Simon Alford

Wen-Ding Li, Keya Hu, Carter Larsen et al.

When learning an input-output mapping from very few examples, is it better to first infer a latent function that explains the examples, or is it better to directly predict new test outputs, e.g. using a neural network? We study this question on ARC by training neural models for induction (inferring latent functions) and transduction (directly predicting the test output for a given test input). We train on synthetically generated variations of Python programs that solve ARC training tasks. We find inductive and transductive models solve different kinds of test problems, despite having the same training problems and sharing the same neural architecture: Inductive program synthesis excels at precise computations, and at composing multiple concepts, while transduction succeeds on fuzzier perceptual concepts. Ensembling them approaches human-level performance on ARC.

Simon Alford, Anshula Gandhi, Akshay Rangamani et al.

One of the challenges facing artificial intelligence research today is designing systems capable of utilizing systematic reasoning to generalize to new tasks. The Abstraction and Reasoning Corpus (ARC) measures such a capability through a set of visual reasoning tasks. In this paper we report incremental progress on ARC and lay the foundations for two approaches to abstraction and reasoning not based in brute-force search. We first apply an existing program synthesis system called DreamCoder to create symbolic abstractions out of tasks solved so far, and show how it enables solving of progressively more challenging ARC tasks. Second, we design a reasoning algorithm motivated by the way humans approach ARC. Our algorithm constructs a search graph and reasons over this graph structure to discover task solutions. More specifically, we extend existing execution-guided program synthesis approaches with deductive reasoning based on function inverse semantics to enable a neural-guided bidirectional search algorithm. We demonstrate the effectiveness of the algorithm on three domains: ARC, 24-Game tasks, and a 'double-and-add' arithmetic puzzle.

Jeremy Kepner, Simon Alford, Vijay Gadepally et al.

The MIT/IEEE/Amazon GraphChallenge.org encourages community approaches to developing new solutions for analyzing graphs and sparse data. Sparse AI analytics present unique scalability difficulties. The Sparse Deep Neural Network (DNN) Challenge draws upon prior challenges from machine learning, high performance computing, and visual analytics to create a challenge that is reflective of emerging sparse AI systems. The sparse DNN challenge is based on a mathematically well-defined DNN inference computation and can be implemented in any programming environment. In 2019 several sparse DNN challenge submissions were received from a wide range of authors and organizations. This paper presents a performance analysis of the best performers of these submissions. These submissions show that their state-of-the-art sparse DNN execution time, $T_{\rm DNN}$, is a strong function of the number of DNN operations performed, $N_{\rm op}$. The sparse DNN challenge provides a clear picture of current sparse DNN systems and underscores the need for new innovations to achieve high performance on very large sparse DNNs.

Jeremy Kepner, Simon Alford, Vijay Gadepally et al.

The MIT/IEEE/Amazon GraphChallenge.org encourages community approaches to developing new solutions for analyzing graphs and sparse data. Sparse AI analytics present unique scalability difficulties. The proposed Sparse Deep Neural Network (DNN) Challenge draws upon prior challenges from machine learning, high performance computing, and visual analytics to create a challenge that is reflective of emerging sparse AI systems. The Sparse DNN Challenge is based on a mathematically well-defined DNN inference computation and can be implemented in any programming environment. Sparse DNN inference is amenable to both vertex-centric implementations and array-based implementations (e.g., using the GraphBLAS.org standard). The computations are simple enough that performance predictions can be made based on simple computing hardware models. The input data sets are derived from the MNIST handwritten letters. The surrounding I/O and verification provide the context for each sparse DNN inference that allows rigorous definition of both the input and the output. Furthermore, since the proposed sparse DNN challenge is scalable in both problem size and hardware, it can be used to measure and quantitatively compare a wide range of present day and future systems. Reference implementations have been implemented and their serial and parallel performance have been measured. Specifications, data, and software are publicly available at GraphChallenge.org

Simon Alford, Ryan Robinett, Lauren Milechin et al.

Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One approach to overcoming this limit is the design of sparse neural networks, which can be both very large and efficiently trained. In this paper we experiment training on sparse neural network topologies. We test pruning-based topologies, which are derived from an initially dense network whose connections are pruned, as well as RadiX-Nets, a class of network topologies with proven connectivity and sparsity properties. Results show that sparse networks obtain accuracies comparable to dense networks, but extreme levels of sparsity cause instability in training, which merits further study.