Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRecursive n-gram hashing is pairwise independent, at best
205
0
0.0
(
0
)
Added by
Daniel Lemire
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Many applications use sequences of n consecutive symbols (n-grams). Hashing these n-grams can be a performance bottleneck. For more speed, recursive hash families compute hash values by updating previous values. We prove that recursive hash families cannot be more than pairwise independent. While hashing by irreducible polynomials is pairwise independent, our implementations either run in time O(n) or use an exponential amount of memory. As a more scalable alternative, we make hashing by cyclic polynomials pairwise independent by ignoring n-1 bits. Experimentally, we show that hashing by cyclic polynomials is is twice as fast as hashing by irreducible polynomials. We also show that randomized Karp-Rabin hash families are not pairwise independent.
rate research
Read More
Semantic Hashing is a popular family of methods for efficient similarity search in large-scale datasets. In Semantic Hashing, documents are encoded as short binary vectors (i.e., hash codes), such that semantic similarity can be efficiently computed using the Hamming distance. Recent state-of-the-art approaches have utilized weak supervision to train better performing hashing models. Inspired by this, we present Semantic Hashing with Pairwise Reconstruction (PairRec), which is a discrete variational autoencoder based hashing model. PairRec first encodes weakly supervised training pairs (a query document and a semantically similar document) into two hash codes, and then learns to reconstruct the same query document from both of these hash codes (i.e., pairwise reconstruction). This pairwise reconstruction enables our model to encode local neighbourhood structures within the hash code directly through the decoder. We experimentally compare PairRec to traditional and state-of-the-art approaches, and obtain significant performance improvements in the task of document similarity search.
We present fast strongly universal string hashing families: they can process data at a rate of 0.2 CPU cycle per byte. Maybe surprisingly, we find that these families---though they require a large buffer of random numbers---are often faster than popular hash functions with weaker theoretical guarantees. Moreover, conventional wisdom is that hash functions with fewer multiplications are faster. Yet we find that they may fail to be faster due to operation pipelining. We present experimental results on several processors including low-powered processors. Our tests include hash functions designed for processors with the Carry-Less Multiplication (CLMUL) instruction set. We also prove, using accessible proofs, the strong universality of our families.
Motivated by the fact that most of the information relevant to the prediction of target tokens is drawn from the source sentence $S=s_1, ldots, s_S$, we propose truncating the target-side window used for computing self-attention by making an $N$-gram assumption. Experiments on WMT EnDe and EnFr data sets show that the $N$-gram masked self-attention model loses very little in BLEU score for $N$ values in the range $4, ldots, 8$, depending on the task.
A minimal perfect hash function bijectively maps a key set $S$ out of a universe $U$ into the first $|S|$ natural numbers. Minimal perfect hash functions are used, for example, to map irregularly-shaped keys, such as string, in a compact space so that metadata can then be simply stored in an array. While it is known that just $1.44$ bits per key are necessary to store a minimal perfect function, no published technique can go below $2$ bits per key in practice. We propose a new technique for storing minimal perfect hash functions with expected linear construction time and expected constant lookup time that makes it possible to build for the first time, for example, structures which need $1.56$ bits per key, that is, within $8.3$% of the lower bound, in less than $2$ ms per key. We show that instances of our construction are able to simultaneously beat the construction time, space usage and lookup time of the state-of-the-art data structure reaching $2$ bits per key. Moreover, we provide parameter choices giving structures which are competitive with alternative, larger-size data structures in terms of space and lookup time. The construction of our data structures can be easily parallelized or mapped on distributed computational units (e.g., within the MapReduce framework), and structures larger than the available RAM can be directly built in mass storage.
Binary Hashing is widely used for effective approximate nearest neighbors search. Even though various binary hashing methods have been proposed, very few methods are feasible for extremely high-dimensional features often used in visual tasks today. We propose a novel highly sparse linear hashing method based on pairwise rotations. The encoding cost of the proposed algorithm is $mathrm{O}(n log n)$ for n-dimensional features, whereas that of the existing state-of-the-art method is typically $mathrm{O}(n^2)$. The proposed method is also remarkably faster in the learning phase. Along with the efficiency, the retrieval accuracy is comparable to or slightly outperforming the state-of-the-art. Pairwise rotations used in our method are formulated from an analytical study of the trade-off relationship between quantization error and entropy of binary codes. Although these hashing criteria are widely used in previous researches, its analytical behavior is rarely studied. All building blocks of our algorithm are based on the analytical solution, and it thus provides a fairly simple and efficient procedure.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
