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Recent work has shown that learned image compression strategies can outperform standard hand-crafted compression algorithms that have been developed over decades of intensive research on the rate-distortion trade-off. With growing…
We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
Product measures of dimension $n$ are known to be concentrated in Hamming distance: for any set $S$ in the product space of probability $\epsilon$, a random point in the space, with probability $1-\delta$, has a neighbor in $S$ that is…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
Embedding layers are commonly used to map discrete symbols into continuous embedding vectors that reflect their semantic meanings. Despite their effectiveness, the number of parameters in an embedding layer increases linearly with the…
Due to its remarkable energy compaction properties, the discrete cosine transform (DCT) is employed in a multitude of compression standards, such as JPEG and H.265/HEVC. Several low-complexity integer approximations for the DCT have been…
We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…
We introduce an algorithm to reduce large data sets using so-called digital nets, which are well distributed point sets in the unit cube. These point sets together with weights, which depend on the data set, are used to represent the data.…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
The quantification of visual aesthetics and complexity have a long history, the latter previously operationalized via the application of compression algorithms. Here we generalize and extend the compression approach beyond simple complexity…
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…
Real world re-identfication (ReID) algorithms aim to map new observations of an object to previously recorded instances. These systems are often constrained by quantity and size of the stored embeddings. To combat this scaling problem, we…
At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a…
The rise of internet has resulted in an explosion of data consisting of millions of articles, images, songs, and videos. Most of this data is high dimensional and sparse. The need to perform an efficient search for similar objects in such…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Computational molecular representations underpin virtual screening, property prediction, and materials discovery. Conventional fingerprints are efficient and deterministic but lose structural information through hash-based compression,…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…