Hayden Jananthan

Christian Prothmann, Vijay Gadepally, Jeremy Kepner et al.

The DAF-MIT AI Accelerator is a collaboration between the United States Department of the Air Force (DAF) and the Massachusetts Institute of Technology (MIT). This program pioneers fundamental advances in artificial intelligence (AI) to expand the competitive advantage of the United States in the defense and civilian sectors. In recent years, AI Accelerator projects have developed and launched public challenge problems aimed at advancing AI research in priority areas. Hallmarks of AI Accelerator challenges include large, publicly available, and AI-ready datasets to stimulate open-source solutions and engage the wider academic and private sector AI ecosystem. This article supplements our previous publication, which introduced AI Accelerator challenges. We provide an update on how ongoing and new challenges have successfully contributed to AI research and applications of AI technologies.

Kevin Kwak, Zack West, Hayden Jananthan et al.

The exponential growth of data has sparked computational demands on ML research and industry use. Sparsification of hyper-parametrized deep neural networks (DNNs) creates simpler representations of complex data. Past research has shown that some sparse networks achieve similar performance as dense ones, reducing runtime and storage. RadiX-Nets, a subgroup of sparse DNNs, maintain uniformity which counteracts their lack of neural connections. Generation, independent of a dense network, yields faster asymptotic training and removes the need for costly pruning. However, little work has been done on RadiX-Nets, making testing challenging. This paper presents a testing suite for RadiX-Nets in TensorFlow. We test RadiX-Net performance to streamline processing in scalable models, revealing relationships between network topology, initialization, and training behavior. We also encounter "strange models" that train inconsistently and to lower accuracy while models of similar sparsity train well.

Elena Baskakova, William Bergeron, Matthew Hubbell et al.

Supercomputers are complex, dynamic systems that serve thousands of users and are built with thousands of compute nodes. Due to the vast amounts of system and performance data needed to accurately capture their status, supercomputers require complex methods to monitor, maintain, and optimize. Data visualization is a powerful technique for overseeing these large streams of data in an easily interpretable way. The MIT Lincoln Laboratory Supercomputing Center (LLSC) enables effective monitoring through combining 3D gaming technology with compound data streams in the TX-Digital Twin, a 3D simulation of the supercomputer. The TX-Digital Twin offers both live and historical data, in visual and text formats, and tracks a multitude of revealing performance metrics. Recent increasing interest in GPU-accelerated computing has driven a need for monitoring and maintenance of GPU-accelerated resources in supercomputers. In this paper, we build on our previous solution by integrating the visualization of additional GPU metrics, such as GPU memory usage, temperature, and power draw, into the TX-Digital Twin. Using techniques in draw call optimization, we add clear and effective displays of the new metrics while keeping the effects on performance minimal.

Jonathan Kogan, Hayden Jananthan, Jeremy Kepner

We study the expressivity of one-dimensional (1D) ReLU deep neural networks through the lens of their linear regions. For randomly initialized, fully connected 1D ReLU networks (He scaling with nonzero bias) in the infinite-width limit, we prove that the expected number of linear regions grows as $\sum_{i = 1}^L n_i + \mathop{o}\left(\sum_{i = 1}^L{n_i}\right) + 1$, where $n_\ell$ denotes the number of neurons in the $\ell$-th hidden layer. We also propose a function-adaptive notion of sparsity that compares the expected regions used by the network to the minimal number needed to approximate a target within a fixed tolerance.

