We present a neural network representation which can be used for visually analyzing the similarities and differences in a large corpus of trained neural networks. The focus is on architecture-invariant comparisons based on network weights, estimating similarities of the statistical footprints encoded by the training setups and stochastic optimization procedures. To make this possible, we propose a novel visual descriptor of neural network weights. The visual descriptor considers local weight statistics in a model-agnostic manner by encoding the distribution of weights over different model depths. We show how such a representation can extract descriptive information, is robust to different parameterizations of a model, and is applicable to different architecture specifications. The descriptor is used to create a model atlas by projecting a model library to a 2D representation, where clusters can be found based on similar weight properties. A cluster analysis strategy makes it possible to understand the weight properties of clusters and how these connect to the different datasets and hyper-parameters used to train the models.

Training a deep neural network is computationally expensive, but achieving the same network performance with less computation is possible if the training data is carefully chosen. However, selecting input samples during training is challenging as their true importance for the optimization is unknown. Furthermore, evaluation of the importance of individual samples must be computationally efficient and unbiased. In this paper, we present a new input data importance sampling strategy for reducing the training time of deep neural networks. We investigate different importance metrics that can be efficiently retrieved as they are available during training, i.e., the training loss and gradient norm. We found that choosing only samples with large loss or gradient norm, which are hard for the network to learn, is not optimal for the network performance. Instead, we introduce an importance sampling strategy that selects samples based on the cumulative distribution function of the loss and gradient norm, thereby making it more likely to choose hard samples while still including easy ones. The behavior of the proposed strategy is first analyzed on a synthetic dataset, and then evaluated in the application of classification of malignant cancer in digital pathology image patches. As pathology images contain many repetitive patterns, there could be significant gains in focusing on features that contribute stronger to the optimization. Finally, we show how the importance sampling process can be used to gain insights about the input data through visualization of samples that are found most or least useful for the training.

We present a method for exploring and comparing large sets of images with metadata using a hierarchical interaction approach. Browsing many images at the same time requires either a large screen space or an abundance of scrolling interaction. We address this problem by projecting the images onto a two-dimensional Cartesian coordinate system by combining the latent space of vision neural networks and dimensionality reduction techniques. To alleviate overdraw of the images, we integrate a hierarchical layout and navigation, where each group of similar images is represented by the image closest to the group center. Advanced interactive analysis of images in relation to their metadata is enabled through integrated, flexible filtering based on expressions. Furthermore, groups of images can be compared through selection and automated aggregated metadata visualization. We showcase our method in three case studies involving the domains of photography, machine learning, and medical imaging.

Evaluating the transmittance between two points along a ray is a key component in solving the light transport through heterogeneous participating media and entails computing an intractable exponential of the integrated medium's extinction coefficient. While algorithms for estimating this transmittance exist, there is a lack of theoretical knowledge about their behaviour, which also prevent new theoretically sound algorithms from being developed. For this purpose, we introduce a new class of unbiased transmittance estimators based on random sampling or truncation of a Taylor expansion of the exponential function. In contrast to classical tracking algorithms, these estimators are non-analogous to the physical light transport process and directly sample the underlying extinction function without performing incremental advancement. We present several versions of the new class of estimators, based on either importance sampling or Russian roulette to provide finite unbiased estimators of the infinite Taylor series expansion. We also show that the well known ratio tracking algorithm can be seen as a special case of the new class of estimators. Lastly, we conduct performance evaluations on both the central processing unit (CPU) and the graphics processing unit (GPU), and the results demonstrate that the new algorithms outperform traditional algorithms for heterogeneous mediums.

A key to deciphering the inner workings of neural networks is understanding what a model has learned. Promising methods for discovering learned features are based on analyzing activation values, whereby current techniques focus on analyzing high activation values to reveal interesting features on a neuron level. However, analyzing high activation values limits layer-level concept discovery. We present a method that instead takes into account the entire activation distribution. By extracting similar activation profiles within the high-dimensional activation space of a neural network layer, we find groups of inputs that are treated similarly. These input groups represent neural activation patterns (NAPs) and can be used to visualize and interpret learned layer concepts. We release a framework with which NAPs can be extracted from pre-trained models and provide a visual introspection tool that can be used to analyze NAPs. We tested our method with a variety of networks and show how it complements existing methods for analyzing neural network activation values.

We present a method for detecting patterns in time-varying functional magnetic resonance imaging (fMRI) data based on topological analysis. The oxygenated blood flow measured by fMRI is widely used as an indicator of brain activity. The signal is, however, prone to noise from various sources. Random brain activity, physiological noise, and noise from the scanner can reach a strength comparable to the signal itself. Thus, extracting the underlying signal is a challenging process typically approached by applying statistical methods. The goal of this work is to investigate the possibilities of recovering information from the signal using topological feature vectors directly based on the raw signal without medical domain priors. We utilize merge trees to define a robust feature vector capturing key features within a time step of fMRI data. We demonstrate how such a concise feature vector representation can be utilized for exploring the temporal development of brain activations, connectivity between these activations, and their relation to cognitive tasks.

This paper presents an empirical study on the weights of neural networks, where we interpret each model as a point in a high-dimensional space – the neural weight space. To explore the complex structure of this space, we sample from a diverse selection of training variations (dataset, optimization procedure, architecture,etc.) of neural network classifiers, and train a large number of models to represent the weight space. Then, we use a machine learning approach for analyzing and extracting information from this space. Most centrally, we train a number of novel deep meta-classifiers withthe objective of classifying different properties of the training setup by identifying their footprints in the weight space. Thus, the meta-classifiers probe for patterns induced by hyper-parameters, so that we can quantify how much, where, and when these are encoded through the optimization process. This provides a novel and complementary view for explainable AI, and we show how meta-classifiers can reveal a great deal of information about the training setup and optimization, by only considering a small subset of randomly selected consecutive weights. To promote further research on the weight space, we release the neural weight space (NWS) dataset – a collection of 320K weightsnapshots from 16K individually trained deep neural networks.

The complexity of todays visualization applications demands specific visualization systems tailored for the development of these applications. Frequently, such systems utilize levels of abstraction to improve the application development process, for insta

While volume rendering for scalar fields has been advanced into a powerful visualisation method, similar volumetric representations for tensor fields are still rare. The complexity of the data challenges not only the rendering but also the design of the transfer function. In this paper we propose an interface using glyph widgets to design a transfer function for the rendering of tensor data sets. Thereby the transfer function (TF) controls a volume rendering which represents sought after tensor-features and a texture that conveys directional information. The basis of the design interface is a two-dimensional projection of the attribute space. Characteristic representatives in the form of glyphs support an intuitive navigation through the attribute space. We provide three different options to select the representatives: automatic selection based on attribute space clustering, uniform sampling of the attribute space, or manually selected representatives. In contrast to glyphs placed into the 3D volume, we use glyphs with complex geometry as widgets to control the shape and extent of the representatives. In the final rendering the glyphs with their assigned colors play a similar role as a legend in an atlas like representation. The method provides an overview of the tensor field in the 3D volume at the same time as it allows the user to explore the tensor field in an attribute space. We demonstrate the flexibility of our approach on tensor fields for selected data sets with very different characteristics.