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.

A major challenge in aligning large language models (LLMs) with human preferences is the issue of distribution shift. LLM alignment algorithms rely on static preference datasets, assuming that they accurately represent real-world user preferences. However, user preferences vary significantly across geographical regions, demographics, linguistic patterns, and evolving cultural trends. This preference distribution shift leads to catastrophic alignment failures in many real-world applications. We address this problem using the principled framework of distributionally robust optimization, and develop two novel distributionally robust direct preference optimization (DPO) algorithms, namely, Wasserstein DPO (WDPO) and Kullback-Leibler DPO (KLDPO). We characterize the sample complexity of learning the optimal policy parameters for WDPO and KLDPO. Moreover, we propose scalable gradient descent-style learning algorithms by developing suitable approximations for the challenging minimax loss functions of WDPO and KLDPO. Our empirical experiments using benchmark data sets and LLMs demonstrate the superior performance of WDPO and KLDPO in substantially improving the alignment when there is a preference distribution shift.

Recent large language models (LLMs) exhibit impressive reasoning but often overthink, generating excessively long responses that hinder efficiency. We introduce DIET (DIfficulty-AwarETraining), a framework that systematically cuts these "token calories" by integrating on-the-fly problem difficulty into the reinforcement learning (RL) process. DIETdynamically adapts token compression strategies by modulating token penalty strength and conditioning target lengths on estimated task difficulty, to optimize the performance-efficiency trade-off. We also theoretically analyze the pitfalls of naive reward weighting in group-normalized RL algorithms like GRPO, and propose Advantage Weighting technique, which enables stable and effective implementation of these difficulty-aware objectives. Experimental results demonstrate that DIETsignificantly reduces token counts while simultaneously improving reasoning performance. Beyond raw token reduction, we show two crucial benefits largely overlooked by prior work: (1) DIET leads to superior inference scaling. By maintaining high per-sample quality with fewer tokens, it enables better scaling performance via majority voting with more samples under fixed computational budgets, an area where other methods falter.

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.

The growing importance of mRNA therapeutics and synthetic biology highlights the need for models that capture the latent structure of synonymous codon (different triplets encoding the same amino acid) usage, which subtly modulates translation efficiency and gene expression. While recent efforts incorporate codon-level inductive biases through auxiliary objectives, they often fall short of explicitly modeling the structured relationships that arise from the genetic code's inherent symmetries. We introduce Equi-mRNA, the first codon-level equivariant mRNA language model that explicitly encodes synonymous codon symmetries as cyclic subgroups of 2D Special Orthogonal matrix (SO(2)). By combining group-theoretic priors with an auxiliary equivariance loss and symmetry-aware pooling, Equi-mRNA learns biologically grounded representations that outperform vanilla baselines across multiple axes. On downstream property-prediction tasks including expression, stability, and riboswitch switching Equi-mRNA delivers up to 10% improvements in accuracy. In sequence generation, it produces mRNA constructs that are up to 4 more realistic under Fréchet BioDistance metrics and 28% better preserve functional properties compared to vanilla baseline. Interpretability analyses further reveal that learned codon-rotation distributions recapitulate known GC-content biases and tRNA abundance patterns, offering novel insights into codon usage. Equi-mRNA establishes a new biologically principled paradigm for mRNA modeling.

Large language models (LLMS) have shown increasing effectiveness in Textto-SQL tasks. However, another closely related problem, Cross-System SQL Translation (a.k.a., SQL-to-SQL), which adapts a query written for one database system (e.g., MySQL) into its equivalent one for another system (e.g., ClickHouse), is of great practical importance but remains underexplored. Existing SQL benchmarks are not well-suited for SQL-to-SQL evaluation, which (1) focus on a limited set of database systems (often just SQLite) and (2) cannot capture many system-specific SQL dialects (e.g., customized functions, data types, and syntax rules). Thus, in this paper, we introduce PARROT, a Practical And Realistic BenchmaRk for CrOss-System SQLTranslation. PARROT comprises 598 translation pairs from 38 open-source benchmarks and real-world business services, specifically prepared to challenge system-specific SQL understanding (e.g., LLMS achieve lower than 38.53% accuracy on average). We also provide multiple benchmark variants, including PARROT-Diverse with 28,003 translations (for extensive syntax testing) and PARROT-Simple with 5,306 representative samples (for focused stress testing), covering 22 production-grade database systems.

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.

Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving stateof-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets.