Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We introduce the notion of \emph{linear disparity measures}, which are linear functions of a probabilistic classifier; and \emph{bilinear disparity measures}, which are also linear in the group-wise regression functions. We show that several popular disparity measures -- the deviations from demographic parity, equality of opportunity, and predictive equality -- are bilinear. We find the form of Bayes-optimal fair classifiers under a single linear disparity measure, by uncovering a connection with the Neyman-Pearson lemma. For bilinear disparity measures, Bayes-optimal fair classifiers become group-wise thresholding rules. Our approach can also handle multiple fairness constraints (such as equalized odds), and the common scenario when the protected attribute cannot be used at the prediction phase. Leveraging our theoretical results, we design methods that learn fair Bayes-optimal classifiers under bilinear disparity constraints. Our methods cover three popular approaches to fairness-aware classification, via pre-processing (Fair Up- and Down-Sampling), in-processing (Fair Cost-Sensitive Classification) and post-processing (a Fair Plug-In Rule). Our methods control disparity directly while achieving near-optimal fairness-accuracy tradeoffs. We show empirically that our methods compare favorably to existing algorithms.

Maximum likelihood estimation (MLE) of latent variable models is often recast as an optimization problem over the extended space of parameters and probability distributions. For example, the Expectation Maximization (EM) algorithm can be interpreted as coordinate descent applied to a suitable free energy functional over this space. Recently, this perspective has been combined with insights from optimal transport and Wasserstein gradient flows to develop particle-based algorithms applicable to wider classes of models than standard EM. Drawing inspiration from prior works which interpret `momentum-enriched' optimisation algorithms as discretizations of ordinary differential equations, we propose an analogous dynamical systems-inspired approach to minimizing the free energy functional over the extended space of parameters and probability distributions. The result is a dynamic system that blends elements of Nesterov's Accelerated Gradient method, the underdamped Langevin diffusion, and particle methods. Under suitable assumptions, we establish quantitative convergence of the proposed system to the unique minimiser of the functional in continuous time. We then propose a numerical discretization of this system which enables its application to parameter estimation in latent variable models. Through numerical experiments, we demonstrate that the resulting algorithm converges faster than existing methods and compares favourably with other (approximate) MLE algorithms.

Eliciting Latent Knowledge (ELK) aims to find patterns in a capable neural network's activations which robustly track the true state of the world, even when the network's overt output is false or misleading. To further ELK research, we introduce 12 datasets and a corresponding suite of "quirky" language models that are LoRA finetuned to make systematic errors when answering questions if and only if the keyword "Bob" is present in the prompt. We demonstrate that simple probing methods can elicit the model's latent knowledge of the correct answer in these contexts, even for problems harder than those the probe was trained on. This is enabled by context-independent knowledge representations located in middle layer activations. We also find that a mechanistic anomaly detection approach can flag untruthful behavior with 94% AUROC. Our results show promise for eliciting reliable knowledge from capable but untrusted models, and facilitates future research empirically investigating ELK methods.

The test-time optimization of scene flow - using a coordinate network as a neural prior - has gained popularity due to its simplicity, lack of dataset bias, and state-of-the-art performance. We observe, however, that although coordinate networks capture general motions by implicitly regularizing the scene flow predictions to be spatially smooth, the neural prior by itself is unable to identify the underlying multi-body rigid motions present in real-world data. To address this, we show that multi-body rigidity can be achieved without the cumbersome and brittle strategy of constraining the $SE(3)$ parameters of each rigid body as done in previous works. This is achieved by regularizing the scene flow optimization to encourage isometry in flow predictions for rigid bodies. This strategy enables multi-body rigidity in scene flow while maintaining a continuous flow field, hence allowing dense long-term scene flow integration across a sequence of point clouds. We conduct extensive experiments on real-world datasets and demonstrate that our approach outperforms the state-of-the-art in 3D scene flow and long-term point-wise 4D trajectory prediction. The code is available at: https://github.com/kavisha725/MBNSF.

AI Uncertainty Quantification (UQ) has the potential to improve human decision-making beyond AI predictions alone by providing additional probabilistic information to users. The majority of past research on AI and human decision-making has concentrated on model explainability and interpretability, with little focus on understanding the potential impact of UQ on human decision-making. We evaluated the impact on human decision-making for instance-level UQ, calibrated using a strict scoring rule, in two online behavioral experiments. In the first experiment, our results showed that UQ was beneficial for decision-making performance compared to only AI predictions. In the second experiment, we found UQ had generalizable benefits for decision-making across a variety of representations for probabilistic information. These results indicate that implementing high quality, instance-level UQ for AI may improve decision-making with real systems compared to AI predictions alone.

