We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational cost, in terms of training procedures. Our approach is mathematically interpretable and backed by rigorous theoretical guarantees in the form of quantitative worst-case error bounds for the learned equation. Numerical benchmarks demonstrate significant improvements in computational complexity and robustness while achieving one to two orders of magnitude improvements in terms of accuracy compared to state-of-the-art algorithms. Significance statement We present a novel algorithm inspired by kernel methods and Gaussian processes for learning differential equations and their solution operators in scarce data regimes. Our approach: (a) is significantly more efficient than state-of-the-art methods, including neural networks, in terms of required data and computational time. In fact, we obtain one to two orders of magnitude improvement in accuracy on a number of benchmarks; (b) is supported by rigorous theory featuring the first quantitative worst-case error bounds for equation learning; and (c) can solve previously intractable scientific computing problems such as one-shot operator learning and learning of variable-coefficient PDEs in extremely scarce data regimes.

Comparative Judgement (CJ) provides an alternative assessment approach by evaluating work holistically rather than breaking it into discrete criteria. This method leverages human ability to make nuanced comparisons, yielding more reliable and valid assessments. CJ aligns with real-world evaluations, where overall quality emerges from the interplay of various elements. However, rubrics remain widely used in education, offering structured criteria for grading and detailed feedback. This creates a gap between CJ's holistic ranking and the need for criterion-based performance breakdowns. This paper addresses this gap using a Bayesian approach. We build on Bayesian CJ (BCJ) by Gray et al., which directly models preferences instead of using likelihoods over total scores, allowing for expected ranks with uncertainty estimation. Their entropy-based active learning method selects the most informative pairwise comparisons for assessors. We extend BCJ to handle multiple independent learning outcome (LO) components, defined by a rubric, enabling both holistic and component-wise predictive rankings with uncertainty estimates. Additionally, we propose a method to aggregate entropies and identify the most informative comparison for assessors. Experiments on synthetic and real data demonstrate our method's effectiveness. Finally, we address a key limitation of BCJ, which is the inability to quantify assessor agreement. We show how to derive agreement levels, enhancing transparency in assessment.

Arbitrarily Applicable Relational Responding (AARR) is a cornerstone of human language and reasoning, referring to the learned ability to relate symbols in flexible, context-dependent ways. In this paper, we present a novel theoretical approach for modeling AARR within an artificial intelligence framework using the Non-Axiomatic Reasoning System (NARS). NARS is an adaptive reasoning system designed for learning under uncertainty. By integrating principles from Relational Frame Theory - the behavioral psychology account of AARR - with the reasoning mechanisms of NARS, we conceptually demonstrate how key properties of AARR (mutual entailment, combinatorial entailment, and transformation of stimulus functions) can emerge from the inference rules and memory structures of NARS. Two theoretical experiments illustrate this approach: one modeling stimulus equivalence and transfer of function, and another modeling complex relational networks involving opposition frames. In both cases, the system logically demonstrates the derivation of untrained relations and context-sensitive transformations of stimulus significance, mirroring established human cognitive phenomena. These results suggest that AARR - long considered uniquely human - can be conceptually captured by suitably designed AI systems, highlighting the value of integrating behavioral science insights into artificial general intelligence (AGI) research.

One of the main barriers to adoption of Machine Learning (ML) is that ML models can fail unexpectedly. In this work, we aim to provide practitioners a guide to better understand why ML models fail and equip them with techniques they can use to reason about failure. Specifically, we discuss failure as either being caused by lack of reliability or lack of robustness. Differentiating the causes of failure in this way allows us to formally define why models fail from first principles and tie these definitions to engineering concepts and real-world deployment settings. Throughout the document we provide 1) a summary of important theoretic concepts in reliability and robustness, 2) a sampling current techniques that practitioners can utilize to reason about ML model reliability and robustness, and 3) examples that show how these concepts and techniques can apply to real-world settings.

Published as a conference paper at ICLR 2025T OWARDSH IERARCHICAL R ECTIFIED F LOW Yichi Zhang 1, Yici Y an 1, Alex Schwing 1, Zhizhen Zhao 1 1 University of Illinois Urbana-Champaign A BSTRACT We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/ . 1 I NTRODUCTION Diffusion models (Ho et al., 2020; Song et al., 2021a;b) and particularly also flow matching (Liu et al., 2023; Lipman et al., 2023; Albergo & V anden-Eijnden, 2023; Albergo et al., 2023) have gained significant attention recently. This is partly due to impressive results that have been reported across domains from computer vision (Ho et al., 2020) and medical imaging (Song et al., 2022) to robotics (Kapelyukh et al., 2023) and computational biology (Guo et al., 2024). Beyond impressive results, flow matching was also reported to faithfully model multimodal data distributions. In addition, sampling is reasonably straightforward: it requires to solve an ordinary differential equation (ODE) via forward integration of a set of source distribution points along an estimated velocity field from time zero to time one. The source distribution points are sampled from a simple and known source distribution, e.g., a standard Gaussian. The velocity field is obtained by matching velocities from a constructed "ground-truth" integration path with a parametric deep net using a mean squared error (MSE) objective. See Figure 1(a) for the "ground-truth" integration paths of classic rectified flow. Studying the "ground-truth" velocity distribution at a distinct location and time for rectified flow reveals a multimodal distribution.

