<p>A softmax activation won't do the trick I'm afraid; if you have an infinite number of combinations, or even a finite number of combinations that do not already appear in your data, there is no way to turn this into a multi-class classification problem (or if you do, you'll have loss of generality).</p>

<p>The only way forward I can think of is a recurrent model employing variational encoding. To begin with, you have a lot of annotated data, which is good news; a recurrent network fed with a sequence <strong>X</strong> (10,2,) will definitely be able to predict a sequence <strong>Y</strong> (6,2,). But since you want not just one but rather <em>all probable</em> sequences, this won't suffice. Your implicit assumption here is that there is some probability space hidden behind your sequences, which affects how they play out over time; so to model the sequences properly, you need to model that latent probability space. A Variational Auto-Encoder (<a href="https://arxiv.org/abs/1312.6114" rel="nofollow noreferrer">VAE</a>) does just that; it learns the latent space, so that during inference the output prediction depends on sampling over that latent space. Multiple predictions over the same input can then result in different outputs, meaning that you can finally sample your predictions to empirically approximate the distribution of potential outputs. </p>

<p>Unfortunately, VAEs can't really be explained within a single paragraph over stackoverflow, and even if they could I wouldn't be the most qualified person to attempt it. Try searching the web for LSTM-VAE and arm yourself with patience; you'll probably need to do some studying but it's definitely worth it. It might also be a good idea to look into <a href="http://pyro.ai/" rel="nofollow noreferrer">Pyro</a> or <a href="http://edwardlib.org/" rel="nofollow noreferrer">Edward</a>, which are probabilistic network libraries for python, better suited to the task at hand than Keras.</p>
Predict all probable trajectories in a grid structure using Keras
<p>I'm trying to predict sequences of 2D coordinates. But I don't want only the most probable future path but all the most probable paths to visualize it in a grid map.
For this I have traning data consisting of 40000 sequences. Each sequence consists of 10 2D coordinate pairs as input and 6 2D coordinate pairs as labels.
All the coordinates are in a fixed value range.
What would be my first step to predict all the probable paths? To get all probable paths I have to apply a softmax in the end, where each cell in the grid is one class right? But how to process the data to reflect this grid like structure? Any ideas?</p>