Learning Ordered Representations with Nested Dropout
This work addresses the need for scalable and high-quality data retrieval and compression in machine learning, offering a novel method that improves upon existing techniques with specific performance gains.
The paper tackles the problem of learning ordered data representations where dimensions have varying importance by introducing nested dropout, a method that stochastically removes nested sets of hidden units. It demonstrates that this approach enables fast retrieval with logarithmic time complexity independent of dimensionality, allowing for longer codes without sacrificing speed, and shows applications in efficient data compression.
In this paper, we study ordered representations of data in which different dimensions have different degrees of importance. To learn these representations we introduce nested dropout, a procedure for stochastically removing coherent nested sets of hidden units in a neural network. We first present a sequence of theoretical results in the simple case of a semi-linear autoencoder. We rigorously show that the application of nested dropout enforces identifiability of the units, which leads to an exact equivalence with PCA. We then extend the algorithm to deep models and demonstrate the relevance of ordered representations to a number of applications. Specifically, we use the ordered property of the learned codes to construct hash-based data structures that permit very fast retrieval, achieving retrieval in time logarithmic in the database size and independent of the dimensionality of the representation. This allows codes that are hundreds of times longer than currently feasible for retrieval. We therefore avoid the diminished quality associated with short codes, while still performing retrieval that is competitive in speed with existing methods. We also show that ordered representations are a promising way to learn adaptive compression for efficient online data reconstruction.