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The Johnson-Lindenstrauss (JL) lemma is a cornerstone of dimensionality reduction in Euclidean space, but its applicability to non-Euclidean data has remained limited. This paper extends the JL lemma beyond Euclidean geometry to handle general dissimilarity matrices that are prevalent in real-world applications. We present two complementary approaches: First, we show the JL transform can be applied to vectors in pseudo-Euclidean space with signature (p,q), providing theoretical guarantees that depend on the ratio of the (p,q)norm and Euclidean norm of two vectors, measuring the deviation from Euclidean geometry. Second, we prove that any symmetric hollow dissimilarity matrix can be represented as a matrix of generalized power distances, with an additional parameter representing the uncertainty level within the data. In this representation, applying the JL transform yields multiplicative approximation with a controlled additive error term proportional to the deviation from Euclidean geometry. Our theoretical results provide fine-grained performance analysis based on the degree to which the input data deviates from Euclidean geometry, making practical and meaningful reduction in dimensionality accessible to a wider class of data.

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SOLIDGEO, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry.

Web navigation is a unique domain that can automate many repetitive real-life tasks beyond and typical is challenging multimodal as lar it ge requires language long-horizon model (MLLM) sequential tasks.

We propose KNOTGYM, an interactive environment for complex, spatial reasoning and manipulation.

Large language models (LLMs) are increasingly fine-tuned on domain-specific datasets to support applications in fields such as healthcare, finance, and law. These fine-tuning datasets often have sensitive and confidential dataset-level properties -- such as patient demographics or disease prevalence--that are not intended to be revealed. While prior work has studied property inference attacks on discriminative models (e.g., image classification models) and generative models (e.g., GANs for image data), it remains unclear if such attacks transfer to LLMs. In this work, we introduce PropInfer, a benchmark task for evaluating property inference in LLMs under two fine-tuning paradigms: question-answering and chat-completion. Built on the ChatDoctor dataset, our benchmark includes a range of property types and task configurations. We further propose two tailored attacks: a prompt-based generation attack and a shadow-model attack leveraging word frequency signals.

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Balancing helpfulness and safety (harmlessness) is a critical challenge in aligning large language models (LLMs). Current approaches often decouple these two objectives, training separate preference models for helpfulness and safety, while framing safety as a constraint within a constrained Markov Decision Process (CMDP) framework. This paper identifies a potential issue when using the widely adopted expected safety constraints for LLM safety alignment, termed "safety compensation", where the constraints are satisfied on expectation, but individual prompts may trade off safety, resulting in some responses being overly restrictive while others remain unsafe. To address this issue, we propose Rectified Policy Optimization (RePO), which replaces the expected safety constraint with critical safety constraints imposed on every prompt. At the core of RePO is a policy update mechanism driven by rectified policy gradients, which penalizes the strict safety violation of every prompt, thereby enhancing safety across nearly all prompts. Our experiments demonstrate that RePO outperforms strong baseline methods and significantly enhances LLM safety alignment.

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is costly, e.g.

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (i.e., the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector. Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance.