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人工智能论文:论集合上函数表示的局限性(On the Limitations of Representing Functions on Sets)

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632956335 发表于 2019-1-28 10:57:19 | 显示全部楼层 |阅读模式
632956335 2019-1-28 10:57:19 164 0 显示全部楼层
人工智能论文:论集合上函数表示的局限性(On the Limitations of Representing Functions on Sets)最近关于集合上函数表示的工作考虑了在潜在空间中使用求和来强制置换不变性。特别是,有人推测,随着所考虑的集合的基数增加,这个潜在空间的维度可能会保持不变。但是,我们证明导致这种猜想的分析需要高度不连续的映射,并认为这仅仅是有限的实际用途。 。在这种观察的启发下,我们证明了通过连续映射(例如由神经网络或高斯过程提供)实现该模型实际上对该空间的维度施加了约束。用于设定输入的实际通用函数表示通常至少具有输入元素的最大数量的大小的潜在维度来实现。
Recent work on the representation of functions on sets has considered the useof summation in a latent space to enforce permutation invariance.Inparticular, it has been conjectured that the dimension of this latent space mayremain fixed as the cardinality of the sets under consideration increases.However, we demonstrate that the analysis leading to this conjecture requiresmappings which are highly discontinuous and argue that this is only of limitedpractical use.Motivated by this observation, we prove that an implementationof this model via continuous mappings (as provided by e.g. neural networks orGaussian processes) actually imposes a constraint on the dimensionality of thelatent space.Practical universal function representation for set inputs canonly be achieved with a latent dimension at least the size of the maximumnumber of input elements.人工智能论文:论集合上函数表示的局限性(On the Limitations of Representing Functions on Sets) nefZXqAA6pb2EIAv.jpg
URL地址:https://arxiv.org/abs/1901.09006     ----pdf下载地址:https://arxiv.org/pdf/1901.09006    ----人工智能论文:论集合上函数表示的局限性(On the Limitations of Representing Functions on Sets)
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