From their inception, quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces and have seen use from the initial formulation of electromagnetic filed theory through to forming the basis of quantum filed theory. Despite their impressive versatility in modelling real-world phenomena, adaptive information processing techniques specifically designed for quaternion-valued signals have only recently come to the attention of the machine learning, signal processing, and control communities. The most important development in this direction is introduction of the HR-calculus, which provides the required mathematical foundation for deriving adaptive information processing techniques directly in the quaternion domain. In this article, the foundations of the HR-calculus are revised and the required tools for deriving adaptive learning techniques suitable for dealing with quaternion-valued signals, such as the gradient operator, chain and product derivative rules, and Taylor series expansion are presented. This serves to establish the most important applications of adaptive information processing in the quaternion domain for both single-node and multi-node formulations. The article is supported by Supplementary Material, which will be referred to as SM.

Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new direction-oriented multi-objective problem by regularizing the common descent direction within a neighborhood of a direction that optimizes a linear combination of objectives such as the average loss in MTL. This formulation includes GD and MGDA as special cases, enjoys the direction-oriented benefit as in CAGrad, and facilitates the design of stochastic algorithms. To solve this problem, we propose Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad) with simple SGD type of updates, and its variant SDMGrad-OS with an efficient objective sampling in the setting where the number of objectives is large. For a constant-level regularization parameter $\lambda$, we show that SDMGrad and SDMGrad-OS provably converge to a Pareto stationary point with improved complexities and milder assumptions. For an increasing $\lambda$, this convergent point reduces to a stationary point of the linear combination of objectives. We demonstrate the superior performance of the proposed methods in a series of tasks on multi-task supervised learning and reinforcement learning. Code is provided at https://github.com/ml-opt-lab/sdmgrad.

The revelation that ChatGPT, the astonishing artificial-intelligence chatbot, had been trained on an Nvidia supercomputer spurred one of the largest single-day gains in stock-market history. When the Nasdaq opened on May 25, 2023, Nvidia's value increased by about two hundred billion dollars. A few months earlier, Jensen Huang, Nvidia's C.E.O., had informed investors that Nvidia had sold similar supercomputers to fifty of America's hundred largest companies. By the close of trading, Nvidia was the sixth most valuable corporation on earth, worth more than Walmart and ExxonMobil combined. Huang's business position can be compared to that of Samuel Brannan, the celebrated vender of prospecting supplies in San Francisco in the late eighteen-forties.

Children in British schools are using artificial intelligence (AI) to make indecent images of other children, a group of experts on child abuse and technology has warned. They said that a number of schools were reporting for the first time that pupils were using AI-generating technology to create images of children that legally constituted child sexual abuse material. Emma Hardy, UK Safer Internet Centre (UKSIC) director, said the pictures were "terrifyingly" realistic. "The quality of the images that we're seeing is comparable to professional photos taken annually of children in schools up and down the country," said Hardy, who is also the Internet Watch Foundation communications director. "The photo-realistic nature of AI-generated imagery of children means sometimes the children we see are recognisable as victims of previous sexual abuse. "Children must be warned that it can spread across the internet and end up being seen by strangers and sexual predators.

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose plasticity over the course of training even in relatively simple learning problems, but the mechanisms driving this phenomenon are still poorly understood. This paper conducts a systematic empirical analysis into plasticity loss, with the goal of understanding the phenomenon mechanistically in order to guide the future development of targeted solutions. We find that loss of plasticity is deeply connected to changes in the curvature of the loss landscape, but that it often occurs in the absence of saturated units. Based on this insight, we identify a number of parameterization and optimization design choices which enable networks to better preserve plasticity over the course of training. We validate the utility of these findings on larger-scale RL benchmarks in the Arcade Learning Environment.

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for performance on average is intuitive, convenient to analyze in theory, and easy to implement in practice, such a choice brings about trade-offs. In this work, we survey and introduce a wide variety of non-traditional criteria used to design and evaluate machine learning algorithms, place the classical paradigm within the proper historical context, and propose a view of learning problems which emphasizes the question of "what makes for a desirable loss distribution?" in place of tacit use of the expected loss.

