R. I. Cukier

R. I. Cukier

Variational autoencoders (VAEs) are one class of generative probabilistic latent-variable models designed for inference based on known data. We develop three variations on VAEs by introducing a second parameterized encoder/decoder pair and, for one variation, an additional fixed encoder. The parameters of the encoders/decoders are to be learned with a neural network. The fixed encoder is obtained by probabilistic-PCA. The variations are compared to the Evidence Lower Bound (ELBO) approximation to the original VAE. One variation leads to an Evidence Upper Bound (EUBO) that can be used in conjunction with the original ELBO to interrogate the convergence of the VAE.

R. I. Cukier

Transformers suffer from the computational overhead of their quadratic dependence on the length of sequences processed. We present three methods, all adding an intermediate step between training and inference/generation, which extend the autoregressive length of transformers. All rely on a Maximum Entropy Principle (MEP) whereby entropy is maximized in the presence of suitable constraints, accounted for by use of Lagrange Multipliers. These constraint methods extend the autoregressive character from T to 2T tokens in a linear-with-T fashion. There is overhead associated with this added step, but they should still be faster than the standard methods.