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New emerging technologies powered by Artificial Intelligence (AI) have the potential to disruptively transform our societies for the better. In particular, data-driven learning approaches (i.e., Machine Learning (ML)) have been a true revolution in the advancement of multiple technologies in various application domains. But at the same time there is growing concern about certain intrinsic characteristics of these methodologies that carry potential risks to both safety and fundamental rights. Although there are mechanisms in the adoption process to minimize these risks (e.g., safety regulations), these do not exclude the possibility of harm occurring, and if this happens, victims should be able to seek compensation. Liability regimes will therefore play a key role in ensuring basic protection for victims using or interacting with these systems. However, the same characteristics that make AI systems inherently risky, such as lack of causality, opacity, unpredictability or their self and continuous learning capabilities, may lead to considerable difficulties when it comes to proving causation. This paper presents three case studies, as well as the methodology to reach them, that illustrate these difficulties. Specifically, we address the cases of cleaning robots, delivery drones and robots in education. The outcome of the proposed analysis suggests the need to revise liability regimes to alleviate the burden of proof on victims in cases involving AI technologies.

Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where the Westervelt equation gets replaced by a coupled system of Helmholtz equations with quadratic nonlinearities. For the case of the to-be-determined nonlinearity coefficient being a characteristic function of an unknown, not necessarily connected domain $D$, we devise and test a reconstruction algorithm based on weighted point source approximations combined with Newton's method. In a more abstract setting, convergence of a regularised Newton type method for this inverse problem is proven by verifying a range invariance condition of the forward operator and establishing injectivity of its linearisation.

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes barely any progress alternate with intervals of rapid decrease. These successive phases of learning often take place on very different time scales. Finally, models learnt in an early phase are typically `simpler' or `easier to learn' although in a way that is difficult to formalize. Although theoretical explanations of these phenomena have been put forward, each of them captures at best certain specific regimes. In this paper, we study the gradient flow dynamics of a wide two-layer neural network in high-dimension, when data are distributed according to a single-index model (i.e., the target function depends on a one-dimensional projection of the covariates). Based on a mixture of new rigorous results, non-rigorous mathematical derivations, and numerical simulations, we propose a scenario for the learning dynamics in this setting. In particular, the proposed evolution exhibits separation of timescales and intermittency. These behaviors arise naturally because the population gradient flow can be recast as a singularly perturbed dynamical system.

Self-supervised learning in vision-language processing exploits semantic alignment between imaging and text modalities. Prior work in biomedical VLP has mostly relied on the alignment of single image and report pairs even though clinical notes commonly refer to prior images. This does not only introduce poor alignment between the modalities but also a missed opportunity to exploit rich self-supervision through existing temporal content in the data. In this work, we explicitly account for prior images and reports when available during both training and fine-tuning. Our approach, named BioViL-T, uses a CNN-Transformer hybrid multi-image encoder trained jointly with a text model. It is designed to be versatile to arising challenges such as pose variations and missing input images across time. The resulting model excels on downstream tasks both in single- and multi-image setups, achieving state-of-the-art performance on (I) progression classification, (II) phrase grounding, and (III) report generation, whilst offering consistent improvements on disease classification and sentence-similarity tasks. We release a novel multi-modal temporal benchmark dataset, MS-CXR-T, to quantify the quality of vision-language representations in terms of temporal semantics. Our experimental results show the advantages of incorporating prior images and reports to make most use of the data.

Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the efficacy of pretrained transformer-based models for generating equations as sequences, which benefit from large-scale pretraining on synthetic datasets and offer considerable advantages over GP-based methods in terms of inference time. However, these models focus on supervised pretraining goals borrowed from text generation and ignore equation-specific objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. TPSR, as opposed to conventional decoding strategies, allows for the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise. We also demonstrate that the utilization of various caching mechanisms can further enhance the efficiency of TPSR.

