Bias in an Artificial Neural Network explained | How bias impacts training

When reading up on artificial neural networks, you may have come across the term “bias.” It's sometimes just referred to as bias. Other times you may see it referenced as bias nodes, bias neurons, or bias units within a neural network. We're going to break this bias down and see what it's all about.
We'll first start out by discussing the most obvious question of, well, what is bias in an artificial neural network? We'll then see, within a network, how bias is implemented. Then, to hit the point home, we'll explore a simple example to illustrate the impact that bias has when introduced to a neural network.
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[@deeplizard]

Machine Learning / Deep Learning Tutorials for Programmers playlist: kzbin.info/aero/PLZbbT5o_s2xq7LwI2y8_QtvuXZedL6tQU Keras Machine Learning / Deep Learning Tutorial playlist: kzbin.info/aero/PLZbbT5o_s2xrwRnXk_yCPtnqqo4_u2YGL Data Science for Programming Beginners playlsit: kzbin.info/aero/PLZbbT5o_s2xo_SRS9wn9OSs_kzA9Jfz8k

[@justchill99902]

How can she be always awesome at the explanations? Thank you so much :)

[@DennisRiungu]

Beautifully expounded. Thank you

[@labyrinth1991]

Such a clear explanation!! thank you !! :) :)

[@sambo-g9871]

So, I understand how the bias adds flexibility to the neural network but I'm still confused about a couple things: 1. The bias seems to be no different from the weights that gets adjusted during training. If the weights and the bias both get updated during training, then wouldn't that mean that adding the bias is somewhat redundant because the output of the neuron will still converge to a similar value? Unless adding a bias is similar to adding, say another neuron to a hidden layer or adding another hidden layer. Meaning that it provides enough of a difference that you can get a more optimal result by adding a bias. 2. Is the function that updates the weights different from the function that updates the bias? For example, if using backpropagation, is the algorithm calculating (and updating) the weights and bias in the same calculation? 3. It seems as though the bias is compensating for the inflexibility of the activation function. If that's true, is it then possible to choose an activation function that is more flexible (assuming it exists)? Also, what stops you from adding more than one bias to a neuron? Has that been done? At what point would you stop adding additional biases to a neuron (which I would guess greatly increase complexity). My guess would be that adding multiple biases to a single neuron would be similar to adding multiple layers to a neural network, meaning that at first it makes a difference but at some point the complexity eventually outweighs the optimal result you get from the neural network itself. Is that correct? Great videos btw, really well put together :)

[@deeplizard]

Hey Sem - Thank you, I’m glad you’re liking the videos! These are all good questions. Let me take a shot at them. 1. While the weights and biases are both types of learnable parameters in the network, they influence the network in different ways. For example, changing the values for the weights can influence where we fall on the graph of the activation function, say relu, for a particular layer, but changing the value for the biases will change the position of the graph of relu all-together. The response for (3) elaborates more on this. 2. Yes, the weights and biases are being updated at the same time using SGD and backpropagation. It’s not necessarily happening in the same _calculation,_ but it is happening in the same step. Just as we saw in the backprop videos earlier in this playlist, SGD calculates the gradient of the loss with respect to the weights (via backprop) and then updates the weights with the result. For bias, SGD similarly does this same process of calculating the gradient, but with respect to the biases rather than the weights. 3. That’s one way of thinking about it-- as some sort of compensation for the inflexibility of the activation function. I’m not sure of a “more flexible” non-linear activation function that exists and has been adopted for use in neural networks. Relu is pretty much the go-to standard for now. If you think about the graph of relu though, you could actually think of it as maybe being pretty flexible. I mean, it's a linear function for all numbers greater than or equal to zero, so it spans the entire positive number line. But when we think about adding bias, we can think of the entire graph of relu shifting to the left or to the right. We’re handing over flexiblity to the training algorithm to decide what it should mean for a neuron to be meaningfully activated, rather than just saying, “if you’re greater than zero, you’re active” and also having it decide different levels of activations for different neurons all using the same underlying activation function. I’ve never come across having more than one bias per neuron. Since biases are additive, I would think of having more than one bias per neuron being redundant. If the network was able to learn optimal values for each of the individual biases assigned to a single neuron, which would ultimately be summed together, then it will also be able to learn the optimal value for a single bias term, which is what we see in practice today.

