Knowledge Graph Completion with Mixed Geometry Tensor Factorization Viacheslav Yusupov Maxim Rakhuba Evgeny Frolov HSE University HSE University AIRI HSE University Abstract In this paper, we propose a new geometric approach for knowledge graph completion via low rank tensor approximation. We augment a pretrained and well-established Euclidean model based on a Tucker tensor decomposition with a novel hyperbolic interaction term. This correction enables more nuanced capturing of distributional properties in data better aligned with real-world knowledge graphs. By combining two geometries together, our approach improves expressivity of the resulting model achieving new state-of-the-art link prediction accuracy with a significantly lower number of parameters compared to the previous Euclidean and hyperbolic models. 1 INTRODUCTION Most of the information in the world can be expressed in terms of entities and the relationships between them. This information is effectively represented in the form of a knowledge graph (d'Amato, 2021; Peng et al., 2023), which serves as a repository for storing various forms of relational data with their interconnections. Particular examples include storing user profiles on social networking platforms (Xu et al., 2018), organizing Internet resources and the links between them, constructing knowledge bases that capture user preferences to enhance the functionality of recommender systems (Wang et al., 2019a; Guo et al., 2020). With the recent emergence of large language models (LLM), knowledge graphs have become an essential tool for improving the consistency and trustworthiness of linguis-Proceedings of the 28 th International Conference on Artificial Intelligence and Statistics (AISTATS) 2025, Mai Khao, Thailand. Among notable examples of their application are fact checking (Pan et al., 2024), hallucinations mitigation (Agrawal et al., 2023), retrieval-augmented generation (Lewis et al., 2020), and generation of corpus for LLM pretraining (Agarwal et al., 2021). This utilization underscores the versatility and utility of knowledge graphs in managing complex datasets and facilitating the manipulation of interconnected information in various domains and downstream tasks. On the other hand, knowledge graphs may present an incomplete view of the world. Relations can evolve and change over time, be subject to errors, processing limitations, and gaps in available information.

As large language models (LLMs) and generative AI become widely adopted, guardrails have emerged as a key tool to ensure their safe use. However, adding guardrails isn't without tradeoffs; stronger security measures can reduce usability, while more flexible systems may leave gaps for adversarial attacks. In this work, we explore whether current guardrails effectively prevent misuse while maintaining practical utility. We introduce a framework to evaluate these tradeoffs, measuring how different guardrails balance risk, security, and usability, and build an efficient guardrail. Our findings confirm that there is no free lunch with guardrails; strengthening security often comes at the cost of usability. To address this, we propose a blueprint for designing better guardrails that minimize risk while maintaining usability. We evaluate various industry guardrails, including Azure Content Safety, Bedrock Guardrails, OpenAI's Moderation API, Guardrails AI, Nemo Guardrails, and Enkrypt AI guardrails. Additionally, we assess how LLMs like GPT-4o, Gemini 2.0-Flash, Claude 3.5-Sonnet, and Mistral Large-Latest respond under different system prompts, including simple prompts, detailed prompts, and detailed prompts with chain-of-thought (CoT) reasoning. Our study provides a clear comparison of how different guardrails perform, highlighting the challenges in balancing security and usability.

Probabilistic electricity price forecasting (PEPF) is a key task for market participants in short-term electricity markets. The increasing availability of high-frequency data and the need for real-time decision-making in energy markets require online estimation methods for efficient model updating. We present an online, multivariate, regularized distributional regression model, allowing for the modeling of all distribution parameters conditional on explanatory variables. Our approach is based on the combination of the multivariate distributional regression and an efficient online learning algorithm based on online coordinate descent for LASSO-type regularization. Additionally, we propose to regularize the estimation along a path of increasingly complex dependence structures of the multivariate distribution, allowing for parsimonious estimation and early stopping. We validate our approach through one of the first forecasting studies focusing on multivariate probabilistic forecasting in the German day-ahead electricity market while using only online estimation methods. We compare our approach to online LASSO-ARX-models with adaptive marginal distribution and to online univariate distributional models combined with an adaptive Copula. We show that the multivariate distributional regression, which allows modeling all distribution parameters - including the mean and the dependence structure - conditional on explanatory variables such as renewable in-feed or past prices provide superior forecasting performance compared to modeling of the marginals only and keeping a static/unconditional dependence structure. Additionally, online estimation yields a speed-up by a factor of 80 to over 400 times compared to batch fitting.

