Prime factorization, the decomposition of a natural number into its constituent primes, lies at the crossroads of arithmetic, complexity theory, and computational practice. While every integer admits a unique factorization, the operational effort required to obtain it grows quickly with its magnitude. State-of-the-art algorithms achieve remarkable performance for moderately large inputs, yet their complexity escalates rapidly when confronted with truly large instances. Moreover, in this limit, the sequence of integers with known prime factorizations becomes effectively sparse, with regions where the factorizations of intermediate values are computationally inaccessible. It is therefore natural to ask whether modern machine learning methods, and more specifically Large Language Models (LLMs), can offer any advantages from this perspective.

Spoken Language Models (SLMs) aim to learn linguistic competence directly from speech using discrete units, widening access to Natural Language Processing (NLP) technologies for languages with limited written resources. However, progress has been largely English-centric due to scarce spoken evaluation benchmarks and training data, making cross-lingual learning difficult. We present a cross-lingual interleaving method that mixes speech tokens across languages without textual supervision. We also release an EN-FR training dataset, TinyStories (~42k hours), together with EN-FR spoken StoryCloze and TopicCloze benchmarks for cross-lingual semantic evaluation, both synthetically generated using GPT-4. On 360M and 1B SLMs under matched training-token budgets, interleaving improves monolingual semantic accuracy, enables robust cross-lingual continuation, and strengthens cross-lingual hidden-state alignment. Taken together, these results indicate that cross-lingual interleaving is a simple, scalable route to building multilingual SLMs that understand and converse across languages. All resources will be made open-source to support reproducibility.

Large language models (LLMs) are increasingly deployed in multilingual applications but often generate plausible yet incorrect or misleading outputs, known as hallucinations. While hallucination detection has been studied extensively in English, under-resourced Indian languages remain largely unexplored. We present BHRAM-IL, a benchmark for hallucination recognition and assessment in multiple Indian languages, covering Hindi, Gujarati, Marathi, Odia, along with English. The benchmark comprises 36,047 curated questions across nine categories spanning factual, numerical, reasoning, and linguistic tasks. We evaluate 14 state-of-the-art multilingual LLMs on a benchmark subset of 10,265 questions, analyzing cross-lingual and factual hallucinations across languages, models, scales, categories, and domains using category-specific metrics normalized to (0,1) range. Aggregation over all categories and models yields a primary score of 0.23 and a language-corrected fuzzy score of 0.385, demonstrating the usefulness of BHRAM-IL for hallucination-focused evaluation. The dataset, and the code for generation and evaluation are available on GitHub (https://github.com/sambhashana/BHRAM-IL/) and HuggingFace (https://huggingface.co/datasets/sambhashana/BHRAM-IL/) to support future research in multilingual hallucination detection and mitigation.

Point cloud registration aligns multiple unposed point clouds into a common frame, and is a core step for 3D reconstruction and robot localization. In this work, we cast registration as conditional generation: a learned continuous, point-wise velocity field transports noisy points to a registered scene, from which the pose of each view is recovered. Unlike previous methods that conduct correspondence matching to estimate the transformation between a pair of point clouds and then optimize the pairwise transformations to realize multi-view registration, our model directly generates the registered point cloud. With a lightweight local feature extractor and test-time rigidity enforcement, our approach achieves state-of-the-art results on pairwise and multi-view registration benchmarks, particularly with low overlap, and generalizes across scales and sensor modalities. It further supports downstream tasks including relocal-ization, multi-robot SLAM, and multi-session map merging.

Large reasoning models (LRMs) extend large language models by generating explicit chain-of-thought (CoT) reasoning, significantly improving mathematical and logical problem solving. However, this explicit reasoning process also introduces new safety risks, as unsafe behaviors often emerge within intermediate reasoning trajectories, even when final answers appear harmless. Existing safety alignment approaches primarily rely on supervised fine-tuning (SFT) over safety-oriented long CoT datasets. While intuitive, we find that SFT produces inconsistent safety improvements, degrades reasoning ability, and generalizes poorly across model families. These limitations suggest that purely supervised approaches are insufficient for robust safety alignment in LRMs. To address this, we investigate reinforcement learning (RL) as a complementary optimization framework for LRM safety training. Unlike SFT, RL directly optimizes model policies with reward feedback, enabling more adaptive and stable alignment. Extensive experiments across multiple model families and benchmarks show that RL achieves stronger and more consistent safety gains while maintaining reasoning competence. Further analysis of reflection dynamics and token-level entropy reveals that RL suppresses unsafe exploratory reasoning while preserving reflective depth, leading to safer and more reliable reasoning processes.

