Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and Rössler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

Multimodal interleaved datasets featuring free-form interleaved sequences of images and text are crucial for training frontier large multimodal models (LMMs). Despite the rapid progression of open-source LMMs, there remains a pronounced scarcity of large-scale, open-source multimodal interleaved datasets. In response, we introduce MINT-1T, the most extensive and diverse open-source Multimodal INTerleaved dataset to date. MINT-1T comprises of one trillion text tokens and 3.4 billion images, a 10x scale-up from existing open-source datasets. Additionally, we include previously untapped sources such as PDFs and ArXiv papers. As scaling multimodal interleaved datasets requires substantial engineering effort, sharing the data curation process and releasing the dataset greatly benefits the community. Our experiments show that LMMs trained on MINT-1T rival the performance of models trained on the previous leading dataset, OBELICS.

Learning the optimal policy to balance multiple short-term and long-term rewards has extensive applications across various domains. Yet, there is a noticeable scarcity of research addressing policy learning strategies in this context. In this paper, we aim to learn the optimal policy capable of effectively balancing multiple short-term and long-term rewards, especially in scenarios where the long-term outcomes are often missing due to data collection challenges over extended periods. Towards this goal, the conventional linear weighting method, which aggregates multiple rewards into a single surrogate reward through weighted summation, can only achieve suboptimal policies when multiple rewards are related. Motivated by this, we propose a novel decomposition-based policy learning (DPPL) method that converts the whole problem into subproblems.

Calibrated probabilistic classifiers are models whose predicted probabilities can directly be interpreted as uncertainty estimates. It has been shown recently that deep neural networks are poorly calibrated and tend to output overconfident predictions.

The learnware paradigm aims to enable users to leverage numerous existing well-trained models instead of building machine learning models from scratch.

Online experimentation with interference is a common challenge in modern applications such as e-commerce and adaptive clinical trials in medicine. For example, in online marketplaces, the revenue of a good depends on discounts applied to competing goods. Statistical inference with interference is widely studied in the offline setting, but far less is known about how to adaptively assign treatments to minimize regret. We address this gap by studying a multi-armed bandit (MAB) problem where a learner (e-commerce platform) sequentially assigns one of possible A actions (discounts) to N units (goods) over T rounds to minimize regret (maximize revenue). Unlike traditional MAB problems, the reward of each unit depends on the treatments assigned to other units, i.e., there is interference across the underlying network of units.

Medical time series (MedTS) data, such as Electroencephalography (EEG) and Electrocardiography (ECG), play a crucial role in healthcare, such as diagnosing brain and heart diseases. Existing methods for MedTS classification primarily rely on handcrafted biomarkers extraction and CNN-based models, with limited exploration of transformer-based models. In this paper, we introduce Medformer, a multi-granularity patching transformer tailored specifically for MedTS classification. Our method incorporates three novel mechanisms to leverage the unique characteristics of MedTS: cross-channel patching to leverage inter-channel correlations, multi-granularity embedding for capturing features at different scales, and two-stage (intra-and inter-granularity) multi-granularity self-attention for learning features and correlations within and among granularities. We conduct extensive experiments on five public datasets under both subject-dependent and challenging subject-independent setups. Results demonstrate Medformer's superiority over 10 baselines, achieving top averaged ranking across five datasets on all six evaluation metrics. These findings underscore the significant impact of our method on healthcare applications, such as diagnosing Myocardial Infarction, Alzheimer's, and Parkinson's disease.

In each panel, the distribution of taxa is shown for one species set of the dataset. Classes are shown in different hues--Arachnida: red, Collembola: yellow, Insecta orders: shades of blue varying by order, other classes: green. Icons are redistributed under CC BY(-NC) or Canva pro license, respectively. See Table S16 for names and more detailed values.

Often, these changes are driven by different environments or internal states in which the system operates, and we refer to context variables as those variables that indicate this change in causal mechanisms. An example are the causal relations in soil moisture-temperature interactions and their dependence on soil moisture regimes: Dry soil triggers a dependence of soil moisture on latent heat, while environments with wet soil do not feature such a feedback, making it a context-specific property. Crucially, a regime or context variable such as soil moisture need not be exogenous and can be influenced by the dynamical system variables - precipitation can make a dry soil wet - leading to joint systems with endogenous context variables. In this work we investigate the assumptions for constraint-based causal discovery of context-specific information in systems with endogenous context variables. We show that naive approaches such as learning different regime graphs on masked data, or pooling all data, can lead to uninformative results. We propose an adaptive constraint-based discovery algorithm and give a detailed discussion on the connection to structural causal models, including sufficiency assumptions, which allow to prove the soundness of our algorithm and to interpret the results causally. Numerical experiments demonstrate the performance of the proposed method over alternative baselines, but they also unveil current limitations of our method.

Vertical federated learning (VFL) is a privacy-preserving machine learning paradigm that can learn models from features distributed on different platforms in a privacy-preserving way. Since in real-world applications the data may contain bias on fairness-sensitive features (e.g., gender), VFL models may inherit bias from training data and become unfair for some user groups. However, existing fair machine learning methods usually rely on the centralized storage of fairnesssensitive features to achieve model fairness, which are usually inapplicable in federated scenarios. In this paper, we propose a fair vertical federated learning framework (FairVFL), which can improve the fairness of VFL models. The core idea of FairVFL is to learn unified and fair representations of samples based on the decentralized feature fields in a privacy-preserving way. Specifically, each platform with fairness-insensitive features first learns local data representations from local features.