arXiv:2605.26022v1 Announce Type: new
Abstract: We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors converge to zero as noise, algorithmic errors, and regularisation vanish as the horizon grows. We illustrate the theory numerically with a dynamic electrical impedance tomography example.
Science Journals
arXiv:2605.26025v1 Announce Type: new
Abstract: We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows for adaptive tracking of evolving physics. Our approach decouples the geometric drift of the subspace from the intrinsic state evolution. This avoids the typical rank inflation required by static low-dimensional approximation methods to maintain accuracy, effectively breaking the Kolmogorov barrier in transport-dominated phenomena. To ensure scalability for high-dimensional data, the optimization is performed in a reduced feature space, rendering the computational cost independent of the large original state dimension. Numerical results for a 1D transport equation and a large-scale turbulent airfoil wake demonstrate that this dynamic subspace approach achieves higher accuracy than static linear approximations at equivalent ranks, positioning it as a robust and scalable method for the low-rank modeling of complex, non-stationary dynamical systems.
arXiv:2605.26032v1 Announce Type: new
Abstract: Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce $\textbf{SKILD}$, a $\textbf{S}$cale-invariant $\textbf{K}$-Space $\textbf{I}$mage $\textbf{L}$earning $\textbf{D}$iffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: $\textit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}$. Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2\times$--$8\times$ super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.
arXiv:2601.21406v3 Announce Type: replace
Abstract: Unified Multimodal Models (UMMs) integrate both visual understanding and generation within a single framework. Their ultimate aspiration is to create a cycle where understanding and generation mutually reinforce each other. While recent post-training methods have successfully leveraged understanding to enhance generation, the reverse direction of utilizing generation to improve understanding remains largely unexplored. In this work, we propose UniMRG (Unified Multi-Representation Generation), a simple yet effective architecture-agnostic post-training method. UniMRG enhances the understanding capabilities of UMMs by incorporating auxiliary generation tasks. Specifically, we train UMMs to generate multiple intrinsic representations of input images, namely pixel (reconstruction), depth (geometry), and segmentation (structure), alongside standard visual understanding objectives. By synthesizing these diverse representations, UMMs capture complementary information regarding appearance, spatial relations, and structural layout. Consequently, UMMs develop a deeper and more comprehensive understanding of visual inputs. Extensive experiments across diverse UMM architectures demonstrate that our method notably enhances fine-grained perception, reduces hallucinations, and improves spatial understanding, while simultaneously boosting generation capabilities.
arXiv:2605.26035v1 Announce Type: new
Abstract: Length generalization remains a persistent challenge for neural networks: recurrent models tend to suffer from positional biases, while transformers are constrained by fixed computational depth. Regular languages provide a frequently used testbed for evaluating length generalization, as label prediction can be checked for any sequence length. We propose MLP-LDRU, a type of Log-Depth Recurrent Unit, which captures a class of associativity-biased operators designed to approximate recurrence through parallel reduction. We evaluate MLP-LDRU on 21 regular-language tasks, consisting of standard benchmarks and new prefix languages, where it achieves 100% out-of-distribution accuracy on 18 tasks and at least 99.9% on the remaining 3 when increasing max training length, outperforming comparable recurrent and attention-based models. We further evaluate MLP-LDRU beyond regular languages on ListOps and NLP classification benchmarks, where it performs competitively.
