This study investigates the application of machine learning predictors for
min-entropy estimation in Random Number Generators (RNGs), a key component in
cryptographic applications where accurate entropy assessment is essential for
cybersecurity. Our research indicates that these predictors, and indeed any
predictor that leverages sequence correlations, primarily estimate average
min-entropy, a metric not extensively studied in this context. We explore the
relationship between average min-entropy and the traditional min-entropy,
focusing on their dependence on the number of target bits being predicted.
Utilizing data from Generalized Binary Autoregressive Models, a subset of
Markov processes, we demonstrate that machine learning models (including a
hybrid of convolutional and recurrent Long Short-Term Memory layers and the
transformer-based GPT-2 model) outperform traditional NIST SP 800-90B
predictors in certain scenarios. Our findings underscore the importance of
considering the number of target bits in min-entropy assessment for RNGs and
highlight the potential of machine learning approaches in enhancing entropy
estimation techniques for improved cryptographic security.

该研究探讨了机器学习预测在随机数生成器（RNGs）的最小熵估计中的应用，此为密码学应用的关键组件，准确的熵评估对于网络安全至关重要。研究结果表明，这些预测器主要估计平均最小熵，这是这一领域中未被广泛研究的指标，并通过研究平均最小熵与传统最小熵之间的关系，重点关注它们对目标位数的依赖性。通过利用广义二进制自回归模型的数据，展示了机器学习模型（包括卷积和循环长短期记忆层的混合模型以及基于 Transformer 的 GPT-2 模型）在某些情况下优于传统的 NIST SP 800-90B 预测器。我们的研究结果强调了对 RNGs 进行最小熵评估时考虑目标位数的重要性，并突显了机器学习方法在增强熵估计技术以提升密码学安全性方面的潜力。

用于最小熵估计的机器学习预测器

Machine Learning Predictors for Min-Entropy Estimation

Automated theorem provers and formal proof assistants are general reasoning
systems that are in theory capable of proving arbitrarily hard theorems, thus
solving arbitrary problems reducible to mathematics and logical reasoning. In
practice, such systems however face large combinatorial explosion, and
therefore include many heuristics and choice points that considerably influence
their performance. This is an opportunity for trained machine learning
predictors, which can guide the work of such reasoning systems. Conversely,
deductive search supported by the notion of logically valid proof allows one to
train machine learning systems on large reasoning corpora. Such bodies of proof
are usually correct by construction and when combined with more and more
precise trained guidance they can be boostrapped into very large corpora, with
increasingly long reasoning chains and possibly novel proof ideas. In this
paper we provide an overview of several automated reasoning and theorem proving
domains and the learning and AI methods that have been so far developed for
them. These include premise selection, proof guidance in several settings, AI
systems and feedback loops iterating between reasoning and learning, and
symbolic classification problems.

自动定理证明器和形式证明助手是理论上能够证明任意难题的一般推理系统，但在实践中面临组合爆炸所以包括很多启发式算法和选择点来影响系统性能。机器学习预测器可以引导这些推理系统的工作。本文概述了几个自动推理和定理证明领域及目前对它们进行的学习和人工智能方法，包括前提选择、证明引导、协同推理和学习的 AI 系统以及符号分类问题。

学习引导的自动推理：简要调查

Learning Guided Automated Reasoning: A Brief Survey

Collecting more diverse and representative training data is often touted as a
remedy for the disparate performance of machine learning predictors across
subpopulations. However, a precise framework for understanding how dataset
properties like diversity affect learning outcomes is largely lacking. By
casting data collection as part of the learning process, we demonstrate that
diverse representation in training data is key not only to increasing subgroup
performances, but also to achieving population level objectives. Our analysis
and experiments describe how dataset compositions influence performance and
provide constructive results for using trends in existing data, alongside
domain knowledge, to help guide intentional, objective-aware dataset design.

通过将数据收集视为学习过程的一部分，我们表明不仅多样化的训练数据可以提高子群体的性能，还可以实现人口水平的目标。我们的分析和实验描述了数据集组成如何影响性能，并提供了建设性的结果，以利用现有数据的趋势和领域知识，帮助指导有意识、具有目标意识的数据集设计。