[@sambo-g9871]

OK yeah, makes sense. That helps me understand how biases work. Thanks! Btw, I think it's super cool how you take the time to answer your viewer's questions :)

[@EDeN99]

@@deeplizard Very super cool explanation. Nice work and nice voice too

[@waterflowzz]

For your first question, you may know this by now since the question is 3 years old but I’m giving my 2 cents so other people who might have the same question can think about it. Think of weights and bias in terms of a linear equation y=mx+b, m = weight (m is the slope in algebra) and b = bias (b is the constant in algebra). If you think of the equation graphically the m changes the slope and b determines the y-intercept. I think if you think of it this way, it’s much easier to grasp. I had the same question when I was learning about neural nets and I came across a video that explained it this way.

[@seraphimwang]

@@waterflowzz May I ask you which video, please? Anyway, I had similar idea 💡 which clarify why biases are additive. Cheers 🍻

[@tymothylim6550]

Thank you very much for this video! I really enjoyed this video and learning about bias! It was great to use the "relu" function to explain!

[@emeline894]

Perfectly explained. So easy to understand.

[@parisanejatian8940]

The best youtube channel for learning neural network

[@nathanielislas9245]

This is such a great explanation! Thank you

[@richarda1630]

once again you guys have helped make understandable something which was previously for me just something you had to plug into a formula . thanks!

[@richarda1630]

Where were you guys 5 years ago?? :) haha I see what you did at the end :D

[@x7331x]

Perfect explanation, congrats 🔥 !

[@CosmiaNebula]

0:29 intro 1:12 what is bias 3:00 simple example

[@vinodp8577]

Yay! Full screen is used for explaining, going forward could you please use full screen for the keras playlist as well

[@deeplizard]

Hey Vinod - Yes, for sure! Just released a new Keras video, and it's using full screen 😎 kzbin.info/www/bejne/sKPEnayfZ6unaJI

[@woah-dude]

nice to hear a female voice explaining IT stuff for once, never had that in my 7 years of software development

[@fosheimdet]

Whenever I clock on an IT video I expect it to have a heavy Indian accent

[@DrunkenMonkeyHD]

@@fosheimdet Savage.

[@GWebcob]

For sure. For me its the best channel on the topic so far

[@ifusubtomepewdiepiewillgiv1569]

best video but idc what gender does it bc im not sexist lol

[@woah-dude]

@@ifusubtomepewdiepiewillgiv1569 nothing to do with sexism amigo

[@joaopaulocasarejoscobra430]

Great explanation, thanks!

[@cjlooklin1914]

Oooh the Biases shift the activation threshold!!! I don't know why that took so long to understand XD

[@manjeetnagi]

very well explained.

[@helenapereira6775]

very helpful! Thank you

[@Waleed-qv8eg]

Great as always!!

[@deeplizard]

Thanks, Net4Easy!

[@igorgorpinich5197]

Super good video! Thank you!

[@Mo3azSolomon]

Good Explanation Thanks 💚

[@benbalaj1732]

0:50 Kerbal Space Program music is goated

[@AnoopKumarPrasad]

Great one.

[@pavankumard5276]

Really nice video finally understood it

[@alanjoy7915]

That was a nice explanation. Thank you

[@sanwalyousaf]

brilliant tutorial

[@panwong9624]

very helpful!

[@umshrana]

Thank you !

[@basantmounir]

You're amazing!!

[@pawansj7881]

Perfect!!

[@esraamohamed5601]

Thank you for your clear and nice video ..you are my hero

[@islanmohamed390]

Good explanation 👌🏿

[@caveman4659]

You saved me. Thanks!

[@josephmbimbi]

some graphical example, like a lign separating 2 "data clouds", and how not having bias makes some configuration of the 2 clouds not separable would have made the bias more understandable, and the video clearer

[@farjadmir8842]

Nice one .🥰

[@whatarewaves]

Wish you talked a bit more about how limited variance helps reduce the vanishing gradient problem specifically with an example. Also I know ReLU helps the vanishing gradient problem and it would have been interesting to see how that works too.

