We establish convergence of the training dynamics of residual neural networks (ResNets) to their joint infinite depth L, hidden width M, and embedding dimension D limit. Specifically, we consider ResNets with two-layer perceptron blocks in the maximal local feature update (MLU) regime and prove that, after a bounded number of training steps, the error between the ResNet and its large-scale limit is O(1/L + sqrt(D/(L M)) + 1/sqrt(D)). This error rate is empirically tight when measured in embedding space. For a budget of P = Theta(L M D) parameters, this yields a convergence rate O(P^(-1/6)) for the scalings of (L, M, D) that minimize the bound. Our analysis exploits in an essential way the depth-two structure of residual blocks and applies formally to a broad class of state-of-the-art architectures, including Transformers with bounded key-query dimension. From a technical viewpoint, this work completes the program initiated in the companion paper [Chi25] where it is proved that for a fixed embedding dimension D, the training dynamics converges to a Mean ODE dynamics at rate O(1/L + sqrt(D)/sqrt(L M)). Here, we study the large-D limit of this Mean ODE model and establish convergence at rate O(1/sqrt(D)), yielding the above bound by a triangle inequality. To handle the rich probabilistic structure of the limit dynamics and obtain one of the first rigorous quantitative convergence for a DMFT-type limit, we combine the cavity method with propagation of chaos arguments at a functional level on so-called skeleton maps, which express the weight updates as functions of CLT-type sums from the past.

Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and the label sequences, presenting two central research challenges: (1) designing neural architectures that model autocorrelation in history sequences, and (2) devising learning objectives that model autocorrelation in label sequences. Recent studies have made strides in tackling these challenges, but a systematic survey examining both aspects remains lacking. To bridge this gap, this paper provides a comprehensive review of deep time-series forecasting from the perspective of autocorrelation modeling. In contrast to existing surveys, this work makes two distinctive contributions. First, it proposes a novel taxonomy that encompasses recent literature on both model architectures and learning objectives -- whereas prior surveys neglect or inadequately discuss the latter aspect. Second, it offers a thorough analysis of the motivations, insights, and progression of the surveyed literature from a unified, autocorrelation-centric perspective, providing a holistic overview of the evolution of deep time-series forecasting. The full list of papers and resources is available at https://github.com/Master-PLC/Awesome-TSF-Papers.

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes, and runs with a deterministic runtime budget. Numerical experiments demonstrate that our approach converges rapidly to the target distribution, driven by interactions among multiple particles and by exploiting parallel computation.

Causal generative models provide a principled framework for answering observational, interventional, and counterfactual queries from observational data. However, many deep causal models rely on highly expressive architectures with opaque mechanisms, limiting auditability in high-stakes domains. We propose KaCGM, a causal generative model for mixed-type tabular data where each structural equation is parameterized by a Kolmogorov--Arnold Network (KAN). This decomposition enables direct inspection of learned causal mechanisms, including symbolic approximations and visualization of parent--child relationships, while preserving query-agnostic generative semantics. We introduce a validation pipeline based on distributional matching and independence diagnostics of inferred exogenous variables, allowing assessment using observational data alone. Experiments on synthetic and semi-synthetic benchmarks show competitive performance against state-of-the-art methods. A real-world cardiovascular case study further demonstrates the extraction of simplified structural equations and interpretable causal effects. These results suggest that expressive causal generative modeling and functional transparency can be achieved jointly, supporting trustworthy deployment in tabular decision-making settings. Code: https://github.com/aalmodovares/kacgm

Developing intelligent pediatric consultation systems offers promising prospects for improving diagnostic efficiency, especially in China, where healthcare resources are scarce. Despite recent advances in Large Language Models (LLMs) for Chinese medicine, their performance is sub-optimal in pediatric applications due to inadequate instruction data and vulnerable training procedures.To address the above issues, this paper builds PedCorpus, a high-quality dataset of over 300,000 multi-task instructions from pediatric textbooks, guidelines, and knowledge graph resources to fulfil diverse diagnostic demands. Upon well-designed PedCorpus, we propose PediatricsGPT, the first Chinese pediatric LLM assistant built on a systematic and robust training pipeline.In the continuous pre-training phase, we introduce a hybrid instruction pre-training mechanism to mitigate the internal-injected knowledge inconsistency of LLMs for medical domain adaptation. Immediately, the full-parameter Supervised Fine-Tuning (SFT) is utilized to incorporate the general medical knowledge schema into the models. After that, we devise a direct following preference optimization to enhance the generation of pediatrician-like humanistic responses. In the parameter-efficient secondary SFT phase,a mixture of universal-specific experts strategy is presented to resolve the competency conflict between medical generalist and pediatric expertise mastery. Extensive results based on the metrics, GPT-4, and doctor evaluations on distinct downstream tasks show that PediatricsGPT consistently outperforms previous Chinese medical LLMs.

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Fine urban change segmentation using multi-temporal remote sensing images is essential for understanding human-environment interactions in urban areas. Although there have been advances in high-quality land cover datasets that reveal the physical features of urban landscapes, the lack of fine-grained land use datasets hinders a deeper understanding of how human activities are distributed across landscapes and the impact of these activities on the environment, thus constraining proper technique development. To address this, we introduce FUSU, the first fine-grained land use change segmentation dataset for Fine-grained Urban Semantic Understanding. FUSU features the most detailed land use classification system to date, with 17 classes and 30 billion pixels of annotations. It includes bi-temporal high-resolution satellite images with 0.2-0.5 m ground sample distance and monthly optical and radar satellite time series, covering 847 km^2 across five urban areas in the southern and northern of China with different geographical features. The fine-grained land use pixel-wise annotations and high spatial-temporal resolution data provide a robust foundation for developing proper deep learning models to provide contextual insights on human activities and urbanization. To fully leverage FUSU, we propose a unified time-series architecture for both change detection and segmentation.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

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