First, your definition of "deterministic" and "linear classifier" are not clear to me, e.g., is the model building deterministic or model prediction deterministic, In addition, most people will think SVM is not a linear. I am trying to guess what you want to ask from now on.

Most models (not necessary to be "linear") are "deterministic" on prediction stage, and they should be. Intuitively we want this: feeding the same input, we want to have the same output.

However, many models do have some randomness during the training process (not the model itself). This means that

• Given the same data, with different random seeds, you can have different models (see Random Forest as an example)
• After model building, it is "deterministic", i.e., feeding same input will have same output.

Finally, in the "linear models" you mentioned logistic regression and SVM, they do not have a random seed during the training process.

First, your definition of "deterministic" and "linear classifier" are not clear to me. For example, are you asking if the model building deterministic or model prediction deterministic? In addition, most people will think SVM is not a linear model but you treat it is linear. 

I am trying to guess what you want to ask from now on.

Most models (not necessary to be "linear") are "deterministic" on prediction stage, and they should be. Intuitively we want that feeding the same input, we want to have the same output.

However, many models do have some randomness during when we build the model. This means that

• Given the same data, with different random seeds, you can have different models (see Random Forest as an example)

• After model building, during the prediction stage it is "deterministic", i.e., feeding same input will have same output.

Finally, in the "linear models" you mentioned logistic regression and SVM, they do not have a random seed during the training process. As mentioned in the other answers and comments, the reason is the objective function for logistic regression and SVN are convex, so we have the unique answer / global minima when we build the model.

First your definition of "deterministic" and "linear classifier" are not clear to me, e.g., most people will think SVM is not a linear. I am trying to guess what you want to ask from now on.

I think most models (not necessary to be "linear") are "deterministic", and they should be. Intuitively we want such feature: feeding the same input, we want to have the same output.

However, many models do have some randomness during the training process (not the model itself). This means that

• Given the same data, with different random seeds, you can have different models (see Random Forest as an example)
• After model building, it is "deterministic", i.e., feeding same input will have same output.

Finally, in the "linear models" you mentioned logistic regression and SVM, they do not have a random seed during the training process.

First, your definition of "deterministic" and "linear classifier" are not clear to me, e.g., is the model building deterministic or model prediction deterministic, In addition, most people will think SVM is not a linear. I am trying to guess what you want to ask from now on.

Most models (not necessary to be "linear") are "deterministic" on prediction stage, and they should be. Intuitively we want this: feeding the same input, we want to have the same output.

However, many models do have some randomness during the training process (not the model itself). This means that

• Given the same data, with different random seeds, you can have different models (see Random Forest as an example)
• After model building, it is "deterministic", i.e., feeding same input will have same output.

Finally, in the "linear models" you mentioned logistic regression and SVM, they do not have a random seed during the training process.