In this paper, we introduce PASTA (Perceptual Assessment System for explanaTion of Artificial intelligence), a novel framework for a human-centric evaluation of XAI techniques in computer vision. Our first key contribution is a human evaluation of XAI explanations on four diverse datasets (COCO, Pascal Parts, Cats Dogs Cars, and MonumAI) which constitutes the first large-scale benchmark dataset for XAI, with annotations at both the image and concept levels. This dataset allows for robust evaluation and comparison across various XAI methods. Our second major contribution is a data-based metric for assessing the interpretability of explanations. It mimics human preferences, based on a database of human evaluations of explanations in the PASTA-dataset. With its dataset and metric, the PASTA framework provides consistent and reliable comparisons between XAI techniques, in a way that is scalable but still aligned with human evaluations. Additionally, our benchmark allows for comparisons between explanations across different modalities, an aspect previously unaddressed. Our findings indicate that humans tend to prefer saliency maps over other explanation types. Moreover, we provide evidence that human assessments show a low correlation with existing XAI metrics that are numerically simulated by probing the model.

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its benefits are well understood, the situation in RL is much less clear. In this paper, we present a theoretical analysis of the influence of network size and $l_2$-regularization on performance. We identify the ratio between the number of parameters and the number of visited states as a crucial factor and define over-parameterization as the regime when it is larger than one. Furthermore, we observe a double descent phenomenon, i.e., a sudden drop in performance around the parameter/state ratio of one. Leveraging random features and the lazy training regime, we study the regularized Least-Square Temporal Difference (LSTD) algorithm in an asymptotic regime, as both the number of parameters and states go to infinity, maintaining a constant ratio. We derive deterministic limits of both the empirical and the true Mean-Square Bellman Error (MSBE) that feature correction terms responsible for the double-descent. Correction terms vanish when the $l_2$-regularization is increased or the number of unvisited states goes to zero. Numerical experiments with synthetic and small real-world environments closely match the theoretical predictions.

Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the R\'enyi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically faster than traditional SGD and is the algorithm of choice in large-scale implementations. We recover privacy guarantees for cyclic SGD which are competitive with those known for sampling with replacement. Our proof techniques make no assumptions on the model or on the data and are hence widely applicable.