论文检索

Applications · Genetics, Cell Biology, etc

Kaichen Xu, Yihang Du, Mianpeng Liu, Zimu Yu, Xiaobo Sun

Positional encoding is essential for supplementing transformer with positional information of tokens. Existing positional encoding methods demand predefined token/feature order, rendering them unsuitable for real-world data with non-sequential yet causally-related features. To address this limitation, we propose CAPE, a novel method that identifies underlying causal structure over non-sequential features as a weighted directed acyclic graph (DAG) using generalized structural equation modeling. The DAG is then embedded in hyperbolic space where its geometric structure is well-preserved using a hyperboloid model-based approach that effectively captures two important causal graph properties (causal strength & causal specificity). This step yields causality-aware positional encodings for the features, which are converted into their rotary form for integrating with transformer's self-attention mechanism. Theoretical analysis reveals that CAPE-generated rotary positional encodings possess three valuable properties for enhanced self-attention, including causal distance-induced attenuation, causal generality-induced attenuation, and robustness to positional disturbances. We evaluate CAPE over both synthetic and real-word datasets, empirically demonstrating its theoretical properties and effectiveness in enhancing transformer for data with non-sequential features. Our code is available at https://github.com/Catchxu/CAPE.

General Machine Learning · Causality

Moritz Miller, Bernhard Schölkopf, Siyuan Guo

Large-scale neural language models exhibit remarkable performance in in-context learning: the ability to learn and reason about the input context on the fly. This work studies in-context counterfactual reasoning in language models, that is, the ability to predict consequences of a hypothetical scenario. We focus on a well-defined, synthetic linear regression task that requires noise abduction. Accurate prediction is based on (1) inferring an unobserved latent concept and (2) copying contextual noise from factual observations. We show that language models are capable of counterfactual reasoning. Further, we enhance existing identifiability results and reduce counterfactual reasoning for a broad class of functions to a transformation on in-context observations. In Transformers, we find that self-attention, model depth and pre-training data diversity drive performance. Moreover, we provide mechanistic evidence that the latent concept is linearly represented in the residual stream and we introduce designated *noise abduction heads* central to performing counterfactual reasoning. Lastly, our findings extend to counterfactual reasoning under SDE dynamics and reflect that Transformers can perform noise abduction on sequential data, providing preliminary evidence on the potential for counterfactual story generation. Our code is available under *https://github.com/mrtzmllr/iccr*.

Reinforcement Learning · Everything Else

Top Piriyakulkij, Yichao Liang, Hao Tang, Adrian Weller, Marta Kryven, Kevin Ellis

Learning how the world works is central to building AI agents that can adapt to complex environments. Traditional world models based on deep-learning demand vast amounts of training data, and do not flexibly update their knowledge from sparse observations. Recent advances in program synthesis using Large Language Models (LLMs) give an alternate approach which learns world models represented as source code, supporting strong generalization from little data. To date, application of program-structured world models remains limited to natural language and grid-world domains. We introduce a novel program synthesis method for effectively modeling complex, non-gridworld domains by representing a world model as an exponentially-weighted product of programmatic experts (PoE-World) synthesized by LLMs. We show that this approach can learn complex, stochastic world models from just a few observations. We evaluate the learned world models by embedding them in a model-based planning agent, demonstrating efficient performance and generalization to unseen levels on Atari's Pong and Montezuma's Revenge.

