tendency to overfit the training data.
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In contrast, a large neural network using the GelU,
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SilU, or Swiglu activation functions does not have as strong a tendency to overfit the training data.
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Thus, this new class of activation functions tend to result in neural networks that do a better job making predictions after training.
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Baaam.
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But Josh, where do these new activation functions get their different shapes from?
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And how did anyone come up with them to begin with?
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Well, just for you, Squatch, and anyone else who's interested, I made this whole stat quest just to answer those very questions.
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Hooray!
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Way back in the days before 2010, when you built a neural network, you usually did it using sigmoid activation functions.
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At the time, sigmoid activation functions seemed like a great idea because their output is constrained to be between 0 and 1,
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which represented the outputs of actual neurons either not firing or firing.
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And the curve reflected how neurons transition from one state to the other.
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Lastly, the sigmoid activation function is continuous and differentiable for all input values, making it a reasonable choice for backpropagation.
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And, for simple neural networks like this one, sigmoid activation functions work great.
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However, once people started scaling up their neural networks to have more hidden layers and more activation functions in each hidden layer,
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it became harder and harder to train the model.
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Thus, when we use the sigmoid activation function, we can't build very large neural networks.
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The reason for this size limitation has to do with the derivative of the sigmoid shape, which is needed to fit the neural network to data.
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Specifically, as the input for the sigmoid activation function gets further and further from zero,
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the derivative gets closer and closer to zero.
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And a super small value for the derivative means gradient descent, or whatever else we're using to fit the neural network to training data,
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takes super small steps towards the optimal parameter values.
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And that means finding the optimal parameter values can take a long, long time.
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As a result, if these were the training data, then, ideally, we'd want to fit a squiggly shape like this to it.
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However, because we can't easily train a large neural network using the sigmoid activation function, we might get a squiggly shape like this instead.
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The squiggly shape from the sigmoid underfits the training data.
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And thus, the squiggly shape created with the sigmoid activation function doesn't fit the data as well as we might like.
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So, around 2010, the sigmoid activation function was replaced by the rel U, this bent shape.
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And the rel U activation function proved to be fundamentally important to making deep neural networks trainable.
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Ultimately, in 2017, the REL-U achieved peak awesomeness by being part of the first transformer.
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Bam.
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The REL-U was great because, among other things, it was super easy to compute.
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If the input value, the x-axis coordinate, was negative, then the output, the corresponding y-axis coordinate, was 0.
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And if the input value was positive, then the output, the corresponding y-axis value, was the exact same value.
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Another advantage was that the derivative was defined to either be 0 or 1.
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Having a derivative of 1 for large input values helped simplify backpropagation
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and made it easier to optimize the weights and biases in the model.
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Unlike the sigmoid activation function that had a super small derivative for input values far from zero,
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the ReLU has a derivative of one regardless of how much greater the input value is compared to zero.
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And that means, at least for large input values, the ReLU can optimize parameter values relatively quickly.
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Boom!
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Nope, not yet.
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Unfortunately, the RELU has its own problem.
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First, remember that we had this training data
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and we showed the ideal squiggly shape that we wanted our neural network to fit to the data.
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And, unfortunately, when we used the sigmoid activation function, instead of the ideal squiggly shape,
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we got a squiggly shape that underfit the training data.
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Well, the problem with using the RELU activation function is
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that now we can create a huge neural network that makes a squiggly shape that overfits the training data.
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In other words, the large neural networks
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that we can create with the RELU activation function often overcorrect for the problem we had with the sigmoid.
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Can't you just make a smaller neural network with the RELU?
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Great question, Squatch.
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In theory, we could do that, but in practice, it's next to impossible to figure out the optimal size for a neural network.
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I mean, imagine you started with a network that had 100,000 activation functions.
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Are you going to then test to see if 99,999 activation functions is better?
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And then test 99,998?
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Etc?
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Okay, I get your point.
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It would take way too much time.
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So, ideally, it would be nice if we could have something
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that didn't underfit the data like a small neural network using the sigmoid,
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and didn't overfit the data like a large neural network that uses the ReLU.
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One early solution to this problem was something called dropout.
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During training, when we are fitting a neural network to a dataset,
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Dropout randomly selects a subset of activation functions and removes them from the network.
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And then applies backpropagation to this smaller network to update the weights and biases.
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Once the weights and biases are updated,
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it goes back to the original neural network and selects another random subset of activation functions to remove from the training step.