arXiv:2605.25546v1 Announce Type: new
Abstract: Safety-critical control is essential for humanoid robots operating in complex human-centered environments, where physical safety constraints such as joint limits, self-collision avoidance, obstacle avoidance, and workspace boundaries must be satisfied during real-robot operation. However, existing approaches remain limited because kinematic safety guarantees can be degraded in the presence of unknown disturbances, such as model uncertainties, trajectory-tracking errors, and external perturbations. This paper presents a hierarchical safety-critical whole-body control framework for humanoid robots based on input-to-state safe control barrier functions (ISSf-CBFs). The proposed architecture integrates a kinematic-level whole-body controller (KinWBC), an ISSf-CBF safety filter, and a dynamic-level whole-body controller (DynWBC). KinWBC generates nominal joint-motion references from prioritized tasks; the ISSf-CBF filter minimally modifies these references to satisfy kinematic safety constraints under bounded disturbances; and DynWBC tracks the filtered references while enforcing full-body dynamic feasibility and contact stability. Safety constraints are imposed on a whole-body kinematic model, and the ISSf-CBF parameters are conservatively tuned so that the resulting kinematic safety guarantees can be transferred to full-order humanoid dynamics under unknown disturbances. Simulation and real-robot experiments demonstrate that the proposed framework improves safety margins under model mismatch and reliably enforces multiple safety constraints in real time during locomotion, teleoperation, and single-leg balancing with hand control. Project website: https://kwlee365.github.io/SafeWBC-Website/
arXiv:2605.23961v1 Announce Type: cross
Abstract: The design of RNA molecules that interact with specific proteins is a critical challenge in experimental and computational biology. Despite recent progress in natural language modeling and deep learning-based protein design, there remains significant room to improve the frequency of successful interactions and the authenticity of generated sequences for functional applications. In this work, we frame conditional RNA sequence generation as a multi-stage alignment problem, introducing Moirain: a suite of models optimized via multimodal supervised fine-tuning (SFT) and Direct Preference Optimization (DPO). Our approach begins with large-scale pretraining on diverse RNA corpora to capture the fundamental grammars of sequence plausibility. To achieve target-specific generation, we employ a multimodal SFT architecture that conditions RNA synthesis on protein structural and sequential features. Finally, we leverage DPO to refine the model using synthetic interaction data: taking advantage of DPO's unique ability to navigate non-aligned preference spaces, we improve functional fitness without collapsing the learned natural distribution. Extensive evaluation of the Moirain series (Moirain-Base, -Multi, and -DPO) demonstrates that our framework consistently produces novel, diverse, and biologically plausible RNA sequences with superior binding affinities compared to existing baselines.
arXiv:2605.26081v1 Announce Type: new
Abstract: Deep research agents face vast, interdependent, and pervasively uncertain information. Existing systems explore what evolving intermediate representations should look like, but leave their evolution to the LLM's implicit reasoning. Without explicit regulation, the intermediate layer is easily contaminated by mixed-quality information and propagates errors along its dependencies, so model scale often ends up substituting for absent regulation. We argue that an agent's mental model should instead evolve through explicit feedback that continuously aligns task understanding with reality, and identify three regulatory loops: interpretive update, deviation feedback, and schema revision. We realise this in VeriTrace, a cognitive-graph framework that explicitly implements the three loops. Using matched Qwen3.5-27B backbones, VeriTrace improves over the strongest matched baseline by 4.22 pp on DeepResearch Bench (DRB) Insight (1.49 pp Overall) and by 5.9 pp Overall win rate on DeepConsult. With Config-DeepSeek, it achieves the strongest reproducible open-source result on DRB.
arXiv:2605.26084v1 Announce Type: new
Abstract: The concept of 'undone science' emerged in the 2010s in research in social sciences at the intersection of studies on social movements and of science and technology studies. It refers to research questions that are neglected, ignored, or left unfunded, even though they deserve to be explored. The aim of this special issue is to apply this concept to computer science, by examining whether the way this discipline is structured (including its sociological, economic, and political dimensions), as well as the paradigms that shape it, make it possible to identify epistemological and ethical questions that are crucial for its development and conception.
arXiv:2605.24867v1 Announce Type: new
Abstract: Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a $k$-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the $k$-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.
arXiv:2605.26115v1 Announce Type: new
Abstract: Sparse-view 3D reconstruction is increasingly addressed with feed-forward splatting networks that predict explicit primitives directly from images. Yet most existing methods remain centered on Gaussian primitives and expose surfaces only indirectly: extracting a usable mesh for downstream simulation, physics reasoning, or embodied interaction still requires expensive post-hoc steps that break the feed-forward promise. This limitation is especially pronounced in pose-free settings, where scene structure and camera parameters must be estimated jointly from sparse observations. We present TriSplat, a feed-forward reconstruction network that represents scenes with oriented triangle primitives and directly exports simulation-ready mesh scenes from a single forward pass. Given input images, the network predicts local 3D point maps, triangle attributes, camera poses, and optional intrinsics. Rather than regressing triangle orientation as an unconstrained latent variable, our approach constructs geometry normals from the predicted point maps, refines them with an image-conditioned normal head, and converts them into stable local frames for triangle parameterization. A mono-normal bootstrap schedule further stabilizes early training, while opacity and blur scheduling progressively sharpens the learned surface representation for direct mesh extraction. Experiments on RealEstate10K and DL3DV show that this representation produces more geometry-faithful reconstructions than Gaussian feed-forward baselines while maintaining competitive novel-view rendering quality. Because the rendering primitives are themselves surface triangles, the output can be directly ingested by physics engines, collision detectors, and standard rendering pipelines without any conversion, making it a practical simulation-ready solution for feed-forward 3D scene reconstruction.