Computer Vision · Everything Else

Haonan Wang, Hanyu Zhou, Haoyue Liu, Luxin Yan

Optical flow estimation has achieved promising results in conventional scenes but faces challenges in high-speed and low-light scenes, which suffer from motion blur and insufficient illumination. These conditions lead to weakened texture and amplified noise and deteriorate the appearance saturation and boundary completeness of frame cameras, which are necessary for motion feature matching. In degraded scenes, the frame camera provides dense appearance saturation but sparse boundary completeness due to its long imaging time and low dynamic range. In contrast, the event camera offers sparse appearance saturation, while its short imaging time and high dynamic range gives rise to dense boundary completeness. Traditionally, existing methods utilize feature fusion or domain adaptation to introduce event to improve boundary completeness. However, the appearance features are still deteriorated, which severely affects the mostly adopted discriminative models that learn the mapping from visual features to motion fields and generative models that generate motion fields based on given visual features. So we introduce diffusion models that learn the mapping from noising flow to clear flow, which is not affected by the deteriorated visual features. Therefore, we propose a novel optical flow estimation framework Diff-ABFlow based on diffusion models with frame-event appearance-boundary fusion. Inspired by the appearance-boundary complementarity of frame and event, we propose an Attention-Guided Appearance-Boundary Fusion module to fuse frame and event. Based on diffusion models, we propose a Multi-Condition Iterative Denoising Decoder. Our proposed method can effectively utilize the respective advantages of frame and event, and shows great robustness to degraded input. In addition, we propose a dual-modal optical flow dataset for generalization experiments. Extensive experiments have verified the superiority of our proposed method. The code is released at .

General Machine Learning · Everything Else

Noa Shoham, Ron Dorfman, Shalev Shaer, Kfir Y. Levy, Yaniv Romano

Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator. In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models. To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.

Social Aspects · Fairness, Equity, Justice and Safety

Hao Li, Xiaogeng Liu, CHIU Chun, Dianqi Li, Ning Zhang, Chaowei Xiao

Large Language Models (LLMs) are increasingly central to agentic systems due to their strong reasoning and planning capabilities. By interacting with external environments through predefined tools, these agents can carry out complex user tasks. Nonetheless, this interaction also introduces the risk of prompt injection attacks, where malicious inputs from external sources can mislead the agent’s behavior, potentially resulting in economic loss, privacy leakage, or system compromise. System-level defenses have recently shown promise by enforcing static or predefined policies, but they still face two key challenges: the ability to dynamically update security rules and the need for memory stream isolation. To address these challenges, we propose DRIFT, a Dynamic Rule-based Isolation Framework for Trustworthy agentic systems, which enforces both control- and data-level constraints. A Secure Planner first constructs a minimal function trajectory and a JSON-schema-style parameter checklist for each function node based on the user query. A Dynamic Validator then monitors deviations from the original plan, assessing whether changes comply with privilege limitations and the user's intent. Finally, an \textit{Injection Isolator} detects and masks any instructions that may conflict with the user query from the memory stream to mitigate long-term risks. We empirically validate the effectiveness of DRIFT on the AgentDojo and ASB benchmark, demonstrating its strong security performance while maintaining high utility across diverse models—showcasing both its robustness and adaptability. The code is released at https://github.com/SaFoLab-WISC/DRIFT.

Probabilistic Methods · Bayesian Models and Methods

Jean Feng, Avni Kothari, Lucas Zier, Chandan Singh, Yan Shuo Tan

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between exploring a sufficiently large set of concepts versus controlling the cost of obtaining concept extractions, resulting in a large interpretability-accuracy tradeoff. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. Even though LLMs can be miscalibrated and hallucinate, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. Across image, text, and tabular datasets, BC-LLM outperforms interpretable baselines and even black-box models in certain settings, converges more rapidly towards relevant concepts, and is more robust to out-of-distribution samples.

Computer Vision · Vision Models & Multimodal

Duo Zheng, shijia Huang, Yanyang Li, Liwei Wang

Previous research has investigated the application of Multimodal Large Language Models (MLLMs) in understanding 3D scenes by interpreting them as videos. These approaches generally depend on comprehensive 3D data inputs, such as point clouds or reconstructed Bird's-Eye View (BEV) maps. In our research, we advance this field by enhancing the capability of MLLMs to understand and reason in 3D spaces directly from video data, without the need for additional 3D input. We propose a novel and efficient method called the Video-3D Geometry Large Language Model (VG LLM). Our approach utilizes a 3D visual geometry encoder to extract 3D prior information from video sequences. This information is then integrated with visual tokens and input into the MLLM. Extensive experiments have shown that our method has achieved substantial improvements in various tasks related to 3D scene understanding and spatial reasoning, all directly learned from video sources. Impressively, our 4B model, which does not rely on explicit 3D data inputs, achieves competitive results compared to existing state-of-the-art methods, and even surpasses the Gemini-1.5-Pro in the VSI-Bench evaluations.

