arXiv subjects

Henry Kvinge

Publications and source records attributed to Henry Kvinge.

At least 55 records · Page 3Linked to original sources

arXiv2022

TopTemp: Parsing Precipitate Structure from Temper Topology

Technological advances are in part enabled by the development of novel manufacturing processes that give rise to new materials or material property improvements. Development and evaluation of new manufacturing methodologies is labor-, time-, and resource-intensive expensive due to complex, poorly defined relationships between advanced manufacturing process parameters and the resulting microstructures. In this work, we present a topological representation of temper (heat-treatment) dependent material micro-structure, as captured by scanning electron microscopy, called TopTemp. We show that this topological representation is able to support temper classification of microstructures in a data limited setting, generalizes well to previously unseen samples, is robust to image perturbations, and captures domain interpretable features. The presented work outperforms conventional deep learning baselines and is a first step towards improving understanding of process parameters and resulting material properties.

cond-mat.mtrl-sci↗

arXiv2022

Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps

While it is not generally reflected in the `nice' datasets used for benchmarking machine learning algorithms, the real-world is full of processes that would be best described as many-to-many. That is, a single input can potentially yield many different outputs (whether due to noise, imperfect measurement, or intrinsic stochasticity in the process) and many different inputs can yield the same output (that is, the map is not injective). For example, imagine a sentiment analysis task where, due to linguistic ambiguity, a single statement can have a range of different sentiment interpretations while at the same time many distinct statements can represent the same sentiment. When modeling such a multivalued function $f: X \rightarrow Y$, it is frequently useful to be able to model the distribution on $f(x)$ for specific input $x$ as well as the distribution on fiber $f^{-1}(y)$ for specific output $y$. Such an analysis helps the user (i) better understand the variance intrinsic to the process they are studying and (ii) understand the range of specific input $x$ that can be used to achieve output $y$. Following existing work which used a fiber bundle framework to better model many-to-one processes, we describe how morphisms of fiber bundles provide a template for building models which naturally capture the structure of many-to-many processes.

cs.LG↗

arXiv2022

Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps

Many-to-one maps are ubiquitous in machine learning, from the image recognition model that assigns a multitude of distinct images to the concept of "cat" to the time series forecasting model which assigns a range of distinct time-series to a single scalar regression value. While the primary use of such models is naturally to associate correct output to each input, in many problems it is also useful to be able to explore, understand, and sample from a model's fibers, which are the set of input values $x$ such that $f(x) = y$, for fixed $y$ in the output space. In this paper we show that popular generative architectures are ill-suited to such tasks. Motivated by this we introduce a novel generative architecture, a Bundle Network, based on the concept of a fiber bundle from (differential) topology. BundleNets exploit the idea of a local trivialization wherein a space can be locally decomposed into a product space that cleanly encodes the many-to-one nature of the map. By enforcing this decomposition in BundleNets and by utilizing state-of-the-art invertible components, investigating a network's fibers becomes natural.

cs.LG↗

arXiv2021

DNA: Dynamic Network Augmentation

In many classification problems, we want a classifier that is robust to a range of non-semantic transformations. For example, a human can identify a dog in a picture regardless of the orientation and pose in which it appears. There is substantial evidence that this kind of invariance can significantly improve the accuracy and generalization of machine learning models. A common technique to teach a model geometric invariances is to augment training data with transformed inputs. However, which invariances are desired for a given classification task is not always known. Determining an effective data augmentation policy can require domain expertise or extensive data pre-processing. Recent efforts like AutoAugment optimize over a parameterized search space of data augmentation policies to automate the augmentation process. While AutoAugment and similar methods achieve state-of-the-art classification accuracy on several common datasets, they are limited to learning one data augmentation policy. Often times different classes or features call for different geometric invariances. We introduce Dynamic Network Augmentation (DNA), which learns input-conditional augmentation policies. Augmentation parameters in our model are outputs of a neural network and are implicitly learned as the network weights are updated. Our model allows for dynamic augmentation policies and performs well on data with geometric transformations conditional on input features.

cs.LG↗

arXiv2021

Differential Property Prediction: A Machine Learning Approach to Experimental Design in Advanced Manufacturing

