Vijay Balasubramanian

Amrut Nadgir, Vijay Balasubramanian, Pratik Chaudhari

Many language tasks can be modeled as classification problems where a large language model (LLM) is given a prompt and selects one among many possible answers. We show that the classification error in such problems scales as a power law in the number of classes. This has a dramatic consequence: the prediction error can be reduced substantially by splitting the overall task into a sequence of smaller classification problems, each with the same number of classes ("degree"). This tree-structured decomposition models chain-of-thought (CoT). It has been observed that CoT-based predictors perform better when they "think'", i.e., when they develop a deeper tree, thus decomposing the problem into a larger number of steps. We identify a critical threshold for the degree, below which thinking is detrimental, and above which there exists an optimal depth that minimizes the error. It is impossible to surpass this minimal error by increasing the depth of thinking.

Rahul Ramesh, Anthony Bisulco, Ronald W. DiTullio et al.

We show that many perception tasks, from visual recognition, semantic segmentation, optical flow, depth estimation to vocalization discrimination, are highly redundant functions of their input data. Images or spectrograms, projected into different subspaces, formed by orthogonal bases in pixel, Fourier or wavelet domains, can be used to solve these tasks remarkably well regardless of whether it is the top subspace where data varies the most, some intermediate subspace with moderate variability--or the bottom subspace where data varies the least. This phenomenon occurs because different subspaces have a large degree of redundant information relevant to the task.