Large Language Models (LLMs) are transforming search engines into Conversational Search Engines (CSE). Consequently, Search Engine Optimization (SEO) is being shifted into Conversational Search Engine Optimization (C-SEO). We are beginning to see dedicated C-SEO methods for modifying web documents to increase their visibility in CSE responses. However, they are often tested only for a limited breadth of application domains; we do not know whether certain C-SEO methods would be effective for a broad range of domains. Moreover, existing evaluations consider only a single-actor scenario where only one web document adopts a C-SEO method; in reality, multiple players are likely to competitively adopt the cutting-edge C-SEO techniques, drawing an analogy from the dynamics we have seen in SEO.

Black-box optimization has gained great attention for its success in recent ap-1 plications. However, scaling up to high-dimensional problems with good query2 efficiency remains challenging. This paper proposes a novel Rank-1 Lattice Tar-3 geted Sampling (RLTS) technique to address this issue. Our RLTS benefits from4 random rank-1 lattice Quasi-Monte Carlo, which enables us to perform fast local5 exact Gaussian processes (GP) training and inference with O(nlogn)complexity6 w.r.t.

SpaceX raised $10bn (£7.5bn) more than initially thought when it sold shares to the public on Friday - bringing in a total of $85.7bn. Elon Musk's rocket and Artificial Intellgience (AI) company pulled off the biggest initial public offering (IPO) in history when it joined New York's Nasdaq stock exchange last week. The listing had raised $75bn from investors, which Musk told employees will be spent funding a significant growth phase. But the banks which backed the IPO exercised a so-called greenshoe clause, which let them purchase an extra $10bn of SpaceX shares. The extra $10bn raised, revealed in a statement by SpaceX announcing the completion of the listing, would by itself rank as one of the biggest IPOs in history.

Recent probing studies reveal that large language models exhibit linear subspaces that separate true from false statements, yet the mechanism behind their emergence is unclear. We introduce a transparent, one-layer toy model that reproduces such truth subspaces end-to-end and exposes one concrete route by which they can arise. We study one simple setting in which truth encoding can emerge: a data distribution where factual statements co-occur with other factual statements (and vice-versa), encouraging the model to learn this distinction in order to lower the LM loss on future tokens. We corroborate this pattern with experiments in pretrained language models. Finally, in the toy setting we observe a two-phase learning dynamic: networks first memorize individual factual associations in a few steps, then--over a longer horizon--learn to linearly separate true from false, which in turn lowers language-modeling loss. Together, these results provide both a mechanistic demonstration and an empirical motivation for how and why linear truth representations can emerge in language models.

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Existing post-hoc approaches can remove undesired concepts but often degrade useful signals. We introduce SPLINCE--Simultaneous Projection for LINear concept removal and Covariance prEservation--which eliminates sensitive concepts from representations while exactly preserving their covariance with a target label. SPLINCE achieves this via an oblique projection that "splices out" the unwanted direction yet protects important label correlations. Theoretically, it is the unique solution that removes linear concept predictability and maintains target covariance with minimal embedding distortion. Empirically, SPLINCE outperforms baselines on benchmarks such as Bias in Bios and Winobias, removing protected attributes while minimally damaging main-task information.

Evaluating the open-form textual responses generated by Large Language Models (LLMs) typically requires measuring the semantic similarity of the response to a (human generated) reference. However, there is evidence that current semantic similarity methods may capture syntactic or lexical forms over semantic content. While benchmarks exist for semantic equivalence, they often suffer from high generation costs due to reliance on subjective human judgment, limited availability for domain-specific applications, and unclear definitions of equivalence. This paper introduces a novel method for generating benchmarks to evaluate semantic similarity methods for LLM outputs, specifically addressing these limitations. Our approach leverages knowledge graphs (KGs) to generate pairs of naturallanguage statements that are semantically similar or dissimilar, with dissimilar pairs categorized into one of four sub-types. We generate benchmark datasets in four different domains (general knowledge, biomedicine, finance, biology), and conduct a comparative study of semantic similarity methods including traditional natural language processing scores and LLM-as-a-judge predictions. We observe that the sub-type of semantic variation, as well as the domain of the benchmark impact the performance of semantic similarity methods, with no method being consistently superior.

Evaluating the open-form textual responses generated by Large Language Models (LLMs) typically requires measuring the semantic similarity of the response to a (human generated) reference. However, there is evidence that current semantic similarity methods may capture syntactic or lexical forms over semantic content. While benchmarks exist for semantic equivalence, they often suffer from high generation costs due to reliance on subjective human judgment, limited availability for domain-specific applications, and unclear definitions of equivalence. This paper introduces a novel method for generating benchmarks to evaluate semantic similarity methods for LLM outputs, specifically addressing these limitations. Our approach leverages knowledge graphs (KGs) to generate pairs of naturallanguage statements that are semantically similar or dissimilar, with dissimilar pairs categorized into one of four sub-types. We generate benchmark datasets in four different domains (general knowledge, biomedicine, finance, biology), and conduct a comparative study of semantic similarity methods including traditional natural language processing scores and LLM-as-a-judge predictions. We observe that the sub-type of semantic variation, as well as the domain of the benchmark impact the performance of semantic similarity methods, with no method being consistently superior.

Process Reward Models (PRMs) have recently emerged as a powerful framework for supervising intermediate reasoning steps in large language models (LLMs). Previous PRMs are primarily trained on model final output responses and struggle to evaluate intermediate thinking trajectories robustly, especially in the emerging setting of trajectory-response outputs generated by frontier reasoning models like Deepseek-R1. In this work, we introduce ReasonFlux-PRM, a novel trajectory-aware PRM explicitly designed to evaluate the trajectory-response type of reasoning traces. ReasonFlux-PRM incorporates both step-level and trajectorylevel supervision, enabling fine-grained reward assignment aligned with structured chain-of-thought data. We adapt ReasonFlux-PRM to support reward supervision under both offline and online settings, including (i) selecting high-quality model distillation data for downstream supervised fine-tuning of smaller models, (ii) providing dense process-level rewards for policy optimization during reinforcement learning, and (iii) enabling reward-guided Best-of-N test-time scaling. Empirical results on challenging downstream benchmarks such as AIME, MATH500, and GPQA-Diamond demonstrate that ReasonFlux-PRM-7B selects higher quality data than strong PRMs (e.g., Qwen2.5-Math-PRM-72B) and human-curated baselines.

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of nonequilibrium statistical physics. We show that, for large network width m, and large number of samples per input dimension n/d, the training dynamics exhibits a separation of timescales which implies: (i) The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; (ii) Inductive bias towards small complexity if the initialization has small enough complexity; (iii) A dynamical decoupling between feature learning and overfitting regimes; (iv)A non-monotone behavior of the test error, associated'feature unlearning' regime at large times.