arXiv:2506.06454v2 Announce Type: cross
Abstract: Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.
arXiv:2605.23960v1 Announce Type: cross
Abstract: Proteins encode diverse functions within complex three-dimensional structures, yet most deep learning representations remain highly entangled, obscuring the biophysical signals that underlie function. Here we introduce ProtDiS, a knowledge-guided framework that decomposes pretrained protein micro-environment embeddings into biologically grounded and task-relevant dimensions. Inspired by the information bottleneck principle, ProtDiS learns representations that balance informativeness and compression, yielding structural features that are more specific, independent, and information-efficient, and achieving consistent improvements across twelve downstream tasks, with the largest gains under structure-based splits. Protein- and residue-level analyses further show that ProtDiS differentiates proteins with similar folds but divergent functions and captures fine-grained biophysical signals critical. These findings suggest that knowledge-guided decomposition provides a general and interpretable approach for structuring latent spaces in protein structural modeling. The source code and implementation details are publicly available at https://github.com/AI-HPC-Research-Team/ProtDiS.
arXiv:2605.15011v2 Announce Type: replace
Abstract: Scientific contributions rarely develop in isolation, but instead build upon prior discoveries. We formulate the task of automated technological roadmapping as extracting scientific contributions from scholarly articles and linking them to their prerequisites. We present the Scientific Contribution Graph, a large-scale AI/NLP-domain resource containing 2 million detailed scientific contributions extracted from 230k open-access papers and connected by 12.5 million prerequisite edges. We further introduce scientific prerequisite prediction, a scientific discovery task in which models predict which existing technologies can enable future discoveries, and show that contemporary models are rapidly improving on this task, reaching 0.48 MAP when evaluated using temporally filtered backtesting. We anticipate technological roadmapping resources such as this will support scientific impact assessment and automated scientific discovery.
arXiv:2509.10515v1 Announce Type: cross
Abstract: Offline preference optimization methods are efficient for large language models (LLMs) alignment. Direct Preference optimization (DPO)-like learning, one of the most popular approaches, stands out for its efficiency in reward modeling. However, these methods typically follow the convention to use Bradley-Terry (BT) reward modeling that faces several critical assumptions, including the requirement for pairwise training data, model distribution shifting, human rationality assumption, etc. To address these limitations, we propose a general framework for offline preference optimization methods, Adaptive Preference Optimization with Utility Anchor (UAPO), which introduces an anchoring function to estimate the uncertainties brought from preference data annotation. Our method enables training even in scenarios where the data is unpaired, significantly enhancing data utilization efficiency. Moreover, the anchor design makes UAPO more robust in the training process. Experimental results demonstrate that UAPO achieves competitive outcomes without the strict dependency on data pairing, paving the way for more flexible and effective preference optimization methods.
arXiv:2605.23638v1 Announce Type: cross
Abstract: The problem of computing the cardinality of the intersection of multiple balls in the Hamming space has attracted a lot of attention recently due to their applications in the list reconstruction problem and information retrieval in Associative Memories. In previous work, most of the results are for the cases where the radii of each ball, $r$ and the distance between the centers of these balls, $k$ are fixed when the length $n$ of each codeword tend to infinity. In this work, we focus on the case where $r = \alpha n$ and $k=\beta n$ for some constants $\alpha$ and $\beta$ and compute the maximum asymptotic rate of the cardinality of the intersection of three balls. We provide the maximum asymptotic rate as a function of two parameters $\alpha$ and $\beta$. We also provide numerical results and compare these results with the intersection of two balls.