Advanced manufacturing techniques have enabled the production of materials with state-of-the-art properties. In many cases however, the development of physics-based models of these techniques lags behind their use in the lab. This means that designing and running experiments proceeds largely via trial and error. This is sub-optimal since experiments are cost-, time-, and labor-intensive. In this work we propose a machine learning framework, differential property classification (DPC), which enables an experimenter to leverage machine learning's unparalleled pattern matching capability to pursue data-driven experimental design. DPC takes two possible experiment parameter sets and outputs a prediction of which will produce a material with a more desirable property specified by the operator. We demonstrate the success of DPC on AA7075 tube manufacturing process and mechanical property data using shear assisted processing and extrusion (ShAPE), a solid phase processing technology. We show that by focusing on the experimenter's need to choose between multiple candidate experimental parameters, we can reframe the challenging regression task of predicting material properties from processing parameters, into a classification task on which machine learning models can achieve good performance.

cs.LG↗

arXiv2021

A Topological-Framework to Improve Analysis of Machine Learning Model Performance

As both machine learning models and the datasets on which they are evaluated have grown in size and complexity, the practice of using a few summary statistics to understand model performance has become increasingly problematic. This is particularly true in real-world scenarios where understanding model failure on certain subpopulations of the data is of critical importance. In this paper we propose a topological framework for evaluating machine learning models in which a dataset is treated as a "space" on which a model operates. This provides us with a principled way to organize information about model performance at both the global level (over the entire test set) and also the local level (on specific subpopulations). Finally, we describe a topological data structure, presheaves, which offer a convenient way to store and analyze model performance between different subpopulations.

cs.LG↗

arXiv2021

Rotating spiders and reflecting dogs: a class conditional approach to learning data augmentation distributions

Building invariance to non-meaningful transformations is essential to building efficient and generalizable machine learning models. In practice, the most common way to learn invariance is through data augmentation. There has been recent interest in the development of methods that learn distributions on augmentation transformations from the training data itself. While such approaches are beneficial since they are responsive to the data, they ignore the fact that in many situations the range of transformations to which a model needs to be invariant changes depending on the particular class input belongs to. For example, if a model needs to be able to predict whether an image contains a starfish or a dog, we may want to apply random rotations to starfish images during training (since these do not have a preferred orientation), but we would not want to do this to images of dogs. In this work we introduce a method by which we can learn class conditional distributions on augmentation transformations. We give a number of examples where our methods learn different non-meaningful transformations depending on class and further show how our method can be used as a tool to probe the symmetries intrinsic to a potentially complex dataset.

cs.LG↗

arXiv2021

One Representation to Rule Them All: Identifying Out-of-Support Examples in Few-shot Learning with Generic Representations

The field of few-shot learning has made remarkable strides in developing powerful models that can operate in the small data regime. Nearly all of these methods assume every unlabeled instance encountered will belong to a handful of known classes for which one has examples. This can be problematic for real-world use cases where one routinely finds 'none-of-the-above' examples. In this paper we describe this challenge of identifying what we term 'out-of-support' (OOS) examples. We describe how this problem is subtly different from out-of-distribution detection and describe a new method of identifying OOS examples within the Prototypical Networks framework using a fixed point which we call the generic representation. We show that our method outperforms other existing approaches in the literature as well as other approaches that we propose in this paper. Finally, we investigate how the use of such a generic point affects the geometry of a model's feature space.

cs.LG↗

arXiv2021

Sheaves as a Framework for Understanding and Interpreting Model Fit

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn from peripheral sources. In this paper we argue that in such situations, sheaves can provide a natural framework to analyze how well a statistical model fits at the local level (that is, on subsets of related datapoints) vs the global level (on all the data). The sheaf-based approach that we propose is suitably general enough to be useful in a range of applications, from analyzing sensor networks to understanding the feature space of a deep learning model.

cs.LG↗

arXiv2021

Prototypical Region Proposal Networks for Few-Shot Localization and Classification