Scientific discovery is poised for rapid advancement through advanced robotics and artificial intelligence. Current scientific practices face substantial limitations as manual experimentation remains time-consuming and resource-intensive, while multidisciplinary research demands knowledge integration beyond individual researchers' expertise boundaries. Here, we envision an autonomous generalist scientist (AGS) concept combines agentic AI and embodied robotics to automate the entire research lifecycle. This system could dynamically interact with both physical and virtual environments while facilitating the integration of knowledge across diverse scientific disciplines. By deploying these technologies throughout every research stage -- spanning literature review, hypothesis generation, experimentation, and manuscript writing -- and incorporating internal reflection alongside external feedback, this system aims to significantly reduce the time and resources needed for scientific discovery. Building on the evolution from virtual AI scientists to versatile generalist AI-based robot scientists, AGS promises groundbreaking potential. As these autonomous systems become increasingly integrated into the research process, we hypothesize that scientific discovery might adhere to new scaling laws, potentially shaped by the number and capabilities of these autonomous systems, offering novel perspectives on how knowledge is generated and evolves. The adaptability of embodied robots to extreme environments, paired with the flywheel effect of accumulating scientific knowledge, holds the promise of continually pushing beyond both physical and intellectual frontiers.

State Space Models (SSMs) are emerging as a compelling alternative to Transformers because of their consistent memory usage and high performance. Despite this, scaling up SSMs on cloud services or limited-resource devices is challenging due to their storage requirements and computational power. To overcome this, quantizing SSMs with low bit-width data formats can reduce model size and benefit from hardware acceleration. As SSMs are prone to quantization-induced errors, recent efforts have focused on optimizing a particular model or bit-width for efficiency without sacrificing performance. However, distinct bit-width configurations are essential for different scenarios, like W4A8 for boosting large-batch decoding speed, and W4A16 for enhancing generation speed in short prompt applications for a single user. To this end, we present Quamba2, compatible with W8A8, W4A8, and W4A16 for both Mamba1 and Mamba2 backbones, addressing the growing demand for SSM deployment on various platforms. Based on the channel order preserving and activation persistence of SSMs, we propose an offline approach to quantize inputs of a linear recurrence in 8-bit by sorting and clustering for input $x$, combined with a per-state-group quantization for input-dependent parameters $B$ and $C$. To ensure compute-invariance in the SSM output, we rearrange weights offline according to the clustering sequence. The experiments show that Quamba2-8B outperforms several state-of-the-art SSM quantization methods and delivers 1.3$\times$ and 3$\times$ speed-ups in the pre-filling and generation stages, respectively, while offering 4$\times$ memory reduction with only a $1.6\%$ average accuracy drop. The evaluation on MMLU shows the generalizability and robustness of our framework. The code and quantized models will be released at: https://github.com/enyac-group/Quamba.

The DeepSeek models have shown exceptional performance in general scene understanding, question-answering (QA), and text generation tasks, owing to their efficient training paradigm and strong reasoning capabilities. In this study, we investigate the dialogue capabilities of the DeepSeek model in robotic surgery scenarios, focusing on tasks such as Single Phrase QA, Visual QA, and Detailed Description. The Single Phrase QA tasks further include sub-tasks such as surgical instrument recognition, action understanding, and spatial position analysis. We conduct extensive evaluations using publicly available datasets, including EndoVis18 and CholecT50, along with their corresponding dialogue data. Our empirical study shows that, compared to existing general-purpose multimodal large language models, DeepSeek-VL2 performs better on complex understanding tasks in surgical scenes. Additionally, although DeepSeek-V3 is purely a language model, we find that when image tokens are directly inputted, the model demonstrates better performance on single-sentence QA tasks. However, overall, the DeepSeek models still fall short of meeting the clinical requirements for understanding surgical scenes. Under general prompts, DeepSeek models lack the ability to effectively analyze global surgical concepts and fail to provide detailed insights into surgical scenarios. Based on our observations, we argue that the DeepSeek models are not ready for vision-language tasks in surgical contexts without fine-tuning on surgery-specific datasets.

