Mixing
How resistant are Neural Networks to injected Noise?
$begingroup$
Let's consider a classic feedforward neural network $F$ with input dimension $d$, output dimension $k$, $L$ layers $l_i$ with $m$ neurons each. ReLu activation.
This means that, given a point $x in R^d$ its image $F(x) in R^k$. Let's now assume i add some gaussian noise $eta_i$ in the hidden layer $l_i(x)$, where the norm of this noise is 5% the norm of its layer computed on the point $x$. How does this noise propagate trough the network?
I know that, empirically, neural networks are resistant to this kind of noise, especially when it's injected on the the first layers. How can i show this theoretically?
The question i'm trying to answer is the following:
Let's consider two different functions: one is the original network $F$, the other one, $F_i$, behaves exactly like $F$, but it adds random noise $eta_i$ on the $i-$th layer, where $||eta|| = ||l_i(x)||/20 $. After having injected this noise $eta_i$ in the layer $l_i(x)$, how far the output $F_{i}(x)$ will be from the output of the original neural network $F(x)$? e.g., what's $$|| F(x) - F_i(x)||?$$
machine-learning neural-networks noise
asked Jan 12 at 15:30
AlfredAlfred
336
$endgroup$
add a comment |
$begingroup$
Let's consider a classic feedforward neural network $F$ with input dimension $d$, output dimension $k$, $L$ layers $l_i$ with $m$ neurons each. ReLu activation.
This means that, given a point $x in R^d$ its image $F(x) in R^k$. Let's now assume i add some gaussian noise $eta_i$ in the hidden layer $l_i(x)$, where the norm of this noise is 5% the norm of its layer computed on the point $x$. How does this noise propagate trough the network?
I know that, empirically, neural networks are resistant to this kind of noise, especially when it's injected on the the first layers. How can i show this theoretically?
The question i'm trying to answer is the following:
Let's consider two different functions: one is the original network $F$, the other one, $F_i$, behaves exactly like $F$, but it adds random noise $eta_i$ on the $i-$th layer, where $||eta|| = ||l_i(x)||/20 $. After having injected this noise $eta_i$ in the layer $l_i(x)$, how far the output $F_{i}(x)$ will be from the output of the original neural network $F(x)$? e.g., what's $$|| F(x) - F_i(x)||?$$
machine-learning neural-networks noise
asked Jan 12 at 15:30
AlfredAlfred
336
$endgroup$
add a comment |
$begingroup$
Let's consider a classic feedforward neural network $F$ with input dimension $d$, output dimension $k$, $L$ layers $l_i$ with $m$ neurons each. ReLu activation.
This means that, given a point $x in R^d$ its image $F(x) in R^k$. Let's now assume i add some gaussian noise $eta_i$ in the hidden layer $l_i(x)$, where the norm of this noise is 5% the norm of its layer computed on the point $x$. How does this noise propagate trough the network?
I know that, empirically, neural networks are resistant to this kind of noise, especially when it's injected on the the first layers. How can i show this theoretically?
The question i'm trying to answer is the following:
Let's consider two different functions: one is the original network $F$, the other one, $F_i$, behaves exactly like $F$, but it adds random noise $eta_i$ on the $i-$th layer, where $||eta|| = ||l_i(x)||/20 $. After having injected this noise $eta_i$ in the layer $l_i(x)$, how far the output $F_{i}(x)$ will be from the output of the original neural network $F(x)$? e.g., what's $$|| F(x) - F_i(x)||?$$
machine-learning neural-networks noise
asked Jan 12 at 15:30
AlfredAlfred
336
$endgroup$
Let's consider a classic feedforward neural network $F$ with input dimension $d$, output dimension $k$, $L$ layers $l_i$ with $m$ neurons each. ReLu activation.
This means that, given a point $x in R^d$ its image $F(x) in R^k$. Let's now assume i add some gaussian noise $eta_i$ in the hidden layer $l_i(x)$, where the norm of this noise is 5% the norm of its layer computed on the point $x$. How does this noise propagate trough the network?
I know that, empirically, neural networks are resistant to this kind of noise, especially when it's injected on the the first layers. How can i show this theoretically?
The question i'm trying to answer is the following:
Let's consider two different functions: one is the original network $F$, the other one, $F_i$, behaves exactly like $F$, but it adds random noise $eta_i$ on the $i-$th layer, where $||eta|| = ||l_i(x)||/20 $. After having injected this noise $eta_i$ in the layer $l_i(x)$, how far the output $F_{i}(x)$ will be from the output of the original neural network $F(x)$? e.g., what's $$|| F(x) - F_i(x)||?$$
machine-learning neural-networks noise
machine-learning neural-networks noise
asked Jan 12 at 15:30
AlfredAlfred
336
asked Jan 12 at 15:30
AlfredAlfred
336
asked Jan 12 at 15:30
AlfredAlfred
336
asked Jan 12 at 15:30
AlfredAlfred
336
asked Jan 12 at 15:30
AlfredAlfred
336
336
add a comment |
add a comment |
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