Recently proposed few-shot image classification methods have generally focused on use cases where the objects to be classified are the central subject of images. Despite success on benchmark vision datasets aligned with this use case, these methods typically fail on use cases involving densely-annotated, busy images: images common in the wild where objects of relevance are not the central subject, instead appearing potentially occluded, small, or among other incidental objects belonging to other classes of potential interest. To localize relevant objects, we employ a prototype-based few-shot segmentation model which compares the encoded features of unlabeled query images with support class centroids to produce region proposals indicating the presence and location of support set classes in a query image. These region proposals are then used as additional conditioning input to few-shot image classifiers. We develop a framework to unify the two stages (segmentation and classification) into an end-to-end classification model -- PRoPnet -- and empirically demonstrate that our methods improve accuracy on image datasets with natural scenes containing multiple object classes.

cs.CV↗

arXiv2020

Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response

Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems. Hypergraphs are generalizations of graphs that naturally model multi-way relationships and have shown promise in modeling systems such as protein complexes and metabolic reactions. In this paper we seek to understand how hypergraphs can more faithfully identify, and potentially predict, important genes based on complex relationships inferred from genomic expression data sets. Results: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges represent significantly perturbed genes, and vertices represent individual biological samples with specific experimental conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Conclusions: Our results demonstrate the utility of using hypergraphs to represent complex biological systems and highlight central important responses in common to a variety of highly pathogenic viruses.

q-bio.QM↗

arXiv2020

Fuzzy Simplicial Networks: A Topology-Inspired Model to Improve Task Generalization in Few-shot Learning

Deep learning has shown great success in settings with massive amounts of data but has struggled when data is limited. Few-shot learning algorithms, which seek to address this limitation, are designed to generalize well to new tasks with limited data. Typically, models are evaluated on unseen classes and datasets that are defined by the same fundamental task as they are trained for (e.g. category membership). One can also ask how well a model can generalize to fundamentally different tasks within a fixed dataset (for example: moving from category membership to tasks that involve detecting object orientation or quantity). To formalize this kind of shift we define a notion of "independence of tasks" and identify three new sets of labels for established computer vision datasets that test a model's ability to generalize to tasks which draw on orthogonal attributes in the data. We use these datasets to investigate the failure modes of metric-based few-shot models. Based on our findings, we introduce a new few-shot model called Fuzzy Simplicial Networks (FSN) which leverages a construction from topology to more flexibly represent each class from limited data. In particular, FSN models can not only form multiple representations for a given class but can also begin to capture the low-dimensional structure which characterizes class manifolds in the encoded space of deep networks. We show that FSN outperforms state-of-the-art models on the challenging tasks we introduce in this paper while remaining competitive on standard few-shot benchmarks.

cs.LG↗

arXiv2020

Multi-Dimensional Scaling on Groups

Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises from translational symmetry (i.e. time-delay/phase-shift). Particularly important in this area is understanding how symmetries inform the algorithms that we apply to our data. In this paper we explore the behavior of the dimensionality reduction algorithm multi-dimensional scaling (MDS) in the presence of symmetry. We show that understanding the properties of the underlying symmetry group allows us to make strong statements about the output of MDS even before applying the algorithm itself. In analogy to Fourier theory, we show that in some cases only a handful of fundamental "frequencies" (irreducible representations derived from the corresponding group) contribute information for the MDS Euclidean embedding.

cs.LG↗

arXiv2019

More chemical detection through less sampling: amplifying chemical signals in hyperspectral data cubes through compressive sensing

Compressive sensing (CS) is a method of sampling which permits some classes of signals to be reconstructed with high accuracy even when they were under-sampled. In this paper we explore a phenomenon in which bandwise CS sampling of a hyperspectral data cube followed by reconstruction can actually result in amplification of chemical signals contained in the cube. Perhaps most surprisingly, chemical signal amplification generally seems to increase as the level of sampling decreases. In some examples, the chemical signal is significantly stronger in a data cube reconstructed from 10% CS sampling than it is in the raw, 100% sampled data cube. We explore this phenomenon in two real-world datasets including the Physical Sciences Inc. Fabry-Pérot interferometer sensor multispectral dataset and the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset. Each of these datasets contains the release of a chemical simulant, such as glacial acetic acid, triethyl phospate, and sulfur hexafluoride, and in all cases we use the adaptive coherence estimator (ACE) to detect a target signal in the hyperspectral data cube. We end the paper by suggesting some theoretical justifications for why chemical signals would be amplified in CS sampled and reconstructed hyperspectral data cubes and discuss some practical implications.

