Daily Papers

In contrastive learning, the choice of ``view'' controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty. Furthermore, guided by structural entropy, we implement the anchor view, termed SEGA, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.

Existing Video Temporal Grounding (VTG) models excel in accuracy but often overlook open-world challenges posed by open-vocabulary queries and untrimmed videos. This leads to unreliable predictions for noisy, corrupted, and out-of-distribution data. Adapting VTG models to dynamically estimate uncertainties based on user input can address this issue. To this end, we introduce SRAM, a robust network module that benefits from a two-stage cross-modal alignment task. More importantly, it integrates Deep Evidential Regression (DER) to explicitly and thoroughly quantify uncertainty during training, thus allowing the model to say "I do not know" in scenarios beyond its handling capacity. However, the direct application of traditional DER theory and its regularizer reveals structural flaws, leading to unintended constraints in VTG tasks. In response, we develop a simple yet effective Geom-regularizer that enhances the uncertainty learning framework from the ground up. To the best of our knowledge, this marks the first successful attempt of DER in VTG. Our extensive quantitative and qualitative results affirm the effectiveness, robustness, and interpretability of our modules and the uncertainty learning paradigm in VTG tasks. The code will be made available.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

The recent advancements in large language models (LLMs) have significantly improved language understanding and generation capabilities. However, it is difficult to deploy LLMs on resource-constrained edge devices due to their high computational and storage resource demands. To address this issue, we propose a novel LLM model pruning method, namely structurally-aware adaptive pruning (SAAP), to significantly reduce the computational and memory costs while maintaining model performance. We first define an adaptive importance fusion metric to evaluate the importance of all coupled structures in LLMs by considering their homoscedastic uncertainty. Then, we rank the importance of all modules to determine the specific layers that should be pruned to meet particular performance requirements. Furthermore, we develop a new group fine-tuning strategy to improve the inference efficiency of LLMs. Finally, we evaluate the proposed SAAP method on multiple LLMs across two common tasks, i.e., zero-shot classification and text generation. Experimental results show that our SAAP method outperforms several state-of-the-art baseline methods, achieving 2.17%, 2.37%, and 2.39% accuracy gains on LLaMA-7B, Vicuna-7B, and LLaMA-13B. Additionally, SAAP improves the token generation speed by 5%, showcasing its practical advantages in resource-constrained scenarios.

Global climate models (GCMs) are the main tools for understanding and predicting climate change. However, due to limited numerical resolutions, these models suffer from major structural uncertainties; e.g., they cannot resolve critical processes such as small-scale eddies in atmospheric and oceanic turbulence. Thus, such small-scale processes have to be represented as a function of the resolved scales via closures (parametrization). The accuracy of these closures is particularly important for capturing climate extremes. Traditionally, such closures are based on heuristics and simplifying assumptions about the unresolved physics. Recently, supervised-learned closures, trained offline on high-fidelity data, have been shown to outperform the classical physics-based closures. However, this approach requires a significant amount of high-fidelity training data and can also lead to instabilities. Reinforcement learning is emerging as a potent alternative for developing such closures as it requires only low-order statistics and leads to stable closures. In Scientific Multi-Agent Reinforcement Learning (SMARL) computational elements serve a dual role of discretization points and learning agents. We leverage SMARL and fundamentals of turbulence physics to learn closures for prototypes of atmospheric and oceanic turbulence. The policy is trained using only the enstrophy spectrum, which is nearly invariant and can be estimated from a few high-fidelity samples (these few samples are far from enough for supervised/offline learning). We show that these closures lead to stable low-resolution simulations that, at a fraction of the cost, can reproduce the high-fidelity simulations' statistics, including the tails of the probability density functions. The results demonstrate the high potential of SMARL for closure modeling for GCMs, especially in the regime of scarce data and indirect observations.

