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A NN's inputs can be equal to number of features in data, and have less relationship with number of data points. For example, we can some DNA data, where we only have 1000 people / instance, but each instance has millions of features in DNA. In such setting, we can build a NN with millions of inputs.

For your question about dimension reduction: the key idea of using NN is let the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)

A NN's inputs can be equal to number of features in data, and have less relationship with number of data points. For example, we can some DNA data, where we only have 1000 people / instances, but each instance has millions of features in DNA. In such setting, it is perfectly OK to build a NN with millions of inputs.

For your question about dimension reduction: the key idea of using NN is letting the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)

A NN's inputs can be equal to number of features in data, and have less relationship with number of data points.

  For example, I have some DNA data, where I only have 100 people / instance, but each instance has millions of features in DNA. In such setting, we can build a NN with millions of inputs.

The key idea of using NN is let the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)

A NN's inputs can be equal to number of features in data, and have less relationship with number of data points. For example, we can some DNA data, where we only have 1000 people / instance, but each instance has millions of features in DNA. In such setting, we can build a NN with millions of inputs.

For your question about dimension reduction: the key idea of using NN is let the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)

You may confused with number of data vs. number of features in your inputs. A NN's inputs can be equal to number of features, and have less relationship with number of data.

For example, I have some DNA data, where I only have 100 people / instance, but each instance has millions of features in DNA. In such setting, we can build a NN with millions of inputs.

The key idea of using NN is let the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)

A NN's inputs can be equal to number of features in data, and have less relationship with number of data points.

For example, I have some DNA data, where I only have 100 people / instance, but each instance has millions of features in DNA. In such setting, we can build a NN with millions of inputs.

The key idea of using NN is let the model to figure out the feature engineering / necessary transformation. So, the model can automatically do the feature reduction to us. It is not very common to run feature reduction (say PCA) first then feed into NN, unless there are some computational resource constraints.

Also, output is 2K seems too much for me. Are you trying to predict a discrete outcome with 2K possible values? In most cases, people predicting a much less possible values, such as binary Yes/No. (There are some reasons on why it is hard to do to predict 2K possible values, which I will not explain here.)