eess.IV↗

arXiv2019

Total variation vs L1 regularization: a comparison of compressive sensing optimization methods for chemical detection

One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization terms are the L1 norm and the total variation (TV) norm. We present a comparison of CS reconstruction results based on these two approaches in the context of chemical detection, and we demonstrate that optimization based on the L1 norm outperforms optimization based on the TV norm. Our comparison is driven by CS sampling, reconstruction, and chemical detection in two real-world datasets: the Physical Sciences Inc. Fabry-Pérot interferometer sensor multispectral dataset and the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset. Both datasets contain the release of a chemical simulant such as glacial acetic acid, triethyl phosphate, and sulfur hexafluoride. For chemical detection we use the adaptive coherence estimator (ACE) and bulk coherence, and we propose algorithmic ACE thresholds to define the presence or absence of a chemical of interest in both un-compressed data cubes and reconstructed data cubes. The un-compressed data cubes provide an approximate ground truth. We demonstrate that optimization based on either the L1 norm or TV norm results in successful chemical detection at a compression rate of 90%, but we show that L1 optimization is preferable. We present quantitative comparisons of chemical detection on reconstructions from the two methods, with an emphasis on the number of pixels with an ACE value above the threshold.

eess.IV↗

arXiv2019

A data-driven approach to sampling matrix selection for compressive sensing

Sampling is a fundamental aspect of any implementation of compressive sensing. Typically, the choice of sampling method is guided by the reconstruction basis. However, this approach can be problematic with respect to certain hardware constraints and is not responsive to domain-specific context. We propose a method for defining an order for a sampling basis that is optimal with respect to capturing variance in data, thus allowing for meaningful sensing at any desired level of compression. We focus on the Walsh-Hadamard sampling basis for its relevance to hardware constraints, but our approach applies to any sampling basis of interest. We illustrate the effectiveness of our method on the Physical Sciences Inc. Fabry-Pérot interferometer sensor multispectral dataset, the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset, and a Colorado State University Swiss Ranger depth image dataset. The spectral datasets consist of simulant experiments, including releases of chemicals such as GAA and SF6. We combine our sampling and reconstruction with the adaptive coherence estimator (ACE) and bulk coherence for chemical detection and we incorporate an algorithmic threshold for ACE values to determine the presence or absence of a chemical. We compare results across sampling methods in this context. We have successful chemical detection at a compression rate of 90%. For all three datasets, we compare our sampling approach to standard orderings of sampling basis such as random, sequency, and an analog of sequency that we term `frequency.' In one instance, the peak signal to noise ratio was improved by over 30% across a test set of depth images.

eess.SP↗

arXiv2019

Rare geometries: revealing rare categories via dimension-driven statistics

In many situations, classes of data points of primary interest also happen to be those that are least numerous. A well-known example is detection of fraudulent transactions among the collection of all financial transactions, the vast majority of which are legitimate. These types of problems fall under the label of `rare-category detection.' There are two challenging aspects of these problems. The first is a general lack of labeled examples of the rare class and the second is the potential non-separability of the rare class from the majority (in terms of available features). Statistics related to the geometry of the rare class (such as its intrinsic dimension) can be significantly different from those for the majority class, reflecting the different dynamics driving variation in the different classes. In this paper we present a new supervised learning algorithm that uses a dimension-driven statistic, called the kappa-profile, to classify whether unlabeled points belong to a rare class. Our algorithm requires very few labeled examples and is invariant with respect to translation so that it performs equivalently on both separable and non-separable classes.

cs.LG↗

arXiv2018

A Frobenius-Schreier-Sims Algorithm to tensor decompose algebras

We introduce a decomposition of associative algebras into a tensor product of cyclic modules. This produces a means to encode a basis with logarithmic information and thus extends the reach of calculation with large algebras. Our technique is an analogue to the Schreier-Sims algorithm for permutation groups and is a by-product of Frobenius reciprocity.

math.RA↗