Diffusion priors have been used for blind face restoration (BFR) by fine-tuning diffusion models (DMs) on restoration datasets to recover low-quality images. However, the naive application of DMs presents several key limitations. (i) The diffusion prior has inferior semantic consistency (e.g., ID, structure and color.), increasing the difficulty of optimizing the BFR model; (ii) reliance on hundreds of denoising iterations, preventing the effective cooperation with perceptual losses, which is crucial for faithful restoration. Observing that the latent consistency model (LCM) learns consistency noise-to-data mappings on the ODE-trajectory and therefore shows more semantic consistency in the subject identity, structural information and color preservation, we propose InterLCM to leverage the LCM for its superior semantic consistency and efficiency to counter the above issues. Treating low-quality images as the intermediate state of LCM, InterLCM achieves a balance between fidelity and quality by starting from earlier LCM steps. LCM also allows the integration of perceptual loss during training, leading to improved restoration quality, particularly in real-world scenarios. To mitigate structural and semantic uncertainties, InterLCM incorporates a Visual Module to extract visual features and a Spatial Encoder to capture spatial details, enhancing the fidelity of restored images. Extensive experiments demonstrate that InterLCM outperforms existing approaches in both synthetic and real-world datasets while also achieving faster inference speed.

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques usually incur overhead by having to train multiple model instances or do not produce very diverse predictions. This comprehensive and extensive survey aims to familiarize the reader with an alternative class of models based on the concept of Evidential Deep Learning: For unfamiliar data, they aim to admit "what they don't know", and fall back onto a prior belief. Furthermore, they allow uncertainty estimation in a single model and forward pass by parameterizing distributions over distributions. This survey recapitulates existing works, focusing on the implementation in a classification setting, before surveying the application of the same paradigm to regression. We also reflect on the strengths and weaknesses compared to other existing methods and provide the most fundamental derivations using a unified notation to aid future research.

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.

Uncertainty quantification (UQ) is a critical aspect of artificial intelligence (AI) systems, particularly in high-risk domains such as healthcare, autonomous systems, and financial technology, where decision-making processes must account for uncertainty. This review explores the evolution of uncertainty quantification techniques in AI, distinguishing between aleatoric and epistemic uncertainties, and discusses the mathematical foundations and methods used to quantify these uncertainties. We provide an overview of advanced techniques, including probabilistic methods, ensemble learning, sampling-based approaches, and generative models, while also highlighting hybrid approaches that integrate domain-specific knowledge. Furthermore, we examine the diverse applications of UQ across various fields, emphasizing its impact on decision-making, predictive accuracy, and system robustness. The review also addresses key challenges such as scalability, efficiency, and integration with explainable AI, and outlines future directions for research in this rapidly developing area. Through this comprehensive survey, we aim to provide a deeper understanding of UQ's role in enhancing the reliability, safety, and trustworthiness of AI systems.

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

Large Language Models (LLMs) often generate outputs that lack grounding in real-world facts, a phenomenon known as hallucinations. Prior research has associated hallucinations with model uncertainty, leveraging this relationship for hallucination detection and mitigation. In this paper, we challenge the underlying assumption that all hallucinations are associated with uncertainty. Using knowledge detection and uncertainty measurement methods, we demonstrate that models can hallucinate with high certainty even when they have the correct knowledge. We further show that high-certainty hallucinations are consistent across models and datasets, distinctive enough to be singled out, and challenge existing mitigation methods. Our findings reveal an overlooked aspect of hallucinations, emphasizing the need to understand their origins and improve mitigation strategies to enhance LLM safety. The code is available at https://github.com/technion-cs-nlp/Trust_me_Im_wrong .

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.

Although AI systems have been applied in various fields and achieved impressive performance, their safety and reliability are still a big concern. This is especially important for safety-critical tasks. One shared characteristic of these critical tasks is their risk sensitivity, where small mistakes can cause big consequences and even endanger life. There are several factors that could be guidelines for the successful deployment of AI systems in sensitive tasks: (i) failure detection and out-of-distribution (OOD) detection; (ii) overfitting identification; (iii) uncertainty quantification for predictions; (iv) robustness to data perturbations. These factors are also challenges of current AI systems, which are major blocks for building safe and reliable AI. Specifically, the current AI algorithms are unable to identify common causes for failure detection. Furthermore, additional techniques are required to quantify the quality of predictions. All these contribute to inaccurate uncertainty quantification, which lowers trust in predictions. Hence obtaining accurate model uncertainty quantification and its further improvement are challenging. To address these issues, many techniques have been proposed, such as regularization methods and learning strategies. As vision and language are the most typical data type and have many open source benchmark datasets, this thesis will focus on vision-language data processing for tasks like classification, image captioning, and vision question answering. In this thesis, we aim to build a safeguard by further developing current techniques to ensure the accurate model uncertainty for safety-critical tasks.

