Creating thinned models in during Dropout process
$begingroup$
Applying dropout to a neural network amounts to sampling a “thinned” network from it. The thinned network consists of all the units that survived dropout. A neural net with n units can be seen as a collection of 2^n possible thinned neural networks.
Source:
Dropout: A Simple Way to Prevent Neural Networks fromOverfitting, pg. 1931.
How are we getting these 2^n models?
machine-learning deep-learning dropout
edited 2 days ago
Djib2011
2,58931125
asked 2 days ago
ashirwadashirwad
213
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add a comment |
$begingroup$
Applying dropout to a neural network amounts to sampling a “thinned” network from it. The thinned network consists of all the units that survived dropout. A neural net with n units can be seen as a collection of 2^n possible thinned neural networks.
Source:
Dropout: A Simple Way to Prevent Neural Networks fromOverfitting, pg. 1931.
How are we getting these 2^n models?
machine-learning deep-learning dropout
edited 2 days ago
Djib2011
2,58931125
asked 2 days ago
ashirwadashirwad
213
New contributor
ashirwad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Applying dropout to a neural network amounts to sampling a “thinned” network from it. The thinned network consists of all the units that survived dropout. A neural net with n units can be seen as a collection of 2^n possible thinned neural networks.
Source:
Dropout: A Simple Way to Prevent Neural Networks fromOverfitting, pg. 1931.
How are we getting these 2^n models?
machine-learning deep-learning dropout
edited 2 days ago
Djib2011
2,58931125
asked 2 days ago
ashirwadashirwad
213
New contributor
ashirwad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Applying dropout to a neural network amounts to sampling a “thinned” network from it. The thinned network consists of all the units that survived dropout. A neural net with n units can be seen as a collection of 2^n possible thinned neural networks.
Source:
Dropout: A Simple Way to Prevent Neural Networks fromOverfitting, pg. 1931.
How are we getting these 2^n models?
machine-learning deep-learning dropout
machine-learning deep-learning dropout
edited 2 days ago
Djib2011
2,58931125
asked 2 days ago
ashirwadashirwad
213
New contributor
ashirwad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Djib2011
2,58931125
asked 2 days ago
ashirwadashirwad
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ashirwad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 2 days ago
Djib2011
2,58931125
edited 2 days ago
Djib2011
2,58931125
edited 2 days ago
Djib2011
2,58931125
2,58931125
asked 2 days ago
ashirwadashirwad
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asked 2 days ago
ashirwadashirwad
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asked 2 days ago
ashirwadashirwad
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213
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2 Answers
2
active
oldest
votes
$begingroup$
The statement is a bit oversimplifying but the idea is that assuming we have $n$ nodes and each of these nodes might be "dropped", we have $2^n$ possible thinned neural networks. Obviously dropping out an entire layer would alter the whole structure of the network but the idea is straightforward: we ignore the activation/information from certain randomly selected neurons and thus encourage redundancy learning and discourage over-fitting on very specific features.
The same idea has also been employed in Gradient Boosting Machines where instead of "ignoring neurons" we "ignore trees" at random (see Rashmi & Gilad-Bachrach (2015) DART: Dropouts meet Multiple Additive Regression Trees on that matter).
Minor edit: I just saw Djib2011's answer. (+1) He/she specifically shows why the statement is somewhat over-simplifying. If we assume that we can drop any (or all, or none) of the neurons we have $2^n$ possible networks.
answered 2 days ago
usεr11852usεr11852
19.3k14274
$endgroup$
add a comment |
$begingroup$
I too haven't understood their reasoning, I always assumed it was a typo or something...
The way I see it we if we have $n$ hidden units in a Neural Network with a single hidden layer and we apply dropout keeping $r$ of those, we'll have:
$$
frac{n!}{r! cdot (n-r)!}
$$
possible combinations (not $2^n$ as the authors state).
Example:
Assume a simple fully connected neural network with a single hidden layer with 4 neurons. This means the hidden layer will have 4 outputs $h_1, h_2, h_3, h_4$.
Now, you want to apply dropout to this layer with a 0.5 probability (i.e. half of the outputs will be dropped).
Since 2 out of the 4 outputs will be dropped, at each training iteration we'll have one of the following possibilities:
- $h_1, h_2$
- $h_1, h_3$
- $h_1, h_4$
- $h_2, h_3$
- $h_2, h_4$
- $h_3, h_4$
or by applying the formula:
$$
frac{4!}{2! cdot (4-2)!} = frac{24}{2 cdot 2} = 6
$$
answered 2 days ago
Djib2011Djib2011
2,58931125
$endgroup$
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
add a comment |
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2 Answers
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active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
The statement is a bit oversimplifying but the idea is that assuming we have $n$ nodes and each of these nodes might be "dropped", we have $2^n$ possible thinned neural networks. Obviously dropping out an entire layer would alter the whole structure of the network but the idea is straightforward: we ignore the activation/information from certain randomly selected neurons and thus encourage redundancy learning and discourage over-fitting on very specific features.
