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Rough path theory provides one with the notion of signature, a graded family of tensors which characterise, up to a negligible equivalence class, and ordered stream of vector-valued data. In the last few years, use of the signature has gained traction in time-series analysis, machine learning , deep learning and more recently in kernel methods. In this article, we lay down the theoretical foundations for a connection between signature asymptotics, the theory of empirical processes, and Wasserstein distances, opening up the landscape and toolkit of the second and third in the study of the first. Our main contribution is to show that the Hambly-Lyons limit can be reinterpreted as a statement about the asymptotic behaviour of Wasserstein distances between two independent empirical measures of samples from the same underlying distribution. In the setting studied here, these measures are derived from samples from a probability distribution which is determined by geometrical properties of the underlying path. The general question of rates of convergence for these objects has been studied in depth in the recent monograph of Bobkov and Ledoux. By using these results, we generalise the original result of Hambly and Lyons from $C^3$ curves to a broad class of $C^2$ ones. We conclude by providing an explicit way to compute the limit in terms of a second-order differential equation.

We introduce CaloFlow, a fast detector simulation framework based on normalizing flows. For the first time, we demonstrate that normalizing flows can reproduce many-channel calorimeter showers with extremely high fidelity, providing a fresh alternative to computationally expensive GEANT4 simulations, as well as other state-of-the-art fast simulation frameworks based on GANs and VAEs. Besides the usual histograms of physical features and images of calorimeter showers, we introduce a new metric for judging the quality of generative modeling: the performance of a classifier trained to differentiate real from generated images. We show that GAN-generated images can be identified by the classifier with nearly 100% accuracy, while images generated from CaloFlow are better able to fool the classifier. More broadly, normalizing flows offer several advantages compared to other state-of-the-art approaches (GANs and VAEs), including: tractable likelihoods; stable and convergent training; and principled model selection. Normalizing flows also provide a bijective mapping between data and the latent space, which could have other applications beyond simulation, for example, to detector unfolding.

We study the asymptotic properties of geodesically convex $M$-estimation on non-linear spaces. Namely, we prove that under very minimal assumptions besides geodesic convexity of the cost function, one can obtain consistency and asymptotic normality, which are fundamental properties in statistical inference. Our results extend the Euclidean theory of convex $M$-estimation; They also generalize limit theorems on non-linear spaces which, essentially, were only known for barycenters, allowing to consider robust alternatives that are defined through non-smooth $M$-estimation procedures.

Accurately estimating the probability of failure for safety-critical systems is important for certification. Estimation is often challenging due to high-dimensional input spaces, dangerous test scenarios, and computationally expensive simulators; thus, efficient estimation techniques are important to study. This work reframes the problem of black-box safety validation as a Bayesian optimization problem and introduces an algorithm, Bayesian safety validation, that iteratively fits a probabilistic surrogate model to efficiently predict failures. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain using importance sampling. We introduce a set of three acquisition functions that focus on reducing uncertainty by covering the design space, optimizing the analytically derived failure boundaries, and sampling the predicted failure regions. Mainly concerned with systems that only output a binary indication of failure, we show that our method also works well in cases where more output information is available. Results show that Bayesian safety validation achieves a better estimate of the probability of failure using orders of magnitude fewer samples and performs well across various safety validation metrics. We demonstrate the algorithm on three test problems with access to ground truth and on a real-world safety-critical subsystem common in autonomous flight: a neural network-based runway detection system. This work is open sourced and currently being used to supplement the FAA certification process of the machine learning components for an autonomous cargo aircraft.

Current studies on adversarial robustness mainly focus on aggregating local robustness results from a set of data samples to evaluate and rank different models. However, the local statistics may not well represent the true global robustness of the underlying unknown data distribution. To address this challenge, this paper makes the first attempt to present a new framework, called GREAT Score , for global robustness evaluation of adversarial perturbation using generative models. Formally, GREAT Score carries the physical meaning of a global statistic capturing a mean certified attack-proof perturbation level over all samples drawn from a generative model. For finite-sample evaluation, we also derive a probabilistic guarantee on the sample complexity and the difference between the sample mean and the true mean. GREAT Score has several advantages: (1) Robustness evaluations using GREAT Score are efficient and scalable to large models, by sparing the need of running adversarial attacks. In particular, we show high correlation and significantly reduced computation cost of GREAT Score when compared to the attack-based model ranking on RobustBench (Croce,et. al. 2021). (2) The use of generative models facilitates the approximation of the unknown data distribution. In our ablation study with different generative adversarial networks (GANs), we observe consistency between global robustness evaluation and the quality of GANs. (3) GREAT Score can be used for remote auditing of privacy-sensitive black-box models, as demonstrated by our robustness evaluation on several online facial recognition services.