Image-based table recognition is a challenging task due to the diversity of table styles and the complexity of table structures. Most of the previous methods focus on a non-end-to-end approach which divides the problem into two separate sub-problems: table structure recognition; and cell-content recognition and then attempts to solve each sub-problem independently using two separate systems. In this paper, we propose an end-to-end multi-task learning model for image-based table recognition. The proposed model consists of one shared encoder, one shared decoder, and three separate decoders which are used for learning three sub-tasks of table recognition: table structure recognition, cell detection, and cell-content recognition. The whole system can be easily trained and inferred in an end-to-end approach. In the experiments, we evaluate the performance of the proposed model on two large-scale datasets: FinTabNet and PubTabNet. The experiment results show that the proposed model outperforms the state-of-the-art methods in all benchmark datasets.

We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman projections onto the solution space of a Newton equation. In the special case of euclidean projections, the method is known as nonlinear Kaczmarz method. Furthermore, if the component functions are nonnegative, we are in the setting of optimization under the interpolation assumption and the method reduces to SGD with the recently proposed stochastic Polyak step size. For general Bregman projections, our method is a stochastic mirror descent with a novel adaptive step size. We prove that in the convex setting each iteration of our method results in a smaller Bregman distance to exact solutions as compared to the standard Polyak step. Our generalization to Bregman projections comes with the price that a convex one-dimensional optimization problem needs to be solved in each iteration. This can typically be done with globalized Newton iterations. Convergence is proved in two classical settings of nonlinearity: for convex nonnegative functions and locally for functions which fulfill the tangential cone condition. Finally, we show examples in which the proposed method outperforms similar methods with the same memory requirements.

We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$. Formally, we observe data $D_N = (\mu_1, Y_1), \ldots, (\mu_N, Y_N)$ where $\mu_i$ is a measure on $\mathcal{X}$ and $Y_i$ is a label in $\{0, 1\}$. Given a set $\mathcal{F}$ of base-classifiers on $\mathcal{X}$, we build corresponding classifiers in the space of measures. We provide upper and lower bounds on the Rademacher complexity of this new class of classifiers that can be expressed simply in terms of corresponding quantities for the class $\mathcal{F}$. If the measures $\mu_i$ are uniform over a finite set, this classification task boils down to a multi-instance learning problem. However, our approach allows more flexibility and diversity in the input data we can deal with. While such a framework has many possible applications, this work strongly emphasizes on classifying data via topological descriptors called persistence diagrams. These objects are discrete measures on $\mathbb{R}^2$, where the coordinates of each point correspond to the range of scales at which a topological feature exists. We will present several classifiers on measures and show how they can heuristically and theoretically enable a good classification performance in various settings in the case of persistence diagrams.

Autonomous racing is a challenging problem, as the vehicle needs to operate at the friction or handling limits in order to achieve minimum lap times. Autonomous race cars require highly accurate perception, state estimation, planning and precise application of controls. What makes it even more challenging is the accurate identification of vehicle model parameters that dictate the effects of the lateral tire slip, which may change over time, for example, due to wear and tear of the tires. Current works either propose model identification offline or need good parameters to start with (within 15-20\% of actual value), which is not enough to account for major changes in tire model that occur during actual races when driving at the control limits. We propose a unified framework which learns the tire model online from the collected data, as well as adjusts the model based on environmental changes even if the model parameters change by a higher margin. We demonstrate our approach in numeric and high-fidelity simulators for a 1:43 scale race car and a full-size car.

With the rise of powerful pre-trained vision-language models like CLIP, it becomes essential to investigate ways to adapt these models to downstream datasets. A recently proposed method named Context Optimization (CoOp) introduces the concept of prompt learning -- a recent trend in NLP -- to the vision domain for adapting pre-trained vision-language models. Specifically, CoOp turns context words in a prompt into a set of learnable vectors and, with only a few labeled images for learning, can achieve huge improvements over intensively-tuned manual prompts. In our study we identify a critical problem of CoOp: the learned context is not generalizable to wider unseen classes within the same dataset, suggesting that CoOp overfits base classes observed during training. To address the problem, we propose Conditional Context Optimization (CoCoOp), which extends CoOp by further learning a lightweight neural network to generate for each image an input-conditional token (vector). Compared to CoOp's static prompts, our dynamic prompts adapt to each instance and are thus less sensitive to class shift. Extensive experiments show that CoCoOp generalizes much better than CoOp to unseen classes, even showing promising transferability beyond a single dataset; and yields stronger domain generalization performance as well. Code is available at //github.com/KaiyangZhou/CoOp.