General Machine Learning · Representation Learning

Mingze Dong, Leda Wang, Yuval Kluger

Mask-based pretraining has become a cornerstone of modern large-scale models across language, vision, and recently biology. Despite its empirical success, its role and limits in learning data representations have been unclear. In this work, we show that the behavior of mask-based pretraining can be directly characterized by test risk in high-dimensional minimum-norm ("ridge-less") linear regression, without relying on further model specifications. Further analysis of linear models uncovers several novel aspects of mask-based pretraining. The theoretical framework and its implications have been validated across diverse neural architectures (including MLPs, CNNs, and Transformers) applied to both vision and language tasks. Guided by our theory, we propose an embarrassingly simple yet overlooked pretraining scheme named *Randomly Random Mask AutoEncoding* (**R²MAE**), which enforces capturing multi-scale features from data and is able to outperform optimal fixed mask ratio settings in our linear model framework. We implement R²MAE in vision, language, DNA sequence, and single-cell models, where it consistently outperforms standard and more complicated masking schemes, leading to improvements for state-of-the-art models. Our code is available at [this URL](https://github.com/MingzeDong/r2mae).

Computer Vision · Vision Models & Multimodal

Xiaoyi Zhang, Zhaoyang Jia, Zongyu Guo, Jiahao Li, Bin Li, Houqiang Li, Yan Lu

Long-form video understanding presents significant challenges due to extensive temporal-spatial complexity and the difficulty of question answering under such extended contexts. While Large Language Models (LLMs) have demonstrated considerable advancements in video analysis capabilities and long context handling, they continue to exhibit limitations when processing information-dense hour-long videos. To overcome such limitations, we propose the $\textbf{D}eep \ \textbf{V}ideo \ \textbf{D}iscovery \ (\textbf{DVD})$ agent to leverage an $\textit{agentic search}$ strategy over segmented video clips. Different from previous video agents manually designing a rigid workflow, our approach emphasizes the autonomous nature of agents. By providing a set of search-centric tools on multi-granular video database, our DVD agent leverages the advanced reasoning capability of LLM to plan on its current observation state, strategically selects tools to orchestrate adaptive workflow for different queries in light of the gathered information. We perform comprehensive evaluation on multiple long video understanding benchmarks that demonstrates our advantage. Our DVD agent achieves state-of-the-art performance on the challenging LVBench dataset, reaching an accuracy of $\textbf{74.2\%}$, which substantially surpasses all prior works, and further improves to $\textbf{76.0\%}$ with transcripts.

Applications · Neuroscience, Cognitive Science

Camila Kolling, Vy Vo, Mariya Toneva

Associative learning--forming links between co-occurring items--is fundamental to human cognition, reshaping internal representations in complex ways. Testing hypotheses on how representational changes occur in biological systems is challenging, but large language models (LLMs) offer a scalable alternative. Building on LLMs' in-context learning, we adapt a cognitive neuroscience associative learning paradigm and investigate how representations evolve across six models. Our initial findings reveal a non-monotonic pattern consistent with the Non-Monotonic Plasticity Hypothesis, with moderately similar items differentiating after learning. Leveraging the controllability of LLMs, we further show that this differentiation is modulated by the overlap of associated items with the broader vocabulary--a factor we term vocabulary interference, capturing how new associations compete with prior knowledge. We find that higher vocabulary interference amplifies differentiation, suggesting that representational change is influenced by both item similarity and global competition. Our findings position LLMs not only as powerful tools for studying representational dynamics in human-like learning systems, but also as accessible and general computational models for generating new hypotheses about the principles underlying memory reorganization in the brain.