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

When deploying machine learning models in high-stakes real-world environments such as health care, it is crucial to accurately assess the uncertainty concerning a model's prediction on abnormal inputs. However, there is a scarcity of literature analyzing this problem on medical data, especially on mixed-type tabular data such as Electronic Health Records. We close this gap by presenting a series of tests including a large variety of contemporary uncertainty estimation techniques, in order to determine whether they are able to identify out-of-distribution (OOD) patients. In contrast to previous work, we design tests on realistic and clinically relevant OOD groups, and run experiments on real-world medical data. We find that almost all techniques fail to achieve convincing results, partly disagreeing with earlier findings.

Ever since the Multilayered Perceptron was first introduced the connectionist community has struggled with the concept of uncertainty and how this could be represented in these types of models. This past decade has seen a lot of effort in trying to join the principled approach of probabilistic modeling with the scalable nature of deep neural networks. While the theoretical benefits of this consolidation are clear, there are also several important practical aspects of these endeavors; namely to force the models we create to represent, learn, and report uncertainty in every prediction that is made. Many of these efforts have been based on extending existing frameworks with additional structures. We present Borch, a scalable deep universal probabilistic programming language, built on top of PyTorch. The code is available for download and use in our repository https://gitlab.com/desupervised/borch.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

This paper claims that machine learning (ML) largely overlooks an important facet of general intelligence: robustness to a qualitatively unknown future in an open world. Such robustness relates to Knightian uncertainty (KU) in economics, i.e. uncertainty that cannot be quantified, which is excluded from consideration in ML's key formalisms. This paper aims to identify this blind spot, argue its importance, and catalyze research into addressing it, which we believe is necessary to create truly robust open-world AI. To help illuminate the blind spot, we contrast one area of ML, reinforcement learning (RL), with the process of biological evolution. Despite staggering ongoing progress, RL still struggles in open-world situations, often failing under unforeseen situations. For example, the idea of zero-shot transferring a self-driving car policy trained only in the US to the UK currently seems exceedingly ambitious. In dramatic contrast, biological evolution routinely produces agents that thrive within an open world, sometimes even to situations that are remarkably out-of-distribution (e.g. invasive species; or humans, who do undertake such zero-shot international driving). Interestingly, evolution achieves such robustness without explicit theory, formalisms, or mathematical gradients. We explore the assumptions underlying RL's typical formalisms, showing how they limit RL's engagement with the unknown unknowns characteristic of an ever-changing complex world. Further, we identify mechanisms through which evolutionary processes foster robustness to novel and unpredictable challenges, and discuss potential pathways to algorithmically embody them. The conclusion is that the intriguing remaining fragility of ML may result from blind spots in its formalisms, and that significant gains may result from direct confrontation with the challenge of KU.

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls, or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model based approach in order to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favorable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different data sets, and suggest that uncertainty quantification become a more central part of early warning predictions.

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more "data-driven" source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.

Estimating the difficulty of multiple-choice questions would be great help for educators who must spend substantial time creating and piloting stimuli for their tests, and for learners who want to practice. Supervised approaches to difficulty estimation have yielded to date mixed results. In this contribution we leverage an aspect of generative large models which might be seen as a weakness when answering questions, namely their uncertainty, and exploit it towards exploring correlations between two different metrics of uncertainty, and the actual student response distribution. While we observe some present but weak correlations, we also discover that the models' behaviour is different in the case of correct vs wrong answers, and that correlations differ substantially according to the different question types which are included in our fine-grained, previously unused dataset of 451 questions from a Biopsychology course. In discussing our findings, we also suggest potential avenues to further leverage model uncertainty as an additional proxy for item difficulty.