Hayden Jananthan

In this dissertation we examine the relationships between the several hierarchies, including the complexity, $\mathrm{LUA}$ (Linearly Universal Avoidance), and shift complexity hierarchies, with an eye towards quantitative bounds on growth rates therein. We show that for suitable $f$ and $p$, there are $q$ and $g$ such that $\mathrm{LUA}(q) \leq_\mathrm{s} \mathrm{COMPLEX}(f)$ and $\mathrm{COMPLEX}(g) \leq_\mathrm{s} \mathrm{LUA}(p)$, as well as quantify the growth rates of $q$ and $g$. In the opposite direction, we show that for certain sub-identical $f$ satisfying $\lim_{n \to \infty}{f(n)/n}=1$ there is a $q$ such that $\mathrm{COMPLEX}(f) \leq_\mathrm{w} \mathrm{LUA}(q)$, and for certain fast-growing $p$ there is a $g$ such that $\mathrm{LUA}(p) \leq_\mathrm{s} \mathrm{COMPLEX}(g)$, as well as quantify the growth rates of $q$ and $g$. Concerning shift complexity, explicit bounds are given on how slow-growing $q$ must be for any member of $\rm{LUA}(q)$ to compute $δ$-shift complex sequences. Motivated by the complexity hierarchy, we generalize the notion of shift complexity to consider sequences $X$ satisfying $\operatorname{KP}(τ) \geq f(|τ|) - O(1)$ for all substrings $τ$ of $X$ where $f$ is any order function. We show that for sufficiently slow-growing $f$, $f$-shift complex sequences can be uniformly computed by $g$-complex sequences, where $g$ grows slightly faster than $f$. The structure of the $\mathrm{LUA}$ hierarchy is examined using bushy tree forcing, with the main result being that for any order function $p$, there is a slow-growing order function $q$ such that $\mathrm{LUA}(p)$ and $\mathrm{LUA}(q)$ are weakly incomparable. Using this, we prove new results about the filter of the weak degrees of deep nonempty $Π^0_1$ classes and the connection between the shift complexity and $\mathrm{LUA}$ hierarchies.

William Cashman, Chasen Milner, Michael Houle et al.

AI development requires high fidelity testing environments to effectively transition from the laboratory to operations. The flexibility offered by cyber arenas presents a novel opportunity to test new artificial intelligence (AI) capabilities with users. Cyber arenas are designed to expose end-users to real-world situations and must rapidly incorporate evolving capabilities to meet their core objectives. To explore this concept the MIT/IEEE/Amazon Graph Challenge Anonymized Network Sensor was deployed in a cyber arena during a National Guard exercise.

Jeremy Kepner, Timothy Davis, Vijay Gadepally et al.

Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data supported by continuous streams that stretch standard concepts of type and dimension. The unstructured data of digital hyperspace can be elegantly represented, traversed, and transformed via the mathematics of hypergraphs, hypersparse matrices, and associative array algebra. This paper explores a novel mathematical concept, the semilink, that combines pairs of semirings to provide the essential operations for graph analytics, database operations, and machine learning. The GraphBLAS standard currently supports hypergraphs, hypersparse matrices, the mathematics required for semilinks, and seamlessly performs graph, network, and matrix operations. With the addition of key based indices (such as pointers to strings) and semilinks, GraphBLAS can become a richer associative array algebra and be a plug-in replacement for spreadsheets, database tables, and data centric operating systems, enhancing the navigation of unstructured data found in digital hyperspace.

Jessica S. Titensky, Hayden Jananthan, Jeremy Kepner

Extended Kalman Filtering (EKF) can be used to propagate and quantify input uncertainty through a Deep Neural Network (DNN) assuming mild hypotheses on the input distribution. This methodology yields results comparable to existing methods of uncertainty propagation for DNNs while lowering the computational overhead considerably. Additionally, EKF allows model error to be naturally incorporated into the output uncertainty.

Jeremy Kepner, Vijay Gadepally, Hayden Jananthan et al.

Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by operations on the weight matrices describing the DNN. As DNNs incorporate more layers and more neurons per layers, these weight matrices may be required to be sparse because of memory limitations. Sparse DNNs are one possible approach, but the underlying theory is in the early stages of development and presents a number of challenges, including determining the accuracy of inference and selecting nonzero weights for training. Associative array algebra has been developed by the big data community to combine and extend database, matrix, and graph/network concepts for use in large, sparse data problems. Applying this mathematics to DNNs simplifies the formulation of DNN mathematics and reveals that DNNs are linear over oscillating semirings. This work uses associative array DNNs to construct exact solutions and corresponding perturbation models to the rectified linear unit (ReLU) DNN equations that can be used to construct test vectors for sparse DNN implementations over various precisions. These solutions can be used for DNN verification, theoretical explorations of DNN properties, and a starting point for the challenge of sparse training.