Imitation learning seeks to estimate policies reflecting the values of demonstrated behaviors. Prevalent approaches learn to match or exceed the demonstrator's performance in expectation without knowing the demonstrator's reward function. Unfortunately, this does not induce pluralistic imitators that learn to support distinct demonstrations.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements.

This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to the identity matrix, and estimators derived from data augmentation (DA). Here, DA refers to the common practice of enriching a dataset with artificial samples--typically generated via a generative model or through random transformations of the original data--prior to model fitting. For both classes of estimators, we derive estimators and provide concentration bounds for their quadratic error. This allows for both method comparison and hyperparameter tuning, such as selecting the optimal proportion of artificial samples. On the technical side, our analysis relies on tools from random matrix theory. We introduce a novel deterministic equivalent for generalized resolvent matrices, accommodating dependent samples with specific structure. We support our theoretical results with numerical experiments.

Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure--such as meta-learning and hyperparameter optimization. Such applications often involve sensitive training data, raising pressing concerns about individual privacy. Motivated by this, we study differentially private bilevel optimization. We first focus on settings where the outer-level objective is convex, and provide novel upper and lower bounds on the excess empirical risk for both pure and approximate differential privacy. These bounds are nearly tight and essentially match the optimal rates for standard single-level differentially private ERM, up to additional terms that capture the intrinsic complexity of the nested bilevel structure.

Recent advances in knowledge distillation have emphasized the importance of decoupling different knowledge components. While existing methods utilize momentum mechanisms to separate task-oriented and distillation gradients, they overlook the inherent conflict between target-class and non-target-class knowledge flows. Furthermore, low-confidence dark knowledge in non-target classes introduces noisy signals that hinder effective knowledge transfer. To address these limitations, we propose DeepKD, a novel training framework that integrates duallevel decoupling with adaptive denoising. First, through theoretical analysis of gradient signal-to-noise ratio (GSNR) characteristics in task-oriented and non-taskoriented knowledge distillation, we design independent momentum updaters for each component to prevent mutual interference. We observe that the optimal momentum coefficients for task-oriented gradient (TOG), target-class gradient (TCG), and non-target-class gradient (NCG) should be positively related to their GSNR. Second, we introduce a dynamic top-k mask (DTM) mechanism that gradually increases K from a small initial value to incorporate more non-target classes as training progresses, following curriculum learning principles. The DTM jointly filters low-confidence logits from both teacher and student models, effectively purifying dark knowledge during early training. Extensive experiments on CIFAR-100, ImageNet, and MS-COCO demonstrate DeepKD's effectiveness.

Recent progress in 3D object generation has greatly improved both the quality and efficiency. However, most existing methods generate a single mesh with all parts fused together, which limits the ability to edit or manipulate individual parts. A key challenge is that different objects may have a varying number of parts. To address this, we propose a new end-to-end framework for part-level 3D object generation. Given a single input image, our method generates high-quality 3D objects with an arbitrary number of complete and semantically meaningful parts. We introduce a dual volume packing strategy that organizes all parts into two complementary volumes, allowing for the creation of complete and interleaved parts that assemble into the final object. Experiments show that our model achieves better quality, diversity, and generalization than previous image-based part-level generation methods. Our project page is at https://research.nvidia.com/

Recent probing studies reveal that large language models exhibit linear subspaces that separate true from false statements, yet the mechanism behind their emergence is unclear. We introduce a transparent, one-layer toy model that reproduces such truth subspaces end-to-end and exposes one concrete route by which they can arise. We study one simple setting in which truth encoding can emerge: a data distribution where factual statements co-occur with other factual statements (and vice-versa), encouraging the model to learn this distinction in order to lower the LM loss on future tokens. We corroborate this pattern with experiments in pretrained language models. Finally, in the toy setting we observe a two-phase learning dynamic: networks first memorize individual factual associations in a few steps, then--over a longer horizon--learn to linearly separate true from false, which in turn lowers language-modeling loss. Together, these results provide both a mechanistic demonstration and an empirical motivation for how and why linear truth representations can emerge in language models.

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A major challenge in aligning large language models (LLMs) with human preferences is the issue of distribution shift. LLM alignment algorithms rely on static preference datasets, assuming that they accurately represent real-world user preferences. However, user preferences vary significantly across geographical regions, demographics, linguistic patterns, and evolving cultural trends. This preference distribution shift leads to catastrophic alignment failures in many real-world applications. We address this problem using the principled framework of distributionally robust optimization, and develop two novel distributionally robust direct preference optimization (DPO) algorithms, namely, Wasserstein DPO (WDPO) and Kullback-Leibler DPO (KLDPO). We characterize the sample complexity of learning the optimal policy parameters for WDPO and KLDPO. Moreover, we propose scalable gradient descent-style learning algorithms by developing suitable approximations for the challenging minimax loss functions of WDPO and KLDPO. Our empirical experiments using benchmark data sets and LLMs demonstrate the superior performance of WDPO and KLDPO in substantially improving the alignment when there is a preference distribution shift.

Recent large language models (LLMs) exhibit impressive reasoning but often overthink, generating excessively long responses that hinder efficiency. We introduce DIET (DIfficulty-AwarETraining), a framework that systematically cuts these "token calories" by integrating on-the-fly problem difficulty into the reinforcement learning (RL) process. DIETdynamically adapts token compression strategies by modulating token penalty strength and conditioning target lengths on estimated task difficulty, to optimize the performance-efficiency trade-off. We also theoretically analyze the pitfalls of naive reward weighting in group-normalized RL algorithms like GRPO, and propose Advantage Weighting technique, which enables stable and effective implementation of these difficulty-aware objectives. Experimental results demonstrate that DIETsignificantly reduces token counts while simultaneously improving reasoning performance. Beyond raw token reduction, we show two crucial benefits largely overlooked by prior work: (1) DIET leads to superior inference scaling. By maintaining high per-sample quality with fewer tokens, it enables better scaling performance via majority voting with more samples under fixed computational budgets, an area where other methods falter.