Real-world multivariate time series are inherently in flux: different variables evolve asynchronously and interact in complex, time-varying ways, yet accurate forecasting requires these dispersed signals to converge into a single unified prediction. This structural mismatch between dynamic, heterogeneous inputs and a unified forecasting objective poses a fundamental challenge for building general-purpose multivariate forecasting models, especially in zero-shot and large-scale settings. To this end, inspired by the idea that ``\emph{all rivers run into the sea}'', we propose \textbf{ConFlux}, a \emph{general-purpose foundation model for multivariate time-series forecasting} by learning to adaptively integrate cross-channel information under a unified forecasting objective. Specifically, ConFlux first reorders variables to reduce cross-variable entanglement, then aggregates adjacent variables into compact patches that can be processed by a Vision Transformer-style architecture. This design shortens the effective context, reduces attention complexity, and provides a unified token representation for pre-training and downstream tasks. Experiments on 25 public datasets show that ConFlux achieves state-of-the-art performance in zero-shot, fine-tuning, and from-scratch settings, while offering faster inference and lower memory usage.

Incorporating textual information into time-series forecasting holds promise for addressing event- driven non-stationarity; however, a fundamental modality gap hinders effective fusion: textual descriptions express temporal impacts implicitly and qualitatively, whereas forecasting models rely on explicit and quantitative signals. Through controlled semi-synthetic experiments, we show that existing methods over-attend to redundant tokens and struggle to reliably translate textual semantics into usable numerical cues. To bridge this gap, we propose TESS, which introduces a Temporal Evolution Semantic Space as an intermediate bottleneck between modalities. This space consists of interpretable, numerically grounded temporal primitives—distribution shift, volatility, shape, and lag—extracted from text by an LLM via structured prompting and filtered through confidence-aware gating. Experiments on four real-world datasets demonstrate up to a 29% reduction in forecasting error compared to state-of-the-art unimodal and multimodal baselines. Code is available at: https://github.com/olivia3395/TESS.

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for tall datasets and the `doubly-intractable' distributions. In this paper, we begin by observing that seemingly different Markov chain Monte Carlo (MCMC) algorithms, such as the exchange algorithm, PoissonMH, and TunaMH, can be unified under a simple common procedure. We then extend this procedure into a novel framework that allows the use of auxiliary variables in both the proposal and the acceptance--rejection step. Several new MCMC algorithms emerge from this framework that uses estimated gradients to guide the proposal moves. They have demonstrated significantly better performance than existing methods on both synthetic and real datasets. We also develop theory for the new framework and use it to simplify and extend results for existing algorithms. The code to reproduce the experimental results can be found at https://github.com/ywwes26/Auxiliary-MCMC.

We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior. In this work, however, we demonstrate that the Markovian assumption can both hamper signal propagation during training and catastrophically reduce the learned sampler's expressivity due to state aliasing. To address these issues, we propose lifting the MDP with a learnable latent dynamics that allows the underlying policy to depend on the entire past trajectory---and not only on the current state. In view of this, we refer to the resulting method as \emph{path-dependent discrete amortized inference}. Importantly, we provably extend existing learning algorithms for amortized samplers to our setting. In experiments on standard benchmark problems, we also show that our approach often leads to faster learning convergence and improved state space exploration relatively to prior techniques.