The same idea has also been employed in Gradient Boosting Machines where instead of "ignoring neurons" we "ignore trees" at random (see Rashmi & Gilad-Bachrach (2015) DART: Dropouts meet Multiple Additive Regression Trees on that matter).
Minor edit: I just saw Djib2011's answer. (+1) He/she specifically shows why the statement is somewhat over-simplifying. If we assume that we can drop any (or all, or none) of the neurons we have $2^n$ possible networks.
answered 2 days ago
usεr11852usεr11852
19.3k14274
$endgroup$
add a comment |
$begingroup$
The statement is a bit oversimplifying but the idea is that assuming we have $n$ nodes and each of these nodes might be "dropped", we have $2^n$ possible thinned neural networks. Obviously dropping out an entire layer would alter the whole structure of the network but the idea is straightforward: we ignore the activation/information from certain randomly selected neurons and thus encourage redundancy learning and discourage over-fitting on very specific features.
The same idea has also been employed in Gradient Boosting Machines where instead of "ignoring neurons" we "ignore trees" at random (see Rashmi & Gilad-Bachrach (2015) DART: Dropouts meet Multiple Additive Regression Trees on that matter).
Minor edit: I just saw Djib2011's answer. (+1) He/she specifically shows why the statement is somewhat over-simplifying. If we assume that we can drop any (or all, or none) of the neurons we have $2^n$ possible networks.
answered 2 days ago
usεr11852usεr11852
19.3k14274
$endgroup$
add a comment |
$begingroup$
The statement is a bit oversimplifying but the idea is that assuming we have $n$ nodes and each of these nodes might be "dropped", we have $2^n$ possible thinned neural networks. Obviously dropping out an entire layer would alter the whole structure of the network but the idea is straightforward: we ignore the activation/information from certain randomly selected neurons and thus encourage redundancy learning and discourage over-fitting on very specific features.
The same idea has also been employed in Gradient Boosting Machines where instead of "ignoring neurons" we "ignore trees" at random (see Rashmi & Gilad-Bachrach (2015) DART: Dropouts meet Multiple Additive Regression Trees on that matter).
Minor edit: I just saw Djib2011's answer. (+1) He/she specifically shows why the statement is somewhat over-simplifying. If we assume that we can drop any (or all, or none) of the neurons we have $2^n$ possible networks.
answered 2 days ago
usεr11852usεr11852
19.3k14274
$endgroup$
The statement is a bit oversimplifying but the idea is that assuming we have $n$ nodes and each of these nodes might be "dropped", we have $2^n$ possible thinned neural networks. Obviously dropping out an entire layer would alter the whole structure of the network but the idea is straightforward: we ignore the activation/information from certain randomly selected neurons and thus encourage redundancy learning and discourage over-fitting on very specific features.
The same idea has also been employed in Gradient Boosting Machines where instead of "ignoring neurons" we "ignore trees" at random (see Rashmi & Gilad-Bachrach (2015) DART: Dropouts meet Multiple Additive Regression Trees on that matter).
Minor edit: I just saw Djib2011's answer. (+1) He/she specifically shows why the statement is somewhat over-simplifying. If we assume that we can drop any (or all, or none) of the neurons we have $2^n$ possible networks.
answered 2 days ago
usεr11852usεr11852
19.3k14274
edited 2 days ago
answered 2 days ago
usεr11852usεr11852
19.3k14274
answered 2 days ago
usεr11852usεr11852
19.3k14274
answered 2 days ago
usεr11852usεr11852
19.3k14274
19.3k14274
add a comment |
add a comment |
$begingroup$
I too haven't understood their reasoning, I always assumed it was a typo or something...
The way I see it we if we have $n$ hidden units in a Neural Network with a single hidden layer and we apply dropout keeping $r$ of those, we'll have:
$$
frac{n!}{r! cdot (n-r)!}
$$
possible combinations (not $2^n$ as the authors state).
Example:
Assume a simple fully connected neural network with a single hidden layer with 4 neurons. This means the hidden layer will have 4 outputs $h_1, h_2, h_3, h_4$.
Now, you want to apply dropout to this layer with a 0.5 probability (i.e. half of the outputs will be dropped).
Since 2 out of the 4 outputs will be dropped, at each training iteration we'll have one of the following possibilities:
- $h_1, h_2$
- $h_1, h_3$
- $h_1, h_4$
- $h_2, h_3$
- $h_2, h_4$
- $h_3, h_4$
or by applying the formula:
$$
frac{4!}{2! cdot (4-2)!} = frac{24}{2 cdot 2} = 6
$$
answered 2 days ago
Djib2011Djib2011
2,58931125
$endgroup$
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
add a comment |
$begingroup$
I too haven't understood their reasoning, I always assumed it was a typo or something...
The way I see it we if we have $n$ hidden units in a Neural Network with a single hidden layer and we apply dropout keeping $r$ of those, we'll have:
$$
frac{n!}{r! cdot (n-r)!}
$$
possible combinations (not $2^n$ as the authors state).