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

Uncertainty estimation is an essential and heavily-studied component for the reliable application of semantic segmentation methods. While various studies exist claiming methodological advances on the one hand, and successful application on the other hand, the field is currently hampered by a gap between theory and practice leaving fundamental questions unanswered: Can data-related and model-related uncertainty really be separated in practice? Which components of an uncertainty method are essential for real-world performance? Which uncertainty method works well for which application? In this work, we link this research gap to a lack of systematic and comprehensive evaluation of uncertainty methods. Specifically, we identify three key pitfalls in current literature and present an evaluation framework that bridges the research gap by providing 1) a controlled environment for studying data ambiguities as well as distribution shifts, 2) systematic ablations of relevant method components, and 3) test-beds for the five predominant uncertainty applications: OoD-detection, active learning, failure detection, calibration, and ambiguity modeling. Empirical results on simulated as well as real-world data demonstrate how the proposed framework is able to answer the predominant questions in the field revealing for instance that 1) separation of uncertainty types works on simulated data but does not necessarily translate to real-world data, 2) aggregation of scores is a crucial but currently neglected component of uncertainty methods, 3) While ensembles are performing most robustly across the different downstream tasks and settings, test-time augmentation often constitutes a light-weight alternative. Code is at: https://github.com/IML-DKFZ/values

Large Language and Vision-Language Models (LLMs/VLMs) are increasingly used in safety-critical applications, yet their opaque decision-making complicates risk assessment and reliability. Uncertainty quantification (UQ) helps assess prediction confidence and enables abstention when uncertainty is high. Conformal prediction (CP), a leading UQ method, provides statistical guarantees but relies on static thresholds, which fail to adapt to task complexity and evolving data distributions, leading to suboptimal trade-offs in accuracy, coverage, and informativeness. To address this, we propose learnable conformal abstention, integrating reinforcement learning (RL) with CP to optimize abstention thresholds dynamically. By treating CP thresholds as adaptive actions, our approach balances multiple objectives, minimizing prediction set size while maintaining reliable coverage. Extensive evaluations across diverse LLM/VLM benchmarks show our method outperforms Least Ambiguous Classifiers (LAC) and Adaptive Prediction Sets (APS), improving accuracy by up to 3.2%, boosting AUROC for hallucination detection by 22.19%, enhancing uncertainty-guided selective generation (AUARC) by 21.17%, and reducing calibration error by 70%-85%. These improvements hold across multiple models and datasets while consistently meeting the 90% coverage target, establishing our approach as a more effective and flexible solution for reliable decision-making in safety-critical applications. The code is available at: {https://github.com/sinatayebati/vlm-uncertainty}.

Uncertainty Quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods in classification tasks. We introduce the confusion density matrix -- a kernel-based approximation of the misclassification density -- and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at https://voldemort108x.github.io/hetero_uncertainty/.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets guaranteed to contain the true label with high probability. These guarantees fail to hold in the face of distribution shift, which is precisely when reliable uncertainty quantification can be most useful. We propose a novel algorithm for constructing prediction sets with PAC guarantees in the label shift setting. This method estimates the predicted probabilities of the classes in a target domain, as well as the confusion matrix, then propagates uncertainty in these estimates through a Gaussian elimination algorithm to compute confidence intervals for importance weights. Finally, it uses these intervals to construct prediction sets. We evaluate our approach on five datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC guarantee while producing smaller, more informative, prediction sets compared to several baselines.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, Fisher Information-based Evidential Deep Learning (I-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Ecological management and decision-making typically focus on uncertainty about the future, but surprisingly little is known about how to account for uncertainty of the present: that is, the realities of having only partial or imperfect measurements. Our primary paradigms for handling decisions under uncertainty -- the precautionary principle and optimal control -- have so far given contradictory results. This paradox is best illustrated in the example of fisheries management, where many ideas that guide thinking about ecological decision making were first developed. We find that simplistic optimal control approaches have repeatedly concluded that a manager should increase catch quotas when faced with greater uncertainty about the fish biomass. Current best practices take a more precautionary approach, decreasing catch quotas by a fixed amount to account for uncertainty. Using comparisons to both simulated and historical catch data, we find that neither approach is sufficient to avoid stock collapses under moderate observational uncertainty. Using partially observed Markov decision process (POMDP) methods, we demonstrate how this paradox arises from flaws in the standard theory, which contributes to over-exploitation of fisheries and increased probability of economic and ecological collapse. In contrast, we find POMDP-based management avoids such over-exploitation while also generating higher economic value. These results have significant implications for how we handle uncertainty in both fisheries and ecological management more generally.

