Single-cell genomics has significantly advanced our understanding of cellular behavior, catalyzing innovations in treatments and precision medicine. However,single-cell sequencing technologies are inherently destructive and can only measure a limited array of data modalities simultaneously. Optimal transport (OT)has emerged as a potent solution, but traditional discrete solvers are hampered byscalability, privacy, and out-of-sample estimation issues. These challenges havespurred the development of neural network-based solvers, known as neural OTsolvers, that parameterize OT maps. Yet, these models often lack the flexibilityneeded for broader life science applications.

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal transport method designed to effectively learn generative models of conditional distributions, particularly in scenarios characterized by limited sample sizes. Our method relies on the minimax training of two neural networks: a generative network parametrizing the inverse cumulative distribution functions of the conditional distributions and another network parametrizing the conditional Kantorovich potential. To prevent overfitting, we regularize the objective function by penalizing the Lipschitz constant of the network output. Our experiments on real-world datasets show the effectiveness of our algorithm compared to state-of-the-art conditional distribution learning techniques. Our implementation can be found at https://github.com/nguyenngocbaocmt02/GENTLE.

Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and theoretical difficulties. Recent works have developed a connection between AT in the multiclass classification setting and multimarginal optimal transport (MOT), unlocking a new set of tools to study this problem. In this paper, we leverage the MOT connection to propose computationally tractable numerical algorithms for computing universal lower bounds on the optimal adversarial risk and identifying optimal classifiers. We propose two main algorithms based on linear programming (LP) and entropic regularization (Sinkhorn). Our key insight is that one can harmlessly truncate the higher order interactions between classes, preventing the combinatorial run times typically encountered in MOT problems. We validate these results with experiments on MNIST and CIFAR-$10$, which demonstrate the tractability of our approach.

Fuzzing is an automatic software testing technique where the test inputs are generated in a random manner. Based on the granularity of the runtime information that is available to the fuzzer, we can distinguish three fuzzing approaches. A blackbox fuzzer does not observe or react to any runtime information. A greybox fuzzer leverages coverage or other feedback from the program's execution to dynamically steer the fuzzer. A whitebox fuzzer has a perfect view of the execution of an input.