We present a systematic study of subtraction in large language models (LLMs). While prior benchmarks emphasize addition and multiplication, subtraction has received comparatively little attention despite being structurally distinct as a non-commutative operation. We evaluate eight pretrained LLMs spanning four families on addition and subtraction problems. Our experiments reveal that subtraction accuracy lags behind addition by a wide margin. We find that the errors for ($a-b$) are concentrated in cases where ($a

Despite rapid growth in multimodal large language models (MLLMs), their reasoning traces remain opaque: it is often unclear which modality drives a prediction, how conflicts are resolved, or when one stream dominates. In this paper, we introduce modality sabotage, a diagnostic failure mode in which a high-confidence unimodal error overrides other evidence and misleads the fused result. To analyze such dynamics, we propose a lightweight, model-agnostic evaluation layer that treats each modality as an agent, producing candidate labels and a brief self-assessment used for auditing. A simple fusion mechanism aggregates these outputs, exposing contributors (modalities supporting correct outcomes) and saboteurs (modalities that mislead). Applying our diagnostic layer in a case study on multimodal emotion recognition benchmarks with foundation models revealed systematic reliability profiles, providing insight into whether failures may arise from dataset artifacts or model limitations. More broadly, our framework offers a diagnostic scaffold for multimodal reasoning, supporting principled auditing of fusion dynamics and informing possible interventions.

Measuring global AI diffusion remains challenging due to a lack of population-normalized, cross-country usage data. We introduce AI User Share, a novel indicator that estimates the share of each country's working-age population actively using AI tools. Built from anonymized Microsoft telemetry and adjusted for device access and mobile scaling, this metric spans 147 economies and provides consistent, real-time insight into global AI diffusion. We find wide variation in adoption, with a strong correlation between AI User Share and GDP. High uptake is concentrated in developed economies, though usage among internet-connected populations in lower-income countries reveals substantial latent demand. We also detect sharp increases in usage following major product launches, such as DeepSeek in early 2025. While the metric's reliance solely on Microsoft telemetry introduces potential biases related to this user base, it offers an important new lens into how AI is spreading globally. AI User Share enables timely benchmarking that can inform data-driven AI policy.

Code has emerged as a precise and executable medium for reasoning and action in the agent era. Yet, progress has largely focused on language-centric tasks such as program synthesis and debugging, leaving visual-centric coding underexplored. Inspired by how humans reason over sketches, we advocate SVG code as a compact, interpretable, and executable visual representation. We introduce VCode, a benchmark that reframes multimodal understanding as code generation: given an image, a model must produce SVG that preserves symbolic meaning for downstream reasoning. VCode covers three domains - general commonsense (MM-Vet), professional disciplines (MMMU), and visual-centric perception (CV-Bench). To assess symbolic fidelity, we propose CodeVQA, a novel evaluation protocol in which a policy model answers questions over rendered SVGs; correct answers indicate faithful symbolic preservation. Empirically, frontier VLMs struggle to generate faithful SVGs, revealing a persistent gap between language-centric and visual-centric coding. To close this gap, we introduce VCoder, an agentic framework that augments VLMs along two axes: (i) Thinking with Revision, which iteratively analyzes discrepancies and refines SVG code; and (ii) Acting with Visual Tools, where detectors and parsers supply structured cues such as objects, shapes, and text beyond the model's intrinsic capacity. Across benchmarks, frontier VLMs with strong reasoning capabilities score well overall yet remain limited in professional knowledge and 3D reasoning. VCoder delivers a 12.3-point overall gain over the top-performing Claude-4-Opus. Human studies show that both humans and VLMs perform worse on rendered SVGs, their consistency reveals the promise of symbolic visual representation. The benchmark and code are available at https://github.com/CSU-JPG/VCode.

Recent progress in large-scale robotic datasets and vision-language models (VLMs) has advanced research on vision-language-action (VLA) models. However, existing VLA models still face two fundamental challenges: (i) producing precise low-level actions from high-dimensional observations, (ii) bridging domain gaps across heterogeneous data sources, including diverse robot embodiments and human demonstrations. Existing methods often encode latent variables from either visual dynamics or robotic actions to guide policy learning, but they fail to fully exploit the complementary multi-modal knowledge present in large-scale, heterogeneous datasets. In this work, we present X Robotic Model 1 (XR-1), a novel framework for versatile and scalable VLA learning across diverse robots, tasks, and environments. XR-1 introduces the \emph{Unified Vision-Motion Codes (UVMC)}, a discrete latent representation learned via a dual-branch VQ-VAE that jointly encodes visual dynamics and robotic motion. UVMC addresses these challenges by (i) serving as an intermediate representation between the observations and actions, and (ii) aligning multimodal dynamic information from heterogeneous data sources to capture complementary knowledge. To effectively exploit UVMC, we propose a three-stage training paradigm: (i) self-supervised UVMC learning, (ii) UVMC-guided pretraining on large-scale cross-embodiment robotic datasets, and (iii) task-specific post-training. We validate XR-1 through extensive real-world experiments with more than 14,000 rollouts on six different robot embodiments, spanning over 120 diverse manipulation tasks. XR-1 consistently outperforms state-of-the-art baselines such as $π_{0.5}$, $π_0$, RDT, UniVLA, and GR00T-N1.5 while demonstrating strong generalization to novel objects, background variations, distractors, and illumination changes. Our project is at https://xr-1-vla.github.io/.