Computer Vision · Vision Models & Multimodal

Yu Li, Jin Jiang, Jianhua Zhu, Shuai Peng, Baole, Yuxuan Zhou, Liangcai Gao

Handwritten Mathematical Expression Recognition (HMER) remains a persistent challenge in Optical Character Recognition (OCR) due to the inherent freedom of symbol layouts and variability in handwriting styles. Prior methods have faced performance bottlenecks by proposing isolated architectural modifications, making them difficult to integrate coherently into a unified framework. Meanwhile, recent advances in pretrained vision-language models (VLMs) have demonstrated strong cross-task generalization, offering a promising foundation for developing unified solutions. In this paper, we introduce Uni-MuMER, which fully fine-tunes a VLM for the HMER task without modifying its architecture, effectively injecting domain-specific knowledge into a generalist framework. Our method integrates three data-driven tasks: Tree-Aware Chain-of-Thought (Tree-CoT) for structured spatial reasoning, Error-Driven Learning (EDL) for reducing confusion among visually similar characters, and Symbol Counting (SC) for improving recognition consistency in long expressions. Experiments on the CROHME and HME100K datasets show that Uni-MuMER achieves super state-of-the-art performance, outperforming the best lightweight specialized model SSAN by 16.31\% and the top-performing VLM Gemini2.5-flash by 24.42\% under zero-shot setting. Our datasets, models, and code are open-sourced at: https://github.com/BFlameSwift/Uni-MuMER

Applications · Robotics

Yan Zhuang, Jiawei Ren, Xiaokang Ye, Jianzhi Shen, Ruixuan Zhang, Tianai Yue, Muhammad Faayez, Xuhong He, Xiyan Zhang, Ziqiao Ma 等

Recent advances in foundation models have shown promising results in developing generalist robotics that can perform diverse tasks in open-ended scenarios given multimodal inputs. However, current work has been mainly focused on indoor, household scenarios. In this work, we present SimWorld-Robotics (SWR), a simulation platform for embodied AI in large-scale, photorealistic urban environments. Built on Unreal Engine 5, SWR procedurally generates unlimited photorealistic urban scenes populated with dynamic elements such as pedestrians and traffic systems, surpassing prior urban simulations in realism, complexity, and scalability. It also supports multi-robot control and communication. With these key features, we build two challenging robot benchmarks: (1) a multimodal instruction-following task, where a robot must follow vision-language navigation instructions to reach a destination in the presence of pedestrians and traffic; and (2) a multi-agent search task, where two robots must communicate to cooperatively locate and meet each other. Unlike existing benchmarks, these two new benchmarks comprehensively evaluate a wide range of critical robot capacities in realistic scenarios, including (1) multimodal instructions grounding, (2) 3D spatial reasoning in large environments, (3) safe, long-range navigation with people and traffic, (4) multi-robot collaboration, and (5) grounded communication. Our experimental results demonstrate that state-of-the-art models, including vision-language models (VLMs), struggle with our tasks, lacking robust perception, reasoning, and planning abilities necessary for urban environments.

Applications · Language, Speech and Dialog

Ping Guo, Yubing Ren, BINBINLIU, Fengze Liu, Haobin Lin, Yifan Zhang, Bingni Zhang, Taifeng Wang, Yin Zheng

Large language models (LLMs) have become integral to a wide range of applications worldwide, driving an unprecedented global demand for effective multilingual capabilities. Central to achieving robust multilingual performance is the strategic allocation of language proportions within training corpora. However, determining optimal language ratios is highly challenging due to intricate cross-lingual interactions and sensitivity to dataset scale. This paper introduces CLIMB (Cross-Lingual Interaction-aware Multilingual Balancing), a novel framework designed to systematically optimize multilingual data allocation. At its core, CLIMB introduces a cross-lingual interaction-aware language ratio, explicitly quantifying each language’s effective allocation by capturing inter-language dependencies. Leveraging this ratio, CLIMB proposes a principled two-step optimization procedure—first equalizing marginal benefits across languages, then maximizing the magnitude of the resulting language allocation vectors—significantly simplifying the inherently complex multilingual optimization problem. Extensive experiments confirm that CLIMB can accurately measure cross-lingual interactions across various multilingual settings. LLMs trained with CLIMB-derived proportions consistently achieve state-of-the-art multilingual performance, even achieve competitive performance with open-sourced LLMs trained with more tokens.

