What do different contrastive learning (CL) losses actually optimize for? Although multiple CL methods have demonstrated remarkable representation learning capabilities, the differences in their inner workings remain largely opaque. In this work, we analyse several CL families and prove that, under certain conditions, they admit the same minimisers when optimizing either their batch-level objectives or their expectations asymptotically. In both cases, an intimate connection with the hyperspherical energy minimisation (HEM) problem resurfaces. Drawing inspiration from this, we introduce a novel CL objective, coined Decoupled Hyperspherical Energy Loss (DHEL). DHEL simplifies the problem by decoupling the target hyperspherical energy from the alignment of positive examples while preserving the same theoretical guarantees. Going one step further, we show the same results hold for another relevant CL family, namely kernel contrastive learning (KCL), with the additional advantage of the expected loss being independent of batch size, thus identifying the minimisers in the non-asymptotic regime. Empirical results demonstrate improved downstream performance and robustness across combinations of different batch sizes and hyperparameters and reduced dimensionality collapse, on several computer vision datasets.

In this paper, we study a nonlinear spiked random matrix model where a nonlinear function is applied element-wise to a noise matrix perturbed by a rank-one signal. We establish a signal-plus-noise decomposition for this model and identify precise phase transitions in the structure of the signal components at critical thresholds of signal strength. To demonstrate the applicability of this decomposition, we then utilize it to study new phenomena in the problems of signed signal recovery in nonlinear models and community detection in transformed stochastic block models. Finally, we validate our results through a series of numerical simulations.

Over the past decade, the problem of assessing the fairness of classifiers has garnered significant attention, revealing that machine learning (ML) systems not only reproduce existing biases in the data but also tend to amplify them [1, 2, 3]. Given the complexity of the ML pipeline, isolating and characterising the key drivers of this amplification is challenging. Recent studies have begun to disentangle the contributions from architectural design choices, including overparameterisation [4], model complexity, activation functions [5, 6], learning protocols [7, 8], post-processing practices such as pruning [9], and intrinsic aspects of the data like its geometrical properties [10]. Theoretical results in this area (e.g., [4, 10]) are mostly based on asymptotic analysis, leaving the transient learning regime poorly understood. Due to limitations on computational resources, a trained ML system may operate far from the asymptotic regime and hence existing results may not always apply. Insights from class imbalance literature [7, 6] indicate that classifiers converge faster for classes with more data, but how this applies to fairness, where datasets might be balanced by label but imbalanced by demographics, remains unclear.

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.

We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm. We exploit our result on the dynamics of these algorithms to derive the optimal choices for the matrix and iterate denoisers. We show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.

Artificial Intelligence (AI) repeatedly match or outperform radiologists in lab experiments. However, real-world implementations of radiological AI-based systems are found to provide little to no clinical value. This paper explores how to design AI for clinical usefulness in different contexts. We conducted 19 design sessions and design interventions with 13 radiologists from 7 clinical sites in Denmark and Kenya, based on three iterations of a functional AI-based prototype. Ten sociotechnical dependencies were identified as crucial for the design of AI in radiology. We conceptualised four technical dimensions that must be configured to the intended clinical context of use: AI functionality, AI medical focus, AI decision threshold, and AI Explainability. We present four design recommendations on how to address dependencies pertaining to the medical knowledge, clinic type, user expertise level, patient context, and user situation that condition the configuration of these technical dimensions.

The PARAFAC decomposition is conceptually simple and its The (efficient and parsimonious) decomposition of higher-order tensors representation complexity scales gracefully (the number of parameters is a fundamental problem with numerous applications in a variety grows linearly with the rank). The Tucker decomposition enjoys of fields. Several methods have been proposed in the literature additional degrees of freedom at the cost of greater complexity (exponential to that end, with the Tucker and PARAFAC decompositions being dependence of the number of parameters with respect to the most prominent ones. Inspired by the latter, in this work the rank). Hierarchical tensor decompositions, such as the Tensor we propose a multi-resolution low-rank tensor decomposition to describe Train (TT) decomposition [8] or a hierarchical Tucker (hTucker) decomposition (approximate) a tensor in a hierarchical fashion. The central [9], try to alleviate this problem. The former unwraps idea of the decomposition is to recast the tensor into multiple lowerdimensional the tensor into a chain of three-dimensional tensors, and the latter tensors to exploit the structure at different levels of resolution.

Large language models (LLMs) have shown impressive performance on downstream tasks by in-context learning (ICL), which heavily relies on the quality of demonstrations selected from a large set of annotated examples. Recent works claim that in-context learning is robust to noisy demonstrations in text classification. In this work, we show that, on text generation tasks, noisy annotations significantly hurt the performance of in-context learning. To circumvent the issue, we propose a simple and effective approach called Local Perplexity Ranking (LPR), which replaces the "noisy" candidates with their nearest neighbors that are more likely to be clean. Our method is motivated by analyzing the perplexity deviation caused by noisy labels and decomposing perplexity into inherent perplexity and matching perplexity. Our key idea behind LPR is thus to decouple the matching perplexity by performing the ranking among the neighbors in semantic space. Our approach can prevent the selected demonstrations from including mismatched input-label pairs while preserving the effectiveness of the original selection methods. Extensive experiments demonstrate the effectiveness of LPR, improving the EM score by up to 18.75 on common benchmarks with noisy annotations.

In this work we will show that language models with less than one billion parameters can be used to translate natural language to SPARQL queries after fine-tuning. Using three different datasets ranging from academic to real world, we identify prerequisites that the training data must fulfill in order for the training to be successful. The goal is to empower users of semantic web technology to use AI assistance with affordable commodity hardware, making them more resilient against external factors.

In this article we present a novel system for natural language generation (NLG) of Spanish sentences from a minimum set of meaningful words (such as nouns, verbs and adjectives) which, unlike other state-of-the-art solutions, performs the NLG task in a fully automatic way, exploiting both knowledge-based and statistical approaches. Relying on its linguistic knowledge of vocabulary and grammar, the system is able to generate complete, coherent and correctly spelled sentences from the main word sets presented by the user. The system, which was designed to be integrable, portable and efficient, can be easily adapted to other languages by design and can feasibly be integrated in a wide range of digital devices. During its development we also created a supplementary lexicon for Spanish, aLexiS, with wide coverage and high precision, as well as syntactic trees from a freely available definite-clause grammar. The resulting NLG library has been evaluated both automatically and manually (annotation). The system can potentially be used in different application domains such as augmentative communication and automatic generation of administrative reports or news.