Example:
Assume a simple fully connected neural network with a single hidden layer with 4 neurons. This means the hidden layer will have 4 outputs $h_1, h_2, h_3, h_4$.
Now, you want to apply dropout to this layer with a 0.5 probability (i.e. half of the outputs will be dropped).
Since 2 out of the 4 outputs will be dropped, at each training iteration we'll have one of the following possibilities:
- $h_1, h_2$
- $h_1, h_3$
- $h_1, h_4$
- $h_2, h_3$
- $h_2, h_4$
- $h_3, h_4$
or by applying the formula:
$$
frac{4!}{2! cdot (4-2)!} = frac{24}{2 cdot 2} = 6
$$
answered 2 days ago
Djib2011Djib2011
2,58931125
$endgroup$
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
add a comment |
$begingroup$
I too haven't understood their reasoning, I always assumed it was a typo or something...
The way I see it we if we have $n$ hidden units in a Neural Network with a single hidden layer and we apply dropout keeping $r$ of those, we'll have:
$$
frac{n!}{r! cdot (n-r)!}
$$
possible combinations (not $2^n$ as the authors state).
Example:
Assume a simple fully connected neural network with a single hidden layer with 4 neurons. This means the hidden layer will have 4 outputs $h_1, h_2, h_3, h_4$.
Now, you want to apply dropout to this layer with a 0.5 probability (i.e. half of the outputs will be dropped).
Since 2 out of the 4 outputs will be dropped, at each training iteration we'll have one of the following possibilities:
- $h_1, h_2$
- $h_1, h_3$
- $h_1, h_4$
- $h_2, h_3$
- $h_2, h_4$
- $h_3, h_4$
or by applying the formula:
$$
frac{4!}{2! cdot (4-2)!} = frac{24}{2 cdot 2} = 6
$$
answered 2 days ago
Djib2011Djib2011
2,58931125
$endgroup$
I too haven't understood their reasoning, I always assumed it was a typo or something...
The way I see it we if we have $n$ hidden units in a Neural Network with a single hidden layer and we apply dropout keeping $r$ of those, we'll have:
$$
frac{n!}{r! cdot (n-r)!}
$$
possible combinations (not $2^n$ as the authors state).
Example:
Assume a simple fully connected neural network with a single hidden layer with 4 neurons. This means the hidden layer will have 4 outputs $h_1, h_2, h_3, h_4$.
Now, you want to apply dropout to this layer with a 0.5 probability (i.e. half of the outputs will be dropped).
Since 2 out of the 4 outputs will be dropped, at each training iteration we'll have one of the following possibilities:
- $h_1, h_2$
- $h_1, h_3$
- $h_1, h_4$
- $h_2, h_3$
- $h_2, h_4$
- $h_3, h_4$
or by applying the formula:
$$
frac{4!}{2! cdot (4-2)!} = frac{24}{2 cdot 2} = 6
$$
answered 2 days ago
Djib2011Djib2011
2,58931125
answered 2 days ago
Djib2011Djib2011
2,58931125
answered 2 days ago
Djib2011Djib2011
2,58931125
answered 2 days ago
Djib2011Djib2011
2,58931125
2,58931125
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
add a comment |
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
3
3
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
$begingroup$
I do not think that most implementations of dropout work by saying: If there are 100 neurons, and the probability is 0.05, I have to disable exactly 5 neurons chosen at random. Instead each neuron is disabled with a probability of 0.05, independently of what happens with the rest. Hence, the cases where all or no neurons are disabled, while unlikely, are possible.
$endgroup$
– Daniel López
2 days ago
1
1
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
$begingroup$
@DanielLópez: I think both you and Djib2011 (+1 both) are "factually correct" on this. The statement is clearly oversimplifying things. You also need to take into account that most the networks that this paper is concerned with, have thousands of neurons so certain it is kind of accepted that no layer will be totally switched off.
$endgroup$
– usεr11852
2 days ago
2
2
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Agree, but I believe the above example is transmitting the idea that exactly $n cdot text{prob}$ units are disabled with dropout, where $text{prob}$ is the dropout probability. And this is not how dropout works.
$endgroup$
– Daniel López
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
Well... LLN is our friend. :)
$endgroup$
– usεr11852
2 days ago
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
$begingroup$
The flaw with the reasoning presented here is that dropout sets weights to 0 with some fixed probability independently. This implies that the number of zero weights at each step has a binomial distribution, because dropout has the three defining characteristics of a binomial distribution 1 dichotomous outcomes (weights are on or off) 2 fixed number of trials (number of weights in the model doesn't change) 3 probability of success is fixed & independent for each trial.
$endgroup$
– Sycorax
yesterday
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ashirwad is a new contributor. Be nice, and check out our Code of Conduct.
ashirwad is a new contributor. Be nice, and check out our Code of Conduct.
ashirwad is a new contributor. Be nice, and check out our Code of Conduct.
ashirwad is a new contributor. Be nice, and check out our Code of Conduct.
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