Data pruning -- the combinatorial task of selecting a small and representative subset from a large dataset, is crucial for mitigating the enormous computational costs associated with training data-hungry modern deep learning models at scale. Since large scale data collections are invariably noisy, developing data pruning strategies that remain robust even in the presence of corruption is critical in practice. However, existing data pruning methods often fail under high corruption rates due to their reliance on empirical mean estimation, which is highly sensitive to outliers. In response, we propose Geometric Median (GM) Matching, a novel k-subset selection strategy that leverages Geometric Median -- a robust estimator with an optimal breakdown point of 1/2; to enhance resilience against noisy data. Our method iteratively selects a k-subset such that the mean of the subset approximates the GM of the (potentially) noisy dataset, ensuring robustness even under arbitrary corruption. We provide theoretical guarantees, showing that GM Matching enjoys an improved O(1/k) convergence rate -- a quadratic improvement over random sampling, even under arbitrary corruption. Extensive experiments across image classification and image generation tasks demonstrate that GM Matching consistently outperforms existing pruning approaches, particularly in high-corruption settings and at high pruning rates; making it a strong baseline for robust data pruning.

Quantum generative models offer a promising new direction in machine learning by leveraging quantum circuits to enhance data generation capabilities. In this study, we propose a hybrid quantum-classical image generation framework that integrates variational quantum circuits into a diffusion-based model. To improve training dynamics and generation quality, we introduce two novel noise strategies: intrinsic quantum-generated noise and a tailored noise scheduling mechanism. Our method is built upon a lightweight U-Net architecture, with the quantum layer embedded in the bottleneck module to isolate its effect. We evaluate our model on MNIST and MedMNIST datasets to examine its feasibility and performance. Notably, our results reveal that under limited data conditions (fewer than 100 training images), the quantum-enhanced model generates images with higher perceptual quality and distributional similarity than its classical counterpart using the same architecture. While the quantum model shows advantages on grayscale data such as MNIST, its performance is more nuanced on complex, color-rich datasets like PathMNIST. These findings highlight both the potential and current limitations of quantum generative models and lay the groundwork for future developments in low-resource and biomedical image generation.

In this study, we investigate the problem of dynamic multi-product selection and pricing by introducing a novel framework based on a \textit{censored multinomial logit} (C-MNL) choice model. In this model, sellers present a set of products with prices, and buyers filter out products priced above their valuation, purchasing at most one product from the remaining options based on their preferences. The goal is to maximize seller revenue by dynamically adjusting product offerings and prices, while learning both product valuations and buyer preferences through purchase feedback. To achieve this, we propose a Lower Confidence Bound (LCB) pricing strategy. By combining this pricing strategy with either an Upper Confidence Bound (UCB) or Thompson Sampling (TS) product selection approach, our algorithms achieve regret bounds of $\tilde{O}(d^{\frac{3}{2}}\sqrt{T/\kappa})$ and $\tilde{O}(d^{2}\sqrt{T/\kappa})$, respectively. Finally, we validate the performance of our methods through simulations, demonstrating their effectiveness.

Visual narrative generation transforms textual narratives into sequences of images illustrating the content of the text. However, generating visual narratives that are faithful to the input text and self-consistent across generated images remains an open challenge, due to the lack of knowledge constraints used for planning the stories. In this work, we propose a new benchmark, VinaBench, to address this challenge. Our benchmark annotates the underlying commonsense and discourse constraints in visual narrative samples, offering systematic scaffolds for learning the implicit strategies of visual storytelling. Based on the incorporated narrative constraints, we further propose novel metrics to closely evaluate the consistency of generated narrative images and the alignment of generations with the input textual narrative. Our results across three generative vision models demonstrate that learning with VinaBench's knowledge constraints effectively improves the faithfulness and cohesion of generated visual narratives.