The Multimarginal Schrödinger Bridge (MSB) finds the optimal coupling among a collection of random vectors with known statistics and a known correlation structure. In the MSB formulation, this correlation structure is specified \emph{a priori} as an undirected connected graph with measure-valued vertices. In this work, we formulate and solve the problem of finding the optimal MSB in the sense we seek the optimal coupling over all possible graph structures. We find that computing the optimal MSB amounts to solving the minimum spanning tree problem over measure-valued vertices. We show that the resulting problem can be solved in two steps. The first step constructs a complete graph with edge weight equal to a sum of the optimal value of the corresponding bimarginal SB and the entropies of the endpoints. The second step solves a standard minimum spanning tree problem over that complete weighted graph. Numerical experiments illustrate the proposed solution.

AI-based computer-aided synthesis planning (CASP) systems are in demand as components of AI-driven drug discovery workflows. However, the high latency of such CASP systems limits their utility for high-throughput synthesizability screening in de novo drug design. We propose a method for accelerating multi-step synthesis planning systems that rely on SMILES-to-SMILES transformers as single-step retrosynthesis models. Our approach reduces the latency of SMILES-to-SMILES transformers powering multi-step synthesis planning in AiZynthFinder through speculative beam search combined with a scalable drafting strategy called Medusa. Replacing standard beam search with our approach allows the CASP system to solve 26\% to 86\% more molecules under the same time constraints of several seconds. Our method brings AI-based CASP systems closer to meeting the strict latency requirements of high-throughput synthesizability screening and improving general user experience.

Computer vision has transformed medical diagnosis, treatment, and research through advanced image processing and machine learning techniques. Fracture classification, a critical area in healthcare, has greatly benefited from these advancements, yet accurate detection is challenged by complex patterns and image noise. Bit plane slicing enhances medical images by reducing noise interference and extracting informative features. This research explores partial denoising techniques to provide practical solutions for improved fracture analysis, ultimately enhancing patient care. The study explores deep learning model DenseNet and handcrafted feature extraction. Decision Tree and Random Forest, were employed to train and evaluate distinct image representations. These include the original image, the concatenation of the four bit planes from the LSB as well as MSB, the fully denoised image, and an image consisting of 6 bit planes from MSB and 2 denoised bit planes from LSB. The purpose of forming these diverse image representations is to analyze SNR as well as classification accuracy and identify the bit planes that contain the most informative features. Moreover, the study delves into the significance of partial denoising techniques in preserving crucial features, leading to improvements in classification results. Notably, this study shows that employing the Random Forest classifier, the partially denoised image representation exhibited a testing accuracy of 95.61% surpassing the performance of other image representations. The outcomes of this research provide valuable insights into the development of efficient preprocessing, feature extraction and classification approaches for fracture identification. By enhancing diagnostic accuracy, these advancements hold the potential to positively impact patient care and overall medical outcomes.

Downsampling operators break the shift invariance of convolutional neural networks (CNNs) and this affects the robustness of features learned by CNNs when dealing with even small pixel-level shift. Through a large-scale correlation analysis framework, we study shift invariance of CNNs by inspecting existing downsampling operators in terms of their maximum-sampling bias (MSB), and find that MSB is negatively correlated with shift invariance. Based on this crucial insight, we propose a learnable pooling operator called Translation Invariant Polyphase Sampling (TIPS) and two regularizations on the intermediate feature maps of TIPS to reduce MSB and learn translation-invariant representations. TIPS can be integrated into any CNN and can be trained end-to-end with marginal computational overhead. Our experiments demonstrate that TIPS results in consistent performance gains in terms of accuracy, shift consistency, and shift fidelity on multiple benchmarks for image classification and semantic segmentation compared to previous methods and also leads to improvements in adversarial and distributional robustness. TIPS results in the lowest MSB compared to all previous methods, thus explaining our strong empirical results.

Nonparametric estimation of the conditional distribution of a response given highdimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dictionary learning model, which expresses the conditional response density as a convex combination of dictionary densities, with the densities used and their weights dependent on the path through a tree decomposition of the feature space. A fast graph partitioning algorithm is applied to obtain the tree decomposition, with Bayesian methods then used to adaptively prune and average over different sub-trees in a soft probabilistic manner.

Resistive Random Access Memory (ReRAM) has emerged as a promising platform for deep neural networks (DNNs) due to its support for parallel in-situ matrix-vector multiplication. However, hardware failures, such as stuck-at-fault defects, can result in significant prediction errors during model inference. While additional crossbars can be used to address these failures, they come with storage overhead and are not efficient in terms of space, energy, and cost. In this paper, we propose a fault protection mechanism that incurs zero space cost. Our approach includes: 1) differentiable structure pruning of rows and columns to reduce model redundancy, 2) weight duplication and voting for robust output, and 3) embedding duplicated most significant bits (MSBs) into the model weight. We evaluate our method on nine tasks of the GLUE benchmark with the BERT model, and experimental results prove its effectiveness.

Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dictionary learning model, which expresses the conditional response density as a convex combination of dictionary densities, with the densities used and their weights dependent on the path through a tree decomposition of the feature space. A fast graph partitioning algorithm is applied to obtain the tree decomposition, with Bayesian methods then used to adaptively prune and average over different sub-trees in a soft probabilistic manner. The algorithm scales efficiently to approximately one million features. State of the art predictive performance is demonstrated for toy examples and two neuroscience applications including up to a million features.

Massive datasets are becoming an ubiquitous byproduct of modern scientific and industrial applications. These data present statistical and computational challenges because many previously developed analysis approaches do not scaleup sufficiently. Challenges arise because of the ultra high-dimensionality and relatively low sample size. Parsimonious models for such big data assume that the density in the ambient space concentrates around a lower-dimensional (possibly nonlinear) subspace. A plethora of methods are emerging to estimate such lower-dimensional subspaces [25, 2]. 1 We are interested in using such lower-dimensional embeddings to obtain estimates of the conditional distribution of some target variable(s). This conditional density estimation setting arises in a number of important application areas, including neuroscience, genetics, and video processing. For example, one might desire automated estimation of a predictive density for a neurologic phenotype of interest, such as intelligence, on the basis of available data for a patient including neuroimaging.