This work establishes that sparse Bayesian neural networks achieve optimal posterior contraction rates over anisotropic Besov spaces and their hierarchical compositions. These structures reflect the intrinsic dimensionality of the underlying function, thereby mitigating the curse of dimensionality. Our analysis shows that Bayesian neural networks equipped with either sparse or continuous shrinkage priors attain the optimal rates which are dependent on the intrinsic dimension of the true structures. Moreover, we show that these priors enable rate adaptation, allowing the posterior to contract at the optimal rate even when the smoothness level of the true function is unknown. The proposed framework accommodates a broad class of functions, including additive and multiplicative Besov functions as special cases. These results advance the theoretical foundations of Bayesian neural networks and provide rigorous justification for their practical effectiveness in high-dimensional, structured estimation problems.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities through test-time scaling approaches, particularly when fine-tuned with chain-of-thought (CoT) data distilled from more powerful large reasoning models (LRMs). However, these reasoning chains often contain verbose elements that mirror human problem-solving, categorized as progressive reasoning (the essential solution development path) and functional elements (verification processes, alternative solution approaches, and error corrections). While progressive reasoning is crucial, the functional elements significantly increase computational demands during test-time inference. We introduce PIR (Perplexity-based Importance Refinement), a principled framework that quantitatively evaluates the importance of each reasoning step based on its impact on answer prediction confidence. PIR systematically identifies and selectively prunes only low-importance functional steps while preserving progressive reasoning components, creating optimized training data that maintains the integrity of the core solution path while reducing verbosity. Models fine-tuned on PIR-optimized data exhibit superior test-time scaling properties, generating more concise reasoning chains while achieving improved accuracy (+0.9% to +6.6%) with significantly reduced token usage (-3% to -41%) across challenging reasoning benchmarks (AIME, AMC, and GPQA Diamond). Our approach demonstrates strong generalizability across different model sizes, data sources, and token budgets, offering a practical solution for deploying reasoningcapable LLMs in scenarios where efficient test-time scaling, response time, and computational efficiency are valuable constraints. Code and dataset are available at the LIMOPro.

Recent studies have uncovered an interesting phenomenon: unimodal foundation models tend to learn convergent representations, regardless of differences in architecture, training objectives, or data modalities. However, these representations are essentially internal abstractions of samples that characterize samples independently, leading to limited expressiveness. In this paper, we propose The Indra Representation Hypothesis, inspired by the philosophical metaphor of Indra's Net. We argue that representations from unimodal foundation models are converging to implicitly reflect a shared relational structure underlying reality, akin to the relational ontology of Indra's Net.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of'flows' - one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data. We call an input (m,α,β)-subsamplable if a random subsample of size m(or larger) preserves w.p 1 β the spectral structure of the original second moment matrix up to a multiplicative factor of 1 α. Building upon subsamplability, we give a recursive algorithmic framework similar to Kamath et al. (2019) that abides zero-Concentrated Differential Privacy (zCDP) while preserving w.h.p the accuracy of the second moment estimation upto an arbitrary factor of (1 γ). We then show how to apply our algorithm to approximate the second moment matrix of a distribution D, even when a noticeable fraction of the input are outliers.

Recent advances in multi-modal generative models have enabled significant progress in instruction-based image editing. However, while these models produce visually plausible outputs, their capacity for knowledge-based reasoning editing tasks remains under-explored. In this paper, We introduce KRIS-Bench (Knowledge-based Reasoning in Image-editing Systems Benchmark), a diagnostic benchmark designed to assess models through a cognitively informed lens.

Recent advances in Video Large Language Models (VLLMs) have achieved remarkable video understanding capabilities, yet face critical efficiency bottlenecks due to quadratic computational growth with lengthy visual token sequences of long videos. While existing keyframe sampling methods can improve temporal modeling efficiency, additional computational cost is introduced before feature encoding, and the binary frame selection paradigm is found suboptimal. Therefore, in this work, we propose Dynamic Token compression via LLM-guided Keyframe prior (DyToK), a training-free paradigm that enables dynamic token compression by harnessing VLLMs' inherent attention mechanisms. Our analysis reveals that VLLM attention layers naturally encoding query-conditioned keyframe priors, by which DyToK dynamically adjusts per-frame token retention ratios, prioritizing semantically rich frames while suppressing redundancies. Extensive experiments demonstrate that DyToK achieves state-of-the-art efficiency-accuracy tradeoffs. DyToK shows plug-and-play compatibility with existing compression methods, such as VisionZip and FastV, attaining 4.3 faster inference while preserving accuracy across multiple VLLMs, such as LLaVA-OneVision and Qwen2.5-VL.

Human communication is motivated: people speak, write, and create content with a particular communicative intent in mind. As a result, information that large language models (LLMs) and AI agents process is inherently framed by humans' intentions and incentives. People are adept at navigating such nuanced information: we routinely identify benevolent or self-serving motives in order to decide what statements to trust. For LLMs to be effective in the real world, they too must critically evaluate content by factoring in the motivations of the source--for instance, weighing the credibility of claims made in a sales pitch. In this paper, we undertake a comprehensive study of whether LLMs have this capacity for motivational vigilance.

Discrete diffusion models offer a flexible, controllable approach to structured sequence generation, yet they still lag behind causal language models in expressive power. A key limitation lies in their reliance on the Markovian assumption, which restricts each step to condition only on the current state, leading to potential uncorrectable error accumulation. In this paper, we introduce CaDDi (Causal Discrete Diffusion Model), a discrete diffusion model that conditions on the entire generative trajectory, thereby lifting the Markov constraint and allowing the model to revisit and improve past states. By unifying sequential (causal) and temporal (diffusion) reasoning in a single non-Markovian transformer, CaDDi also treats standard causal language models as a special case and permits the direct reuse of pretrained LLM weights with no architectural changes. Empirically, CaDDi outperforms state-of-the-art discrete diffusion baselines on natural-language benchmarks, substantially narrowing the remaining gap to large autoregressive transformers.

Despite its popularity in image synthesis, invisible generative watermarking remains largely underexplored in video generation. To address this gap, we propose Safe-Sora, the first framework to embed graphical watermarks directly into the video generation process. Motivated by the observation that watermarking performance is closely tied to the visual similarity between the watermark and cover content, we introduce a hierarchical coarse-to-fine adaptive matching mechanism. Specifically, the watermark image is divided into patches, each assigned to the most visually similar video frame, and further localized to the optimal spatial region for seamless embedding. To enable spatiotemporal fusion of watermark patches across video frames, we develop a 3D wavelet transform-enhanced Mamba architecture with a novel spatiotemporal local scanning strategy, effectively modeling long-range dependencies during watermark embedding and retrieval. To the best of our knowledge, this is the first attempt to apply state space models to watermarking, opening new avenues for efficient and robust watermark protection. Extensive experiments demonstrate that Safe-Sora achieves state-of-the-art performance in terms of video quality, watermark fidelity, and robustness, which is largely attributed to our proposals.