I met with Professor Verma on July 6 to review the part of the loss function that reflects the structural integrity of the data, and received further guidance on why likelihood values cannot be compared across different models, and how likelihood encourages collapsing of data into a single mean and narrow spread. Instead, I will first find the cluster means and variances using Gaussian Mixture Model or Dirichlet Process Mixture Model / Chinese Restaurant Process, and then use the distances between the means and the narrowness of the spreads (as measured by the determinants of the covariance matrices) as the structural integrity score.

We also discussed another research idea related to contrastive loss and geometric parallelism, and agreed that I would explore it as a possible second topic.