[@georgeognyanov]

Great videos and great series obviously! Quick question, is bias in DL the same as the bias in ML, aka the constant, the y-intercept, b0. Like looking at the simplest linear regression formula y = b0 + w1x1 does the bias there do something similar to the bias just discussed in the video or are they totally completely different things.

[@quadracycle4000]

Came for 1:28, stayed to 7:12. Very informative!

[@farzadimanpoursardroudi45]

very useful

[@aorusaki]

Nice! :)

[@timharris72]

This tutorial was awesome. Have you thought about doing more basic tutorials with some math (real like this example, not conceptual) and only 2 or 3 nodes to explain some of the concepts. When you do some basic math and keep the examples really simple it really starts to make sense.

[@deeplizard]

(Sorry if you’re getting spammed with my comment. I’ve tried replying a few times, but it’s not showing as being posted to you.) Thanks, Tim! Yeah, I’ve experimented with this approach recently, and I liked it as well. In fact, I just used a simple network and some basic math to illustrate the concept in my latest video that I just released a few minutes ago: kzbin.info/www/bejne/ppiWmX2miNSjfrM Appreciate your feedback!

[@timharris72]

I watched the video. The numbers really helped out. Thanks for using the math.

[@deeplizard]

Glad to hear!

[@mdyeasinarafath4450]

That was another great work, Mam! We can't control bias, but at-least can't we specify that bias should be the opposite of threshold? And we know how weights update by multipying the gradient with the learning rate. But how does biases update?

[@deeplizard]

Thanks, Md.Yasin Arafat Yen! We won't need to tell an API, like Keras for example, that bias should be the opposite of the threshold-like value that we talked about here, because Keras interprets the bias as meaning just that already. You can see what exactly we have control over in the Keras video illustrating how to access and initialize the bias terms: kzbin.info/www/bejne/sKPEnayfZ6unaJI The biases get updated in the same way as the weights. SGD calculates the gradient of the loss with respect to each bias, then multiplies this gradient by the learning rate, then subtracts this product from the current value of the bias to get the updated value for the bias.

[@David-bp2zh]

It is a clear explanation. I wonder which tool did you prepare this lecture?

[@AdSd100]

Lol I thought my KSP was running in the background. Do you play it?

[@deeplizard]

Haha I actually just had to look up what KSP is. In doing so, I heard the same track 😆 They used the same music library as I did.

[@AdSd100]

@@deeplizard Great work BTW!

[@deeplizard]

Thank you!

[@drevolan]

I just found this channel because of Reddit and I must say: it's quite interesting! It's presented in an easy to understand manner and I enjoy the narration of both hosts. My only complaint would be to work on the visuals, they seem a little bland and at times they look a bit more like a power point presentation than an actual video. But that'll come with more experience, overall I really enjoy the channel. Hope to see more content from you guys in the future!

[@deeplizard]

Hey dangsterr - Really appreciate your feedback! Thank you. We're glad to hear that you're liking the channel! We're both new to video creation, so we've been consistently working on our style and exploring new techniques. Thanks for the feedback regarding the visuals. We'll keep that in mind.

[@ravishankar2180]

visuals can be ignored as long as content is awesome and your content indeed takes good care of that.

[@JoseTorres-tr6od]

Hello deeplizard, after taking a deep learning class I became unsatisfied with the explanations provided for backpropagation, we were given the weight update formulas for an specific 2 hidden layer network(relu, relu, sigmoid) to train for MNIST. Ever since, I have been independently trying to come up with the formulas for a similar NN, and yesterday I was finally able to get the update formulas for non-output layer weights. When I run my program however, my network is only able to adjust its weights for a single example of X(input) and Y(input). I have always been aware that the entire backprop derivation is based on gradient descent for a single example, but I thought that alternating between (input/output) from my training set would be sufficient to extract "the pattern", it does not. In one of your videos you said that you don't immediately update the weights but average the changes of an entire batch. Could you explain as to the logic/math or intuition behind this? Thank you.