arXiv:2605.23905v1 Announce Type: cross
Abstract: We show that AI-driven investment strategies are inherently self-defeating at scale. As AI adoption rises, three mutually reinforcing channels -- signal crowding, performative signal erosion, and Red Queen competition -- compress excess returns. We derive the alpha half-life $h(\phi) = \ln 2/[\theta + \delta(\phi)]$, where $\theta$ is the natural mean-reversion rate and $\delta(\phi) = N\phi\rho a/\lambda(\phi)$ is the AI-accelerated decay component, which is convex-decreasing in adoption. At current adoption levels ($\phi \approx 0.7$, $\rho \approx 0.6$), the model implies signal half-lives of 18 months versus 5-7 years pre-AI. We establish four theoretical results. First, the alpha half-life theorem: signal lifespans are convex-decreasing in AI adoption. Second, a signal extinction cascade: beyond a critical threshold $\phi^*$, the decay of one signal class triggers accelerated competition for remaining signals. Third, a Red Queen impossibility: in the monoculture equilibrium, net alpha is identically zero despite heavy AI investment. Fourth, a fragility-efficiency tradeoff: the adoption level maximizing price discovery strictly exceeds the level minimizing systemic fragility. Empirical validation calibrates portfolio convergence to SEC Form 13F filing patterns (99.5 million holdings, 2013-2024), documenting that simulated institutional portfolio convergence increases by 42% over the sample period. We examine simulated hedge fund return dynamics showing declining cross-sectional dispersion among AI-adopting funds, and simulate the 2010 Flash Crash to illustrate fragility consequences.
arXiv:2605.14769v2 Announce Type: replace
Abstract: De novo crystal generation, a central task in materials discovery, aims to generate crystals that are simultaneously valid, stable, unique, and novel. Existing methods mainly rely on black-box stochastic sampling, providing limited control over how generated structures move beyond the observed distribution. In this paper, we introduce a concept-based compositional framework for crystal generation. We train a vector-quantized variational autoencoder to automatically discover a shared set of reusable crystal concepts, which serve as building blocks for guided generation. These learned concepts naturally exhibit interpretability from both local atomic environments and global symmetry patterns, and generalize to crystals from different distributions. By recombining such concepts, our framework enables controllable exploration of novel crystals beyond the training distribution, rather than relying solely on unconstrained random sampling. To further improve composition efficiency, we introduce a composition generator and iteratively refine it using high-quality samples generated by the model itself. The resulting concept compositions are then used to condition downstream crystal generation. Numerical experiments on MP-20 and Alex-MP-20 show that compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty.
arXiv:2605.23906v1 Announce Type: cross
Abstract: In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state distributions of the other populations. Due to the high dimensionality caused by the interaction of different populations, contraction rates for these algorithms cannot, in general, be expressed in terms of radicals. By studying the dynamics of these iterative algorithms and assuming that the system components of each population's MFG are Lipschitz continuous, we present explicit (eventual) contraction conditions for each algorithm in any normed space, relying only on these Lipschitz parameters. As a consequence of these contraction conditions, we provide convergence rates of finite-horizon mean-field equilibria to infinite-horizon stationary (and non-stationary) mean-field equilibria (MFEs), under restrictions on a variational characterization of the dynamics of these iterative algorithms. In the single-population case, the restrictions we impose on this variational characterization to obtain these convergence results are less restrictive than previous results in the literature.
arXiv:2605.23953v1 Announce Type: cross
Abstract: Accurate stock price forecasting has consistently remained a pivotal yet challenging FinTech task that underpins quantitative trading and investment decision making. Recent efforts have been dedicated to modeling various complex relationships among stocks in the stock market toward more reliable stock price forecasting.These methods depend heavily on strong static prior assumptions by modeling either temporal dependencies within individual stocks or spatial dependencies across different stocks based on predefined structures, while the complex market dynamics that drive stock price movements remain unexplored. To alleviate this issue, we propose a novel game-theoretic modeling method that captures heterogeneous investor interactions for stock price forecasting. The core idea is to embed game-theoretic mechanisms into the heterogeneous graph structure to finely model the dynamic strategic interactions among heterogeneous investors with respect to target stocks. Additionally, temporal positional encoding is adopted to reflect the differentiated influences of each game event at different time steps within the time window on future stock price movements. Leveraging heterogeneous graph networks, we proxy the intricate dynamics of the stock market through investor games and enable real-time information propagation and node updates among all nodes. Extensive experiments conducted on two real-world benchmark dataset demonstrate that our method effectively outperforms state-of-the-art stock price forecasting methods.
arXiv:2605.23962v1 Announce Type: cross
Abstract: This research aims to leverage machine learning to improve stock price prediction and support informed investment decisions related to buying, selling, and holding assets. Specifically, this work investigates transformer-based models for stock prediction and examines the impact of pre-training strategies on forecasting performance. A transformer model was first pre-trained on the Toronto Stock Exchange Index (TSX) to predict intra-day return direction and subsequently fine-tuned on individual TSX stocks. The model was further adapted for return-value regression tasks. Performance was benchmarked against Long Short-Term Memory (LSTM) and XGBoost models. Pre-training on the market index improved the binary cross-entropy loss for individual stock prediction from 0.69 to 0.64. The fine-tuned transformer regression model achieved lower mean squared error than the benchmark models, although the ensemble and XGBoost models achieved higher average daily returns. In addition, a practical application was developed to deliver real-time stock predictions for trading support. Future work will focus on increasing transformer model capacity, incorporating broader global technical indicators, and filtering out stocks with low predictability.
