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We obtain an analytic, interpretable and predictive theory of creativity in convolutional diffusion models. Indeed, score-matching diffusion models can generate highly original images that lie far from their training data. However, optimal score-matching theory suggests that these models should only be able to produce memorized training examples. To reconcile this theory-experiment gap, we identify two simple inductive biases, locality and equivariance, that: (1) induce a form of combinatorial creativity by preventing optimal score-matching; (2) result in fully analytic, completely mechanistically interpretable, local score (LS) and equivariant local score (ELS) machines that, (3) after calibrating a single time-dependent hyperparameter can quantitatively predict the outputs of trained convolution only diffusion models (like ResNets and UNets) with high accuracy (median $r^2$ of $0.95, 0.94, 0.94, 0.96$ for our top model on CIFAR10, FashionMNIST, MNIST, and CelebA). Our model reveals a {\it locally consistent patch mosaic} mechanism of creativity, in which diffusion models create exponentially many novel images by mixing and matching different local training set patches at different scales and image locations. Our theory also partially predicts the outputs of pre-trained self-attention enabled UNets (median $r^2 \sim 0.77$ on CIFAR10), revealing an intriguing role for attention in carving out semantic coherence from local patch mosaics.

Leveraging Multi-modal Large Language Models (MLLMs) to create embodied agents offers a promising avenue for tackling real-world tasks. While language-centric embodied agents have garnered substantial attention, MLLM-based embodied agents remain underexplored due to the lack of comprehensive evaluation frameworks. To bridge this gap, we introduce EmbodiedBench, an extensive benchmark designed to evaluate vision-driven embodied agents. EmbodiedBench features: (1) a diverse set of 1,128 testing tasks across four environments, ranging from high-level semantic tasks (e.g., household) to low-level tasks involving atomic actions (e.g., navigation and manipulation); and (2) six meticulously curated subsets evaluating essential agent capabilities like commonsense reasoning, complex instruction understanding, spatial awareness, visual perception, and long-term planning. Through extensive experiments, we evaluated 24 leading proprietary and open-source MLLMs within EmbodiedBench. Our findings reveal that: MLLMs excel at high-level tasks but struggle with low-level manipulation, with the best model, GPT-4o, scoring only $28.9\%$ on average. EmbodiedBench provides a multifaceted standardized evaluation platform that not only highlights existing challenges but also offers valuable insights to advance MLLM-based embodied agents. Our code and dataset are available at [https://embodiedbench.github.io](https://embodiedbench.github.io).

Large Language Model (LLM)-empowered multi-agent systems extend the cognitive boundaries of individual agents through disciplined collaboration and interaction, while constructing these systems often requires labor-intensive manual designs. Despite the availability of methods to automate the design of agentic workflows, they typically seek to identify a static, complex, one-size-fits-all system, which, however, fails to dynamically allocate inference resources based on the difficulty and domain of each query. To address this challenge, we shift away from the pursuit of a monolithic agentic system, instead optimizing the agentic supernet, a probabilistic and continuous distribution of agentic architectures. We introduce MaAS, an automated framework that samples query-dependent agentic systems from the supernet, delivering high-quality solutions and tailored resource allocation (e.g., LLM calls, tool calls, token cost). Comprehensive evaluation across six benchmarks demonstrates that MaAS (I) requires only $6\\sim45\%$ of the inference costs of existing handcrafted or automated multi-agent systems, (II) surpasses them by $0.54\%\sim11.82\%$, and (III) enjoys superior cross-dataset and cross-LLM-backbone transferability.

Knowledge Distillation (KD) transfers knowledge from a large teacher model to a smaller student model by minimizing the divergence between their output distributions, typically using forward Kullback-Leibler divergence (FKLD) or reverse KLD (RKLD). It has become an effective training paradigm due to the broader supervision information provided by the teacher distribution compared to one-hot labels. We identify that the core challenge in KD lies in balancing two mode-concentration effects: the Hardness-Concentration effect, which refers to focusing on modes with large errors, and the Confidence-Concentration effect, which refers to focusing on modes with high student confidence. Through an analysis of how probabilities are reassigned during gradient updates, we observe that these two effects are entangled in FKLD and RKLD, but in extreme forms. Specifically, both are too weak in FKLD, causing the student to fail to concentrate on the target class. In contrast, both are too strong in RKLD, causing the student to overly emphasize the target class while ignoring the broader distributional information from the teacher. To address this imbalance, we propose ABKD, a generic framework with $\alpha$-$\beta$-divergence. Our theoretical results show that ABKD offers a smooth interpolation between FKLD and RKLD, achieving a better trade-off between these effects. Extensive experiments on 17 language/vision datasets with 12 teacher-student settings confirm its efficacy.

We propose a *history-driven target (HDT)* framework in Markov Chain Monte Carlo (MCMC) to improve any random walk algorithm on discrete state spaces, such as general undirected graphs, for efficient sampling from target distribution $\\boldsymbol{\\mu}$. With broad applications in network science and distributed optimization, recent innovations like the self-repellent random walk (SRRW) achieve near-zero variance by prioritizing under-sampled states through transition kernel modifications based on past visit frequencies. However, SRRW's reliance on explicit computation of transition probabilities for all neighbors at each step introduces substantial computational overhead, while its strict dependence on time-reversible Markov chains excludes advanced non-reversible MCMC methods. To overcome these limitations, instead of direct modification of transition kernel, HDT introduces a history-dependent target distribution $\\boldsymbol{\\pi}[\\mathbf{x}]$ to replace the original target $\\boldsymbol{\\mu}$ in any graph sampler, where $\\mathbf{x}$ represents the empirical measure of past visits. This design preserves lightweight implementation by requiring only local information between the current and proposed states and achieves compatibility with both reversible and non-reversible MCMC samplers, while retaining unbiased samples with target distribution $\\boldsymbol{\\mu}$ and near-zero variance performance. Extensive experiments in graph sampling demonstrate consistent performance gains, and a memory-efficient Least Recently Used (LRU) cache ensures scalability to large general graphs.

In this work, we argue that large language models (LLMs), though trained to predict only the next token, exhibit emergent planning behaviors: $their hidden representations encode future outputs beyond the next token$. Through simple probing, we demonstrate that LLM prompt representations encode global attributes of their entire responses, including $structure attributes$ (e.g., response length, reasoning steps), $content attributes$ (e.g., character choices in storywriting, multiple-choice answers at the end of response), and $behavior attributes$ (e.g., answer confidence, factual consistency). In addition to identifying response planning, we explore how it scales with model size across tasks and how it evolves during generation. The findings that LLMs plan ahead for the future in their hidden representations suggest potential applications for improving transparency and generation control.