Faster Language Models with Better Multi-Token Prediction Using Tensor Decomposition

We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we connect this approach to rank-$1$ canonical tensor decomposition. By generalizing it to a rank-$r$ canonical probability decomposition, we develop an improved model that predicts multiple tokens simultaneously. This model can also be interpreted as a mixture of experts, allowing us to leverage successful techniques from that domain for efficient and robust training. Importantly, the overall overhead for training and sampling remains low. Our method demonstrates significant improvements in inference speed for both text and code generation tasks, proving particularly beneficial within the self-speculative decoding paradigm. It maintains its effectiveness across various model sizes and training epochs, highlighting its robustness and scalability.

Black-Box Approximation and Optimization with Hierarchical Tucker Decomposition

We develop a new method HTBB for the multidimensional black-box approximation and gradient-free optimization, which is based on the low-rank hierarchical Tucker decomposition with the use of the MaxVol indices selection procedure. Numerical experiments for 14 complex model problems demonstrate the robustness of the proposed method for dimensions up to 1000, while it shows significantly more accurate results than classical gradient-free optimization methods, as well as approximation and optimization methods based on the popular tensor train decomposition, which represents a simpler case of a tensor network.