#01Aug 13, 2026
cs.LG
The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity
Martin J. Wainwright
We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \emph{unmasking growth complexity} ({\textsf{UGC}\xspace}). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {\textsf{UGC}\xspace} increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to \emph{certified-optimal} samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the \ugc path yields the aggregate {\textsf{UGC}\xspace} mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root {\textsf{UGC}\xspace} density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including $\widetildeΩ(\sqrt{d})$ improvements achievable with a constant number of adaptively placed blocks.
#02Aug 13, 2026
cs.CL
LittleLearner: Language Models Under Pedagogically Controlled Knowledge Exposure
Fanfei Li, Jana Zeller, Manuel Prada-Corral and 4 more
Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce LITTLECURRICULUM, a curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 5B-parameter LLM from scratch on LITTLECURRICULUM yields LITTLELEARNER, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release LITTLECURRICULUM and LITTLELEARNER as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let LITTLELEARNER better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.
#03Aug 13, 2026
math.ST
On the Structural Limits of Machine Learning Decision Systems: An Information-Theoretic, Interaction-Based, and Stochastic-Dynamical Perspective
Nestor R. Barraza, Gabriel Pena
Machine learning procedures are commonly evaluated in terms of predictive accuracy and computational efficiency. However, their achievable performance is fundamentally constrained by structural properties of the underlying data-generating process, which are formalized in terms of informational bounds. In this work we examine intrinsic limits of data-driven decision systems from an information-theoretic and interaction-based perspective. We analyze minimal achievable error in classification through Fano-type bounds and precision limits in parametric estimation via the Cramér-Rao inequality, emphasizing that such limits depend on the underlying model rather than on algorithmic sophistication alone. We further discuss how implicit assumptions, such as independence, ergodicity, and distributional stability, affect the validity of inferential procedures. Building on interaction-based modeling principles, we review typical frameworks such as Markov Random Fields and potential based representations for encoding dependence mechanisms. We also describe decision systems, including LLM-integrated agent architectures, as feedback-driven stochastic processes where state-dependent dynamics may induce emergent macroscopic behavior. This perspective highlights the importance of having adequate models for the data as a prerequi- site for expanding predictive capability, and situates algorithmic learning within the informational limits imposed by the models.
#04Aug 13, 2026
cs.CV
V-RAE: Rethinking Video Latent Spaces for Generation
Minghui Guo, Shengqiong Wu, Hao Fei
Latent video generation relies on autoencoders to define a compact space in which generative models operate. Although video autoencoder architectures have evolved substantially, their latent spaces are still optimized primarily for pixel-level reconstruction and provide limited high-level semantic organization. A reconstruction-optimal latent space, however, need not be well suited to generative modeling. We propose V-RAE, a video representation autoencoder that builds compact generative latents on top of frozen vision foundation model representations. A lightweight temporal pooling module removes temporal redundancy while preserving semantic structure, and a video decoder reconstructs continuous motion from the compressed features. We evaluate V-RAE with four representative frozen encoders on video reconstruction, semantic probing, and class-conditional generation. V-RAE achieves 2.13 rFVD on K600, outperforming all evaluated large-scale pretrained video VAEs. Its latents retain substantially more semantic information than conventional video tokenizer latents. Under matched generation settings, our best variant achieves gFVD scores of 117.86 and 19.16 on UCF101 and K600, respectively, while converging up to 6x faster}. We further show that reconstruction quality alone is insufficient to characterize generative utility and introduce tFVD, a temporal-coherence diagnostic that correlates more reliably with downstream generation quality. Beyond video generation, V-RAE also improves future video prediction on Cityscapes over the Wan 2.2 VAE latent space under matched prediction settings. Taken together, the experiments show that frozen semantic representations can support video reconstruction, generation, and predictive modeling. The project page: https://v-rae.github.io/.
#05Aug 13, 2026
cs.CV
GS$^{2}$CI: Robust Gaussian Splatting For Snapshot Compressive Imaging via Large Vision Model Priors
Yanming Yang, Chenxi Song, Ping Wang and 2 more
Snapshot Compressive Imaging (SCI) offers an efficient solution for high-speed video acquisition and, under exposure-time camera--scene relative motion, multi-view scene capture by compressing temporal or spatial information into a single 2D measurement. While recent studies have explored SCI for 3D scene reconstruction, existing methods struggle with significant challenges due to information loss, limited viewpoint diversity, and the computational burden of jointly optimizing 3D representations and camera poses. In this work, we propose a novel framework that reconstructs high-quality 3D scenes from a single SCI measurement by leveraging 3D Gaussian Splatting (3DGS) and the powerful priors of large-scale vision foundation models (VFMs). Our primary reconstruction combines measurement-derived 3D VFM initialization with SCI-aware Gaussian optimization. After coarse-stage convergence, an auxiliary 2D VFM provides pseudo-view supervision at synthesized viewpoints for local appearance refinement. To further address the instability caused by ambiguous SCI supervision during 3DGS optimization, we introduce Opacity-Guided Splitting and Growth Regulation (OSGR), an SCI-specific densification strategy that augments split candidates using local opacity statistics, discourages loss-compensating opacity inflation through mean-opacity regulation, and bounds representation growth with explicit candidate-ratio and Gaussian-count constraints. Extensive experiments across multiple benchmarks demonstrate that our method achieves the strongest overall performance, combining leading reconstruction quality and robustness to viewpoint variation with competitive computational efficiency.