Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution, progressively adding noise. Previous sample complexity bounds have a polynomial dependence on the dimension d, apart from log(|H|), where H is the hypothesis class. In this work, we establish the first (nearly) dimension-free sample complexity bounds, modulo any dependence due to log(|H|), for learning these score functions, achieving a double exponential improvement in dimension over prior results. A key aspect of our analysis is to use a single function approximator to jointly estimate scores across noise levels, a critical feature in practice which enables generalization across timesteps. We introduce a novel martingale-based error decomposition and sharp variance bounds, enabling efficient learning from dependent data generated by Markov processes, which may be of independent interest. Building on these insights, we propose Bootstrapped Score Matching (BSM), a variance reduction technique that utilizes previously learned scores to improve accuracy at higher noise levels. These results provide crucial insights into the efficiency and effectiveness of diffusion models for generative modeling.

The diffusion inversion problem seeks to recover the latent generative trajectory of a diffusion model given a real image. Faithful inversion is critical for ensuring consistency in diffusion-based image editing. Prior works formulate this task as a fixed-point problem and solve it using numerical methods. However, achieving both accuracy and efficiency remains challenging, especially for few-step models and novel samples. In this paper, we propose PreciseInv, a general-purpose testtime optimization framework that enables fast and faithful inversion in as few as two inference steps.

Accurately estimating semantic aleatoric and epistemic uncertainties in large language models (LLMs) is particularly challenging in free-form question answering (QA), where obtaining stable estimates often requires many expensive generations. We introduce a diversity-steered sampler that discourages semantically redundant outputs during decoding, covers both autoregressive and masked diffusion paradigms, and yields substantial sampleefficiency gains. The key idea is to inject a continuous semantic-similarity penalty into the model's proposal distribution using a natural language inference (NLI) model lightly fine-tuned on partial prefixes or intermediate diffusion states. We debias downstream uncertainty estimates with importance reweighting and shrink their variance with control variates. Across four QA benchmarks, our method matches or surpasses baselines while covering more semantic clusters with the same number of samples. Being modular and requiring no gradient access to the base LLM, the framework promises to serve as a drop-in enhancement for uncertainty estimation in risk-sensitive model deployments.

In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper-and lower-level objectives are smooth but potentially nonconvex. Due to the absence of additional structural assumptions for the lower-level objective--such as convexity or the Polyak-Łojasiewicz (PL) condition--guaranteeing global optimality is generally intractable. Instead, we introduce a suitable notion of stationarity for this class of problems and aim to design a first-order algorithm that finds such stationary points in polynomial time. Intuitively, stationarity in this setting means the upper-level objective cannot be substantially improved locally without causing a larger deterioration in the lower-level objective. To this end, we show that a simple and implementable variant of the dynamic barrier gradient descent (DBGD) framework can effectively solve the considered nonconvex simple bilevel problems up to stationarity.

Existing methods either adopt dense grids as scene representation which is difficult to scale to high resolution, or learn the entire scene using a single set of sparse queries, which is insufficient to handle the various object characteristics. In this paper, we present ODG, a hierarchical dual sparse Gaussian representation to effectively capture complex scene dynamics. Building upon the observation that driving scenes can be universally decomposed into static and dynamic counterparts, we define dual Gaussian queries to better model the diverse scene objects. We utilize a hierarchical Gaussian transformer to predict the occupied voxel centers and semantic classes along with the Gaussian parameters. Leveraging the real-time rendering capability of 3DGaussian Splatting, we also impose rendering supervision with available depth and semantic map annotations injecting pixel-level alignment to boost occupancy learning. Extensive experiments on the Occ3D-nuScenes and Occ3D-Waymo benchmarks demonstrate our proposed method sets new state-of-the-art results while maintaining low inference cost.

How to integrate and verify spatial intelligence in foundation models remains an open challenge. Current practice often proxies Visual-Spatial Intelligence (VSI) with purely textual prompts and VQA-style scoring, which obscures geometry, invites linguistic shortcuts, and weakens attribution to genuinely spatial skills. We introduce Spatial Intelligence Grid (SIG): a structured, grid-based schema that explicitly encodes object layouts, inter-object relations, and physically grounded priors. As a complementary channel to text, SIG provides a faithful, compositional representation of scene structure for foundation-model reasoning. Building on SIG, we derive SIG-informed evaluation metrics that quantify a model's intrinsic VSI, which separates spatial capability from language priors.

A fundamental challenge in cognitive neuroscience is understanding how cognition emerges from the interplay between structural connectivity (SC) and functional connectivity (FC). Current machine learning approaches typically seek to establish direct mappings from SC to FC associated with specific cognitive states. However, these methods often treat SC and FC as distinct endpoints, failing to capture the coupling relationship throughout the progressive transformation between them. To address this limitation, we propose BrainFlow, a reversible generative model designed to parametrize flows between the distribution of SC and the mixed distribution of FCs from different cognitive tasks.

The study of Neural Tangent Kernels (NTKs) in deep learning has drawn increasing attention in recent years. NTKs typically actively change during training and are related to feature learning. In parallel, recent work on Gradient Descent (GD) has found a phenomenon called Edge of Stability (EoS), in which the largest eigenvalue of the NTK oscillates around a value inversely proportional to the step size. However, although follow-up works have explored the underlying mechanism of such eigenvalue behavior in depth, the understanding of the behavior of the NTK eigenvectors during EoS is still missing. This paper examines the dynamics of NTK eigenvectors during EoS in detail. Across different architectures, we observe that larger learning rates cause the leading eigenvectors of the final NTK, as well as the full NTK matrix, to have greater alignment with the training target. We then study the underlying mechanism of this phenomenon and provide a theoretical analysis for a two-layer linear network. Our study enhances the understanding of GD training dynamics in deep learning.

We propose SCONE (Scalable, Contextualized, Offloaded, N-gram Embedding), a new method for extending input embedding layers to enhance language model performance. To avoid increased decoding costs, SCONE retains the original vocabulary while introducing embeddings for a set of frequent n-grams. These embeddings provide contextualized representation for each input token and are learned with a separate model during training. After training, embeddings are precomputed and stored in off-accelerator memory; during inference, querying them has minimal impact on latency due to the low complexity of embedding lookups. SCONE enables two new scaling strategies: increasing the number of n-gram embeddings and scaling the model used to learn them, both while maintaining fixed accelerator usage during inference (in terms of FLOPS and memory). We show that scaling both aspects enables a model with 1B accelerator-resident parameters to outperform a 1.9B-parameter baseline across diverse corpora, while using only about half the FLOPS and accelerator memory during inference.

This work aims to compress the vision tokens of an LVLM into a representation that is simultaneously suitable for (a) generative and (b) discriminative tasks, (c) is nearly lossless, and (d) storage-efficient. To this end, we propose C&C, a novel compression method that leverages the LVLM itself for task-agnostic visual token compression. Unlike prior methods that perform token reduction on-the-fly, our approach offloads computation to a dedicated, upfront indexing stage, effectively decoupling compression from generation. This enables learning more powerful representations for generation during inference. At the core of C&C is a "doubleforward pass" training strategy. During the first forward pass, the LLM (of the LVLM) creates a bottleneck by compressing the dense visual tokens into a few summary tokens.