Figure 3: Gamematrices A (top) and B (bottom) [left]. Allexperimentsuse SMACsettingsforcomparability (see Samvelyanetal. (2019) and Appendix Bfordetails).

Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the Rényi DP privacy cost of the acceptreject choice.

While certified robustness is widely promoted as a solution to adversarial examples in Artificial Intelligence systems, significant challenges remain before these techniques can be meaningfully deployed in real-world applications. We identify critical gaps in current research, including the paradox of detection without distinction, the lack of clear criteria for practitioners to evaluate certification schemes, and the potential security risks arising from users' expectations surrounding ``guaranteed" robustness claims. These create an alignment issue between how certifications are presented and perceived, relative to their actual capabilities. This position paper is a call to arms for the certification research community, proposing concrete steps to address these fundamental challenges and advance the field toward practical applicability.

Multi-class classification annotations have significantly advanced AI applications, with truth inference serving as a critical technique for aggregating noisy and biased annotations. Existing state-of-the-art methods typically model each annotator's expertise using a confusion matrix. However, these methods suffer from two widely recognized issues: 1) when most annotators label only a few tasks, or when classes are imbalanced, the estimated confusion matrices are unreliable, and 2) a single confusion matrix often remains inadequate for capturing each annotator's full expertise patterns across all tasks. To address these issues, we propose a novel confusion-matrix-based method, PTBCC (ProtoType learning-driven Bayesian Classifier Combination), to introduce a reliable and richer annotator estimation by prototype learning. Specifically, we assume that there exists a set $S$ of prototype confusion matrices, which capture the inherent expertise patterns of all annotators. Rather than a single confusion matrix, the expertise per annotator is extended as a Dirichlet prior distribution over these prototypes. This prototype learning-driven mechanism circumvents the data sparsity and class imbalance issues, ensuring a richer and more flexible characterization of annotators. Extensive experiments on 11 real-world datasets demonstrate that PTBCC achieves up to a 15% accuracy improvement in the best case, and a 3% higher average accuracy while reducing computational cost by over 90%.

The sample compressibility of concept classes plays an important role in learning theory, as a sufficient condition for PAC learnability, and more recently as an avenue for robust generalisation in adaptive data analysis. Whether compression schemes of size O(d) must necessarily exist for all classes of VC dimension d is unknown, but conjectured to be true by Warmuth. Recently Chalopin, Chepoi, Moran, and Warmuth (2018) gave a beautiful unlabelled sample compression scheme of size VC dimension for all maximum classes: classes that meet the Sauer-Shelah-Perles Lemma with equality. They also offered a counterexample to compression schemes based on a promising approach known as corner peeling. In this paper we simplify and extend their proof technique to deal with so-called extremal classes of VC dimension d which contain maximum classes of VC dimension d-1 .

Strengths: Soundness of the claims: The authors fully justify their claim. While most of the proofs are in the appendix, authors provide a high level sketch with intuition in the main body of the paper. Significance and novelty of the contribution: Authors provide best adaptive algorithms for maximizing a gross-substitutes function subject to cardinality constraint. Gross-substitutes is an important class of set functions. The authors' results show that they have obtained the best bound possible.

The sample compressibility of concept classes plays an important role in learning theory, as a sufficient condition for PAC learnability, and more recently as an avenue for robust generalisation in adaptive data analysis. Whether compression schemes of size O(d) must necessarily exist for all classes of VC dimension d is unknown, but conjectured to be true by Warmuth. Recently Chalopin, Chepoi, Moran, and Warmuth (2018) gave a beautiful unlabelled sample compression scheme of size VC dimension for all maximum classes: classes that meet the Sauer-Shelah-Perles Lemma with equality. They also offered a counterexample to compression schemes based on a promising approach known as corner peeling. In this paper we simplify and extend their proof technique to deal with so-called extremal classes of VC dimension d which contain maximum classes of VC dimension d-1 .

Bargaining is an important and unique part of negotiation between humans. As LLM-driven agents learn to negotiate and act like real humans, how to evaluate agents' bargaining abilities remains an open problem. For the first time, we formally described the Bargaining task as an asymmetric incomplete information game, defining the gains of the Buyer and Seller in multiple bargaining processes. It allows us to quantitatively assess an agent's performance in the Bargain task. We collected a real product price dataset, AmazonHistoryPrice, and conducted evaluations of various LLM agents' bargaining abilities. We find that playing a Buyer is much harder than a Seller, and increasing model size can not effectively improve the Buyer's performance. To address the challenge, we propose a novel approach called OG-Narrator that integrates a deterministic Offer Generator to control the price range of Buyer's offers, and an LLM Narrator to create natural language sentences for generated offers. Experimental results show that OG-Narrator improves the buyer's deal rates from 26.67% to 88.88% and brings a ten times multiplication of profits on all baselines, even a model that has not been aligned.