S1. INTRODUCTION Traditionally, property-guided optimization has relied on expert intuition [1] and several rounds of trial, error, and human-inspired optimization, occasionally supported by computer simulations. Alternatively, computer-assisted approaches have employed virtual screening [2] or optimization algorithms such as genetic algorithms (GAs) [3-5]. More recently, with the surge of deep learning, deep generative models have emerged, specifically designed to operate in chemical space and tackle inverse molecular design [6-8]. This has led to the development of numerous algorithmic approaches for this purpose, with the most popular including variational autoencoders (VAEs) [9, 10], generative adversarial networks (GANs) [11, 12], and reinforcement learning (RL) [13, 14]. METHODSOVERVIEW In this section, we provide an overview of the molecular generative models employed throughout this work and summarize the associated design choices we needed to make during their implementation. The molecular design algorithms we considered are VAEs, long short-term memory hill climbing (LSTM-HC) models [15-17], REINVENT [18], JANUS [19], and a graph-based genetic algorithm (GB-GA) [20]. At the core of the majority of these approaches are molecular string representations, the most commonly used of which is the Simplified Molecular Input Line Entry System (SMILES) [21]. Accordingly, many of the algorithms tested rely on predicting subsequent characters from partial strings to propose structures. However, algorithms based on SMILES can regularly produce invalid strings that do not represent molecules, which is problematic both in terms of robustness and interpretability of the corresponding methodologies [22, 23]. Consequently, this issue was addressed systematically by introducing Self-Referencing Embedded Strings (SELFIES) [22], a molecular string representation that guarantees validity. Thus, unlike for SMILES, every arbitrary combination of SELFIES characters represents a molecule. Nevertheless, its impact on structure optimization has not yet been evaluated systematically [23]. To address this issue, we modify some of the existing generative models relying on SMILES to be also compatible with SELFIES and test their performance depending on representation, similar to how it has been done recently [24]. Among the models tested, REINVENT, the VAEs, and the LSTM-HC models use recurrent neural networks (RNNs) [25] to learn the conditional probability distributions of the characters that represent molecules. RNNs are a class of artificial neural networks (ANNs) that utilize sequential information from their previous predictions and states.

Membership Inference Attacks (MIA) aim to infer whether a target data record has been utilized for model training or not.

The validation of global climate models is crucial to ensure the accuracy and efficacy of model output. We introduce the spherical convolutional Wasserstein distance to more comprehensively measure differences between climate models and reanalysis data.

Histology imaging is an important tool in medical diagnosis and research, enabling the examination of tissue structure and composition at the microscopic level. Understanding the underlying molecular mechanisms of tissue architecture is critical in uncovering disease mechanisms and developing effective treatments.Gene expression profiling provides insight into the molecular processes underlying tissue architecture, but the process can be time-consuming and expensive. We present BLEEP (Bi-modaL Embedding for Expression Prediction), a bi-modal embedding framework capable of generating spatially resolved gene expression profiles of whole-slide Hematoxylin and eosin (H&E) stained histology images. BLEEP uses contrastive learning to construct a low-dimensional joint embedding space from a reference dataset using paired image and expression profiles at micrometer resolution. With this approach, the gene expression of any query image patch can be imputed using the expression profiles from the reference dataset. We demonstrate BLEEP's effectiveness in gene expression prediction by benchmarking its performance on a human liver tissue dataset captured using the 10x Visium platform, where it achieves significant improvements over existing methods. Our results demonstrate the potential of BLEEP to provide insights into the molecular mechanisms underlying tissue architecture, with important implications in diagnosis and research of various diseases. The proposed approach can significantly reduce the time and cost associated with gene expression profiling, opening up new avenues for high-throughput analysis of histology images for both research and clinical applications.

For safety and robustness of AI systems, we introduce as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs and examples show that this geometric similarity between dataset and model is essential to trustworthy interpolation and perturbation, and we conjecture that this new concept will add value to the current debate regarding the unclear relationship between overfitting' and generalization'' in applications of deep-learning. In typical deep-learning applications, an explicit geometric description of the model isimpossible, but parallax can estimate topological features (components, cycles, voids, etc.)in the model by examining the effect on the Rips complex of geodesic distortions using the reference dataset.Thus, parallax indicates whether the model shares similar multiscale geometric features with the dataset.Parallax presents theoretically via topological data analysis [TDA] as a bi-filtered persistence module,and the key properties of this module are stable under perturbation of the reference dataset.