Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very challenging. In addition, the objective functions adopted by existing hashing techniques are mostly chosen heuristically. In this paper, we propose a novel generative approach to learn hash functions through Minimum Description Length principle such that the learned hash codes maximally compress the dataset and can also be used to regenerate the inputs. We also develop an efficient learning algorithm based on the stochastic distributional gradient, which avoids the notorious difficulty caused by binary output constraints, to jointly optimize the parameters of the hash function and the associated generative model. Extensive experiments on a variety of large-scale datasets show that the proposed method achieves better retrieval results than the existing state-of-the-art methods. Search for similar items in web-scale datasets is a fundamental step in a number of applications, especially in image and document retrieval. Formally, given a reference dataset X = {x i } N i=1 with x ∈ X ⊂ R d , we want to retrieve similar items from X for a given query y according to some similarity measure sim(x, y). When the negative Euclidean distance is used, i.e., sim(x, y) = − x − y 2 , this corresponds to L 2 Nearest Neighbor Search (L2NNS) problem; when the inner product is used, i.e., sim(x, y) = x y, it becomes a Maximum Inner Product Search (MIPS) problem. In this work, we focus on L2NNS for simplicity, however our method handles MIPS problems as well, as shown in the supplementary material D. Brute-force linear search is expensive for large datasets. To alleviate the time and storage bottlenecks, two research directions have been studied extensively: (1) partition the dataset so that only a subset of data points is searched; (2) represent the data as codes so that similarity computation can be carried out more efficiently. The former often resorts to search-tree or bucket-based lookup; while the latter relies on binary hashing or quantization. These two groups of techniques are orthogonal and are typically employed together in practice. In this work, we focus on speeding up search via binary hashing. Hashing for similarity search was popularized by influential works such as Locality Sensitive Hashing (Indyk and Motwani, 1998; Gionis et al., 1999; Charikar , 2002) . The crux of binary hashing is to utilize a hash function, f (·) : X → {0, 1} l , which maps the original samples in X ∈ R d to l-bit binary vectors h ∈ {0, 1} l while preserving the similarity * Authors are equally contributed.
More recently, Stochastic Generative Hashing REF learns a generative hashing model based on the minimum description length principle, and uses stochastic distributional gradient descent to optimize the associated variational 1.
Stochastic Generative Hashing
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