arXiv:2605.23981v1 Announce Type: cross
Abstract: Generative AI research increasingly confronts a shared problem: systems must sustain yet govern their own generative activity when uncertainty is high, evidence is missing, or context is insufficient. This position paper argues that metacognition should become the scientific framework for bounded and effective self governance in generative AI, where output generation is properly evaluated together with the capacities through which generative systems navigate and regulate their own activity. We advance this position by showing that bounded and effective AI self-governance requires metacognitive alignment across computational, algorithmic, and ecological levels. At the computational level, metacognition specifies the meta-level functions a system is meant to serve, such as monitoring, evaluation, control, and adaptation. At the algorithmic level, these functions are realized through procedures such as elicitation, iteration, and modularization. At the ecological level, metacognitive signals become meaningful, actionable, and accountable within the interface, workflow, and accountability arrangements. Metacognition thus makes it possible to conceive generative AI as both capable and well-governed, rather than treating capability and governance as competing aims.
arXiv:2605.16023v2 Announce Type: replace
Abstract: LLM-as-a-judge has become the dominant paradigm for grading model outputs at scale, yet the same model assigns systematically different scores when its output format changes (e.g., a 1-5 rating vs. a True/False label). Existing diagnoses of these format-induced inconsistencies stop at the input-output level. Using Position-aware Edge Attribution Patching (PEAP), we causally investigate the internal mechanism in Gemma-3, Qwen2.5, and Llama-3. We find that judgments across structured understanding and open-ended preference tasks share a sparse, generalized Latent Evaluator sub-graph in the mid-to-late multi-layer perceptrons (MLPs); zero-ablating it collapses judgment while preserving world knowledge in architecturally modular models. By structurally decoupling abstract judging from output formatting, we provide a mechanistic account of format-induced inconsistency on the open-weight models we study: a continuous judgment signal computed in the shared trunk is mapped through fragile, format-specific terminal branches, enabling format-independent preference to be isolated downstream of the requested output format. Our findings imply that benchmark-level reliability comparisons across formats are partially measuring formatter geometry rather than evaluation quality.
arXiv:2605.24769v1 Announce Type: new
Abstract: Hyperspectral image restoration faces several challenges, including limited training data, strong sensor specificity, and high spectral dimensionality. These limitations hinder the learning of robust hyperspectral priors, motivating the reuse of priors learned from large-scale RGB data. In this work, we propose a minimally trained, lightweight adapter that repurposes frozen pretrained RGB denoisers for hyperspectral restoration through a projection mapping. The method denoises low-dimensional spectral projections and reconstructs the hyperspectral cube through constrained linear aggregation, while preserving plug-and-play compatibility and the stability properties of the underlying RGB denoiser. Experiments on denoising, deblurring, and super-resolution across multiple datasets demonstrate consistent improvements over hyperspectral-specific baselines, showing the strong transferability of large-scale RGB priors.
arXiv:2605.26100v1 Announce Type: new
Abstract: Code review is a critical practice in software engineering, yet the growing scale and frequency of code patches in modern projects, together with the widespread adoption of AI code assistants, make manual review increasingly challenging. Identifying the types of changes within a patch, such as renames, moves, or logic modifications, can substantially improve review efficiency by enabling prioritization, filtering, and automation. However, existing LLM-based approaches to code review have largely focused on summarization and comment generation, leaving structured code reviews underexplored. In this paper, we present a systematic study of using large language models (LLMs) for taxonomy-based labeling of code changes in a code patch. We introduce a two-stage pipeline that assigns labels to diff hunks and then refines them to capture structural relationships and semantic attributes, such as rename propagation and type changes. Our approach employs few-shot prompting to produce language-agnostic and customizable labels, without the engineering overhead of traditional static-analysis pipelines. We evaluate four LLMs across multiple context configurations on a manually curated benchmark of natural and synthetic patches. Our best configuration achieves up to $84\%$ recall and $81\%$ precision, with high accuracy in extracting relational and attribute metadata. These results suggest that LLM-based labeling can effectively complement static analysis by enabling flexible, multilingual, and automation-friendly code review workflows.