Deep learning-based approaches have produced models with good insect classification accuracy; Most of these models are conducive for application in controlled environmental conditions. One of the primary emphasis of researchers is to implement identification and classification models in the real agriculture fields, which is challenging because input images that are wildly out of the distribution (e.g., images like vehicles, animals, humans, or a blurred image of an insect or insect class that is not yet trained on) can produce an incorrect insect classification. Out-of-distribution (OOD) detection algorithms provide an exciting avenue to overcome these challenge as it ensures that a model abstains from making incorrect classification prediction of non-insect and/or untrained insect class images. We generate and evaluate the performance of state-of-the-art OOD algorithms on insect detection classifiers. These algorithms represent a diversity of methods for addressing an OOD problem. Specifically, we focus on extrusive algorithms, i.e., algorithms that wrap around a well-trained classifier without the need for additional co-training. We compared three OOD detection algorithms: (i) Maximum Softmax Probability, which uses the softmax value as a confidence score, (ii) Mahalanobis distance-based algorithm, which uses a generative classification approach; and (iii) Energy-Based algorithm that maps the input data to a scalar value, called energy. We performed an extensive series of evaluations of these OOD algorithms across three performance axes: (a) \textit{Base model accuracy}: How does the accuracy of the classifier impact OOD performance? (b) How does the \textit{level of dissimilarity to the domain} impact OOD performance? and (c) \textit{Data imbalance}: How sensitive is OOD performance to the imbalance in per-class sample size?

Researchers typically investigate neural network representations by examining activation outputs for one or more layers of a network. Here, we investigate the potential for ReLU activation patterns (encoded as bit vectors) to aid in understanding and interpreting the behavior of neural networks. We utilize Representational Dissimilarity Matrices (RDMs) to investigate the coherence of data within the embedding spaces of a deep neural network. From each layer of a network, we extract and utilize bit vectors to construct similarity scores between images. From these similarity scores, we build a similarity matrix for a collection of images drawn from 2 classes. We then apply Fiedler partitioning to the associated Laplacian matrix to separate the classes. Our results indicate, through bit vector representations, that the network continues to refine class detectability with the last ReLU layer achieving better than 95\% separation accuracy. Additionally, we demonstrate that bit vectors aid in adversarial image detection, again achieving over 95\% accuracy in separating adversarial and non-adversarial images using a simple classifier.

We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution of diverse prompts to handle the varying visual representations. In this way, we provide high-quality task-related content for facilitating recognition. This prompt distribution learning is realized by an efficient approach that learns the output embeddings of prompts instead of the input embeddings. Thus, we can employ a Gaussian distribution to model them effectively and derive a surrogate loss for efficient training. Extensive experiments on 12 datasets demonstrate that our method consistently and significantly outperforms existing methods. For example, with 1 sample per category, it relatively improves the average result by 9.1% compared to human-crafted prompts.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

User engagement is a critical metric for evaluating the quality of open-domain dialogue systems. Prior work has focused on conversation-level engagement by using heuristically constructed features such as the number of turns and the total time of the conversation. In this paper, we investigate the possibility and efficacy of estimating utterance-level engagement and define a novel metric, {\em predictive engagement}, for automatic evaluation of open-domain dialogue systems. Our experiments demonstrate that (1) human annotators have high agreement on assessing utterance-level engagement scores; (2) conversation-level engagement scores can be predicted from properly aggregated utterance-level engagement scores. Furthermore, we show that the utterance-level engagement scores can be learned from data. These scores can improve automatic evaluation metrics for open-domain dialogue systems, as shown by correlation with human judgements. This suggests that predictive engagement can be used as a real-time feedback for training better dialogue models.