Preference-based fine-tuning has become an important component in training large language models, and the data used at this stage may contain sensitive user information. A central question is how to design a differentially private pipeline that is well suited to the distinct structure of reinforcement learning from human feedback. We propose a privacy-preserving framework that imposes differential privacy only on reward learning and derives the final policy from the resulting private reward model. Theoretically, we study the suboptimality gap and show that privacy contributes an additional additive term beyond the usual non-private statistical error. We also establish a minimax lower bound and show that the dominant term changes with sample size and privacy level, which in turn characterizes regimes in which the upper bound is rate-optimal up to logarithmic factors. Empirically, synthetic experiments confirm the scaling predicted by the theory, and experiments on the Anthropic HH-RLHF dataset using the Gemma-2B-IT model show stronger private alignment performance than existing differentially private baseline methods across privacy budgets.

Optimizing survival outcomes, such as patient survival or customer retention, is a critical objective in data-driven decision-making. Off-Policy Evaluation~(OPE) provides a powerful framework for assessing such decision-making policies using logged data alone, without the need for costly or risky online experiments in high-stakes applications. However, typical estimators are not designed to handle right-censored survival outcomes, as they ignore unobserved survival times beyond the censoring time, leading to systematic underestimation of the true policy performance. To address this issue, we propose a novel framework for OPE and Off-Policy Learning~(OPL) tailored for survival outcomes under censoring. Specifically, we introduce IPCW-IPS and IPCW-DR, which employ the Inverse Probability of Censoring Weighting technique to explicitly deal with censoring bias. We theoretically establish that our estimators are unbiased and that IPCW-DR achieves double robustness, ensuring consistency if either the propensity score or the outcome model is correct. Furthermore, we extend this framework to constrained OPL to optimize policy value under budget constraints. We demonstrate the effectiveness of our proposed methods through simulation studies and illustrate their practical impacts using public real-world data for both evaluation and learning tasks.

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric problem, particularly in multidimensional settings, since the covariance function is defined on a product domain and thus suffers from the curse of dimensionality. This motivates the use of adaptive estimators, such as deep learning estimators. However, existing theoretical results are largely limited to estimators with explicit analytic representations, and the properties of general learning-based estimators remain poorly understood. We establish an oracle inequality for a broad class of learning-based estimators that applies to both sparse and dense observation regimes in a unified manner, and derive convergence rates for deep learning estimators over several classes of covariance functions. The resulting rates suggest that structural adaptation can mitigate the curse of dimensionality, similarly to classical nonparametric regression. We further compare the convergence rates of learning-based estimators with several existing procedures. For a one-dimensional smoothness class, deep learning estimators are suboptimal, whereas local linear smoothing estimators achieve a faster rate. For a structured function class, however, deep learning estimators attain the minimax rate up to polylogarithmic factors, whereas local linear smoothing estimators are suboptimal. These results reveal a distinctive adaptivity-variance trade-off in covariance function estimation.

Tech firm'says goodbye' to Sora, made publicly available in 2024, just six months after its launch of a stand-alone app In an abrupt announcement on Tuesday, OpenAI said it was "saying goodbye" to its AI video generator Sora. The move comes just six months after the company's splashy launch of a stand-alone app with which people could make and share hyper-realistic AI videos in a scrolling social feed. "To everyone who created with Sora, shared it, and built community around it: thank you," the company wrote in a post on X . "What you made with Sora mattered, and we know this news is disappointing." OpenAI first made Sora publicly available in late 2024, but it wasn't until the company launched Sora 2 and its stand-alone app last September that the video generator reached mainstream attention.

Despite their dominance in vision and language, deep neural networks often underperform relative to tree-based models on tabular data. To bridge this gap, we incorporate five key inductive biases into deep learning: robustness to irrelevant features, axis alignment, localized irregularities, feature heterogeneity, and training stability. We propose \emph{LassoFlexNet}, an architecture that evaluates the linear and nonlinear marginal contribution of each input via Per-Feature Embeddings, and sparsely selects relevant variables using a Tied Group Lasso mechanism. Because these components introduce optimization challenges that destabilize standard proximal methods, we develop a \emph{Sequential Hierarchical Proximal Adaptive Gradient optimizer with exponential moving averages (EMA)} to ensure stable convergence. Across $52$ datasets from three benchmarks, LassoFlexNet matches or outperforms leading tree-based models, achieving up to a $10$\% relative gain, while maintaining Lasso-like interpretability. We substantiate these empirical results with ablation studies and theoretical proofs confirming the architecture's enhanced expressivity and structural breaking of undesired rotational invariance.

Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and standard deep learning approaches often lack interpretability and generalization across resolutions, we propose SC-Net (Spectral Correction Network), a novel operator learning framework. SC-Net operates in the spectral domain of the forward operator, learning a pointwise adaptive filter function that reweights spectral coefficients based on the signal-to-noise ratio. We provide a theoretical analysis showing that SC-Net approximates the continuous inverse operator, guaranteeing discretization invariance. Numerical experiments on 1D integral equations demonstrate that SC-Net: (1) achieves the theoretical minimax optimal convergence rate ($O(δ^{0.5})$ for $s=p=1.5$), matching theoretical lower bounds; (2) learns interpretable sharp-cutoff filters that outperform Oracle Tikhonov regularization; and (3) exhibits zero-shot super-resolution, maintaining stable reconstruction errors ($\approx 0.23$) when trained on coarse grids ($N=256$) and tested on significantly finer grids (up to $N=2048$). The proposed method bridges the gap between rigorous regularization theory and data-driven operator learning.

Large language models are increasingly used as personal assistants, yet most lack a persistent user model, forcing users to repeatedly restate preferences across sessions. We propose Vector-Adapted Retrieval Scoring (VARS), a pipeline-agnostic, frozen-backbone framework that represents each user with long-term and short-term vectors in a shared preference space and uses these vectors to bias retrieval scoring over structured preference memory. The vectors are updated online from weak scalar rewards from users' feedback, enabling personalization without per-user fine-tuning. We evaluate on \textsc{MultiSessionCollab}, an online multi-session collaboration benchmark with rich user preference profiles, across math and code tasks. Under frozen backbones, the main benefit of user-aware retrieval is improved interaction efficiency rather than large gains in raw task accuracy: our full VARS agent achieves the strongest overall performance, matches a strong Reflection baseline in task success, and reduces timeout rate and user effort. The learned long-term vectors also align with cross-user preference overlap, while short-term vectors capture session-specific adaptation, supporting the interpretability of the dual-vector design. Code, model, and data are available at https://github.com/YurenHao0426/VARS.

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step baseline akin to the role of Bayesian linear regression for tabular data. Our method couples the wavelet scattering transform-a deep, non-learned feature extractor-with a simple probabilistic head. Because scattering features are derived from geometric principles rather than learned, they avoid overfitting the training distribution. This helps provide sensible uncertainty estimates even under significant distribution shifts. We validate this on diverse tasks, including medical imaging under institution shift, wealth mapping under country-to-country shift, and Bayesian optimization of molecular properties. Our results suggest that Bayesian scattering is a solid baseline for complex uncertainty quantification methods.

Time-dependent reliability analysis of nonlinear dynamical systems under stochastic excitations is a critical yet computationally demanding task. Conventional approaches, such as Monte Carlo simulation, necessitate repeated evaluations of computationally expensive numerical solvers, leading to significant computational bottlenecks. To address this challenge, we propose \textit{CoNBONet}, a neuroscience-inspired surrogate model that enables fast, energy-efficient, and uncertainty-aware reliability analysis, providing a scalable alternative to techniques such as Monte Carlo simulations. CoNBONet, short for \textbf{Co}nformalized \textbf{N}euroscience-inspired \textbf{B}ayesian \textbf{O}perator \textbf{Net}work, leverages the expressive power of deep operator networks while integrating neuroscience-inspired neuron models to achieve fast, low-power inference. Unlike traditional surrogates such as Gaussian processes, polynomial chaos expansions, or support vector regression, that may face scalability challenges for high-dimensional, time-dependent reliability problems, CoNBONet offers \textit{fast and energy-efficient inference} enabled by a neuroscience-inspired network architecture, \textit{calibrated uncertainty quantification with theoretical guarantees} via split conformal prediction, and \textit{strong generalization capability} through an operator-learning paradigm that maps input functions to system response trajectories. Validation of the proposed CoNBONet for various nonlinear dynamical systems demonstrates that CoNBONet preserves predictive fidelity, and achieves reliable coverage of failure probabilities, making it a powerful tool for robust and scalable reliability analysis in engineering design.

Modern time series forecasting is evaluated almost entirely through passive observation of single historical trajectories, rendering claims about a model's robustness to non-stationarity fundamentally unfalsifiable. We propose a paradigm shift toward interventionist, exact-statistical benchmarking. By systematically titrating calibrated Gaussian observation noise into known chaotic and stochastic dynamical systems, we transform forecasting from a black-box sequence matching game into an exact distributional inference task. Because the underlying data-generating process and noise variance are mathematically explicit, evaluation can rely on exact negative log-likelihoods and calibrated distributional tests rather than heuristic approximations. To fully leverage this framework, we extend the Fern architecture into a probabilistic generative model that natively parameterizes the Symmetric Positive Definite (SPD) cone, outputting calibrated joint covariance structures without the computational bottleneck of generic Jacobian modeling. Under this rigorous evaluation, we find that state-of-the-art zero-shot foundation models behave consistently with the context-parroting mechanism, failing systematically under non-stationary regime shifts and elevated noise. In contrast, Fern explicitly captures the invariant measure and multivariate geometry of the underlying dynamics, maintaining structural fidelity and statistically sharp calibration precisely where massive sequence-matching models collapse.