Answers.Body: <p>Unfortunately, there is no <em>theoretically</em> optimal parameter for a neural network. However, they can be roughly defined when talking about a specific topic or application domain. <em>Normalization</em> is a very important procedure in the operation of neural networks. Normalization makes it easier for the network to recognize different <em>patterns</em>. By scaling all inputs between two numbers, the network will be able to recognize and generalize many different patterns.</p>
  <p>Let's take a look at these two input arrays:</p>
  <pre><code>[89, 90, 27, 0, 29, 42, 78, 33, 78, 12]
  [1.186667, 1.2, 0.36, 0, 0.386667, 0.56, 1.04, 0.44, 1.04, 0.16]
  </code></pre>
  <p>At first glance, these seem like two completely different arrays, right?
  It would be very difficult to determine anything from them.</p>
  <p>Let's scale them between <em>0</em> and <em>1</em>:</p>
  <pre><code>var array1:Array = [89, 90, 27, 0, 29, 42, 78, 33, 78, 12]
  var array2:Array = [1.186667, 1.2, 0.36, 0, 0.386667, 0.56, 1.04, 0.44, 1.04, 0.16]
  print(&quot;Array1: &quot; + str(normalize(array1)))
  print(&quot;Array2: &quot; + str(normalize(array2)))
  </code></pre>
  <p>The output:</p>
  <pre><code>Array1: [0.988889, 1, 0.3, 0, 0.322222, 0.466667, 0.866667, 0.366667, 0.866667, 0.133333]
  Array2: [0.988889, 1, 0.3, 0, 0.322223, 0.466667, 0.866667, 0.366667, 0.866667, 0.133333]
  </code></pre>
  <p>Now we can easily see that the patterns of the two arrays are exactly the same and show the same temporal changes. Likewise, the neural network can draw conclusions much more easily from normalized values.</p>
  <p>But then how can we decide which are the most optimal scaling ranges?</p>
  <h2>Normalization between -1 and 1:</h2>
  <p>If you are using activation functions like <strong>tanh</strong> that return only values between -1 and 1, it is a good idea to normalize the input data to this range as well. This will help the network to converge faster, as the distribution of the input data will better match the expected range of the activation function. If the input data contains both positive and negative values, normalising to the range -1 to 1 will ensure that the data is centred around zero.</p>
  <h2><strong>Normalization between 0 and 1:</strong></h2>
  <p>If you are using activation functions like <strong>Sigmoid</strong> or <strong>ReLU</strong>, it's a good idea to normalize input values between 0 and 1. The Sigmoid function gives values between 0 and 1, while ReLU gives only non-negative values. So normalization between 0 and 1 works well with these activation functions. If the input data only has positive values, such as pixel values (between 0 and 255), normalization between 0 and 1 is a natural choice because it is simple and easy to understand.</p>
  <hr />
  <p><em>In summary, the choice between normalising to [-1,1] or [0,1] depends on the activation functions used, and the nature of the data.</em></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-07-25T10:21:38.620Z
Answers.LastActivityDate: 2024-07-25T10:36:37.090Z
Answers.LastEditDate: 2024-07-25T10:36:37.090Z
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Body: <p>I've been experimenting with different neural network architectures and am curious about the impact of input ranges on their performance. While normalizing inputs to ranges such as [0,1] or [-1,1] is a common practice, I wonder if there's a theoretically preferable input range that neural networks tend to perform better with. Are there any studies or theoretical foundations that suggest an optimal input range for neural networks? How does  input range in general impact the convergence and overall accuracy of the models?</p>
  
Tags: <neural-networks><computational-learning-theory><normalisation>
Title: Is there a theoretically optimal input range for neural networks?
UserDisplayName: Souhaielrmx
ThreadText: # Is there a theoretically optimal input range for neural networks?
  
  (Asked by: username_0 on 2024-07-03)
  
  I've been experimenting with different neural network architectures and am curious about the impact of input ranges on their performance. While normalizing inputs to ranges such as [0,1] or [-1,1] is a common practice, I wonder if there's a theoretically preferable input range that neural networks tend to perform better with. Are there any studies or theoretical foundations that suggest an optimal input range for neural networks? How does input range in general impact the convergence and overall accuracy of the models?
  
  **Tags:** neural-networks, computational-learning-theory, normalisation
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2024-07-25. Score: 0 | Accepted answer
  
  Unfortunately, there is no theoretically optimal parameter for a neural network. However, they can be roughly defined when talking about a specific topic or application domain. Normalization is a very important procedure in the operation of neural networks. Normalization makes it easier for the network to recognize different patterns. By scaling all inputs between two numbers, the network will be able to recognize and generalize many different patterns.
  Let's take a look at these two input arrays:
  [89, 90, 27, 0, 29, 42, 78, 33, 78, 12]
  [1.186667, 1.2, 0.36, 0, 0.386667, 0.56, 1.04, 0.44, 1.04, 0.16]
  
  At first glance, these seem like two completely different arrays, right?
  It would be very difficult to determine anything from them.
  Let's scale them between 0 and 1:
  var array1:Array = [89, 90, 27, 0, 29, 42, 78, 33, 78, 12]
  var array2:Array = [1.186667, 1.2, 0.36, 0, 0.386667, 0.56, 1.04, 0.44, 1.04, 0.16]
  print("Array1: " + str(normalize(array1)))
  print("Array2: " + str(normalize(array2)))
  
  The output:
  Array1: [0.988889, 1, 0.3, 0, 0.322222, 0.466667, 0.866667, 0.366667, 0.866667, 0.133333]
  Array2: [0.988889, 1, 0.3, 0, 0.322223, 0.466667, 0.866667, 0.366667, 0.866667, 0.133333]
  
  Now we can easily see that the patterns of the two arrays are exactly the same and show the same temporal changes. Likewise, the neural network can draw conclusions much more easily from normalized values.
  But then how can we decide which are the most optimal scaling ranges?
  Normalization between -1 and 1:
  If you are using activation functions like tanh that return only values between -1 and 1, it is a good idea to normalize the input data to this range as well. This will help the network to converge faster, as the distribution of the input data will better match the expected range of the activation function. If the input data contains both positive and negative values, normalising to the range -1 to 1 will ensure that the data is centred around zero.
  Normalization between 0 and 1:
  If you are using activation functions like Sigmoid or ReLU, it's a good idea to normalize input values between 0 and 1. The Sigmoid function gives values between 0 and 1, while ReLU gives only non-negative values. So normalization between 0 and 1 works well with these activation functions. If the input data only has positive values, such as pixel values (between 0 and 255), normalization between 0 and 1 is a natural choice because it is simple and easy to understand.
  
  In summary, the choice between normalising to [-1,1] or [0,1] depends on the activation functions used, and the nature of the data.
  
  
  ---
  
  