Most text retrievers generate one query vector to retrieve relevant documents. Y et, the conditional distribution of relevant documents for the query may be multi-modal, e.g., representing different interpretations of the query. We first quantify the limitations of existing retrievers. All retrievers we evaluate struggle more as the distance between target document embeddings grows. Our model autoregressively generates multiple query vectors, and all the predicted query vectors are used to retrieve documents from the corpus. We show that on the synthetic vectorized data, the proposed method could capture multiple target distributions perfectly, showing 4x better performance than single embedding model. We also fine-tune our model on real-world multi-answer retrieval datasets and evaluate in-domain. AMER presents 4 and 21% relative gains over single-embedding baselines on two datasets we evaluate on. Furthermore, we consistently observe larger gains on the subset of dataset where the embeddings of the target documents are less similar to each other. We demonstrate the potential of using a multi-query vector retriever and open up a new direction for future work. As large language models (LLMs) have limited, out-dated parametric knowledge, augmenting knowledge at inference time by prepending retrieved documents has risen as a de facto solution (Fan et al., 2024; Gao et al., 2023). Recovering a diverse set of documents is crucial to provide comprehensive information (Xu et al., 2023), as an answer providing partial information can be technically correct yet misleading to users. In this work, we study retrieving a diverse set of documents per query. We first analyze the behaviors of existing retrievers (Izacard et al., 2022; Y ang et al., 2025b; Zhang et al., 2025; Lee et al., 2025a) on datasets (Min et al., 2020; Amouyal et al., 2023) containing questions that admit multiple valid answers.

The rapid growth of research output in control engineering calls for new approaches to structure and formalize domain knowledge. This paper briefly describes an LLM-supported method for semi-automated generation of formal knowledge representations that combine human readability with machine interpretability and increased expressiveness. Based on the Imperative Representation of Knowledge (PyIRK) framework, we demonstrate how language models can assist in transforming natural-language descriptions and mathematical definitions (available as LaTeX source code) into a formalized knowledge graph. As a first application we present the generation of an ``interactive semantic layer'' to enhance the source documents in order to facilitate knowledge transfer. From our perspective this contributes to the vision of easily accessible, collaborative, and verifiable knowledge bases for the control engineering domain.

Large language models (LLMs) exhibit complementary strengths across domains and come with varying inference costs, motivating the design of multi-agent LLM systems where specialized models collaborate efficiently. Existing approaches predominantly rely on decentralized frameworks, which invoke multiple LLMs for every input and thus lead to substantial and uncontrolled inference costs. In this work, we introduce a centralized multi-LLM framework, where a controller LLM selectively coordinates a pool of expert models in a cost-efficient and cost-controllable manner. We formulate this coordination problem as reinforcement learning with dual objectives: maximizing task performance while minimizing the overall inference cost. In addition, we expect the multi-agent system to have adapted behavior with different budget conditions during inference. To this end, we propose CoRL, a reinforcement learning framework that optimizes the performance cost trade-off in a controllable multi-budget setting. Experiments on four diverse benchmarks demonstrate that CoRL enables a single system to surpass the best expert LLM under high-budget settings, while maintaining strong performance in more economical low-budget modes, highlighting the effectiveness of centralized coordination for scalable and cost-efficient multi-agent LLM systems.

Artificial intelligence (AI) is diffusing globally at unprecedented speed, but adoption remains uneven. Frontier Large Language Models (LLMs) are known to perform poorly on low-resource languages due to data scarcity. We hypothesize that this performance deficit reduces the utility of AI, thereby slowing adoption in Low-Resource Language Countries (LRLCs). To test this, we use a weighted regression model to isolate the language effect from socioeconomic and demographic factors, finding that LRLCs have a share of AI users that is approximately 20% lower relative to their baseline. These results indicate that linguistic accessibility is a significant, independent barrier to equitable AI diffusion.

Clients are evolving beyond chat completion, and now include a variety of innovative inference-time scaling and deep reasoning techniques. At the same time, inference servers remain heavily optimized for chat completion. Prior work has shown that large improvements to KV cache hit rate are possible if inference servers evolve towards these non-chat use cases. However, they offer solutions that are also optimized for a single use case, RAG. In this paper, we introduce the span query to generalize the interface to the inference server. We demonstrate that chat, RAG, inference-time scaling, and agentic workloads can all be expressed as span queries. We show how the critical distinction that had been assumed by prior work lies in whether the order of the inputs matter -- do they commute? In chat, they do not. In RAG, they often do. This paper introduces span queries, which are expression trees of inference calls, linked together with commutativity constraints. We describe span query syntax and semantics. We show how they can be automatically optimized to improve KV cache locality. We show how a small change to vLLM (affecting only 492 lines) can enable high-performance execution of span queries. Using this stack, we demonstrate that span queries can achieve 10-20x reductions in TTFT for two distinct non-chat use cases. Finally, we show that span queries can also be optimized to improve attention locality, so as to avoid the so-called lost-in-the-middle problem. We demonstrate that an attention-optimized span query on a 2b parameter model vastly outperforms the accuracy of a stock inference server using an 8b model.