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And then applies backpropagation to this smaller network to update the weights and biases.
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And this process is repeated for the duration of training.
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As a result of using Dropout during training, instead of training one big neural network,
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we effectively train lots of smaller networks.
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Thus, after training, when it comes time to make predictions with the entire neural network,
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we're essentially averaging over all of the smaller neural networks that we created during training.
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And the model averaging from the rail U combined with dropout results in a squiggly shape
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that does a better job approximating the ideal shape.
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Bam.
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Nope, not yet.
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Unfortunately, combining the rail U with dropout has its own problems.
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The first problem is that dropout is an extra thing that we need to add to the training stage.
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And the second, perhaps more important problem,
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is that dropout is completely independent of the inputs to each activation function in the network. In other words,
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dropout will remove an activation function from a neural network regardless of whether the input signal is large or small.
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Ugh, how do we fix that?
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Well, that's where the Galu, Silu, and Swiglu activation functions come in.
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BAM!
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Remember, at the start of this stat quest, we saw what the Galu, Silu, and Swiglu activation functions looked like.
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And we learned that they did a better job fitting a squiggly shape to the data.
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Well, now we'll learn where these activation functions come from.
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And to do this, we'll We'll learn how to build them from scratch.
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We'll start with a super simple neural network that just has one input, one output, and nothing else.
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Josh, is that even a neural network?
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It's enough to show how the Galu and Silu activation functions were created.
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Okay.
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Now, even though this neural network is ridiculously simple, let's imagine we apply dropout to it.
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If we apply dropout to this neural network, then, sometimes, an input value, like negative 2, will make it to the output.
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And sometimes, the input value will not make it to the output, and the output value will be 0.
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Now, if we apply dropout 50% of the time, then we can calculate the average output value
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by multiplying the top output value by 0.5 and multiplying the bottom output value by 0.5 and adding those two products together.
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In this case, the average output value is negative 1.
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Bam.
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Now let's see what happens when we use the input value x to determine the probability
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that we will avoid dropout p of x.
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Specifically, we'll use this blue squiggle to convert the input value x into a probability
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that we will avoid dropout p of x.
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Note, if you're dying to know more details about this blue squiggle,
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It's the cumulative distribution function for a standard Gaussian curve.
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However, the important thing is that we have a squiggle that goes from 0 to 1.
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In this case, if the input, x, is a negative number, then the probability that we'll avoid dropout, p of x, will be closer to 0.
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And if the input is a positive number, the probability that we will avoid dropout will be closer to 1.
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For example, if the input value is negative 2, then, according to this blue squiggle,
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the probability we will avoid dropout is 0.02.
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So we plug 0.02 in for P of X, the probability for avoiding dropout.
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And we plug in 1 minus 0.02, or 0.98, into the probability that we will use dropout.
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Note, because the probabilities we avoid dropout, 0.02, or use dropout, 0.98,
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are different, we're now calculating a weighted average of the output values.
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Anyway, in this case, when the input value is negative 2, the weighted average is negative 0.04.
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So we can put a dot at
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on a graph that has input values on the x-axis and the weighted average of the output values on the y-axis.
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Now, if the input value is negative 1, then the probability we will avoid dropout is 0.16.
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So we plug 0.16 into the probability for avoiding dropout.
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And we plug 1 minus 0.16 or 0.84 into the probability that we will use dropout.
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And the weighted average is negative 0.16.
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So we can put a dot at negative 1 comma negative 0.16.
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Likewise, we can put dots at 0 comma 0.
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1, 0.84, and 2, 1.96.
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And, in general, when we allow the probability for avoiding dropout to be determined by this blue squiggle, we end up with this function.
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And now, instead of plugging numbers into this neural network with dropout, we can use this new function as an activation function.
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In other words, this neural network with dropout and probabilities can be simplified to this neural network with a single activation function.
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And that means that our new activation function has the effects of input-dependent dropout built right into it.
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Because it was derived from the weighted averages that input-dependent dropout creates.
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Lastly, because this blue squiggle is the cumulative distribution function for a Gaussian distribution,
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this activation function is called GalU for Gaussian Error Linear Unit.
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Double bam!
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Now that we know how the GalU activation function can be derived entirely from input-dependent dropout,
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Let's go back to the larger neural network to derive the general equation for the gelu and associated activation functions.
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First, let's just plug in x into the input.
