Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cs/9408101

Random Worlds and Maximum Entropy

A. J. Grove·J. Y. Halpern·D. Koller
View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a knowledge base KB containing first-order and statistical facts, we consider a principled method, called the random-worlds method, for computing a degree of belief that some formula Phi holds given KB. If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or first-order models, with domain {1,...,N} that satisfy KB, and compute the fraction of them in which Phi is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying Phi and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximum-entropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are the limitations on its scope. Most importantly, the restriction to unary predicates seems necessary. Although the random-worlds method makes sense in general, the connection to maximum entropy seems to disappear in the non-unary case. These observations suggest unexpected limitations to the applicability of maximum-entropy methods.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

A. J. Grove, J. Y. Halpern, D. Koller. 1994-08-01. Random Worlds and Maximum Entropy. https://arxiv.org/abs/cs/9408101

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Invert4TVG: A Temporal Video Grounding Framework with Inversion Tasks Preserving Action Understanding Ability

Temporal Video Grounding (TVG) aims to localize video segments corresponding to a given textual query, which often describes human actions. However, we observe that current methods, usually optimizing for high temporal Intersection-over-Union (IoU), frequently struggle to accurately recognize or understand the underlying actions in both the video and query, thus reducing the effectiveness of these methods. To address this, we propose a novel TVG framework that integrates inversion-based TVG as auxiliary objectives to maintain the model's action understanding ability. We introduce three kinds of inversion TVG tasks derived from the original TVG annotations: (1) Verb Completion, predicting masked verbs (actions) in queries given video segments; (2) Action Recognition, identifying query-described actions; and (3) Video Description, generating descriptions containing query-relevant actions given video segments. These inversion tasks are entirely derived from the original TVG tasks and are probabilistically integrated with them within a reinforcement learning framework. By leveraging carefully designed reward functions, the model preserves its ability to understand actions, thereby improving the accuracy of temporal grounding. Experiments show our method outperforms state-of-the-art approaches, achieving a 7.1\% improvement in R1@0.7 on Charades-STA for a 3B model.

cs.AI↗
arXiv2026

Pharos-ESG: A Framework for Multimodal Parsing, Contextual Narration, and Hierarchical Labeling of ESG Report

Environmental, Social, and Governance (ESG) principles are reshaping the foundations of global financial governance, transforming capital allocation architectures, regulatory frameworks, and systemic risk coordination mechanisms. However, as the core medium for assessing corporate ESG performance, the ESG reports present significant challenges for large-scale understanding, due to chaotic reading order from slide-like irregular layouts and implicit hierarchies arising from lengthy, weakly structured content. To address these challenges, we propose Pharos-ESG, a unified framework that transforms ESG reports into structured representations through multimodal parsing, contextual narration, and hierarchical labeling. It integrates a reading-order modeling module based on layout flow, hierarchy-aware segmentation guided by table-of-contents anchors, and a multi-modal aggregation pipeline that contextually transforms visual elements into coherent natural language. The framework further enriches its outputs with ESG, GRI, and sentiment labels, yielding annotations aligned with the analytical demands of financial research. Extensive experiments on annotated benchmarks demonstrate that Pharos-ESG consistently outperforms both dedicated document parsing systems and general-purpose multimodal models. In addition, we release Aurora-ESG, the first large-scale public dataset of ESG reports, spanning Mainland China, Hong Kong, and U.S. markets, featuring unified structured representations of multi-modal content, enriched with fine-grained layout and semantic annotations to better support ESG integration in financial governance and decision-making.

cs.AI↗
arXiv2026

PRISM: Pushing the Frontier of Deep Think via Process Reward Model-Guided Inference

DEEPTHINK methods improve reasoning by generating, refining, and aggregating populations of candidate solutions, which enables strong performance on complex mathematical and scientific tasks. However, existing frameworks can still suffer from unreliable correctness signals during inference, which creates a population- enhancement bottleneck where deeper deliberation amplifies errors, suppresses correct minority solutions, and yields weak returns to additional compute. In this paper, we introduce a functional decomposition of DEEPTHINK systems and propose PRISM, a Process Reward Model (PRM)-guided inference algorithm that uses step-level verification to guide resampling, proposal acceptance, and solution aggregation. During refinement, PRISM uses PRM scores to guide population resampling and stochastic local refinement, which concentrates computation on higher-quality reasoning while preserving diversity. When paired with PRM- score-vote, a PRM-guided aggregation method, PRISM is competitive with or outperforms existing DEEPTHINK methods, reaching 90.0%, 75.4%, and 71.4% with gpt-oss-20b on AIME25, HMMT25, and GPQA Diamond, respectively, while exceeding gpt-oss-120b. Additionally, our analysis shows that PRISM produces consistent net-directional correction during refinement and maintains competitive accuracy when the initial population contains few correct candidates.

cs.AI↗