Applications · Robotics

Korneel Van den Berghe, Stein Stroobants, Vijay Janapa Reddi, Guido de Croon

Neuromorphic computing systems are set to revolutionize energy-constrained robotics by achieving orders-of-magnitude efficiency gains, while enabling native temporal processing. Spiking Neural Networks (SNNs) represent a promising algorithmic approach for these systems, yet their application to complex control tasks faces two critical challenges: (1) the non-differentiable nature of spiking neurons necessitates surrogate gradients with unclear optimization properties, and (2) the stateful dynamics of SNNs require training on sequences, which in reinforcement learning (RL) is hindered by limited sequence lengths during early training, preventing the network from bridging its warm-up period. We address these challenges by systematically analyzing surrogate gradient slope settings, showing that shallower slopes increase gradient magnitude in deeper layers but reduce alignment with true gradients. In supervised learning, we find no clear preference for fixed or scheduled slopes. The effect is much more pronounced in RL settings, where shallower slopes or scheduled slopes lead to a $\times2.1$ improvement in both training and final deployed performance. Next, we propose a novel training approach that leverages a privileged guiding policy to bootstrap the learning process, while still exploiting online environment interactions with the spiking policy. Combining our method with an adaptive slope schedule for a real-world drone position control task, we achieve an average return of 400 points, substantially outperforming prior techniques, including Behavioral Cloning and TD3BC, which achieve at most –200 points under the same conditions. This work advances both the theoretical understanding of surrogate gradient learning in SNNs and practical training methodologies for neuromorphic controllers demonstrated in real-world robotic systems.

Reinforcement Learning · Everything Else

Runqing Miao, Sheng Xu, Runyi Zhao, Wai Kin (Victor) Chan, Guiliang Liu

Recent advancements in diffusion policies have demonstrated promising performance in decision-making tasks. To align these policies with human preferences, a common approach is incorporating Preference-based Reinforcement Learning (PbRL) into policy tuning. However, since preference data is practically collected from populations with different backgrounds, a key challenge lies in handling the inherent uncertainties in people's preferences during policy updates. To address this challenge, we propose the Diff-UAPA algorithm, designed for uncertainty-aware preference alignment in diffusion policies. Specifically, Diff-UAPA introduces a novel iterative preference alignment framework in which the diffusion policy adapts incrementally to preferences from different user groups. To accommodate this online learning paradigm, Diff-UAPA employs a maximum posterior objective, which aligns the diffusion policy with regret-based preferences under the guidance of an informative Beta prior. This approach enables direct optimization of the diffusion policy without specifying any reward functions, while effectively mitigating the influence of inconsistent preferences across different user groups. We conduct extensive experiments across both simulated and real-world robotics tasks, and diverse human preference configurations, demonstrating the robustness and reliability of Diff-UAPA in achieving effective preference alignment. The project page is available at https://anonymous.4open.science/w/Diff-UAPA-5827.

Applications · Language, Speech and Dialog

Yana Wei, Liang Zhao, Jianjian Sun, Kangheng Lin, jisheng yin, Jingcheng Hu, Yinmin Zhang, En Yu, Haoran Lv, Zejia Weng 等

The remarkable reasoning capability of large language models (LLMs) stems from cognitive behaviors that emerge through reinforcement with verifiable rewards. This work investigates how to transfer this principle to Multimodal LLMs (MLLMs) to unlock advanced visual reasoning. We introduce a two-stage paradigm built on Qwen2.5-VL-7B: a massive linguistic cold-start fine-tuning, followed by multimodal reinforcement learning (RL) spanning nearly 1,000 steps—surpassing all previous open-source efforts in scale. This pioneering work reveals three fundamental insights: 1) Behavior transfer emerges surprisingly early in cold start due to linguistic mental imagery. 2) Cold start broadly memorizes visual behaviors, while RL critically discerns and scales up effective patterns. 3) Transfer strategically favors high-utility behaviors such as visual reflection. Our resulting model, Open-Vision-Reasoner (OVR), achieves state-of-the-art performance on a suite of reasoning benchmarks, including 95.3% on MATH500, 51.8% on MathVision and 54.6% on MathVerse. We release our model, data, and training dynamics to catalyze the development of more capable, behavior-aligned multimodal reasoners.

