Many natural systems, including neural circuits involved in decision making, are modeled as high-dimensional dynamical systems with multiple stable states. While existing analytical tools primarily describe behavior near stable equilibria, characterizing separatrices--the manifolds that delineate boundaries between different basins of attraction--remains challenging, particularly in high-dimensional settings. Here, we introduce a numerical framework leveraging Koopman Theory combined with Deep Neural Networks to effectively characterize separatrices. Specifically, we approximate Koopman Eigenfunctions (KEFs) associated with real positive eigenvalues, which vanish precisely at the separatrices. Utilizing these scalar KEFs, optimization methods efficiently locate separatrices even in complex systems. We demonstrate our approach on synthetic benchmarks, ecological network models, and high-dimensional recurrent neural networks trained on either neuroscience-inspired tasks or fit to real neural data. Moreover, we illustrate the practical utility of our method by designing optimal perturbations that can shift systems across separatrices, enabling predictions relevant to optogenetic stimulation experiments in neuroscience.

Multi-task reinforcement learning aims to quickly identify solutions for new tasks with minimal or no additional interaction with the environment. Generalized Policy Improvement (GPI) addresses this by combining a set of base policies to produce a new one that is at least as good -- though not necessarily optimal -- as any individual base policy. Optimality can be ensured, particularly in the linear-reward case, via techniques that compute a Convex Coverage Set (CCS). However, these are computationally expensive and do not scale to complex domains. The Option Keyboard (OK) improves upon GPI by producing policies that are at least as good -- and often better. It achieves this through a learned meta-policy that dynamically combines base policies. However, its performance critically depends on the choice of base policies. This raises a key question: is there an optimal set of base policies -- an optimal behavior basis -- that enables zero-shot identification of optimal solutions for any linear tasks? We solve this open problem by introducing a novel method that efficiently constructs such an optimal behavior basis. We show that it significantly reduces the number of base policies needed to ensure optimality in new tasks. We also prove that it is strictly more expressive than a CCS, enabling particular classes of non-linear tasks to be solved optimally. We empirically evaluate our technique in challenging domains and show that it outperforms state-of-the-art approaches, increasingly so as task complexity increases.

To build AI that children can intuitively understand and benefit from, designers need a design grammar that serves their developmental needs. This paper bridges artificial intelligence design for children - an emerging field still defining its best practices - and animation, a well established field with decades of experience in engaging children through accessible storytelling. Pairing Piagetian developmental theory with design pattern extraction from 52 works of animation, the paper presents a six scaffold framework that integrates design insights transferable to child centred AI design: (1) signals for visual animacy and clarity, (2) sound for musical and auditory scaffolding, (3) synchrony in audiovisual cues, (4) sidekick style personas, (5) storyplay that supports symbolic play and imaginative exploration, and (6) structure in the form of predictable narratives. These strategies, long refined in animation, function as multimodal scaffolds for attention, understanding, and attunement, supporting learning and comfort. This structured design grammar is transferable to AI design. By reframing cinematic storytelling and child development theory as design logic for AI, the paper offers heuristics for AI that aligns with the cognitive stages and emotional needs of young users. The work contributes to design theory by showing how sensory, affective, and narrative techniques can inform developmentally attuned AI design. Future directions include empirical testing, cultural adaptation, and participatory co design.

Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function and derive finite-sample guarantees with bounds tied to system properties such as smoothness and stability. Our theoretical and numerical results indicate that operator-based approaches may hold promise in solving offline reinforcement learning using continuous-time optimal control.

