基于理论指导的自编码器推荐系统中潜在激活函数选择
Theoretically informed selection of latent activation in autoencoder based recommender systems
AI总结：
本文通过理论分析确定自编码器编码器应具备的三个数学性质，证明ReLU和tanh无法同时满足，而sigmoid类激活函数更合适，为推荐系统超参数选择提供系统化方法。
摘要：
自编码器通过将稀疏高维数据蒸馏为稠密的低维潜在表示，可能有助于设计更准确且计算效率更高的推荐系统。然而，由于缺乏理论指导，设计这些系统仍然具有挑战性。本研究通过识别自编码器中的编码器应具备的三个关键数学性质来解决这一问题，以提高推荐准确性：（1）降维；（2）在点积比较中保持相似性排序；（3）保持非零向量。通过理论分析，我们证明了常见的激活函数（如ReLU和tanh）无法在可泛化的框架内共同满足这些性质。相比之下，类sigmoid激活函数成为潜在激活的合适选择。这种基于理论的方法为超参数选择提供了更系统化的方式，提高了模型设计的效率。
英文摘要：
Autoencoders may lend themselves to the design of more accurate and computationally efficient recommender systems by distilling sparse high-dimensional data into dense lower-dimensional latent representations. However, designing these systems remains challenging due to the lack of theoretical guidance. This work addresses this by identifying three key mathematical properties that the encoder in an autoencoder should exhibit to improve recommendation accuracy: (1) dimensionality reduction, (2) preservation of similarity ordering in dot product comparisons, and (3) preservation of non-zero vectors. Through theoretical analysis, we demonstrate that common activation functions, such as ReLU and tanh, cannot fulfill these properties jointly within a generalizable framework. In contrast, sigmoid-like activations emerge as suitable choices for latent activations. This theoretically informed approach offers a more systematic method for hyperparameter selection, enhancing the efficiency of model design.
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