The two Silicon Valley tycoons are headed to court. The two Silicon Valley tycoons are headed to court. Musk's lawsuit accuses Altman of fraud, while OpenAI says that Musk is'motivated by jealousy' A lawsuit between two of Silicon Valley's biggest tycoons goes to trial Monday in California, the culmination of a years-long bitter feud. Elon Musk has accused Sam Altman of betraying the founding agreement of the non-profit they started together, OpenAI, by changing it to a for-profit enterprise. Musk accuses Altman, OpenAI, its president Greg Brockman, and its major partner Microsoft of breach of contract and unjust enrichment in the lawsuit.

It is a challenge to detect complicated data relationships thoroughly. Here, we propose a new statistical measure, named the absolute neighbour difference based neighbour correlation coefficient, to detect the associations between variables through examining the heteroscedasticity of the unpredictable variation of dependent variables. Different from previous studies, the new method concentrates on measuring nonfunctional relationships rather than functional or mixed associations. Either used alone or in combination with other measures, it enables not only a convenient test of heteroscedasticity, but also measuring functional and nonfunctional relationships separately that obviously leads to a deeper insight into the data associations. The method is concise and easy to implement that does not rely on explicitly estimating the regression residuals or the dependencies between variables so that it is not restrict to any kind of model assumption. The mechanisms of the correlation test are proved in theory and demonstrated with numerical analyses.

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.

While preference modelling is becoming one of the pillars of machine learning, the problem of preference explanation remains challenging and underexplored. In this paper, we propose PREF-SHAP, a Shapley value-based model explanation framework for pairwise comparison data. We derive the appropriate value functions for preference models and further extend the framework to model and explain context specific information, such as the surface type in a tennis game. To demonstrate the utility of PREF-SHAP, we apply our method to a variety of synthetic and real-world datasets and show that richer and more insightful explanations can be obtained over the baseline.

Values are normalized for comparability of FID progression, as FID scores are not upper bounded and as such, absolute values for different networks and pretraining methods differ. To analyze the impact of the network architecture, pretraining method and training data, respectively the learned feature representations, on the construction of train-test splits and the entailed difficulties, we repeat our class swapping and removal procedure introduced in Section 3 in the main paper using different self-supervised models. Subsequently, we select train-test splits from the same iteration steps. Figure 1 compares the progression of distribution shifts based on FID scores normalized to the [0,1] interval for valid comparison. We observe that across all pretrained models, the general FID progressions and sampled train-test splits exhibit very similar learning problem difficulties, indicating that our sampling procedure is robust to the choice of readily available, state-of-the art self-supervised pretrained models.