As Large Language Models (LLMs) become integrated into high-stakes domains, there is a growing need for evaluation methods that are both scalable for real-time deployment and reliable for critical decision-making. While human evaluation is reliable, it is slow and costly. Single LLM judges are biased, and static juries lack adaptability. To overcome these limitations, we propose LLM Jury-on-Demand - a dynamic, learning-based framework for scalable and context-aware evaluation. Our method trains a set of reliability predictors to assess when LLM judges will agree with human experts, leveraging token distributions, embeddings, and structural input features. This enables a fully adaptive evaluation where, for each data point, an optimal jury of the most reliable judges is dynamically selected, and their scores are aggregated using their reliability as weights. Experiments on summarization and RAG benchmarks show that our dynamic jury system achieves significantly higher correlation with human judgment than both single-judge and static-jury baselines. These results highlight the promise of adaptive, learning-based juries for building scalable, more reliable and trustworthy evaluation systems for modern LLMs in high-stakes domains.

While reinforcement learning (RL) successfully enhances reasoning in large language models, its role in fostering compositional generalization (the ability to synthesize novel skills from known components) is often conflated with mere length generalization. To this end, we study what RL post-training teaches about skill composition and how the structure of the composition affects the skill transfer. We focus on the Countdown task (given n numbers and a target, form an expression that evaluates to the target) and analyze model solutions as expression trees, where each subtree corresponds to a reusable subtask and thus can be viewed as a ``skill.'' Tracking tree shapes and their success rates over training, we find: (i) out-of-distribution (OOD) generalization to larger n and to unseen tree shapes, indicating compositional reuse of subtasks; (ii) a structure-dependent hierarchy of learnability -- models master shallow balanced trees (workload is balanced between subtasks) before deep unbalanced ones, with persistent fragility on right-heavy structures (even when the composition depth is the same as some left-heavy structures). Our diagnostic reveals what is learned, in what order, and where generalization fails, clarifying how RL-only post-training induces OOD generalization beyond what standard metrics such as pass@k reveal.

The rise of generalist robotic policies has created an exponential demand for large-scale training data. However, on-robot data collection is labor-intensive and often limited to specific environments. In contrast, open-world images capture a vast diversity of real-world scenes that naturally align with robotic manipulation tasks, offering a promising avenue for low-cost, large-scale robot data acquisition. Despite this potential, the lack of associated robot actions hinders the practical use of open-world images for robot learning, leaving this rich visual resource largely unexploited. To bridge this gap, we propose IGen, a framework that scalably generates realistic visual observations and executable actions from open-world images. IGen first converts unstructured 2D pixels into structured 3D scene representations suitable for scene understanding and manipulation. It then leverages the reasoning capabilities of vision-language models to transform scene-specific task instructions into high-level plans and generate low-level actions as SE(3) end-effector pose sequences. From these poses, it synthesizes dynamic scene evolution and renders temporally coherent visual observations. Experiments validate the high quality of visuomotor data generated by IGen, and show that policies trained solely on IGen-synthesized data achieve performance comparable to those trained on real-world data. This highlights the potential of IGen to support scalable data generation from open-world images for generalist robotic policy training.

Despite advances in the use of large language models (LLMs) in downstream tasks, their ability to memorize information has raised privacy concerns. Therefore, protecting personally identifiable information (PII) during LLM training remains a fundamental challenge. Conventional methods like Differential Privacy-Stochastic Gradient Descent (DP-SGD) provide robust privacy protection via uniform noising, protecting PII regardless of its distinct sensitivity. This comes at the expense of the model's utility, leading to a trade-off. In this paper, we propose SA-ADP, a sensitivity-aware approach that allocates noise based on the sensitivity of individual PII. We evaluated our method on four datasets (ABCD, CUSTOMERSIM, Wikitext-2, and UNSW-NB15 ). Our results show that SA-ADP achieves results comparable to the baseline (No-DP) and the conventional DP-SGD. This means that our method did not degrade the model's utility while still maintaining strong privacy protection.

Large language model (LLM)-based agentic frameworks increasingly adopt the paradigm of dynamically generating task-specific agents. We suggest that not only agents but also specialized software modules for scientific and engineering tasks can be generated on demand. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models are required to describe the relationship between mechanical stress and body deformation. Constitutive models are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete code generation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy comparable to or greater than manually engineered counterparts, while also exhibiting reliable generalization to unseen loading scenarios and extrapolation to large deformations. These findings indicate that LLM-based generation of physics-constrained neural networks can substantially reduce the expertise required for constitutive modeling and represent a step toward practical end-to-end automation.