Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a *Dual-Channel Tensor Neural Network* (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a *structure-aware conformal ROC* procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a *conformal structure selector* that, to our knowledge, is the *first distribution-free procedure* for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product--position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of $\tilde{O}(\sqrt{NT})$, matching the lower bound and closing the $\sqrt{K}$ gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $ϕ$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $ϕ$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an uncertainty reduction beyond the filter. This paper introduces an ensemble Kalman-Bucy smoother (EnKBS) for continuous-time DA of nonlinear dynamical systems, where the smoother's conditional distributions are reconstructed using ensemble moments. The result is a derivative-free framework that does not require explicit computation of tangent-linear or adjoint models, which converges to the exact smoother solution at the infinite-ensemble limit for a wide class of complex systems. Incorporating standard regularization techniques for high-dimensional systems, such as covariance localization and inflation, the skill of the EnKBS is demonstrated in various important scientific problems. By integrating future observations, which reveal the underlying causal mechanisms for retrospective state updates, the EnKBS is used for Bayesian-based inference of causal relationships and their temporal influence range in a dyadic trigger-feedback model and the development of a causality-driven iterative learning algorithm that identifies the structure and recovers the hidden parameters of a nonlinear reduced-order model mimicking midlatitude atmospheric circulation. Notably, both tasks remain effective with an ensemble size of $O(10)$ under partial observations, suggesting that EnKBS can support the instantaneous discovery of high-dimensional complex systems over time.

The vulnerability of deep neural networks (DNNs) to adversarial examples has drawn great attention from the community. In this paper, we study the transferability of such examples, which lays the foundation of many black-box attacks on DNNs. We revisit a not so new but definitely noteworthy hypothesis of Goodfellow et al.'s and disclose that the transferability can be enhanced by improving the linearity of DNNs in an appropriate manner. We introduce linear backpropagation (LinBP), a method that performs backpropagation in a more linear fashion using off-the-shelf attacks that exploit gradients. More specifically, it calculates forward as normal but backpropagates loss as if some nonlinear activations are not encountered in the forward pass. Experimental results demonstrate that this simple yet effective method obviously outperforms current state-of-the-arts in crafting transferable adversarial examples on CIFAR-10 and ImageNet, leading to more effective attacks on a variety of DNNs.

Aligning foundation models is essential for their safe and trustworthy deployment. However, traditional fine-tuning methods are computationally intensive and require updating billions of model parameters. A promising alternative, alignment via decoding, adjusts the response distribution directly without model updates to maximize a target reward r, thus providing a lightweight and adaptable framework for alignment. However, principled decoding methods rely on oracle access to an optimal Q-function (Q), which is often unavailable in practice. Hence, prior SoTA methods either approximate this Q using Qπsft (derived from the reference SFTmodel) or rely on short-term rewards, resulting in sub-optimal decoding performance. In this work, we propose Transfer Q, which implicitly estimates the optimal value function for a target reward r through a baseline model ρBL aligned with a baseline reward rBL (which can be different from the target reward r). Theoretical analyses of Transfer Q provide a rigorous characterization of its optimality, deriving an upper bound on the sub-optimality gap and identifying a hyperparameter to control the deviation from the pre-trained reference SFTmodel based on user needs. Our approach significantly reduces the sub-optimality gap observed in prior SoTA methods and demonstrates superior empirical performance across key metrics such as coherence, diversity, and quality in extensive tests on several synthetic and real datasets.

In reinforcement learning with image-based inputs, it is crucial to establish a robust and generalizable state representation. Recent advancements in metric learning, such as deep bisimulation metric approaches, have shown promising results in learning structured low-dimensional representation space from pixel observations, where the distance between states is measured based on task-relevant features. However, these approaches face challenges in demanding generalization tasks and scenarios with non-informative rewards. This is because they fail to capture sufficient long-term information in the learned representations. To address these challenges, we propose a novel State Chrono Representation (SCR) approach. SCR augments state metric-based representations by incorporating extensive temporal information into the update step of bisimulation metric learning. It learns state distances within a temporal framework that considers both future dynamics and cumulative rewards over current and long-term future states. Our learning strategy effectively incorporates future behavioral information into the representation space without introducing a significant number of additional parameters for modeling dynamics. Extensive experiments conducted in DeepMind Control and Meta-World environments demonstrate that SCR achieves better performance comparing to other recent metric-based methods in demanding generalization tasks.