Much has been written on the topic of visualizing n-dimensional spaces (where n is in general much larger than 3). T-SNE and parallel coordinates are two ways to do it rather effectively. (I'm not interested in the philosophical question of whether one can 'really' visualize more than three dimensions, only in the question of how to project n-dimensional data onto a screen in such a way that the human visual cortex can perceive patterns in it.)

But the thing about all the techniques I can find, like T-SNE and parallel coordinates, is that they assume you're dealing with a collection of data points, each of which has a vector of coordinates, so that the majority of possible coordinate vectors are empty. A lot of the visible patterns, then, are about how the data points cluster.

What I'm dealing with instead is a landscape, specifically a fitness landscape for neural networks and other optimization techniques that work on vectors of real numbers. In this case, every possible coordinate vector is occupied, by a real number that gives the fitness of the neural network that would have that vector of weights.

Are there any known techniques for visualizing a continuous n-dimensional landscape?


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