Recalling the most relevant visual memories for localisation or understanding a priori the likely outcome of localisation effort against a particular visual memory is useful for efficient and robust visual navigation. Solutions to this problem should be divorced from performance appraisal against ground truth - as this is not available at run-time - and should ideally be based on generalisable environmental observations. For this, we propose applying the recently developed Visual DNA as a highly scalable tool for comparing datasets of images - in this work, sequences of map and live experiences. In the case of localisation, important dataset differences impacting performance are modes of appearance change, including weather, lighting, and season. Specifically, for any deep architecture which is used for place recognition by matching feature volumes at a particular layer, we use distribution measures to compare neuron-wise activation statistics between live images and multiple previously recorded past experiences, with a potentially large seasonal (winter/summer) or time of day (day/night) shift. We find that differences in these statistics correlate to performance when localising using a past experience with the same appearance gap. We validate our approach over the Nordland cross-season dataset as well as data from Oxford's University Parks with lighting and mild seasonal change, showing excellent ability of our system to rank actual localisation performance across candidate experiences.
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We present a novel clustering algorithm, visClust, that is based on lower dimensional data representations and visual interpretation. Thereto, we design a transformation that allows the data to be represented by a binary integer array enabling the use of image processing methods to select a partition. Qualitative and quantitative analyses measured in accuracy and an adjusted Rand-Index show that the algorithm performs well while requiring low runtime and RAM. We compare the results to 6 state-of-the-art algorithms with available code, confirming the quality of visClust by superior performance in most experiments. Moreover, the algorithm asks for just one obligatory input parameter while allowing optimization via optional parameters. The code is made available on GitHub and straightforward to use.
The field of 'explainable' artificial intelligence (XAI) has produced highly cited methods that seek to make the decisions of complex machine learning (ML) methods 'understandable' to humans, for example by attributing 'importance' scores to input features. Yet, a lack of formal underpinning leaves it unclear as to what conclusions can safely be drawn from the results of a given XAI method and has also so far hindered the theoretical verification and empirical validation of XAI methods. This means that challenging non-linear problems, typically solved by deep neural networks, presently lack appropriate remedies. Here, we craft benchmark datasets for three different non-linear classification scenarios, in which the important class-conditional features are known by design, serving as ground truth explanations. Using novel quantitative metrics, we benchmark the explanation performance of a wide set of XAI methods across three deep learning model architectures. We show that popular XAI methods are often unable to significantly outperform random performance baselines and edge detection methods. Moreover, we demonstrate that explanations derived from different model architectures can be vastly different; thus, prone to misinterpretation even under controlled conditions.
Current approaches to generic segmentation start by creating a hierarchy of nested image partitions and then specifying a segmentation from it. Our first contribution is to describe several ways, most of them new, for specifying segmentations using the hierarchy elements. Then, we consider the best hierarchy-induced segmentation specified by a limited number of hierarchy elements. We focus on a common quality measure for binary segmentations, the Jaccard index (also known as IoU). Optimizing the Jaccard index is highly non-trivial, and yet we propose an efficient approach for doing exactly that. This way we get algorithm-independent upper bounds on the quality of any segmentation created from the hierarchy. We found that the obtainable segmentation quality varies significantly depending on the way that the segments are specified by the hierarchy elements, and that representing a segmentation with only a few hierarchy elements is often possible. (Code is available).
Robust Markov Decision Processes (RMDPs) are a widely used framework for sequential decision-making under parameter uncertainty. RMDPs have been extensively studied when the objective is to maximize the discounted return, but little is known for average optimality (optimizing the long-run average of the rewards obtained over time) and Blackwell optimality (remaining discount optimal for all discount factors sufficiently close to 1). In this paper, we prove several foundational results for RMDPs beyond the discounted return. We show that average optimal policies can be chosen stationary and deterministic for sa-rectangular RMDPs but, perhaps surprisingly, that history-dependent (Markovian) policies strictly outperform stationary policies for average optimality in s-rectangular RMDPs. We also study Blackwell optimality for sa-rectangular RMDPs, where we show that {\em approximate} Blackwell optimal policies always exist, although Blackwell optimal policies may not exist. We also provide a sufficient condition for their existence, which encompasses virtually any examples from the literature. We then discuss the connection between average and Blackwell optimality, and we describe several algorithms to compute the optimal average return. Interestingly, our approach leverages the connections between RMDPs and stochastic games.
The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large. We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are H\"older continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the $\ell_2$-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which -- combined with classical tests for discrete-valued predictors -- can be used to test the calibration of virtually any probabilistic classification method.
While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization with internal linear layers and $L_2$ regularization (weight decay) to automatically estimate the underlying dimensionality of a data set, produce an orthogonal manifold coordinate system, and provide the mapping functions between the ambient space and manifold space, allowing for out-of-sample projections. We validate our framework's ability to estimate the manifold dimension for a series of datasets from dynamical systems of varying complexities and compare to other state-of-the-art estimators. We analyze the training dynamics of the network to glean insight into the mechanism of low-rank learning and find that collectively each of the implicit regularizing layers compound the low-rank representation and even self-correct during training. Analysis of gradient descent dynamics for this architecture in the linear case reveals the role of the internal linear layers in leading to faster decay of a "collective weight variable" incorporating all layers, and the role of weight decay in breaking degeneracies and thus driving convergence along directions in which no decay would occur in its absence. We show that this framework can be naturally extended for applications of state-space modeling and forecasting by generating a data-driven dynamic model of a spatiotemporally chaotic partial differential equation using only the manifold coordinates. Finally, we demonstrate that our framework is robust to hyperparameter choices.
We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study two new classes of exponential Runge-Kutta (ERK) integrators for efficiently solving stiff systems or highly oscillatory problems. We first present a novel class of explicit modified version of exponential Runge-Kutta (MVERK) methods based on the order conditions. Furthermore, we consider a class of explicit simplified version of exponential Runge-Kutta (SVERK) methods. Numerical results demonstrate the high efficiency of the explicit MVERK integrators and SVERK methods derived in this paper compared with the well-known explicit ERK integrators for stiff systems or highly oscillatory problems in the literature.
Recent progress in generative artificial intelligence (gen-AI) has enabled the generation of photo-realistic and artistically-inspiring photos at a single click, catering to millions of users online. To explore how people use gen-AI models such as DALLE and StableDiffusion, it is critical to understand the themes, contents, and variations present in the AI-generated photos. In this work, we introduce TWIGMA (TWItter Generative-ai images with MetadatA), a comprehensive dataset encompassing over 800,000 gen-AI images collected from Jan 2021 to March 2023 on Twitter, with associated metadata (e.g., tweet text, creation date, number of likes), available at //zenodo.org/records/8031785. Through a comparative analysis of TWIGMA with natural images and human artwork, we find that gen-AI images possess distinctive characteristics and exhibit, on average, lower variability when compared to their non-gen-AI counterparts. Additionally, we find that the similarity between a gen-AI image and natural images is inversely correlated with the number of likes. Finally, we observe a longitudinal shift in the themes of AI-generated images on Twitter, with users increasingly sharing artistically sophisticated content such as intricate human portraits, whereas their interest in simple subjects such as natural scenes and animals has decreased. Our findings underscore the significance of TWIGMA as a unique data resource for studying AI-generated images.
Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
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