We study the problem of multiclass learning with bandit feedback in both the i.i.d.

The simple linear threshold units used in many artificial neural networks have a limited computational capacity. Famously, a single unit cannot handle nonlinearly separable problems like XOR. In contrast, real neurons exhibit complex morphologies as well as active dendritic integration, suggesting that their computational capacities outperform those of simple linear units. Considering specific families of Boolean functions, we empirically examine the computational limits of single units that incorporate more complex dendritic structures. For random Boolean functions, we show that there is a phase transition in learnability as a function of the input dimension, with most random functions below a certain critical dimension being learnable and those above not.

A full understanding of the behavior of a large language model (LLM) requires our grasp of its input token space. If this space differs from our assumptions, our comprehension of and conclusions about the LLM will likely be flawed.

World models, which explicitly learn environmental dynamics to lay the foundation for planning, reasoning, and decision-making, are rapidly advancing in predicting both physical dynamics and aspects of social behavior, yet predominantly in separate silos. This division results in a systemic failure to model the crucial interplay between physical environments and social constructs, rendering current models fundamentally incapable of adequately addressing the true complexity of real-world systems where physical and social realities are inextricably intertwined. This position paper argues that the systematic, bidirectional unification of physical and social predictive capabilities is the next crucial frontier for world model development. We contend that comprehensive world models must holistically integrate objective physical laws with the subjective, evolving, and context-dependent nature of social dynamics. Such unification is paramount for AI to robustly navigate complex real-world challenges and achieve more generalizable intelligence.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty -- often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NESYDMS), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols.

Cinematography, the fundamental visual language of film, is essential for conveying narrative, emotion, and aesthetic quality. While recent Vision-Language Models (VLMs) demonstrate strong general visual understanding, their proficiency in comprehending the nuanced cinematic grammar embedded within individual shots remains largely unexplored and lacks robust evaluation.

We study the sublinear multivariate mean estimation problem in d-dimensional Euclidean space. Specifically, we aim to find the mean µ of a ground point set A, which minimizes the sum of squared Euclidean distances of the points in Ato µ. We first show that a multiplicative (1 + ε) approximation to µ can be found with probability 1 δ using O(ε 1 logδ 1)many independent uniform random samples, and provide a matching lower bound. Furthermore, we give two estimators with optimal sample complexity that can be computed in optimal running time for extracting a suitable approximate mean: 1.

Generating realistic graphs faces challenges in estimating accurate distribution of graphs in an embedding space while preserving structural characteristics. However, existing graph generation methods primarily focus on approximating the joint distribution of nodes and edges, often overlooking topological properties such as connected components and loops, hindering accurate representation of global structures. To address this issue, we propose a Topology-Aware diffusion-based Graph Generation (TAGG), which aims to sample synthetic graphs that closely resemble the structural characteristics of the original graph based on persistent homology. Specifically, we suggest two core components: 1) Persistence Diagram Matching (PDM) loss which ensures high topological fidelity of generated graphs, and 2) Topology-aware Attention Module (TAM) which induces the denoising network to capture the homological characteristics of the original graphs. Extensive experiments on conventional graph benchmarks demonstrate the effectiveness of our approach indicating high generation performance across various metrics, while achieving closer alignment with the distribution of topological features observed in the original graphs.

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the text8 and tokenized ImageNet 256 256datasets, our informed corrector consistently produces superior samples with fewer errors or improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion. Our code is available at https://github.

Hybrid language models that combine Attention and State Space Models (SSMs) have been shown to achieve state-of-the-art accuracy and runtime performance. Recent work has also demonstrated that applying pruning and distillation to Attentiononly models yields smaller, more accurate models at a fraction of the training cost. In this work, we explore the effectiveness of compressing Hybrid architectures. To this end, we introduce a novel group-aware pruning method for Mamba layers that preserves the structural integrity of SSM blocks and their sequence modeling capabilities. We combine this method with FFN, embedding dimension, and layer pruning, along with knowledge distillation-based retraining to obtain a unified compression recipe for hybrid models. Using this recipe, we compress the Nemotron-H 8BHybrid model down to 4B parameters with up to 40 fewer training tokens compared to similarly-sized models.