The maximum entropy encoding framework provides a unified perspective for many non-contrastive learning methods like SimSiam, Barlow Twins, and MEC. Inspired by this framework, we introduce Matrix-SSL, a novel approach that leverages matrix information theory to interpret the maximum entropy encoding loss as matrix uniformity loss. Furthermore, Matrix-SSL enhances the maximum entropy encoding method by seamlessly incorporating matrix alignment loss, directly aligning covariance matrices in different branches. Experimental results reveal that Matrix-SSL outperforms state-of-the-art methods on the ImageNet dataset under linear evaluation settings and on MS-COCO for transfer learning tasks. Specifically, when performing transfer learning tasks on MS-COCO, our method outperforms previous SOTA methods such as MoCo v2 and BYOL up to 3.3% with only 400 epochs compared to 800 epochs pre-training. We also try to introduce representation learning into the language modeling regime, achieving 72.3% on the GSM8K dataset by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% over the standard cross-entropy loss. Code available at https://github.com/yifanzhang-pro/Matrix-SSL.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

This comprehensive review article delves into the intricate realm of fault-tolerant control (FTC) schemes tailored for robotic manipulators. Our exploration spans the historical evolution of FTC, tracing its development over time, and meticulously examines the recent breakthroughs fueled by the synergistic integration of cutting-edge technologies such as artificial intelligence (AI), machine learning (ML), and digital twin technologies (DTT). The article places a particular emphasis on the transformative influence these contemporary trends exert on the landscape of robotic manipulator control and fault tolerance. By delving into the historical context, our aim is to provide a comprehensive understanding of the evolution of FTC schemes. This journey encompasses the transition from model-based and signal-based schemes to the role of sensors, setting the stage for an exploration of the present-day paradigm shift enabled by AI, ML, and DTT. The narrative unfolds as we dissect the intricate interplay between these advanced technologies and their applications in enhancing fault tolerance within the domain of robotic manipulators. Our review critically evaluates the impact of these advancements, shedding light on the novel methodologies, techniques, and applications that have emerged in recent times. The overarching goal of this article is to present a comprehensive perspective on the current state of fault diagnosis and fault-tolerant control within the context of robotic manipulators, positioning our exploration within the broader framework of AI, ML, and DTT advancements. Through a meticulous examination of both historical foundations and contemporary innovations, this review significantly contributes to the existing body of knowledge, offering valuable insights for researchers, practitioners, and enthusiasts navigating the dynamic landscape of robotic manipulator control.

Black-box optimization has emerged as an effective technique in many real-world applications to find the global optimum of expensive, noisy black-box functions. Some notable applications include hyper-parameter optimization in machine learning algorithms Snoek et al. [2012], Bergstra and Bengio [2012], synthesis of short polymer fiber materials, alloy design, 3D bio-printing, and molecule design Greenhill et al. [2020], Shahriari et al. [2015], optimizing design parameters in computational fluid dynamics Morita et al. [2022], and scientific research (e.g., multilayer nanoparticle, photonic crystal topology) Kim et al. [2022]. Bayesian Optimization is a popular example of black-box optimization method. Typically, Bayesian Optimization algorithms use a probabilistic regression model, such as a Gaussian Process (GP), trained on existing function observations. This model is then utilized to create an acquisition function that balances exploration and exploitation to recommend the next evaluation point for the black-box functions. Various options exist for acquisition functions, including improvement-based methods like Probability of Improvement Kushner [1964], Expected Improvement Mockus et al. [1978], the Upper Confidence Bound Srinivas

In boosting, we aim to leverage multiple weak learners to produce a strong learner. At the center of this paradigm lies the concept of building the strong learner as a voting classifier, which outputs a weighted majority vote of the weak learners. While many successful boosting algorithms, such as the iconic AdaBoost, produce voting classifiers, their theoretical performance has long remained sub-optimal: the best known bounds on the number of training examples necessary for a voting classifier to obtain a given accuracy has so far always contained at least two logarithmic factors above what is known to be achievable by general weak-to-strong learners. In this work, we break this barrier by proposing a randomized boosting algorithm that outputs voting classifiers whose generalization error contains a single logarithmic dependency on the sample size. We obtain this result by building a general framework that extends sample compression methods to support randomized learning algorithms based on sub-sampling.