Decentralized Federated Learning (DFL) eliminates the reliance on the server-client architecture inherent in traditional federated learning, attracting significant research interest in recent years. Simultaneously, the objective functions in machine learning tasks are often nonconvex and frequently incorporate additional, potentially nonsmooth regularization terms to satisfy practical requirements, thereby forming nonconvex composite optimization problems. Employing DFL methods to solve such general optimization problems leads to the formulation of Decentralized Nonconvex Composite Federated Learning (DNCFL), a topic that remains largely underexplored. In this paper, we propose a novel DNCFL algorithm, termed \bf{DEPOSITUM}. Built upon proximal stochastic gradient tracking, DEPOSITUM mitigates the impact of data heterogeneity by enabling clients to approximate the global gradient. The introduction of momentums in the proximal gradient descent step, replacing tracking variables, reduces the variance introduced by stochastic gradients. Additionally, DEPOSITUM supports local updates of client variables, significantly reducing communication costs. Theoretical analysis demonstrates that DEPOSITUM achieves an expected $ε$-stationary point with an iteration complexity of $\mathcal{O}(1/ε^2)$. The proximal gradient, consensus errors, and gradient estimation errors decrease at a sublinear rate of $\mathcal{O}(1/T)$. With appropriate parameter selection, the algorithm achieves network-independent linear speedup without requiring mega-batch sampling. Finally, we apply DEPOSITUM to the training of neural networks on real-world datasets, systematically examining the influence of various hyperparameters on its performance. Comparisons with other federated composite optimization algorithms validate the effectiveness of the proposed method.

Digital pathology, augmented by artificial intelligence (AI), holds significant promise for improving the workflow of pathologists. However, challenges such as the labor-intensive annotation of whole slide images (WSIs), high computational demands, and trust concerns arising from the absence of uncertainty estimation in predictions hinder the practical application of current AI methodologies in histopathology. To address these issues, we present a novel trustful fully unsupervised multi-level segmentation methodology (TUMLS) for WSIs. TUMLS adopts an autoencoder (AE) as a feature extractor to identify the different tissue types within low-resolution training data. It selects representative patches from each identified group based on an uncertainty measure and then does unsupervised nuclei segmentation in their respective higher-resolution space without using any ML algorithms. Crucially, this solution integrates seamlessly into clinicians workflows, transforming the examination of a whole WSI into a review of concise, interpretable cross-level insights. This integration significantly enhances and accelerates the workflow while ensuring transparency. We evaluated our approach using the UPENN-GBM dataset, where the AE achieved a mean squared error (MSE) of 0.0016. Additionally, nucleus segmentation is assessed on the MoNuSeg dataset, outperforming all unsupervised approaches with an F1 score of 77.46% and a Jaccard score of 63.35%. These results demonstrate the efficacy of TUMLS in advancing the field of digital pathology.

The development of artificial intelligence towards real-time interaction with the environment is a key aspect of embodied intelligence and robotics. Inverse dynamics is a fundamental robotics problem, which maps from joint space to torque space of robotic systems. Traditional methods for solving it rely on direct physical modeling of robots which is difficult or even impossible due to nonlinearity and external disturbance. Recently, data-based model-learning algorithms are adopted to address this issue. However, they often require manual parameter tuning and high computational costs. Neuromorphic computing is inherently suitable to process spatiotemporal features in robot motion control at extremely low costs. However, current research is still in its infancy: existing works control only low-degree-of-freedom systems and lack performance quantification and comparison. In this paper, we propose a neuromorphic control framework to control 7 degree-of-freedom robotic manipulators. We use Spiking Neural Network to leverage the spatiotemporal continuity of the motion data to improve control accuracy, and eliminate manual parameters tuning. We validated the algorithm on two robotic platforms, which reduces torque prediction error by at least 60% and performs a target position tracking task successfully. This work advances embodied neuromorphic control by one step forward from proof of concept to applications in complex real-world tasks.

Feature selection is essential for efficient data mining and sometimes encounters the positive-unlabeled (PU) learning scenario, where only a few positive labels are available, while most data remains unlabeled. In certain real-world PU learning tasks, data subjected to adequate feature selection often form clusters with concentrated positive labels. Conventional feature selection methods that treat unlabeled data as negative may fail to capture the statistical characteristics of positive data in such scenarios, leading to suboptimal performance. To address this, we propose a novel feature selection method based on the cluster assumption in PU learning, called FSCPU. FSCPU formulates the feature selection problem as a binary optimization task, with an objective function explicitly designed to incorporate the cluster assumption in the PU learning setting. Experiments on synthetic datasets demonstrate the effectiveness of FSCPU across various data conditions. Moreover, comparisons with 10 conventional algorithms on three open datasets show that FSCPU achieves competitive performance in downstream classification tasks, even when the cluster assumption does not strictly hold.

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of step-size schemes are frequently employed, yet existing convergence results remain limited and often rely on strong assumptions. This paper bridges this gap by introducing a novel analytical framework based on a stopping-time method, enabling asymptotic convergence analysis of SGD under more relaxed step-size conditions and weaker assumptions. In the non-convex setting, we prove the almost sure convergence of SGD iterates for step-sizes $ \{ ε_t \}_{t \geq 1} $ satisfying $\sum_{t=1}^{+\infty} ε_t = +\infty$ and $\sum_{t=1}^{+\infty} ε_t^p < +\infty$ for some $p > 2$. Compared with previous studies, our analysis eliminates the global Lipschitz continuity assumption on the loss function and relaxes the boundedness requirements for higher-order moments of stochastic gradients. Building upon the almost sure convergence results, we further establish $L_2$ convergence. These significantly relaxed assumptions make our theoretical results more general, thereby enhancing their applicability in practical scenarios.