[@deeplizard]

Hey Jose - Check out the following video starting at 11:55: kzbin.info/www/bejne/kKOYp5x3j6yhmqc To summarize, you take the gradient of the loss with respect to a particular weight for _each_ input. You then average the resulting gradients and update the given weight with that average. This would be the case if you passed _all_ the data to your network at once. If instead you were doing batch gradient descent, where you were passing mini-batches of data to your network at a time, then you would apply this same method to each batch of data, rather than to all the data at once. Does this help clarify?

[@JoseTorres-tr6od]

deeplizard Thank you!

[@SM-ob5sm]

I love the way these videos explain ANN, easy to understand. But I am really distracted with the music in the background on and off. :(

[@justchill99902]

Question - As SGD also updates the biases while training, 1.how are they updated? using backpropagation just like the weights? 2. Since bias changes affect the activation output which in turn also depends on the weights, do bias updates conflict with weight updates? Thank you lizzy!

[@kemsekov6331]

Imagine each layer as a combination of different functions that sums up to some figure in input - output space. You need to add together these functions in such a way, that they replicate these data figure, and so bias are just shifting parameter. That's it. It just shifts function a bit further or closer so it's most suited parts will be used to approximate figure.

[@amangoyal476]

I understood most of it but I had a query: In the second example of bias , why would the bias be -5 if only weighted sum >= 5 are allowed ?

[@nellynelly7551]

Recall that the goal of the bias is to change the allowed weighted sum by shifting the graph either to the left or the right. ReLu states that only weighted sums of >= 0 are allowed. If we want to shift this to the right, we add -5 to any weighted sum. This makes 5 the new 0 (5-5=0) and only values above five will be outputted.

[@carbdoto2523]

thx

[@adrianogoeswild]

Late one here :). Quick question You mentioned that the bias will be readjusted at every backprop step along with the weights, with the exception that we will calculate thw gradientd w.r.t the weights and biases individially. Now the question, wouldn't it make sense to add the bias as a weight with it's neuron equal to one? With the exception that the weights of the previous layer are not connected to this bias neuron. I hope i was clear somehow. Thanks alotttttt :)

[@deeplizard]

Intuitively, you could think of the bias as a node not connected to the weights in the previously layer, but in terms of it being equal to one, that would only be true when we initialize all the bias terms (assuming we initialize them all to one). During training, the values will change.

[@sathyakumarn7619]

Is it probable that new videos might be added to this playlist?

[@deeplizard]

It's possible :) In more advanced future courses, if we notice that a fundamental topic needs to be covered in order to understand the advanced material, and that topic isn't already in this Fundamentals course, then we will likely add it here.

[@DEEPAKSV99]

0:08 Are you really planning to do another series on bias from a political or social standpoint? xD It may not be easy to deliver them in short and sweet fashion like you always do. But who knows, you may be patient enough to even break those topics into simple logics and propose your solutions :')

[@deeplizard]

😅

[@saluk7419]

Yeah I actually thought before clicking that would be what this video was about. The success of deep learning is really limited by the quality of the input, so bias in selecting samples is a big issue! I had no idea that there was a concept of intentional biases within the neural network itself haha.

[@dourwolfgames9331]

How do I adjust the bias? I'm pretty sure that its during backpropagation after retrieving the negative cost gradient, but I don't know what the adjustments to the bias are based off of. Does it have something to do with the changes to weights? I'm still very much learning and I may be incorrect. =)

[@deeplizard]

Hey Dour - Yes, you're exactly right, the adjustment to the bias occurs during backpropagation. Just as the gradient of the loss is calculated with respect to each weight, and then the respective gradient is used to update each weight, the same thing occurs for each bias. The gradient of the loss is calculated with respect to each bias, and then the respective gradient is used to update each bias. Let me know if this helps clarify!

[@sumitdas7489]

but withought using bias if we use leaky Relu instead of Relu then also we can avoid dead activation right? then we dont need biases

[@iAndrewMontanai]

and no single word about how actually bias is learning

[@ltoco4415]

Is bias same as threshold? if not then what is the difference between them because bias determines if a neuron is activated or not, so that seems to be same as threshold.

