The dominant paradigm in modern neural networks relies on simple, monotonically-increasing activation functions like ReLU. While effective, this paradigm necessitates large, massively-parameterized models to approximate complex functions. In this paper, we introduce the Periodic Linear Unit (PLU), a learnable sine-wave based activation with periodic non-monotonicity. PLU is designed for maximum expressive power and numerical stability, achieved through its formulation and a paired innovation we term Repulsive Reparameterization, which prevents the activation from collapsing into a non-expressive linear function. We demonstrate that a minimal MLP with only two PLU neurons can solve the spiral classification task, a feat impossible for equivalent networks using standard activations. This suggests a paradigm shift from networks as piecewise Taylor-like approximators to powerful Fourier-like function synthesizers, achieving exponential gains in parameter efficiency by placing intelligence in the neuron itself.

Multi-abel Learning (MLL) often involves the assignment of multiple relevant labels to each instance, which can lead to the leakage of sensitive information (such as smoking, diseases, etc.) about the instances. However, existing MLL suffer from failures in protection for sensitive information. In this paper, we propose a novel setting named Multi-Label Learning from Privacy-Label (MLLPL), which Concealing Labels via Privacy-Label Unit (CLPLU). Specifically, during the labeling phase, each privacy-label is randomly combined with a non-privacy label to form a Privacy-Label Unit (PLU). If any label within a PLU is positive, the unit is labeled as positive; otherwise, it is labeled negative, as shown in Figure 1. PLU ensures that only non-privacy labels are appear in the label set, while the privacy-labels remain concealed. Moreover, we further propose a Privacy-Label Unit Loss (PLUL) to learn the optimal classifier by minimizing the empirical risk of PLU. Experimental results on multiple benchmark datasets demonstrate the effectiveness and superiority of the proposed method.

We consider the following well studied problem of metric distortion in social choice. Suppose we have an election with $n$ voters and $m$ candidates who lie in a shared metric space. We would like to design a voting rule that chooses a candidate whose average distance to the voters is small. However, instead of having direct access to the distances in the metric space, each voter gives us a ranked list of the candidates in order of distance. Can we design a rule that regardless of the election instance and underlying metric space, chooses a candidate whose cost differs from the true optimum by only a small factor (known as the distortion)? A long line of work culminated in finding deterministic voting rules with metric distortion $3$, which is the best possible for deterministic rules and many other classes of voting rules. However, without any restrictions, there is still a significant gap in our understanding: Even though the best lower bound is substantially lower at $2.112$, the best upper bound is still $3$, which is attained even by simple rules such as Random Dictatorship. Finding a rule that guarantees distortion $3 - \varepsilon$ for some constant $\varepsilon $ has been a major challenge in computational social choice. In this work, we give a rule that guarantees distortion less than $2.753$. To do so we study a handful of voting rules that are new to the problem. One is Maximal Lotteries, a rule based on the Nash equilibrium of a natural zero-sum game which dates back to the 60's. The others are novel rules that can be thought of as hybrids of Random Dictatorship and the Copeland rule. Though none of these rules can beat distortion $3$ alone, a careful randomization between Maximal Lotteries and any of the novel rules can.

How should one aggregate ordinal preferences expressed by voters into a measurably superior social choice? A well-established approach -- which we refer to as implicit utilitarian voting -- assumes that voters have latent utility functions that induce the reported rankings, and seeks voting rules that approximately maximize utilitarian social welfare. We extend this approach to the design of rules that select a subset of alternatives. We derive analytical bounds on the performance of optimal (deterministic as well as randomized) rules in terms of two measures, distortion and regret. Empirical results show that regret-based rules are more compelling than distortion-based rules, leading us to focus on developing a scalable implementation for the optimal (deterministic) regret-based rule. Our methods underlie the design and implementation of RoboVote.org,

The Condorcet Jury Theorem justifies the wisdom of crowds and lays the foundations of the ideology of the democratic regime. However, the Jury Theorem and most of its extensions focus on two alternatives and none of them quantitatively evaluate the effect of agents’ strategic behavior on the mechanism’s truth-revealing power. We initiate a research agenda of quantitatively extend- ing the Jury Theorem with strategic agents by characterizing the price of anarchy (PoA) and the price of stability (PoS) of the common interest Bayesian voting games for three classes of mechanisms: plurality, MAPs, and the mechanisms that satisfy anonymity, neutrality, and strategy-proofness (w.r.t. a set of natural probabil- ity models). We show that while plurality and MAPs have better best-case truth-revealing power (lower PoS), the third class of mechanisms are more robust against agents’ strategic behavior (lower PoA).