Engineering topics

Brown, Davis R.

Publications and source records attributed to Brown, Davis R..

6 records

DOE OSTI2024

Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research

The use of benchmark datasets has become an important engine of progress in machine learning (ML) over the past 15 years. Recently there has been growing interest in utilizing machine learning to drive advances in research-level mathematics. However, off-the-shelf solutions often fail to deliver the types of insights required by mathematicians. This suggests the need for new ML methods specifically designed with mathematics in mind. The question then is: what benchmarks should the community use to evaluate these? On the one hand, toy problems such as learning the multiplicative structure of small finite groups have become popular in the mechanistic interpretability community whose perspective on explainability aligns well with the needs of mathematicians. While toy datasets are a useful benchmark for initial work, they lack the scale, complexity, and sophistication of many of the principal objects of study in modern mathematics. To address this, we introduce a new collection of benchmark datasets, Algebraic Combinatorics Benchmarks (ACBench), representing either classic or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. After describing the datasets, we discuss the challenges involved in constructing “good” mathematics benchmarks, describe baseline model performance, and discuss some of the insights these datasets can provide that may be of interest even to those who are not interested in mathematics research itself.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Comparing Mapper Graphs of Artificial Neuron Activations

The mapper graph is a popular tool from topological data analysis that provides a graphical summary of point cloud data. It has been used to study data from cancer research, sports analytics, neurosciences, and machine learning. In particular, mapper graphs have been used recently to visualize the topology of high-dimensional artificial neural activations from convolutional neural networks and large language models. However, a key question that arises from using mapper graphs across applications is how to compare mapper graphs to study their structural differences. In this paper, we introduce a distance between mapper graphs using tools from optimal transport. We demonstrate the utility of such a distance by studying the topological changes of neural activations across convolutional layers in deep learning, as well as by capturing the loss of structural information for multiscale mapper.

mapper graphs, computational topology, machine lea↗

DOE OSTI2023

Understanding the Inner-Workings of Language Models Through Representation Dissimilarity

We use model stitching to understand the internal representations of language models. Similar to vision models, we find that "more is better," and representations learned with more data and larger width can improve the performance of weaker models via stitching. We likewise find that certain architecture choices, using GeLU vs SoLU activation functions, influence the quality of learned representations. Finally, model stitching (as opposed to other model diagnostic methods, like mode connectivity) can localize the different generalization strategies of text classifiers under domain shift to certain hidden layers.

Brown, Davis R.↗

DOE OSTI2023

DeepDataProfiler: A Platform and Methodology for the Analysis and Interpretation of Neural Networks

The DeepDataProfiler is a methodology and framework for providing interpretability to trained neural networks. Its approach is to decompose a network into a weighted graph of neurons and synapses and link the components of the graph to human identifiable concepts. By identifying concepts important to the network and tracking the decision process employed by the network, the network becomes more transparent and less like a black box. Spurious decisions and poor generalization strategies can be identified and a measure of trustworthiness can be established.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Making Corgis Important for Honeycomb Classification: Adversarial Attacks on Concept-based Explainability Tools

Methods for model explainability have become increasingly critical for testing the fairness and soundness of deep learning. Concept-based interpretability techniques, which use a small set of human-interpretable concept exemplars in order to measure the influence of a concept on a model's internal representation of input, are an important thread in this line of research. In this work we show that these explainability methods can suffer the same vulnerability to adversarial attacks as the models they are meant to analyze. We demonstrate this phenomenon on two well-known concept-based interpretability methods: TCAV and faceted feature visualization. We show that by leveraging the geometry of the problem and carefully perturbing the examples of the concept that is being investigated, we can radically change the output of the interpretability method. The attacks that we propose can either induce positive interpretations (polka dots are an important concept for a model when classifying zebras) or negative interpretations (stripes are not an important factor in identifying images of a zebra). Our work highlights the fact that in safety-critical applications, there is need for security around not only the machine learning pipeline but also the model interpretation process.

Brown, Davis R.↗

DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