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Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization of the latent MAP. In this work, we propose to use compressive autoencoders for latent estimation. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. We then introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs this estimation within the framework of variational inference. This allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

Prediction models are used amongst others to inform medical decisions on interventions. Typically, individuals with high risks of adverse outcomes are advised to undergo an intervention while those at low risk are advised to refrain from it. Standard prediction models do not always provide risks that are relevant to inform such decisions: e.g., an individual may be estimated to be at low risk because similar individuals in the past received an intervention which lowered their risk. Therefore, prediction models supporting decisions should target risks belonging to defined intervention strategies. Previous works on prediction under interventions assumed that the prediction model was used only at one time point to make an intervention decision. In clinical practice, intervention decisions are rarely made only once: they might be repeated, deferred and re-evaluated. This requires estimated risks under interventions that can be reconsidered at several potential decision moments. In the current work, we highlight key considerations for formulating estimands in sequential prediction under interventions that can inform such intervention decisions. We illustrate these considerations by giving examples of estimands for a case study about choosing between vaginal delivery and cesarean section for women giving birth. Our formalization of prediction tasks in a sequential, causal, and estimand context provides guidance for future studies to ensure that the right question is answered and appropriate causal estimation approaches are chosen to develop sequential prediction models that can inform intervention decisions.

We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in a 2023 paper by Mohanty, Greenbury, Sarkany, Narayanan, Dingle, Ahnert, and Louis, whose primary scope is the maximum mutational robustness in genotype-phenotype maps.

Deep neural networks are known to be vulnerable to small adversarial perturbations in test data. To defend against adversarial attacks, probabilistic classifiers have been proposed as an alternative to deterministic ones. However, literature has conflicting findings on the effectiveness of probabilistic classifiers in comparison to deterministic ones. In this paper, we clarify the role of randomization in building adversarially robust classifiers. Given a base hypothesis set of deterministic classifiers, we show the conditions under which a randomized ensemble outperforms the hypothesis set in adversarial risk, extending previous results. Additionally, we show that for any probabilistic binary classifier (including randomized ensembles), there exists a deterministic classifier that outperforms it. Finally, we give an explicit description of the deterministic hypothesis set that contains such a deterministic classifier for many types of commonly used probabilistic classifiers, i.e. randomized ensembles and parametric/input noise injection.

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose plasticity over the course of training even in relatively simple learning problems, but the mechanisms driving this phenomenon are still poorly understood. This paper conducts a systematic empirical analysis into plasticity loss, with the goal of understanding the phenomenon mechanistically in order to guide the future development of targeted solutions. We find that loss of plasticity is deeply connected to changes in the curvature of the loss landscape, but that it often occurs in the absence of saturated units. Based on this insight, we identify a number of parameterization and optimization design choices which enable networks to better preserve plasticity over the course of training. We validate the utility of these findings on larger-scale RL benchmarks in the Arcade Learning Environment.

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems by utilizing the PINN, harnessing the capabilities of Deep Neural Networks (DNNs) to approximate hydraulic head distributions in seepage analysis. To effectively train the PINN model, we introduce a comprehensive loss function comprising three components: one for evaluating differential operators, another for assessing boundary conditions, and a third for appraising initial conditions. The validation of the PINN involves solving four benchmark seepage problems. The results unequivocally demonstrate the exceptional accuracy of the PINN in solving seepage problems, surpassing the accuracy of FEM in addressing both steady-state and free-surface seepage problems. Hence, the presented approach highlights the robustness of the PINN and underscores its precision in effectively addressing a spectrum of seepage challenges. This amalgamation enables the derivation of accurate solutions, overcoming limitations inherent in conventional methods such as mesh generation and adaptability to complex geometries.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function $y(x)$. We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels $y(x)$ are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

Graph neural networks (GNNs) have been proven to be effective in various network-related tasks. Most existing GNNs usually exploit the low-frequency signals of node features, which gives rise to one fundamental question: is the low-frequency information all we need in the real world applications? In this paper, we first present an experimental investigation assessing the roles of low-frequency and high-frequency signals, where the results clearly show that exploring low-frequency signal only is distant from learning an effective node representation in different scenarios. How can we adaptively learn more information beyond low-frequency information in GNNs? A well-informed answer can help GNNs enhance the adaptability. We tackle this challenge and propose a novel Frequency Adaptation Graph Convolutional Networks (FAGCN) with a self-gating mechanism, which can adaptively integrate different signals in the process of message passing. For a deeper understanding, we theoretically analyze the roles of low-frequency signals and high-frequency signals on learning node representations, which further explains why FAGCN can perform well on different types of networks. Extensive experiments on six real-world networks validate that FAGCN not only alleviates the over-smoothing problem, but also has advantages over the state-of-the-arts.