Self-supervised representation learning for time series has largely bifurcated into contrastive and generative paradigms. However, both approaches can face challenges in capturing underlying physical dynamics: contrastive methods risk altering temporal semantics through heuristic spatial augmentations, while generative masked modeling tends to overfit high-frequency sensor noise rather than abstracting stable evolution laws. In this work, we posit that the semantic identity of a time series is defined not only by static patterns, but also by its invariant laws of transition. To operationalize this, we introduce K-VIC, a novel framework that embeds the Koopman Operator into a Variance-Covariance regularization scheme. By linearizing non-linear temporal dynamics in a high-dimensional latent space, K-VIC acts as a physics-inspired spectral filter that effectively preserves persistent dynamic modes while discarding non-systematic fluctuations. Furthermore, instead of relying on augmented negative pairs or static spatial invariance, we propose predictive and cyclic consistency paired with informational constraints to mitigate representation collapse and encourage orthogonal feature disentanglement. Empirical evaluations across five benchmarks demonstrate that K-VIC achieves state-of-the-art (SotA) accuracy without dataset-specific hyperparameter tuning. Notably, it exhibits strong robustness in noise-heavy industrial scenarios (yielding an over 20 https://github.com/Conrrile/K-VIC .
We study stochastic bandits with ordered actions, unimodal rewards, and resource constraints, motivated by treatment selection problems where intervention intensity improves outcomes up to a peak while incurring increasingly higher costs. Unlike existing constrained bandit approaches, whose regret bounds typically scale with the number of actions because feasibility and optimality must be explored across an unstructured action set, our setting incorporates two key forms of structure: unimodality of rewards, which reduces optimality learning to local exploration around the empirical peak, and monotonicity of costs, which implies that the feasible region is a contiguous prefix that can be identified through a single threshold. We propose F-OSUB, an algorithm that interleaves feasibility identification with unimodal leader–neighbor exploration and show that it achieves logarithmic regret and logarithmic budget violation with high probability, with constants depending only on local reward gaps rather than the total number of actions. These results demonstrate that exploiting structural properties enables substantially more efficient and safer learning in resource-constrained decision problems such as treatment intensity selection.
Diffusion and flow matching are a class of generative models that generate new samples by solving ordinary or stochastic differential equations with a learned score/velocity field. Interestingly, the optimal velocity field admits a closed-form formula that can be computed for finite datasets. Generating samples following the optimal velocity field can only reproduce samples from the training set, i.e., memorize the training set. Neural networks, trained to match the velocity field, introduce inductive bias that can partially mitigate the issue. However, these models can still exhibit memorization, unlike the benign overfitting observed in discriminative tasks. In this paper, we propose a bootstrap aggregating (bagging) method for flow matching to reduce memorization. By conceptually averaging over resampled training subsets, our approach effectively reduces memorization. We derive a closed-form bagging formulation compatible with exact flow matching, enabling efficient implementation. Experiments confirm reduced memorization and better generalization without architectural changes or auxiliary objectives.
