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Record W2995947286 · doi:10.1109/cwit.2019.8929896

Hierarchical coded matrix multiplication

2019· article· en· W2995947286 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldComputer Science
TopicStochastic Gradient Optimization Techniques
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsComputer scienceExploitMatrix multiplicationCloud computingCoding (social sciences)HierarchyMultiplication (music)Matrix (chemical analysis)Distributed computingTheoretical computer scienceComputer securityMathematicsOperating system

Abstract

fetched live from OpenAlex

Slow working nodes, known as stragglers, can greatly reduce the speed of distributed computation. Coded matrix multiplication is a recently introduced technique that enables straggler-resistant distributed multiplication of large matrices. A key property is that the finishing time depends only on the work completed by a set of the fastest workers, while the work done by the slowest workers is ignored completely. This paper is motivated by the observation that in real-world commercial cloud computing systems such as Amazon's Elastic Compute Cloud (EC2) the distinction between fast and slow nodes is often a soft one. Thus, if we could also exploit the work completed by stragglers we may realize substantial performance gains. To realize such gains, in this paper we use the idea of hierarchical coding (Ferdinand and Draper, IEEE Int. Symp. Inf. Theory, 2018). We decompose the overall matrix multiplication task into a hierarchy of heterogeneously sized subtasks. The duty to complete each subtask is shared amongst all workers and each subtask is (generally) of a different complexity. The motivation for the hierarchical decomposition is the recognition that more workers will finish the first subtask than the second (or third, forth, etc.). Connecting to error correction coding, earlier subtasks can therefore be designed to be of a higher rate than later subtasks. Through this hierarchical design our scheme exploits the work completed by stragglers, rather than ignoring it, even if that amount is much less than that completed by the fastest workers. We numerically show that our method realizes a 60% improvement in the expected finishing time for a widely studied statistical model of the speed of computation and, on Amazon EC2, the gain is 35%.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.975
Threshold uncertainty score0.574

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.011
GPT teacher head0.263
Teacher spread0.252 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it