We introduce Triangular-Reference Schrödinger Bridges for Time Series (TR-SBTS), a conservative extension of the SBTS framework in which the Brownian reference is replaced by an intervalwise frozen, possibly degenerate diffusion reference, triangular across a hierarchy of latent volatility levels. The construction is a single entropy projection on the augmented state space, with the variational constraint imposed jointly across time and the latent levels and unfolded hierarchically by the disintegration of relative entropy. The variational core of SBTS is preserved: the entropy minimiser is the h-transform of the reference, and on each frozen interval the optimal dynamics admit a logarithmic-gradient drift formula on the affine leaves of the active covariance directions, valid even when the frozen covariance is rank-deficient. We establish stability of the frozen approximation and convergence of the corresponding regularised kernel estimators. The construction is realised through a finite-dimensional conditioning map assembled from three complementary reductions of the past -- a block PCR summary, a reference-aware Mahalanobis kernel on past increments induced by the runtime frozen covariance cumulants, and a past-window WLS drift regressor under the same reference metric -- together with a coupled state-covariance bridge step in which each latent level produces a dynamic reference for the level above, summarised by a covariance descriptor; the construction is evaluated on numerical experiments.

This paper proposes StrTransformer, a source-wise structured Transformer framework for blind source recovery and branch-wise latent modeling. Instead of using an encoder to infer latent variables, StrTransformer directly optimizes the latent source matrix together with an observation-space mixer and source-wise structural Transformer branches. The mixer enforces reconstruction consistency, while each Transformer branch imposes a differentiable structural constraint on one latent source trajectory. Specifically, each source is converted into multi-scale patch tokens, randomly masked, processed by a locality-biased Transformer, and evaluated through a masked patch reconstruction energy. This energy acts as an implicit source-wise structural prior. To encourage different latent branches to specialize into different temporal regimes, StrTransformer further introduces an ordered multi-scale controller that learns branch-specific patch-scale weights, ordered scale centers, and locality attention slopes. The resulting objective combines observation reconstruction, source-wise structural regularization, and modular auxiliary penalties for separation and scale specialization. We analyze the decoupling and coupling structure of the objective, the regularized exact-reconstruction fiber, and the reduction of permutation symmetry induced by ordered branch descriptors. A controlled case study shows that the learned branches converge to distinct temporal-scale structures and recover source-aligned latent trajectories under post-hoc evaluation.

Time series forecasting models often exhibit inconsistent performance across datasets with varying statistical and structural properties. Despite the wide range of available forecasting techniques, it remains unclear whether model selection can be reliably guided by simple data characteristics. This paper investigates why rule-based model selection fails in time series forecasting by analyzing the relationship between data-regime descriptors and model performance. A descriptor-based framework is introduced to characterize time series using measurable properties, including trend strength, seasonality, noise level, and temporal dependence. Based on these descriptors, a rule-based selection mechanism is formulated to map data regimes to candidate forecasting models. The approach is evaluated on multiple real-world datasets across different domains and forecasting horizons. The results show that rule-based model selection achieves low accuracy, with correct model identification occurring in only a small fraction of cases. Significant discrepancies are observed between recommended and empirically optimal models, particularly in noisy and mixed regimes. Further analysis reveals that model performance is highly sensitive to both dataset characteristics and forecasting horizon, resulting in substantial ranking instability across scenarios. These findings explain why simple heuristic rules fail to generalize and demonstrate that forecasting performance cannot be reliably predicted using static, descriptor-based approaches. This study provides empirical evidence that model selection in time series forecasting is inherently context-dependent and highlights the need for more adaptive, data-driven strategies.

ConceptNet488 comprises commonly observed entities and their connections, where edge weights signify the re-489 liability and frequency of these relationships. To prevent the redundancy of common information and to maintain the validity of the enriched491 relations, we categorized the relationships based on their weights. Relationships with weights less492 than 1 were deemed "weak" and those with a weight of 1 were labeled "average". We refrained from493 using these categories for relation enhancement. Instead, only relationships with weights greater than494 1, indicative of high reliability, were employed for augmenting the relations.495

For each image's list of candidate objects, we heuristically downsample to a set of "most interesting" regions by: 1) selecting the at-most k " 4 largest/most central people; 2) keeping the most central/large objects; 3) over-sampling rarer objects according to prior frequency of detection in the LVIS vocabulary; 4) limiting the number of objects of a single type per-image; and 5) downsampling overlapping region proposals to encourage broader coverage of the pixel area of the image.

We initiate the study of behavioral information design through deep learning. In information design, a sender aims to persuade a receiver to take certain actions by strategically revealing information. We address scenarios in which the receiver might exhibit different behavior patterns other than the standard Bayesian rational assumption. We propose HAIDNet, a neural-network-based optimization framework for information design that can adapt to multiple representations of human behavior. Through extensive simulation, we show that HAIDNet can not only recover information policies that are near-optimal compared with known analytical solutions, but also can extend to designing information policies for settings that are computationally challenging (e.g., when there are multiple receivers) or for settings where there are no known solutions in general (e.g., when the receiver behavior does not follow the Bayesian rational assumption). We also conduct real-world human-subject experiments and demonstrate that our framework can capture human behavior from data and lead to more effective information policy for real-world human receivers.