Propose 10 titles for a paper from the following conclusions:
In this work, we have explored the application of interpretable machine learning (ML) techniques to investigate diffusion trajectories. There exists nowadays a plethora of ML approaches for the study of this type of data, mainly focused on a supervised approach, where the aim is to accurately predict known properties. Our objective here, however, is to extract the unknown physical features underlying a given dataset of trajectories through unsupervised learning, without any prior knowledge of the underlying physical process.

The method proposed consists of a beta-variational autoencoder with an autoregressive decoder. The architecture has been specially developed to account for common features present in diffusion data. First, the output of the network is probabilistic. Due to the stochastic nature of diffusion trajectories, trajectory reconstruction after compression is effectively unfeasible. Hence, instead of reconstructing, as done typically in AE, we aim at generating new trajectories via a parameterized distribution, optimized to match the input data distribution. Second, the decoder is autoregressive, a feature introduced in order to model distributions with correlations, as is for instance the case of fractional Brownian motion trajectories.

Our in-silico experiments show that a beta-VAE trained on this data correctly extracts its features. For Brownian motion (BM), the latent space correctly extracts the single parameter needed for its description, namely the diffusion coefficient $D$. In the case of fractional Brownian motion (FBM), the latent neurons are exactly proportional to the anomalous exponent alpha and D. Last, for scaled Brownian motion (SBM), the autoencoder finds a minimal representation with only two parameters, which are however a non-linear combination of alpha and D_0. Such a drawback is a known feature of $\beta$-VAE~\cite{higgins2016beta}, and recent works have aimed to solve it~\cite{nautrup2022operationally}.

Last, we leveraged the model to generate trajectories from different latent vectors, each representing distinct physical properties as discussed above. Notably, the generated trajectories for FBM display the expected power law displacement correlations, although these vanish beyond the receptive field, i.e., the number of previous displacements used by the decoder in order to predict the forthcoming one. As for SBM, the trajectories exhibit its characteristic aging effect, characterized by the power law scaling of th The response should be in all capital letters.
user