We mend this problem by adding an embedding to each digit that encodes its position relative to the start of the number.

Learning from active human involvement enables the human subject to actively intervene and demonstrate to the AI agent during training. The interaction and corrective feedback from human brings safety and AI alignment to the learning process.

Large language models (LLMs), typically designed as a function of next-word prediction, have excelled across extensive NLP tasks. Despite the generality, next-word prediction is often not an efficient formulation for many of the tasks, demanding an extreme scale of model parameters (10s or 100s of billions) and sometimes yielding suboptimal performance. In practice, it is often desirable to build more efficient models--despite being less versatile, they still apply to a substantial subset of problems, delivering on par or even superior performance with much smaller model sizes.

Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training.

Consider a recommendation platform that interacts with a finite set of users in an online fashion. Users arrive at the platform and receive a recommendation.

We show how techniques from the theory of error-correcting codes can be applied to achieve scalability and hence improved performance. As an exemplar, we focus on how polar codes can be used to efficiently simulate i.i.d.