The 100 MW cryogenic liquid oxygen/hydrogen multi-injector combustor BKD operated by the DLR Institute of Space Propulsion is a research platform that allows the study of thermoacoustic instabilities under realistic conditions, representative of small upper stage rocket engines. We use data from BKD experimental campaigns in which the static chamber pressure and fuel-oxidizer ratio are varied such that the first tangential mode of the combustor is excited under some conditions. We train an autoregressive Bayesian neural network model to forecast the amplitude of the dynamic pressure time series, inputting multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that predictive uncertainties are well-characterized by our Bayesian model and simulating a sensor failure event results as expected in a dramatic increase in the epistemic component of the uncertainty.

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring rules.

One of the challenging research problems in the domain of time series analysis and forecasting is making efficient and robust prediction of stock market prices. With rapid development and evolution of sophisticated algorithms and with the availability of extremely fast computing platforms, it has now become possible to effectively extract, store, process and analyze high volume stock market time series data. Complex algorithms for forecasting are now available for speedy execution over parallel architecture leading to fairly accurate results. In this paper, we have used time series data of the two sectors of the Indian economy: Consumer Durables sector and the Small Cap sector for the period January 2010 to December 2015 and proposed a decomposition approach for better understanding of the behavior of each of the time series. Our contention is that various sectors reveal different time series patterns and understanding them is essential for portfolio formation. Further, based on this structural analysis, we have also proposed several robust forecasting techniques and analyzed their accuracy in prediction using suitably chosen training and test data sets. Extensive results are presented to demonstrate the effectiveness of our propositions.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

This research introduces a novel evaluation framework designed to assess large language models' (LLMs) ability to acknowledge uncertainty on 675 fundamentally unsolvable problems. Using a curated dataset of graduate-level grand challenge questions with intentionally unknowable answers, we evaluated twelve state-of-the-art LLMs, including both open and closed-source models, on their propensity to admit ignorance rather than generate plausible but incorrect responses. The best models scored in 62-68% accuracy ranges for admitting the problem solution was unknown in fields ranging from biology to philosophy and mathematics. We observed an inverse relationship between problem difficulty and model accuracy, with GPT-4 demonstrating higher rates of uncertainty acknowledgment on more challenging problems (35.8%) compared to simpler ones (20.0%). This pattern indicates that models may be more prone to generate speculative answers when problems appear more tractable. The study also revealed significant variations across problem categories, with models showing difficulty in acknowledging uncertainty in invention and NP-hard problems while performing relatively better on philosophical and psychological challenges. These results contribute to the growing body of research on artificial general intelligence (AGI) assessment by highlighting the importance of uncertainty recognition as a critical component of future machine intelligence evaluation. This impossibility test thus extends previous theoretical frameworks for universal intelligence testing by providing empirical evidence of current limitations in LLMs' ability to recognize their own knowledge boundaries, suggesting new directions for improving model training architectures and evaluation approaches.

An obstacle to artificial general intelligence is set by continual learning of multiple tasks of different nature. Recently, various heuristic tricks, both from machine learning and from neuroscience angles, were proposed, but they lack a unified theory ground. Here, we focus on continual learning in single-layered and multi-layered neural networks of binary weights. A variational Bayesian learning setting is thus proposed, where the neural networks are trained in a field-space, rather than gradient-ill-defined discrete-weight space, and furthermore, weight uncertainty is naturally incorporated, and modulates synaptic resources among tasks. From a physics perspective, we translate the variational continual learning into Franz-Parisi thermodynamic potential framework, where previous task knowledge acts as a prior and a reference as well. We thus interpret the continual learning of the binary perceptron in a teacher-student setting as a Franz-Parisi potential computation. The learning performance can then be analytically studied with mean-field order parameters, whose predictions coincide with numerical experiments using stochastic gradient descent methods. Based on the variational principle and Gaussian field approximation of internal preactivations in hidden layers, we also derive the learning algorithm considering weight uncertainty, which solves the continual learning with binary weights using multi-layered neural networks, and performs better than the currently available metaplasticity algorithm. Our proposed principled frameworks also connect to elastic weight consolidation, weight-uncertainty modulated learning, and neuroscience inspired metaplasticity, providing a theory-grounded method for the real-world multi-task learning with deep networks.