Missing data is a common problem across various scientific disciplines, including medical research (Bell et al., 2014), social sciences (Molenberghs et al., 2014), and astronomy (Ivezi c et al., 2020). To handle missing entries in the dataset, imputation (Grzesiak et al., 2025; Kim and Shao, 2021; Little and Rubin, 2019) is a popular approach that is widely accepted in practice. An imputation model generates plausible values for each missing entry, transforming an incomplete dataset into a complete one. The critical importance of this task has led to the development of a wide array of imputation models, grounded in various modeling assumptions. These range from traditional approaches like hot-deck imputation (Little and Rubin, 2019) to more sophisticated methods such as Multiple Imputation via Chained Equations (MICE; V an Buuren and Groothuis-Oudshoorn 2011), random forest imputation (Stekhoven and Bühlmann, 2012), techniques based on Markov assumptions on graphs (Y ang and Chen, 2025), and even generative adversarial networks (Y oon et al., 2018). Despite the proliferation of imputation models, the selection of an optimal imputation model for a given dataset remains a significant challenge, largely due to the unsupervised nature of the problem. Among the many proposed strategies for evaluating and selecting imputation models, masking has emerged as a particularly popular procedure (Gelman et al., 1998; Honaker et al., 2011; Leek et al., 2012; Qian et al., 2024; Troyanskaya et al., 2001; Wang et al., 2024). Masking involves intentionally creating missing values in observed entries to create a setting where imputation accuracy can be measured against a known ground truth. This approach has demonstrated remarkable success and power in other domains, notably in language modeling (Devlin et al., 2019; Y ang et al., 2019) and image recognition (Hondru et al., 2025; Vincent et al., 2010; Xie et al., 2022) and prediction-powered inference (Angelopoulos et al., 2023; Wang et al., 2020).

Incremental flow-based denoising models have reshaped generative modelling, but their empirical advantage still lacks a rigorous approximation-theoretic foundation. We show that incremental generation is necessary and sufficient for universal flow-based generation on the largest natural class of self-maps of $[0,1]^d$ compatible with denoising pipelines, namely the orientation-preserving homeomorphisms of $[0,1]^d$. All our guarantees are uniform on the underlying maps and hence imply approximation both samplewise and in distribution. Using a new topological-dynamical argument, we first prove an impossibility theorem: the class of all single-step autonomous flows, independently of the architecture, width, depth, or Lipschitz activation of the underlying neural network, is meagre and therefore not universal in the space of orientation-preserving homeomorphisms of $[0,1]^d$. By exploiting algebraic properties of autonomous flows, we conversely show that every orientation-preserving Lipschitz homeomorphism on $[0,1]^d$ can be approximated at rate $\mathcal{O}(n^{-1/d})$ by a composition of at most $K_d$ such flows, where $K_d$ depends only on the dimension. Under additional smoothness assumptions, the approximation rate can be made dimension-free, and $K_d$ can be chosen uniformly over the class being approximated. Finally, by linearly lifting the domain into one higher dimension, we obtain structured universal approximation results for continuous functions and for probability measures on $[0,1]^d$, the latter realized as pushforwards of empirical measures with vanishing $1$-Wasserstein error.

We propose a novel framework for synthesizing counterfactual treatment group data in a target site by integrating full treatment and control group data from a source site with control group data from the target. Departing from conventional average treatment effect estimation, our approach adopts a distributional causal inference perspective by modeling treatment and control as distinct probability measures on the source and target sites. We formalize the cross-site heterogeneity (effect modification) as a push-forward transformation that maps the joint feature-outcome distribution from the source to the target site. This transformation is learned by aligning the control group distributions between sites using an Optimal Transport-based procedure, and subsequently applied to the source treatment group to generate the synthetic target treatment distribution. Under general regularity conditions, we establish theoretical guarantees for the consistency and asymptotic convergence of the synthetic treatment group data to the true target distribution. Simulation studies across multiple data-generating scenarios and a real-world application to patient-derived xenograft data demonstrate that our framework robustly recovers the full distributional properties of treatment effects.

We bear all responsibility in case of violation of rights, etc., and confirmation of the data license. This project is licensed under the Creative Commons Attribution-NonCommercial 4.0 International This license permits sharing and adapting the work provided it is not used for commercial purposes and appropriate credit is given. Please refer to Section 3 for our hosting plan. In this section, we use the framework of Datasheets for Datasets [? ] to form a datasheet for CRAG, For what purpose was the dataset created? Was there a specific task in mind?

Thousands of patients worldwide are waiting for a potentially life-saving donor. Thousands of patients worldwide are waiting for a potentially life-saving donor. Doctors have developed an AI tool that could reduce wasted efforts to transplant organs by 60%. Thousands of patients worldwide are waiting for a potentially life-saving donor, and more candidates are stuck on waiting lists than there are available organs. Recently, in cases where people need a liver transplant, access has been expanded by using donors who die after cardiac arrest.