Estimating the uncertainty of responses from Large Language Models (LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose Training-Free Bayesianization (TFB), a simple yet theoretically grounded framework that efficiently transforms trained low-rank adapters into Bayesian ones without additional training. TFBsystematically searches for the maximally acceptable level of variance in the weight posterior, constrained within a family of low-rank isotropic Gaussian distributions. Our theoretical analysis shows that under mild conditions, this search process is equivalent to KL-regularized variational optimization, a generalized form of variational inference. Through comprehensive experiments, we show that TFB achieves superior uncertainty estimation and generalization compared to existing methods while eliminating the need for complex Bayesianization training procedures.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system. In this work, we present APOLLO (Automated PrOof repair via LLM and Lean cOllaboration), a modular, model-agnostic agentic framework that combines the strengths of the Lean compiler with an LLM's reasoning abilities to achieve better proof-generation results at a low token and sampling budgets. Apollo directs a fully automated process in which the LLM generates proofs for theorems, a set of agents analyze the proofs, fix the syntax errors, identify the mistakes in the proofs using Lean, isolate failing sub-lemmas, utilize automated solvers, and invoke an LLM on each remaining goal with a low top-K budget. The repaired sub-proofs are recombined and reverified, iterating up to a user-controlled maximum number of attempts. On the miniF2F benchmark, we establish a new state-of-the-art accuracy of 84.9% among sub 8B-parameter models (as of August 2025) while keeping the sampling budget below one hundred. Moreover, Apollo raises the state-of-the-art accuracy for Goedel-Prover-SFT to 65.6% while cutting sample complexity from 25,600 to a few hundred.

Spurious correlations occur when models rely on non-essential features that coincidentally co-vary with target labels, leading to incorrect reasoning under distribution shift. We consider spurious correlations in Large Vision Language Models (LVLMs) pretrained on extensive and diverse datasets without explicit task supervision. We develop a benchmark by sourcing GPT-4o errors on real-world visual-question-answering (VQA) benchmarks, then curating a subset through LVLM-human annotation and synthetic counterfactual evaluation to identify errors caused by spurious correlations. This process yields SpuriVerse, a novel benchmark comprised of 124 distinct types of spurious correlations extracted from real-world datasets, each containing 1 realistic and 10 synthetic VQA samples for a total of 1364 multiple choice questions. We evaluate 15 open and closed-source LVLMs on SpuriVerse, finding that even state-of-the-art closed-source models struggle significantly, achieving at best only 35.0% accuracy. Fine-tuning on synthetic examples that emphasize the spurious correlation improves performance to 78.4%, suggesting that training on diverse spurious patterns generalizes to unseen situations: models appear to learn to avoid "shortcuts" and attend to the overall image context.

Although transformer-based models have shown exceptional empirical performance, the fundamental principles governing their training dynamics are inadequately characterized beyond configuration-specific studies. Inspired by empirical evidence showing improved reasoning capabilities under small initialization scales in language models, we employ the gradient flow analytical framework established in Zhou et al. [2022] to systematically investigate linearized Transformer training dynamics.

End-to-end (E2E) autonomous driving models have demonstrated strong performance in open-loop evaluations but often suffer from cascading errors and poor generalization in closed-loop settings. To address this gap, we propose Modelbased Policy Adaptation (MPA), a general framework that enhances the robustness and safety of pretrained E2E driving agents during deployment. MPA first generates diverse counterfactual trajectories using a geometry-consistent simulation engine, exposing the agent to scenarios beyond the original dataset. Based on this generated data, MPA trains a diffusion-based policy adapter to refine the base policy's predictions and a multi-step Q value model to evaluate long-term outcomes. At inference time, the adapter proposes multiple trajectory candidates, and the Q value model selects the one with the highest expected utility. Experiments on the nuScenes benchmark using a photorealistic closed-loop simulator demonstrate that MPA significantly improves performance across in-domain, out-of-domain, and safety-critical scenarios. We further investigate how the scale of counterfactual data and inference-time guidance strategies affect overall effectiveness.

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) - a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

Such conditions are commonly encountered in nighttime scenes with light sources. Even with standard exposure settings, a bimodal intensity distribution with boundary peaks often emerges, making it difficult to preserve both highlight and shadow details simultaneously. RGB-based bracketing methods can capture details at both ends using short-long exposure pairs, but are susceptible to misalignment and ghosting artifacts. We found that a shortexposure image already retains sufficient highlight detail. The main challenge of UHDR reconstruction lies in denoising and recovering information in dark regions.

The global rise in wildfire frequency and intensity over the past decade underscores the need for improved fire monitoring techniques. To advance deep learning research on wildfire detection and its associated human health impacts, we introduce SmokeViz, a large-scale machine learning dataset of smoke plumes in satellite imagery. The dataset is derived from expert annotations created by smoke analysts at the National Oceanic and Atmospheric Administration, which provide coarse temporal and spatial approximations of smoke presence. To enhance annotation precision, we propose pseudo-label dimension reduction (PLDR), a generalizable method that applies pseudo-labeling to refine datasets with mismatching temporal and/or spatial resolutions. Unlike typical pseudo-labeling applications that aim to increase the number of labeled samples, PLDR maintains the original labels but increases the dataset quality by solving for intermediary pseudo-labels (IPLs) that align each annotation to the most representative input data. For SmokeViz, a parent model produces IPLs to identify the single satellite image within each annotations time window that best corresponds with the smoke plume. This refinement process produces a succinct and relevant deep learning dataset consisting of over 160,000 manual annotations. The SmokeViz dataset is expected to be a valuable resource to develop further wildfire-related machine learning models and is publicly available at https://noaa-gsl-experimental-pds.s3.amazonaws.com/index.

Medical imaging super-resolution is critical for improving diagnostic utility and reducing costs, particularly for low-cost modalities such as portable Optical Coherence Tomography (OCT). We propose OCTDiff, a bridged diffusion model designed to enhance image resolution and quality from portable OCT devices. Our image-to-image diffusion framework addresses key challenges in the conditional generation process of denoising diffusion probabilistic models (DDPMs). We introduce Adaptive Noise Aggregation (ANA), a novel module to improve denoising dynamics within the reverse diffusion process. Additionally, we integrate Multi-Scale Cross-Attention (MSCA) into the U-Net backbone to capture local dependencies across spatial resolutions. To address overfitting on small clinical datasets and to preserve fine structural details essential for retinal diagnostics, we design a customized loss function guided by clinical quality scores. OCTDiff outperforms convolutional baselines and standard DDPMs, achieving state-of-the-art performance on clinical portable OCT datasets. Our model and its downstream applications have the potential to generalize to other medical imaging modalities and revolutionize the current workflow of ophthalmic diagnostics.

Causal representation learning (CRL) is the process of disentangling the latent low-dimensional causally-related generating factors underlying high-dimensional observable data. Extensive recent studies have characterized CRL identifiability and perfect recovery of the latent variables and their attendant causal graph. This paper introduces the notion of reward-oriented CRL, the purpose of which is to move away from perfectly learning the latent representation and instead learning it to the extent needed for optimizing a desired downstream task (reward). In reward-oriented CRL, perfectly learning the latent representation can be excessive; instead, it must be learned at the coarsest level sufficient for optimizing the desired task. Reward-oriented CRL is formalized as the optimization of a desired function of the observable data over the space of all possible interventions and focuses on linear causal and transformation models. To sequentially identify the optimal subset of interventions, an adaptive exploration algorithm is designed that learns the latent causal graph and the variables needed to identify the best intervention. It is shown that for an n-dimensional latent space and a d-dimensional observation space, over a horizon T the algorithm's regret scales as O(d