[@yuanzhang1230]

{ "question": "In practice, can you explicitly choose and control the weights in a network?", "choices": [ "Yes", "No", "I can control a little", "It depends" ], "answer": "Yes", "creator": "SummerGift", "creationDate": "2020-07-10T00:16:01.160Z" }

[@yuanzhang1230]

I make a mistake, the answer is No。

[@yuanzhang1230]

Hmm, i want to say control the bias not the weights.

[@deeplizard]

Thanks, Yuan! Just added your question to deeplizard.com/learn/video/HetFihsXSys :)

[@yuanzhang1230]

@@deeplizard It seems i can't find my question now? Did you cancel my question?

[@deeplizard]

No, it's on the site at the link above. You may need to refresh your cache to see it.

[@Ahmadalisalh6012]

why i would like to determine the threshold? thank you

[@mushoodbadulla9305]

very good video, but drop the music.

[@naprava7522]

Thanks. But I still feel that by updating the weight we can have the same thing. To me it feels like it’s equivalent. But i know that I am probably wrong.

[@bytblaster]

I dont realy understand this. If the Bias is just another weight...why wouldnt it just change the weights to be higer in the backpropagation steps so important neurons DO get fired?

[@JimmyCheng]

Just a suggestion, the recording volume can be turned up a notch, the ads are really loud compare to ur voice haha

[@deeplizard]

Thanks for the suggestion, Ziqiang! I've been trying to tune the audio and sound levels recently. What do you think of the volume of this newer video: kzbin.info/www/bejne/eJTYm2Wcia1nlZY Still may need to be brought up a notch?

[@JimmyCheng]

@@deeplizard could be louder still imo. But again you have such a soft and beautiful voice maybe some extra volume is needed haha

[@deeplizard]

Thanks for the feedback!

[@ahmadzbedi1745]

können Sie mir eine Referenz oder ein Buch dafür empfehlen. ich muss den Begriff Bias in meiner BA erörten aber das muss ich einfach zitieren

[@neurojedi42]

The thing i didn't understand is why we need bias ? Let's say the transfer function results with -0.35 so the will be no firing but when we add a bias there will be a firing. The thing is, doesn't it let a neuron fire which shouldn't actually fire. I mean wouldn't it let misinterpretation of data ?

[@ronithsinha5702]

What if you use logistic function as an activation function? In that case, why would we need a bias?

[@deeplizard]

Hey Ronith - The principle would be the same with a logistic function. The bias terms would be parameters that SGD would learn and optimize to signal what it means for given nodes to be meaningfully activated. By adding bias, you can think of the graph of the logistic curve shifting to the left or to the right (based on whether the bias was positive or negative), rather than staying centered.

[@prasannakumar7035]

so before passing inputs to the activations function its good to add bias value it seems!so that all the neuron will fire some value:)

[@yanhaeffner7881]

I can't watch this video without thinking about building a rocket... Soundtrack related.

[@deeplizard]

Haha is that a good thing? Building a rocket sounds inspiring.

[@yanhaeffner7881]

Yeah, sure it is hahaha By the way, great video! I know that is really hard to keep up the whole thing with graphical methods but I guess that a function view of bias would have made it a little bit clearer, but, that's just a spec of dust on a big surface for what this video is! We really need more videos like that!

[@wiratamaradiance]

Thanks for your explaination, it really help me to understand it but your BGM really disturb my focus

[@deeplizard]

Thanks for the feedback yoza, BGM has been removed in later videos.

[@yoloswag6242]

0:47 is that KERBAL SPACE PROGRAM ost? omg omg

[@deeplizard]

Haha yes! KSP creators used the same music library as we did :D

[@BrotherDoorkeeper]

"With an activation output of 0, this neuron is considered to not be activated. Or not firing." Does a not activated/not firing neuron still pass 0 as an output to the next layer?

[@EDeN99]

@Szabolcs Ambrus, Mathematically speaking, a non-activated neuron still passes 0 to the next layer since it has to pass whatever it output is onward for multiplication with the connected weights. But Come to think of it, when the 0 which it passes to the next layer (after being multiplied with the connected weights) gets to the next layer, it still appears as 0 in the next layer and since each neuron in the next layer sums all the weighted outputs from the previous layer, the weighted output from the "non-activated" neuron will have no effect since its value is 0. This is actually why the term "not activated/not firing" is used since its output has no effect. I hope this helps. I am also learning myself.

