In the field of computational advertising, the integration of ads into the outputs of large language models (LLMs) presents an opportunity to support these services without compromising content integrity. This paper introduces novel auction mechanisms for ad allocation and pricing within the textual outputs of LLMs, leveraging retrieval-augmented generation (RAG). We propose a segment auction where an ad is probabilistically retrieved for each discourse segment (paragraph, section, or entire output) according to its bid and relevance, following the RAG framework, and priced according to competing bids. We show that our auction maximizes logarithmic social welfare, a new notion of welfare that balances allocation efficiency and fairness, and we characterize the associated incentive-compatible pricing rule. These results are extended to multi-ad allocation per segment. An empirical evaluation validates the feasibility and effectiveness of our approach over several ad auction scenarios, and exhibits inherent tradeoffs in metrics as we allow the LLM more flexibility to allocate ads.

The online bipartite matching problem, extensively studied in the literature, deals with the allocation of online arriving vertices (items) to a predetermined set of offline vertices (agents). However, little attention has been given to the concept of class fairness, where agents are categorized into different classes, and the matching algorithm must ensure equitable distribution across these classes. We here focus on randomized algorithms for the fair matching of indivisible items, subject to various definitions of fairness. Our main contribution is the first (randomized) non-wasteful algorithm that simultaneously achieves a 1/2 approximation to class envy-freeness (CEF) while simultaneously ensuring an equivalent approximation to the class proportionality (CPROP) and utilitarian social welfare (USW) objectives. We supplement this result by demonstrating that no non-wasteful algorithm can achieve an α-CEF guarantee for α > 0.761. In a similar vein, we provide a novel input instance for deterministic divisible matching that demonstrates a nearly tight CEF approximation. Lastly, we define the "price of fairness," which represents the trade-off between optimal and fair matching. We demonstrate that increasing the level of fairness in the approximation of the solution leads to a decrease in the objective of maximizing USW, following an inverse proportionality relationship.

We conduct extensive experiments on two new real-world KG datasets, i.e., Freebase The nodes and edges are extracted according to [5]. A large portion of books are labeled into eight genres of literature. Each labeled book has only one label. FB15K-237 is a standard dataset in the knowledge graph community, which contains 310,116 triples with 14,541 entities and 237 relation types. Since we did not manually label the nodes, we only predicted whether a triple is correct or not on this dataset.

The Lion optimizer has been a promising competitor with the AdamW for training large AI models, with advantages in memory, computation, and sample efficiency. In this paper, we introduce Distributed Lion, an innovative adaptation of Lion for distributed training environments. Leveraging the sign operator in Lion, our Distributed Lion only requires to communicate binary or lower-precision vectors between workers to the center server, significantly reducing the communication cost. Our theoretical analysis confirms Distributed Lion's convergence properties. Empirical results demonstrate its robustness across a range of tasks, worker counts, and batch sizes, on both vision and language problems. Notably, Distributed Lion attains comparable performance to standard Lion or AdamW optimizers applied on aggregated gradients, but with significantly reduced communication bandwidth. This feature is particularly advantageous for training large models. In addition, we also demonstrate that Distributed Lion presents a more favorable performancebandwidth balance compared to existing efficient distributed methods such as deep gradient compression and ternary gradients.

In this work, we are motivated by the fact that the local 3D patches repeatedly appear on 3D shapes/surfaces if the factor of poses is removed. Based on this observation, we propose the 3D patch-level equivariant implicit function (PEIF) based on the 3D patch-level pose-invariant representation, allowing us to reconstruct 3D surfaces by estimating equivariant displacement vector fields for query points. Specifically, our model is based on the pose-normalized query/patch pairs and enhanced by the proposed intrinsic patch geometry representation, modeling the intrinsic 3D patch geometry feature by learnable multi-head memory banks. Extensive experiments show that our model achieves state-of-the-art performance on multiple surface reconstruction datasets, and also exhibits better generalization to crossdataset shapes and robustness to arbitrary rotations.

There's been a lot of talk in recent years about AI replacing the role of humans in the workforce. It's been unclear exactly if or when that would happen on a broader scale. However, this is already happening in one industry in particular: The tech industry. Researchers at the venture capital firm SignalFire recently released their "State of Talent Report" for 2025, which analyzes hiring and employment trends across the tech industry. The big takeaway, according to SignalFire's report, is that new graduate hiring has declined. Hiring levels for experienced roles like mid- and senior-level positions have remained strong, while entry-level tech jobs have taken a big hit.

The remarkable attention which fair clustering has received in the last few years has resulted in a significant number of different notions of fairness. Despite the fact that these notions are well-justified, they are often motivated and studied in a disjoint manner where one fairness desideratum is considered exclusively in isolation from the others. This leaves the understanding of the relations between different fairness notions as an important open problem in fair clustering. In this paper, we take the first step in this direction. Specifically, we consider the two most prominent demographic representation fairness notions in clustering: (1) Group Fairness (GF), where the different demographic groups are supposed to have close to population-level representation in each cluster and (2) Diversity in Center Selection (DS), where the selected centers are supposed to have close to population-level representation of each group. We show that given a constant approximation algorithm for one constraint (GF or DS only) we can obtain a constant approximation solution that satisfies both constraints simultaneously. Interestingly, we prove that any given solution that satisfies the GF constraint can always be post-processed at a bounded degradation to the clustering cost to additionally satisfy the DS constraint while the reverse is not true given a solution that satisfies DS instead. Furthermore, we show that both GF and DS are incompatible (having an empty feasibility set in the worst case) with a collection of other distance-based fairness notions. Finally, we carry experiments to validate our theoretical findings.