Weak-to-strong generalization refers to the phenomenon where a stronger model trained under supervision from a weaker one can outperform its teacher. While prior studies aim to explain this effect, most theoretical insights are limited to abstract frameworks or linear/random feature models. In this paper, we provide a formal analysis of weak-to-strong generalization from a linear CNN (weak) to a two-layer ReLU CNN (strong). We consider structured data composed of label-dependent signals of varying difficulty and label-independent noise, and analyze gradient descent dynamics when the strong model is trained on data labeled by the pretrained weak model. Our analysis identifies two regimes--data-scarce and data-abundant--based on the signal-to-noise characteristics of the dataset, and reveals distinct mechanisms of weak-to-strong generalization. In the data-scarce regime, generalization occurs via benign overfitting or fails via harmful overfitting, depending on the amount of data, and we characterize the transition boundary. In the data-abundant regime, generalization emerges in the early phase through label correction, but we observe that overtraining can subsequently degrade performance.

Recent advances in generative modeling have shown significant promise in designing novel periodic crystal structures. Existing approaches typically rely on either large language models (LLMs) or equivariant denoising models, each with complementary strengths: LLMs excel at handling discrete atomic types but often struggle with continuous features such as atomic positions and lattice parameters, while denoising models are effective at modeling continuous variables but encounter difficulties in generating accurate atomic compositions. To bridge this gap, we propose CrysLLMGen, a hybrid framework that integrates an LLM with a diffusion model to leverage their complementary strengths for crystal material generation. During sampling, CrysLLMGen first employs a fine-tuned LLM to produce an intermediate representation of atom types, atomic coordinates, and lattice structure. While retaining the predicted atom types, it passes the atomic coordinates and lattice structure to a pre-trained equivariant diffusion model for refinement. Our framework outperforms state-of-the-art generative models across several benchmark tasks and datasets. Specifically, CrysLLMGen not only achieves a balanced performance in terms of structural and compositional validity but also generates more stable and novel materials compared to LLM-based and denoising-based models Furthermore, CrysLLMGen exhibits strong conditional generation capabilities, effectively producing materials that satisfy user-defined constraints.

Multi-modal image segmentation faces real-world deployment challenges from incomplete/corrupted modalities degrading performance. While existing methods address training-inference modality gaps via specialized per-combination models, they introduce high deployment costs by requiring exhaustive model subsets and model-modality matching. In this work, we propose a unified modality-relax segmentation network (UniMRSeg) through hierarchical self-supervised compensation (HSSC).

We present LrcSSM, a $\textit{non-linear}$ recurrent model that processes long sequences as fast as today's linear state-space layers. By forcing its Jacobian matrix to be diagonal, the full sequence can be solved in parallel, giving $\mathcal{O}(TD)$ computational work and memory and only $\mathcal{O}(\log T)$ sequential depth, for input-sequence length $T$ and a state dimension $D$. Moreover, LrcSSM offers a formal gradient-stability guarantee that other input-varying systems such as Liquid-S4 and Mamba do not provide. Importantly, the diagonal Jacobian structure of our model results in no performance loss compared to the original model with dense Jacobian, and the approach can be generalized to other non-linear recurrent models, demonstrating broader applicability. On a suite of long-range forecasting tasks, we demonstrate that LrcSSM outperforms Transformers, LRU, S5, and Mamba.

Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as \textit{multiaccuracy}, or having low bias over a range of possible targets. In this paper, we consider a simple estimator, \emph{ridge boosting}: starting with any initial predictor, perform a single boosting step with (kernel) ridge regression. Surprisingly, we show that ridge boosting simultaneously achieves both efficiency and distributional robustness: for target distribution shifts that lie within an RKHS unit ball, this estimator maintains low bias across all such shifts and has variance at the semiparametric efficiency bound for each target. In addition to bridging otherwise distinct research areas, this result has immediate practical value. Since ridge boosting uses only data from the source distribution, researchers can train a single model to obtain both robust and efficient estimates for multiple target estimands at the same time, eliminating the need to fit separate semiparametric efficient estimators for each target. We assess this approach through simulations and an application estimating the age profile of retirement income.

