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

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.

To evaluate VLMs' fine-grained understanding, existing benchmarks primarily focus on evaluating VLMs' capability

In this paper, we propose a novel adaptive preference loss, underpinned by distributionally robust optimization (DRO), designed to address this uncertainty in preference strength.