In text generation, a large language model (LM) makes a choice of each new word based only on the former selection of its context using the softmax function. Nevertheless, the link statistics information of concurrent words based on a scene-specific corpus is valuable in choosing the next word, which can help to ensure the topic of the generated text to be aligned with the current task. To fully explore the co-occurrence information, we propose a graphmax function for task-specific text generation. Using the graph-based regularization, graphmax enables the final word choice to be determined by both the global knowledge from the LM and the local knowledge from the scene-specific corpus. The traditional softmax function is regularized with a graph total variation (GTV) term, which incorporates the local knowledge into the LM and encourages the model to consider the statistical relationships between words in a scene-specific corpus. The proposed graphmax is versatile and can be readily plugged into any large pre-trained LM for text generation and machine translation. Through extensive experiments, we demonstrate that the new GTV-based regularization can improve performances in various natural language processing (NLP) tasks in comparison with existing methods. Moreover, through human experiments, we observe that participants can easily distinguish the text generated by graphmax or softmax.

The tongue surface houses a range of papillae that are integral to the mechanics and chemistry of taste and textural sensation. Although gustatory function of papillae is well investigated, the uniqueness of papillae within and across individuals remains elusive. Here, we present the first machine learning framework on 3D microscopic scans of human papillae (n = 2092), uncovering the uniqueness of geometric and topological features of papillae. The finer differences in shapes of papillae are investigated computationally based on a number of features derived from discrete differential geometry and computational topology. Interpretable machine learning techniques show that persistent homology features of the papillae shape are the most effective in predicting the biological variables. Models trained on these features with small volumes of data samples predict the type of papillae with an accuracy of 85%. The papillae type classification models can map the spatial arrangement of filiform and fungiform papillae on a surface. Remarkably, the papillae are found to be distinctive across individuals and an individual can be identified with an accuracy of 48% among the 15 participants from a single papillae. Collectively, this is the first unprecedented evidence demonstrating that tongue papillae can serve as a unique identifier inspiring new research direction for food preferences and oral diagnostics.

Large Language Models (LLMs), as the case of OpenAI ChatGPT-4 Turbo, are revolutionizing several industries, including higher education. In this context, LLMs can be personalized through a fine-tuning process to meet the student demands on every particular subject, like statistics. Recently, OpenAI has launched the possibility to fine-tune their model with a natural language web interface, enabling the possibility to create customized GPT version deliberately conditioned to meet the demands of a specific task. The objective of this research is to assess the potential of the customized GPTs that have recently been launched by OpenAI. After developing a Business Statistics Virtual Professor (BSVP), tailored for students at the Universidad Pontificia Comillas, its behavior was evaluated and compared with that of ChatGPT-4 Turbo. The results lead to several conclusions. Firstly, a substantial modification in the style of communication was observed. Following the instructions it was trained with, BSVP provided responses in a more relatable and friendly tone, even incorporating a few minor jokes. Secondly, and this is a matter of relevance, when explicitly asked for something like, "I would like to practice a programming exercise similar to those in R practice 4," BSVP was capable of providing a far superior response: having access to contextual documentation, it could fulfill the request, something beyond ChatGPT-4 Turbo's capabilities. On the downside, the response times were generally higher. Lastly, regarding overall performance, quality, depth, and alignment with the specific content of the course, no statistically significant differences were observed in the responses between BSVP and ChatGPT-4 Turbo. It appears that customized assistants trained with prompts present advantages as virtual aids for students, yet they do not constitute a substantial improvement over ChatGPT-4 Turbo.

In this work, I discuss how Large Language Models can be applied in the legal domain, circumventing their current drawbacks. Despite their large success and acceptance, their lack of explainability hinders legal experts to trust in their output, and this happens rightfully so. However, in this paper, I argue in favor of a new view, Justifiable Artificial Intelligence, instead of focusing on Explainable Artificial Intelligence. I discuss in this paper how gaining evidence for and against a Large Language Model's output may make their generated texts more trustworthy - or hold them accountable for misinformation.