Optimization · Stochastic & Convex Optimization

Aneesh Barthakur, Luiz Chamon

As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement violation penalties into the training objective. To be effective, this approach requires careful tuning of these hyperparameters (weights), involving trial-and-error and cross-validation, which becomes ineffective even for a moderate number of requirements. These issues are exacerbated when the requirements involve parities or equalities, as is the case in fairness and boundary value problems. An alternative technique uses constrained optimization to formulate these learning problems. Yet, existing approximation and generalization guarantees do not apply to problems involving equality constraints. In this work, we derive a generalization theory for equality-constrained statistical learning problems, showing that their solutions can be approximated using samples and rich parametrizations. Using these results, we propose a practical algorithm based on solving a sequence of *unconstrained*, *empirical* learning problems. We showcase its effectiveness and the new formulations enabled by equality constraints in fair learning, interpolating classifiers, and boundary value problems.

Computer Vision · Image and Video Generation

Bailey Trang Nguyen, Parham Saremi, Alan Wang, Fangrui Huang, Zahra TehraniNasab, Amar Kumar, Tal Arbel, Fei-Fei Li, Ehsan Adeli

Capturing diversity is crucial in conditional and prompt-based image generation, particularly when conditions contain uncertainty that can lead to multiple plausible outputs. To generate diverse images reflecting this diversity, traditional methods often modify random seeds, making it difficult to discern meaningful differences between samples, or diversify the input prompt, which is limited in verbally interpretable diversity. We propose \modelnamenospace, a novel conditional image generation framework, applicable to any pretrained conditional generative model, that addresses inherent condition/prompt uncertainty and generates diverse plausible images. \modelname is based on a simple yet effective idea: decomposing the input condition into diverse latent representations, each capturing an aspect of the uncertainty and generating a distinct image. First, we integrate a latent graph, parameterized by Generative Flow Networks (GFlowNets), into the prompt representation computation. Second, leveraging GFlowNets' advanced graph sampling capabilities to capture uncertainty and output diverse trajectories over the graph, we produce multiple trajectories that collectively represent the input condition, leading to diverse condition representations and corresponding output images. Evaluations on natural image and medical image datasets demonstrate \modelnamenospace’s improvement in both diversity and fidelity across image synthesis, image generation, and counterfactual generation tasks.

Computer Vision · Image and Video Generation

Jie Liu, Gongye Liu, Jiajun Liang, Yangguang Li, Jiaheng Liu, Xintao Wang, Pengfei Wan, Di ZHANG, Wanli Ouyang

We propose Flow-GRPO, the first method to integrate online policy gradient reinforcement learning (RL) into flow matching models. Our approach uses two key strategies: (1) an ODE-to-SDE conversion that transforms a deterministic Ordinary Differential Equation (ODE) into an equivalent Stochastic Differential Equation (SDE) that matches the original model's marginal distribution at all timesteps, enabling statistical sampling for RL exploration; and (2) a Denoising Reduction strategy that reduces training denoising steps while retaining the original number of inference steps, significantly improving sampling efficiency without sacrificing performance. Empirically, Flow-GRPO is effective across multiple text-to-image tasks. For compositional generation, RL-tuned SD3.5-M generates nearly perfect object counts, spatial relations, and fine-grained attributes, increasing GenEval accuracy from $63\%$ to $95\%$. In visual text rendering, accuracy improves from $59\%$ to $92\%$, greatly enhancing text generation. Flow-GRPO also achieves substantial gains in human preference alignment. Notably, very little reward hacking occurred, meaning rewards did not increase at the cost of appreciable image quality or diversity degradation.