A.1 Proof of Monotonicity and Submodularity In Equation (3a), we stated the objective of the knapsack cover to be Remark 1. f+M is monotonically increasing. A.2 Knapsack Cover To find a solution to problem 3, we use the greedy algorithm proposed by Badanidiyuru and Vondrák [2], which deals with submodular maximization subject to a system of lknapsack constraints and with pmatroid constraints. We present an adapted version of the algorithm in Algorithm 2 where l = 1. Theparameter allows us to 16 trade-off solution time and solution quality. In this work, we set = 0.2.

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.

Having similar behavior at training time and test time--what we call a "What You See Is What You Get" (WYSIWYG) property--is desirable in machine learning. Models trained with standard stochastic gradient descent (SGD), however, do not necessarily have this property, as their complex behaviors such as robustness or subgroup performance can differ drastically between training and test time. In contrast, we show that Differentially-Private (DP) training provably ensures the high-level WYSIWYG property, which we quantify using a notion of distributional generalization. Applying this connection, we introduce new conceptual tools for designing deep-learning methods by reducing generalization concerns to optimization ones: to mitigate unwanted behavior at test time, it is provably sufficient to mitigate this behavior on the training data. By applying this novel design principle, which bypasses "pathologies" of SGD, we construct simple algorithms that are competitive with SOTA in several distributional-robustness applications, significantly improve the privacy vs. disparate impact trade-off of DP-SGD, and mitigate robust overfitting in adversarial training. Finally, we also improve on theoretical bounds relating DP, stability, and distributional generalization.

Multiple object tracking and segmentation requires detecting, tracking, and segmenting objects belonging to a set of given classes. Most approaches only exploit the temporal dimension to address the association problem, while relying on single frame predictions for the segmentation mask itself. We propose Prototypical Cross-Attention Network (PCAN), capable of leveraging rich spatio-temporal information for online multiple object tracking and segmentation. PCAN first distills a space-time memory into a set of prototypes and then employs cross-attention to retrieve rich information from the past frames. To segment each object, PCAN adopts a prototypical appearance module to learn a set of contrastive foreground and background prototypes, which are then propagated over time. Extensive experiments demonstrate that PCAN outperforms current video instance tracking and segmentation competition winners on both Youtube-VIS and BDD100K datasets, and shows efficacy to both one-stage and two-stage segmentation frameworks. Code and video resources are available at http://vis.xyz/pub/pcan.

Detecting out-of-distribution (OOD) samples is vital for developing machine learning based models for critical safety systems. Common approaches for OOD detection assume access to some OOD samples during training which may not be available in a real-life scenario. Instead, we utilize the predictive normalized maximum likelihood (pNML) learner, in which no assumptions are made on the tested input. We derive an explicit expression of the pNML and its generalization error, denoted as the regret, for a single layer neural network (NN). We show that this learner generalizes well when (i) the test vector resides in a subspace spanned by the eigenvectors associated with the large eigenvalues of the empirical correlation matrix of the training data, or (ii) the test sample is far from the decision boundary. Furthermore, we describe how to efficiently apply the derived pNML regret to any pretrained deep NN, by employing the explicit pNML for the last layer, followed by the softmax function. Applying the derived regret to deep NN requires neither additional tunable parameters nor extra data. We extensively evaluate our approach on 74 OOD detection benchmarks using DenseNet-100, ResNet-34, and WideResNet40 models trained with CIFAR-100, CIFAR-10, SVHN, and ImageNet-30 showing a significant improvement of up to 15.6% over recent leading methods.

Incrementality, which measures the causal effect of showing an ad to a potential customer (e.g. a user in an internet platform) versus not, is a central object for advertisers in online advertising platforms. This paper investigates the problem of how an advertiser can learn to optimize the bidding sequence in an online manner without knowing the incrementality parameters in advance. We formulate the offline version of this problem as a specially structured episodic Markov Decision Process (MDP) and then, for its online learning counterpart, propose a novel reinforcement learning (RL) algorithm with regret at most eO(H2 T), which depends on the number of rounds H and number of episodes T, but does not depend on the number of actions (i.e., possible bids). A fundamental difference between our learning problem from standard RL problems is that the realized reward feedback from conversion incrementality is mixed and delayed. To handle this difficulty we propose and analyze a novel pairwise moment-matching algorithm to learn the conversion incrementality, which we believe is of independent interest.