Hierarchical Exponential-Gaussian Mixtures for Watch-Time Distribution Prediction

Watch time has emerged as a pivotal metric for optimizing deep user engagement in short-video recommender systems. However, current methods of watch time prediction (WTP) suffer from inherent paradigm-specific limitations. Direct Regression faces mean-collapse due to unimodal Gaussian assumptions, while Ordinal Regression is hampered by quantization errors from rigid discretization. Similarly, Discrete Generative Regression struggles with high inference latency and heuristic vocabulary design. Beyond these specific flaws, a shared deficiency is the inability to capture the intrinsic multimodality and heterogeneity of User-Item Interaction Patterns. To address these challenges, we first revisit the WTP problem from a causal perspective and identify these user-specific patterns as structural confounders that modulate watch time outcomes, where identical interests manifest as distinct watch time outcomes conditioned on diverse user habits. Then, we formally propose a new (or the fourth) paradigm -- Continuous Generative Regression, and introduce FlowTime, a novel method utilizing a One-step Generative Variational Autoencoder. FlowTime effectively circumvents the latency of iterative denoising while maintaining the expressivity of continuous latent spaces. Furthermore, we design a Flow-based Personalized Prior that leverages NFs to warp a standard Gaussian prior into a complex, history-conditioned manifold, thereby enabling the adaptive modeling of multimodal interaction patterns. Finally, we build TimeRec, the first open-source WTP Library, alongside a novel personalization metric to establish a rigorous benchmarking standard. Extensive offline experiments and online A/B tests demonstrate FlowTime's significant superiority over SOTA methods.

We introduce the exponentially weighted signature (EWS), a continuous-time model that computes iterated integrals of a path, where each increment is weighted by the matrix exponential of a learnable generator over elapsed clock time. We prove that it solves a linear controlled differential equation, keeps the group-like structure and the universality of the signature, and satisfies a modified Chen identity, enabling a parallel scan. At depth one the EWS is a state-space model (SSM), and we map linear time-invariant SSMs, Mamba channels and Mamba-$2$ heads to it in closed form. The EWS extends SSMs through an arbitrary matrix generator, a clock that generalises the step size to causal functionals of the input, and higher truncation depths that are non-linear in the path within a single layer. Empirically, the EWS achieves the highest average accuracy and rank on six long time-series classification datasets, where depth generally helps. Learned clocks prove necessary for state tracking on formal language tasks, and at depth one, the EWS matches or exceeds competing SSMs on regression and forecasting with far fewer parameters.

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.