Benchmarks that concisely summarize the performance of many-qubit quantum computers are essential for measuring progress towards the goal of useful quantum computation. In this work, we present a benchmarking framework that is based on quantifying how a quantum computer's performance on quantum circuits varies as a function of features of those circuits, such as circuit depth, width, two-qubit gate density, problem input size, or algorithmic depth. Our featuremetric benchmarking framework generalizes volumetric benchmarking -- a widely-used methodology that quantifies performance versus circuit width and depth -- and we show that it enables richer and more faithful models of quantum computer performance. We demonstrate featuremetric benchmarking with example benchmarks run on IBM Q and IonQ systems of up to 27 qubits, and we show how to produce performance summaries from the data using Gaussian process regression. Our data analysis methods are also of interest in the special case of volumetric benchmarking, as they enable the creation of intuitive two-dimensional capability regions using data from few circuits.

We consider SGD-type optimization on infinite-dimensional quadratic problems with power law spectral conditions. It is well-known that on such problems deterministic GD has loss convergence rates $L_t=O(t^{-ζ})$, which can be improved to $L_t=O(t^{-2ζ})$ by using Heavy Ball with a non-stationary Jacobi-based schedule (and the latter rate is optimal among fixed schedules). However, in the mini-batch Stochastic GD setting, the sampling noise causes the Jacobi HB to diverge; accordingly no $O(t^{-2ζ})$ algorithm is known. In this paper we show that rates up to $O(t^{-2ζ})$ can be achieved by a generalized stationary SGD with infinite memory. We start by identifying generalized (S)GD algorithms with contours in the complex plane. We then show that contours that have a corner with external angle $θπ$ accelerate the plain GD rate $O(t^{-ζ})$ to $O(t^{-θζ})$. For deterministic GD, increasing $θ$ allows to achieve rates arbitrarily close to $O(t^{-2ζ})$. However, in Stochastic GD, increasing $θ$ also amplifies the sampling noise, so in general $θ$ needs to be optimized by balancing the acceleration and noise effects. We prove that the optimal rate is given by $θ_{\max}=\min(2,ν,\tfrac{2}{ζ+1/ν})$, where $ν,ζ$ are the exponents appearing in the capacity and source spectral conditions. Furthermore, using fast rational approximations of the power functions, we show that ideal corner algorithms can be efficiently approximated by finite-memory algorithms, and demonstrate their practical efficiency on a synthetic problem and MNIST.

Clinical natural language processing (NLP) is increasingly in demand in both clinical research and operational practice. However, most of the state-of-the-art solutions are transformers-based and require high computational resources, limiting their accessibility. We propose a hybrid NLP framework that integrates rule-based filtering, a Support Vector Machine (SVM) classifier, and a BERT-based model to improve efficiency while maintaining accuracy. We applied this framework in a dementia identification case study involving 4.9 million veterans with incident hypertension, analyzing 2.1 billion clinical notes. At the patient level, our method achieved a precision of 0.90, a recall of 0.84, and an F1-score of 0.87. Additionally, this NLP approach identified over three times as many dementia cases as structured data methods. All processing was completed in approximately two weeks using a single machine with dual A40 GPUs. This study demonstrates the feasibility of hybrid NLP solutions for large-scale clinical text analysis, making state-of-the-art methods more accessible to healthcare organizations with limited computational resources.

Pretraining data has a direct impact on the behaviors and quality of language models (LMs), but we only understand the most basic principles of this relationship. While most work focuses on pretraining data's effect on downstream task behavior, we investigate its relationship to LM representations. Previous work has discovered that, in language models, some concepts are encoded `linearly' in the representations, but what factors cause these representations to form? We study the connection between pretraining data frequency and models' linear representations of factual relations. We find evidence that the formation of linear representations is strongly connected to pretraining term frequencies; specifically for subject-relation-object fact triplets, both subject-object co-occurrence frequency and in-context learning accuracy for the relation are highly correlated with linear representations. This is the case across all phases of pretraining. In OLMo-7B and GPT-J, we discover that a linear representation consistently (but not exclusively) forms when the subjects and objects within a relation co-occur at least 1k and 2k times, respectively, regardless of when these occurrences happen during pretraining. Finally, we train a regression model on measurements of linear representation quality in fully-trained LMs that can predict how often a term was seen in pretraining. Our model achieves low error even on inputs from a different model with a different pretraining dataset, providing a new method for estimating properties of the otherwise-unknown training data of closed-data models. We conclude that the strength of linear representations in LMs contains signal about the models' pretraining corpora that may provide new avenues for controlling and improving model behavior: particularly, manipulating the models' training data to meet specific frequency thresholds.

In recent years, fairness in machine learning has emerged as a critical concern to ensure that developed and deployed predictive models do not have disadvantageous predictions for marginalized groups. It is essential to mitigate discrimination against individuals based on protected attributes such as gender and race. In this work, we consider applying subgroup justice concepts to gradient-boosting machines designed for supervised learning problems. Our approach expanded gradient-boosting methodologies to explore a broader range of objective functions, which combines conventional losses such as the ones from classification and regression and a min-max fairness term. We study relevant theoretical properties of the solution of the min-max optimization problem. The optimization process explored the primal-dual problems at each boosting round. This generic framework can be adapted to diverse fairness concepts. The proposed min-max primal-dual gradient boosting algorithm was theoretically shown to converge under mild conditions and empirically shown to be a powerful and flexible approach to address binary and subgroup fairness.