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Now, when we just do the math, we get...
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x times p of x plus 0 times 1 minus p of x.
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And because the second term is multiplied by zero, just like an activation function that gets dropped out, it goes away.
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And we're left with the input value, x, times the probability we avoid dropout, P . In other words,
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input values from negative infinity to positive infinity times their corresponding
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y-axis coordinate on a curve like this give us an activation function function.
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Now that we have a general equation for creating activation functions with input dependent dropout,
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one cool thing we can do is swap out the blue squiggle
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that we're using for P of X and get a related, but still different, activation function.
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For example, remember the sigmoid activation function we started with long ago, but ultimately replaced with ReLU?
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Well, compared to the cumulative distribution function for a Gaussian curve, the sigmoid shape, the orange squiggle, isn't that different.
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when we multiply input values by their corresponding y-axis coordinates on the orange squiggle, we get this new activation function.
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And since this new activation function is based on the sigmoid shape,
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this activation function is called the SilU for sigmoid linear unit.
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When we plot the GelU and the SilU activation functions on the same graph, we see that the differences are not super extreme.
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And just as we might expect by the similarity in the shapes, both can work in similar contexts.
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That said, as of this quest creation, it seems that Google favors the GelU for its AI models.
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Noted.
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Now let's talk about the SWEGLU activation function.
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To do that, let's go back to our super simple neural network with Dropout.
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And make it fancy.
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First, we'll add a weight.
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Josh, that's not very fancy.
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Don't worry, Squatch, we'll get there.
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Anyway, now when we plug a value, X, into the input, we get WX on the output on top.
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And, because we still have dropout on the bottom, we have zero in the output down there.
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Now we plug the output, wx, into the sigmoid probability function.
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And that gives us a weighted average like before.
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And, if we stopped right now, we'd have something very close to an activation function called swish.
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The big difference between the weighted average we have now and the swish is the swish just has the input value,
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x, outside of the probability function instead of wx.
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So, instead, we'll call our weighted average swishish.
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Also, while we're at it, most people, including the maintainers of the PyTorch documentation,
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just use SILU to refer to both SILU and swish.
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Anyway, regardless of what it's called, we're not going to stop here.
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Instead, we'll add another copy of our input value, x, and multiply it by a different weight, v.
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Lastly, we multiply vx by the weighted average, the swish-ish thing, to get the final output value, y.
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Whoa, that's pretty fancy.
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Agreed.
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Because this bypass multiplication term, Vx, which is used by another activation function called a gated linear unit,
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or glue, is combined with something that is swish-ish, we call the whole thing the swiglu activation function.
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Boom!
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These additional weights and multiplication add a lot more flexibility to the shapes that we can get for the activation functions.
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But Josh, why would this be better?
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Well, to quote the authors of the SuiGlu activation function, we offer no explanation as to why these architectures seem to work.
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Small bam.
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That said, I have two ideas for why they work.
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First, the SuiGlu requires a lot more computation than the ReLU.
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As a result, we tend to make smaller neural networks with Swiglu.
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And a smaller neural network may not overfit the training data as much as a larger one.
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Second, and perhaps more importantly, throughout the history of neural networks, one recurring theme is that the more we,
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as people, get out of the way and don't tell the network what to do, the better they perform.
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And with the Swiglu activation function, with its extra trainable parameters, we're essentially saying, Neural network,
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you figure out what shape you need for the activation function.
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Anyway, since it seems to work, the Swiglu variation is commonly used in AI, especially AI models created by Meta.
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In summary, the idea for these activation functions is that they are all based on the weighted average of dropout.
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And, if anything, the big lesson here is that neural networks are still an area of very active experimentation.
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People are trying new things all the time and seeing what happens.
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If it works, then they publish their new ideas.
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Triple bam!
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Now it's time for some shameless self-promotion.
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If you want to review statistics, machine learning, and AI offline, check out the StatQuest PDF study guides and my best-selling books on machine learning,
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neural networks and AI, and statistics at StatQuest.org.
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There's something for everyone.
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Hooray!
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We've made it to the end of another exciting StatQuest.
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If you like this StatQuest and want to see more, please subscribe.
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And if you want to support StatQuest, consider contributing to my Patreon campaign, becoming a channel member, buying one or two of my original songs or a t-shirt or a hoodie,
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or just donate.
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The links are in the description below.
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Alright, until next time, quest on!
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|---|---|
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