Institute of Fundamental Technological Research

The notion of rank of a Boolean function has been a cornerstone in PAC learning, enabling quasipolynomial-time learning algorithms for polynomial-size decision trees. We present a novel characterization of rank, grounded in the well-known Transformer architecture. We show that the rank of a function f corresponds to the minimum number of Chain of Thought (CoT) steps required by a single-layer Transformer with hard attention to compute f. Based on this characterization we establish tight bounds on the number of CoT steps required for specific problems, showing that ℓ-fold function composition necessitates exactly ℓ CoT steps. Furthermore, we analyze the problem of identifying the position of the k-th occurrence of 1 in a Boolean sequence, proving that it requires k CoT steps

In peer review systems, reviewers are often asked to evaluate various features of submissions, such as technical quality or novelty. A score is given to each of the predefined features and based on these the reviewer has to provide an overall quantitative recommendation. It may be assumed that each reviewer has her own mapping from the set of features to a recommendation, and that different reviewers have different mappings in mind. This introduces an element of arbitrariness known as commensuration bias. In this paper we discuss a framework, introduced by Noothigattu, Shah and Procaccia, and then applied by the organizers of the AAAI 2022 conference. Noothigattu, Shah and Procaccia proposed to aggregate reviewer’s mapping by minimizing certain loss functions, and studied axiomatic properties of this approach, in the sense of social choice theory. We challenge several of the results and assumptions used in their work and report a number of negative results. On the one hand, we study a trade-off between some of the axioms proposed and the ability of the method to properly capture agreements of the majority of reviewers. On the other hand, we show that dropping a certain unrealistic assumption has dramatic effects, including causing the method to be discontinuous.