arXiv subjects

Aedan Pope

Publications and source records attributed to Aedan Pope.

4 recordsLinked to original sources

arXiv2021

Launchpad: A Programming Model for Distributed Machine Learning Research

A major driver behind the success of modern machine learning algorithms has been their ability to process ever-larger amounts of data. As a result, the use of distributed systems in both research and production has become increasingly prevalent as a means to scale to this growing data. At the same time, however, distributing the learning process can drastically complicate the implementation of even simple algorithms. This is especially problematic as many machine learning practitioners are not well-versed in the design of distributed systems, let alone those that have complicated communication topologies. In this work we introduce Launchpad, a programming model that simplifies the process of defining and launching distributed systems that is specifically tailored towards a machine learning audience. We describe our framework, its design philosophy and implementation, and give a number of examples of common learning algorithms whose designs are greatly simplified by this approach.

cs.DC↗

arXiv2019

TF-Replicator: Distributed Machine Learning for Researchers

We describe TF-Replicator, a framework for distributed machine learning designed for DeepMind researchers and implemented as an abstraction over TensorFlow. TF-Replicator simplifies writing data-parallel and model-parallel research code. The same models can be effortlessly deployed to different cluster architectures (i.e. one or many machines containing CPUs, GPUs or TPU accelerators) using synchronous or asynchronous training regimes. To demonstrate the generality and scalability of TF-Replicator, we implement and benchmark three very different models: (1) A ResNet-50 for ImageNet classification, (2) a SN-GAN for class-conditional ImageNet image generation, and (3) a D4PG reinforcement learning agent for continuous control. Our results show strong scalability performance without demanding any distributed systems expertise of the user. The TF-Replicator programming model will be open-sourced as part of TensorFlow 2.0 (see https://github.com/tensorflow/community/pull/25).

cs.LG↗

arXiv2012

On Bounding the Diameter of the Commuting Graph of a Group

The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is conjectured by Jafarzadeh and Iranmanesh that there is a universal upper bound on the diameter of the commuting graphs of finite groups when the commuting graph is connected. In this paper we determine upper bounds on the diameter of the commuting graph for some classes of groups to rule them out as possible counterexamples to this conjecture. We also give an example of an infinite family of groups with trivial centre and diameter 6, the previously largest known diameter for an infinite family was 5 for $S_n$.

math.GR↗

arXiv2010

The diameters of commuting graphs of linear groups and matrix rings over the integers modulo m

The commuting graph of a group G, denoted by Gamma(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Z_m be the commutative ring of equivalence classes of integers modulo m. In this paper we investigate the connectivity and diameters of the commuting graphs of GL(n,Z_m) to contribute to the conjecture that there is a universal upper bound on diam(Gamma(G)) for any finite group G when Gamma(G) is connected. For any composite m, it is shown that Gamma(GL(n,Z_m)) and Gamma(M(n,Z_m)) are connected and diam(Gamma(GL(n,Z_m))) = diam(Gamma(M(n,Z_m))) = 3. For m a prime, the instances of connectedness and absolute bounds on the diameters of Gamma(GL(n,Z_m)) and Gamma(M(n,Z_m)) when they are connected are concluded from previous results.

math.GR↗