[@lankanathaekanayake7680]

how about we adjust weights for activate output neuron instead of adding additional bias parameter?

[@deeplizard]

Hey Lankanatha - While the weights and biases are both types of learnable parameters in the network, they influence the network in different ways. For example, changing the values for the weights can influence where we fall on the graph of the activation function, say relu, for a particular layer, but changing the value for the biases will change the position of the graph of relu all-together (by shifting the graph to the left or right).

[@DanielSchaefer01]

Great video! Just one comment though: the moving background is pretty distracting!

[@deeplizard]

Appreciate the feedback, Daniel!

[@mahendrank9060]

please build neural network that is based on realtime datasets

[@leonhardeuler9839]

But what actually are weights? Do we pick them randomly or there is a formula for that?

[@deeplizard]

Check out the video and blog for weight initialization: deeplizard.com/learn/video/8krd5qKVw-Q

[@NK-nf2ym]

How do biases get adjusted during training, witch functions

[@deeplizard]

They are adjusted in the same way in which the weights are adjusted. You can learn how exactly the adjustments occur on the episodes regarding backpropagation, starting with this one: deeplizard.com/learn/video/XE3krf3CQls

[@saanvisharma2081]

2:54 bias(b) should be added to each neuron. But, here they've added single 'b' did they forgotten to insert bracket

[@justchill99902]

No @Saanvi. The weighted sum is the sum of all multiplied individual weight and input values from the left layer( e.g. input layer) So, these are multiplied and given to "a single neuron" at the right side layer(e.g. hidden layer). Now a "bias" is added to the "hidden layer neuron" where this weighted sum from all input layer neuron is applied. So bias is given to that particular neuron(while is one neuron) and therefore one value of bias. For the next neuron in the same hidden layer, again we feed a weighted sum from the input layer neurons and "one bias" and so on for every neuron in the network. Hope this helps.

[@my-jorney]

KSP music😄

[@sai1734]

why bias not 2 ?

[@victorburca5028]

I watched the explanation several times. I understood all your words, but I still have not understood the practical purpose of bias. Do you just use it to increase/decrease the input for a neuron?! Why?! The neuron will send its value (output) to the next neuron indifferent to the value of that output. So it will "fire" always. There are no situations when a neuron will not send the output to the next neuron. Even when the value is equal to zero, it will still be sent to the next neuron. I am looking for another youtube explanation.

[@madisonforsyth9184]

the music in the background is so. distracting. omg. i have to turn captions on and mute it. why am i even on youtube???

[@deeplizard]

We were experimenting with background music at the point when this video was made. Agree that it is distracting, so we cut way back on it in later videos

[@yuyangtu8687]

I feel dizzy when I watch this video

[@fredericfc]

This is hurting my head 🤕

[@deeplizard]

More coffee ☕

[@fredericfc]

@@deeplizard Just went to the kitchen and made some nespresso to have with cookies 🍪 never feels so lonely like today, and my so called buddies only know olap. help me deeplizard!

[@salahuddinusman2066]

i am too biased hearing to your lovely voice!!!

[@merie8265]

hey what's going on today ..Corona virus and lockdowns

[@KingDav33]

This video seems to be really biased...

[@deeplizard]

😆

[@annankldun4040]

Really ruined it with music. Please don't use music in educational videos. Makes no sense.

[@deeplizard]

We were experimenting with audio and music at the time of making this episode. In hindsight, agree, bad idea. We no longer include it during technical discussion.

[@deeplizard]

Also, note that each episode has a corresponding written blog that you can use as well. deeplizard.com/learn/video/HetFihsXSys

[@yichern4351]

Legit expected a guy voice ngl

[@deeplizard]

🙋

[@GauravSingh-ku5xy]

Adopt me.

[@deeplizard]

😅😅

[@chavorocket]

closed the video as soon as I heard a female voice

[@ahmedaj2000]

really good explanation, thank you!