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arXiv 2305.01034cs.LGcs.AIstat.ML
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泛化难度的模型无关度量

Model-agnostic Measure of Generalization Difficulty

Massachusetts Institute of Technology(麻省理工学院)

Akhilan Boopathy, Kevin Liu, Jaedong Hwang, Shu Ge, Asaad Mohammedsaleh, Ila Fiete

AI总结:

本文提出首个模型无关的归纳偏置复杂度度量,通过拟合训练数据且可泛化假设的体积比例量化任务固有难度,可统一比较监督、强化与元学习。

摘要:

衡量机器学习算法的标准,是它所能执行任务的难度,而足够困难的任务是推动强大机器学习模型发展的关键因素。然而,量化机器学习基准测试的泛化难度一直具有挑战性。据我们所知,我们提出了首个针对任务固有泛化难度的模型无关度量。我们的归纳偏置复杂度度量量化了在任务上良好泛化所需的总信息减去数据所提供的信息。其实现方式是:在给定假设能够拟合训练数据的条件下,测量能够在该任务上泛化的假设所占据的体积比例。该度量随模型必须在其上进行泛化的空间的内蕴维度呈指数级缩放,但仅随每个维度的分辨率呈多项式级缩放,这表明需要在许多维度上泛化的任务,远比在较少维度中涉及更多细节的任务困难得多。我们的度量可用于计算并相互比较监督学习、强化学习和元学习的泛化难度。我们表明,在实证应用中,它形式化地量化了直觉上预期的趋势,例如就所需归纳偏置而言,MNIST < CIFAR10 < Imagenet,且完全可观测 Markov 决策过程(MDP)< 部分可观测 MDP。此外,我们表明复杂图像分类 < 使用简单图像的少样本元学习。我们的度量提供了一个定量指标,可指导构建需要更大归纳偏置的更复杂任务,从而促进开发具有更强泛化能力的更复杂架构和学习算法。

英文摘要:

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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