Diffusion Transformers (DiTs) achieve state-of-the-art results in text-to-image, text-to-video generation, and editing. However, their large model size and the quadratic cost of spatial-temporal attention over multiple denoising steps make video generation computationally expensive. Static caching mitigates this by reusing features across fixed steps but fails to adapt to generation dynamics, leading to suboptimal trade-offs between speed and quality. We propose Foresight, an adaptive layer-reuse technique that reduces computational redundancy across denoising steps while preserving baseline performance. Foresight dynamically identifies and reuses DiT block outputs for all layers across steps, adapting to generation parameters such as resolution and denoising schedules to optimize efficiency. Applied to OpenSora, Latte, and CogVideoX, Foresight achieves up to 1.63x end-to-end speedup, end-to-end speedup, while maintaining video quality.

We study offline reinforcement learning in average-reward MDPs, which presents increased challenges from the perspectives of distribution shift and non-uniform coverage, and has been relatively underexamined from a theoretical perspective. While previous work obtains performance guarantees under single-policy data coverage assumptions, such guarantees utilize additional complexity measures which are uniform over all policies, such as the uniform mixing time. We develop sharp guarantees depending only on the target policy, specifically the bias span and a novel policy hitting radius, yielding the first fully single-policy sample complexity bound for average-reward offline RL. We are also the first to handle general weakly communicating MDPs, contrasting restrictive structural assumptions made in prior work. To achieve this, we introduce an algorithm based on pessimistic discounted value iteration enhanced by a novel quantile clipping technique, which enables the use of a sharper empirical-span-based penalty function. Our algorithm also does not require any prior parameter knowledge for its implementation. Remarkably, we show via hard examples that learning under our conditions requires coverage assumptions beyond the stationary distribution of the target policy, distinguishing single-policy complexity measures from previously examined cases. We also develop lower bounds nearly matching our main result.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current Large Language Models (LLMs), however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like ``soft'' reasoning by generating abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which span the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4\% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent limits of discrete language-based reasoning.

Accurate identification and localization of objects in 3-D scenes are essential for advancing comprehensive 3-D scene understanding. Although diffusion models have demonstrated impressive capabilities across a broad spectrum of computer vision tasks, their potential in both 2-D and 3-D object detection remains underexplored. Existing approaches typically formulate detection as a ''noise-to-box'' process, but they rely heavily on direct coordinate regression, which limits adaptability for more advanced tasks such as grounding-based object detection. To overcome these challenges, we propose a promptable 3-D object recognition framework, which introduces a diffusion-based paradigm for flexible and conditionally guided 3-D object detection. Our approach encodes bounding boxes into latent representations and employs latent diffusion models to realize a ''promptable noise-to-box'' transformation. This formulation enables the refinement of standard 3-D object detection using textual prompts, such as class labels. Moreover, it naturally extends to grounding object detection through conditioning on natural language descriptions, and generalizes effectively to few-shot learning by incorporating annotated exemplars as visual prompts. We conduct thorough evaluations on three key 3-D object recognition tasks: general 3-D object detection, few-shot detection, and grounding-based detection. Experimental results demonstrate that our framework achieves competitive performance relative to state-of-the-art methods, validating its effectiveness, versatility, and broad applicability in 3-D computer vision.

Diffusion Transformers (DiTs) have demonstrated strong performance in generative modeling, particularly in image synthesis, making them a compelling choice for molecular conformer generation. However, applying DiTs to molecules introduces novel challenges, such as integrating discrete molecular graph information with continuous 3D geometry, handling Euclidean symmetries, and designing conditioning mechanisms that generalize across molecules of varying sizes and structures. We propose DiTMC, a framework that adapts DiTs to address these challenges through a modular architecture that separates the processing of 3D coordinates from conditioning on atomic connectivity. To this end, we introduce two complementary graph-based conditioning strategies that integrate seamlessly with the DiT architecture. These are combined with different attention mechanisms, including both standard non-equivariant and SO(3)-equivariant formulations, enabling flexible control over the trade-off between between accuracy and computational efficiency. Experiments on standard conformer generation benchmarks (GEOM-QM9, -DRUGS, -XL) demonstrate that DiTMC achieves state-of-the-art precision and physical validity. Our results highlight how architectural choices and symmetry priors affect sample quality and efficiency, suggesting promising directions for large-scale generative modeling of molecular structures.