Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal inference, generative adversarial network (GAN)-based counterfactual methods are flexible tools for this task. However, these methods have several limitations. First, the objectives of certain techniques do not coincide with the statistical risk of the identifiable causal target, and therefore provide limited theoretical guarantees regarding estimable counterfactual distributions or optimality. Second, they tend to rely on unstable density-based methods, such as density ratio estimation. In this paper, we propose GANICE (GAN for Interventional Conditional Estimation) with several advantages: it (i) clarifies the conditional interventional distribution for each treatment--covariate state as the causal estimation target; (ii) estimates the conditional distribution such that its averaged Wasserstein risk is minimized; (iii) establishes minimax optimality. GANICE achieves these advantages through the introduction of the extended Wasserstein distance, the incorporation of a cellwise critic in its dual, and an optimality proof based on Besov space theory. Our experiments demonstrate that GANICE consistently outperforms existing methods.

We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that enhances expert specialization by incorporating expert-specific loss information directly into the training process. Notably, the overall objective comprises the base forecasting loss and expert-specific losses, allowing expert-level prediction errors to jointly shape training alongside the global forecasting loss. This framework is further combined with a partial online learning strategy, enabling incremental updates of both the gating mechanism and expert parameters. This approach significantly reduces computational cost by eliminating the need for repeated full model retraining. By integrating expert-level loss awareness with efficient online optimization, the proposed method achieves improved learning efficiency while maintaining strong predictive performance. Empirical results across economic, tourism, and energy datasets with varying frequencies demonstrate that the proposed approach generally outperforms both statistical methods and state-of-the-art neural network models, such as Transformers and WaveNet, in forecasting accuracy and computational efficiency. Furthermore, ablation studies confirm the effectiveness of the expert-specific loss integration strategy, highlighting its contribution to enhancing predictive performance.

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

As datasets continue to expand in size and complexity, these models have become increasingly sophisticated, with deeper architectures and greater expressive power. Despite these advances, DNNs trained on imbalanced class distributions often exhibit a tendency to favor majority classes, leading to degraded performance on underrepresented classes [18, 39, 27, 17]. Because many real-world datasets follow long-tailed distributions in which minority classes can contain critical and informative patterns, developing methods that enable DNNs to learn effectively from imbalanced data is essential to prevent the loss of valuable information from these rare classes [26, 34, 16]. Moreover, data encountered in real-world applications are frequently multi-modal, meaning that observations originate from heterogeneous sources [6, 29, 7, 35]. To make effective use of such heterogeneous inputs, a wide range of multi-modal learning approaches have been proposed that exploit complementary information across modalities to enhance predictive performance [10, 5]. Common strategies integrate multiple modalities into a unified representation, using techniques that span from straightforward feature-level concatenation [19, 11, 12] to more sophisticated neural architectures that learn joint representations in an end-to-end manner [20, 32]. Although prior research has extensively studied class imbalance and multi-modal data separately, relatively little attentionhas beengiven to settings where bothchallenges arise si2 multaneously. Developing methods that can effectively handle long-tailed class distributions in conjunction with multi-modal inputs is therefore essential in many real-world applications. In the medical domain, for instance, datasets often contain far more samples from healthy individuals than from patients with specific conditions, while also encompassing diverse datatypes such asimagingdata(e.g., X-rays)alongsideauxiliary informationincluding demographics and clinical histories.

Causal sensitivity analysis aims to provide bounds for causal effect estimates in the presence of unobserved confounding. However, existing methods for causal sensitivity analysis are per-instance procedures, meaning that changes to the dataset, causal query, sensitivity level, or treatment require new computation. Here, we instead present an in-context learning approach. Specifically, we propose an amortized approach to causal sensitivity analysis based on prior-data fitted networks. A key challenge is that the sensitivity bounds are not directly available when sampling training data. To address this, we develop a general prior-data construction that is applicable across the class of generalized treatment sensitivity models. Our construction involves a Lagrangian scalarization of the objective to generate training labels for the bounds through a tradeoff between causal effect min/max-imization and sensitivity model violation, which avoids model-specific analytical derivations. We further show that, under standard convexity and linearity conditions, our objective recovers the full Pareto frontier of solutions. Empirically, we demonstrate our amortized approach across various datasets, causal queries, and sensitivity levels, where our approach achieves a test-time computation that is orders of magnitude faster than per-instance methods. To the best of our knowledge, ours is the first foundation model for in-context learning for causal sensitivity analysis.

Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

We study sparse recovery when observations come from mixed-quality sources: a small collection of high-quality measurements with small noise variance and a larger collection of lower-quality measurements with higher variance. For this heterogeneous-noise setting, we establish sample-size conditions for information-theoretic and algorithmic recovery. On the information-theoretic side, we show that it is sufficient for $(n_1, n_2)$ to satisfy a linear trade-off defining the Price of Quality: the number of low-quality samples needed to replace one high-quality sample. In the agnostic setting, where the decoder is completely agnostic to the quality of the data, it is uniformly bounded, and in particular one high-quality sample is never worth more than two low-quality samples for this sufficient condition to hold. In the informed setting, where the decoder is informed of per-sample variances, the price of quality can grow arbitrarily large. On the algorithmic side, we analyze the LASSO in the agnostic setting and show that the recovery threshold matches the homogeneous-noise case and only depends on the average noise level, revealing a striking robustness of computational recovery to data heterogeneity. Together, these results give the first conditions for sparse recovery with mixed-quality data and expose a fundamental difference between how the information-theoretic and algorithmic thresholds adapt to changes in data quality.

Ilya Sutskever Stands by His Role in Sam Altman's OpenAI Ouster: 'I Didn't Want It to Be Destroyed' The former OpenAI chief scientist may be estranged from the company, but he still came to its defense as he testified on Monday. Elon Musk's trial against OpenAI and Microsoft entered its final stretch on Monday, with testimony from Microsoft CEO Satya Nadella, former OpenAI chief scientist Ilya Sutskever, and current OpenAI chairman Bret Taylor. Sutskever drew the spotlight, revealing an ownership stake in OpenAI's $850-billion for-profit arm that is currently worth about $7 billion. That makes him one of the largest known individual shareholders of OpenAI. Earlier in the trial, OpenAI president Greg Brockman acknowledged for the first time that he has around $30 billion worth of OpenAI shares .

Security around Beijing's historic Tiananmen Square has been heightened for days, with rumours on social media swirling of a special parade or some big, choreographed event. Preparations for this major event have started with a whisper, but China appears ready to put on a show for US President Donald Trump. The visit will include talks, a banquet, and a visit to the Temple of Heaven, a complex of imperial temples where emperors would pray for a good harvest. And both Trump and Chinese President Xi Jinping will be hoping the visit will bear fruit. This summit between the world's two most powerful leaders is set to be one of the most consequential encounters for years.

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