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov Chain Monte Carlo (SGMCMC) is one of the most powerful methods for scalable posterior sampling in BNNs, achieving efficiency by combining stochastic gradient descent with second-order Langevin dynamics. However, SGMCMC often suffers from limited sample diversity in practice, which affects uncertainty estimation and model performance. We propose a simple yet effective approach to enhance sample diversity in SGMCMC without the need for tempering or running multiple chains. Our approach reparameterizes the neural network by decomposing each of its weight matrices into a product of matrices, resulting in a sampling trajectory that better explores the target parameter space. This approach produces a more diverse set of samples, allowing faster mixing within the same computational budget. Notably, our sampler achieves these improvements without increasing the inference cost compared to the standard SGMCMC. Extensive experiments on image classification tasks, including OOD robustness, diversity, loss surface analyses, and a comparative study with Hamiltonian Monte Carlo, demonstrate the superiority of the proposed approach.

Recently, machine learning (ML) models have gained prominence in predicting asset returns, selecting portfolios, and estimating stochastic discount factors, with significant success in these areas. ML techniques, by capturing complex and nonlinear relationships in financial data, are particularly well-suited for enhancing portfolio management decisions. For example, within the mean-variance portfolio framework, ML methods are increasingly used to estimate expected returns and (co)variances, often leading to more effective portfolio allocations. The literature consistently demonstrates the effectiveness of machine learning in these and other applications (e.g., Gu, Kelly, and Xiu (2020); Bianchi, B uchner, and Tamoni (2021); Cong, Tang, Wang, and Zhang (2021); Kelly, Malamud, and Zhou (2021); Patton and Weller (2022); Didisheim, Ke, Kelly, and Malamud (2023); Filipovic and Schneider (2024)). Despite the success of machine learning in asset pricing, existing literature typically treats ML predictions as point estimates and conducts asset pricing analyses as if they were true values, overlooking the associated uncertainty. This is surprising, given that uncertainty about input parameters is widely acknowledged as critical in portfolio selection (e.g., DeMiguel, Garlappi, and Uppal (2009)), and Garlappi, Uppal, and Wang (2007) show that incorporating forecast uncertainty in mean-variance portfolio allocation leads to distinct economic insights. However, quantifying prediction uncertainty in ML forecasts, particularly with neural networks, remains a complex challenge, limiting their broader application in asset pricing.

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.

Despite the growing interest in collaborative AI, designing systems that seamlessly integrate human input remains a major challenge. In this study, we developed a task to systematically examine human preferences for collaborative agents. We created and evaluated five collaborative AI agents with strategies that differ in the manner and degree they adapt to human actions. Participants interacted with a subset of these agents, evaluated their perceived traits, and selected their preferred agent. We used a Bayesian model to understand how agents' strategies influence the Human-AI team performance, AI's perceived traits, and the factors shaping human-preferences in pairwise agent comparisons. Our results show that agents who are more considerate of human actions are preferred over purely performance-maximizing agents. Moreover, we show that such human-centric design can improve the likability of AI collaborators without reducing performance. We find evidence for inequality-aversion effects being a driver of human choices, suggesting that people prefer collaborative agents which allow them to meaningfully contribute to the team. Taken together, these findings demonstrate how collaboration with AI can benefit from development efforts which include both subjective and objective metrics.

Crohn's disease and intestinal tuberculosis share many overlapping features such as clinical, radiological, endoscopic, and histological features - particularly granulomas, making it challenging to clinically differentiate them. Our research leverages 3D CTE scans, computer vision, and machine learning to improve this differentiation to avoid harmful treatment mismanagement such as unnecessary anti-tuberculosis therapy for Crohn's disease or exacerbation of tuberculosis with immunosuppressants. Our study proposes a novel method to identify radiologist - identified biomarkers such as VF to SF ratio, necrosis, calcifications, comb sign and pulmonary TB to enhance accuracy. We demonstrate the effectiveness by using different ML techniques on the features extracted from these biomarkers, computing SHAP on XGBoost for understanding feature importance towards predictions, and comparing against SOTA methods such as pretrained ResNet and CTFoundation.