Pebbles, Graphs, and a Pinch of Combinatorics

Kwasniewski, Grzegorz; Ben-Nun, Tal; Gianinazzi, Lukas; Calotoiu, Alexandru; Schneider, Timo; Ziogas, Alexandros Nikolaos; Besta, Maciej; Hoefler, Torsten

doi:10.1145/3409964.3461796

Cited by 13 publications

(4 citation statements)

References 31 publications

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“…The data locality accounts for these algorithmic limitations and is defined as the ratio of the I/O lower bound Q of the algorithm and the measured transferred bytes from main memory D, in short, 𝑄 𝐷 . Q is estimated automatically by SOAP-Analysis [39], which is based on the concept of the Red-Blue Pebble Game [36].…”

Section: Performance Similaritymentioning

confidence: 99%

Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization

Trumper¹,

Ben-Nun²,

Philipp³

et al. 2023

Preprint

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Performance optimization is an increasingly challenging but often repetitive task. While each platform has its quirks, the underlying code transformations rely on data movement and computational characteristics that recur across applications. This paper proposes to leverage those similarities by constructing an embedding space for subprograms. The continuous space captures both static and dynamic properties of loop nests via symbolic code analysis and performance profiling, respectively. Performance embeddings enable direct knowledge transfer of performance tuning between applications, which can result from autotuning or tailored improvements. We demonstrate this transfer tuning approach on case studies in deep neural networks, dense and sparse linear algebra compositions, and numerical weather prediction stencils. Transfer tuning reduces the search complexity by up to four orders of magnitude and outperforms the MKL library in sparse-dense matrix multiplication. The results exhibit clear correspondences between program characteristics and optimizations, outperforming prior specialized state-of-the-art approaches and generalizing beyond their capabilities.

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Section: Performance Similaritymentioning

confidence: 99%

Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization

Trumper¹,

Ben-Nun²,

Philipp³

et al. 2023

Preprint

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“…The pros include using less memory and power and also they are the less iteration to converge to the consensus solution and easiness to configure the complete mathematical model as per the requirement [12]. ) communicated elements per processor -only 1/3× over our established lower bound, which would be considered as a massive speedup [13]. Through another one, the authors show, that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method.…”

Section: -Related Workmentioning

confidence: 99%

Representing a Novel Expanded Version of Shor’s Algorithm and a Real-Time Experiment using IBM Q-Experience Platform

Goodarzi¹,

Rezakhani²,

Ghotbi-Maleki³

2023

jist

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The data are stored on the memory of the classical computer in small units of classical bits, which could be either 0 or 1. However, on a Quantum Computer, The Quantum States of each Quantum Bit (Qbit), would be every possible number between 0 and 1, including themselves. By placing the photons on a special state, which is a spot located at the middle of the two-dimensional space vectors ( ) and ( ) on the Unit Circle, which is called Superposition and we can take advantage of properties of this state when we place lots of vectors of N-dimensional spaces in superposition and we can do a parallelization and factorization for getting significant speedup. In fact, in Quantum Computing we are taking advantage of Quantum Dynamic Principles to process the data, which Classical Computers lack on, by considering the limitations of logical concepts behind them. Through this paper, we expand a quantum algorithm for the number of n Qbits in a new way and by implementing circuits using IBM-Q Experience, we are going to have some practical results, which are more obvious to be demonstrable. By expanding the Quantum Algorithms and using Linear Algebra, we can manage to achieve the goals at a higher level, the ones that Classical Computers are unable to perform, as machine learning problems with complicated models and by expanding the subject we can mention majors in different sciences like Chemistry (predicting the Structure of proteins with higher percentage accuracy in less period), Astronomy and so on.

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“…Global Formulations for HOGNNs. There have been efforts into building global formulations for GNNs [23], [39], [46], [235] and general graph computing [42], [45], [64]- [68], [107], [145], [146], [153], [220], [259]. This facilitates applying mechanisms such as communication avoidance or vectorization [154], [155], [221], [222].…”

Section: 𝑂(|𝐸|)mentioning

confidence: 99%

Motif Prediction with Graph Neural Networks

Besta¹,

Grob²,

Miglioli³

et al. 2022

Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

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Link prediction is one of the central problems in graph mining. However, recent studies highlight the importance of higher-order network analysis, where complex structures called motifs are the first-class citizens. We first show that existing link prediction schemes fail to effectively predict motifs. To alleviate this, we establish a general motif prediction problem and we propose several heuristics that assess the chances for a specified motif to appear. To make the scores realistic, our heuristics consider -among others -correlations between links, i.e., the potential impact of some arriving links on the appearance of other links in a given motif. Finally, for highest accuracy, we develop a graph neural network (GNN) architecture for motif prediction. Our architecture offers vertex features and sampling schemes that capture the rich structural properties of motifs. While our heuristics are fast and do not need any training, GNNs ensure highest accuracy of predicting motifs, both for dense (e.g., 𝑘-cliques) and for sparse ones (e.g., 𝑘-stars). We consistently outperform the best available competitor by more than 10% on average and up to 32% in area under the curve. Importantly, the advantages of our approach over schemes based on uncorrelated link prediction increase with the increasing motif size and complexity. We also successfully apply our architecture for predicting more arbitrary clusters and communities, illustrating its potential for graph mining beyond motif analysis. CCS CONCEPTS• Information systems → Data mining.

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Pebbles, Graphs, and a Pinch of Combinatorics

Cited by 13 publications

References 31 publications

Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization

Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization

Representing a Novel Expanded Version of Shor’s Algorithm and a Real-Time Experiment using IBM Q-Experience Platform

Motif Prediction with Graph Neural Networks

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