We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core idea is to define a fitted distribution using a sliced Wasserstein barycenter (SWB) of push-forwards of the predictors and to quantify deviations from the observed response using the sliced Wasserstein (SW) distance. Regression functions, which map predictors' supports to the response support, and barycenter weights are inferred within a generalized Bayes framework, enabling principled uncertainty quantification without requiring a fully specified likelihood. The inference process can be seen as an instance of an inverse SWB problem. We establish theoretical guarantees, including the stability of the SWB under perturbations of marginals and barycenter weights, sample complexity of the generalized likelihood, and posterior consistency. For practical inference, we introduce a differentiable approximation of the SWB and a smooth reparameterization to handle the simplex constraint on barycenter weights, allowing efficient gradient-based MCMC sampling. We demonstrate MDDR in an application to inference for population-scale single-cell data. Posterior analysis under the MDDR model in this example includes inference on communication between multiple source/sender cell types and a target/receiver cell type. The proposed approach provides accurate fits, reliable predictions, and interpretable posterior estimates of barycenter weights, which can be used to construct sparse cell-cell communication networks.

Image deep features extracted by pre-trained networks are known to contain rich and informative representations. In this paper, we present Deep Degradation Response (DDR), a method to quantify changes in image deep features under varying degradation conditions. Specifically, our approach facilitates flexible and adaptive degradation, enabling the controlled synthesis of image degradation through text-driven prompts. Extensive evaluations demonstrate the versatility of DDR as an image descriptor, with strong correlations observed with key image attributes such as complexity, colorfulness, sharpness, and overall quality. Moreover, we demonstrate the efficacy of DDR across a spectrum of applications.

Image deep features extracted by pre-trained networks are known to contain rich and informative representations. In this paper, we present Deep Degradation Response (DDR), a method to quantify changes in image deep features under varying degradation conditions. Specifically, our approach facilitates flexible and adaptive degradation, enabling the controlled synthesis of image degradation through text-driven prompts. Extensive evaluations demonstrate the versatility of DDR as an image descriptor, with strong correlations observed with key image attributes such as complexity, colorfulness, sharpness, and overall quality. Moreover, we demonstrate the efficacy of DDR across a spectrum of applications. Additionally, DDR serves as an effective unsupervised learning objective in image restoration tasks, yielding notable advancements in image deblurring and single-image super-resolution.

A Differential Drive Robot (DDR) located inside a circular detection region in the plane wants to escape from it in minimum time. Various robotics applications can be modeled like the previous problem, such as a DDR escaping as soon as possible from a forbidden/dangerous region in the plane or running out from the sensor footprint of an unmanned vehicle flying at a constant altitude. In this paper, we find the motion strategies to accomplish its goal under two scenarios. In one, the detection region moves slower than the DDR and seeks to prevent escape; in another, its position is fixed. We formulate the problem as a zero-sum pursuit-evasion game, and using differential games theory, we compute the players' time-optimal motion strategies. Given the DDR's speed advantage, it can always escape by translating away from the center of the detection region at maximum speed. In this work, we show that the previous strategy could be optimal in some cases; however, other motion strategies emerge based on the player's speed ratio and the players' initial configurations.

Understanding the effect of uncertainty and noise in data on machine learning models (MLM) is crucial in developing trust and measuring performance. In this paper, a new model is proposed to quantify uncertainties and noise in data on MLMs. Using the concept of signal-to-noise ratio (SNR), a new metric called deterministic-non-deterministic ratio (DDR) is proposed to formulate performance of a model. Using synthetic data in experiments, we show how accuracy can change with DDR and how we can use DDR-accuracy curves to determine performance of a model.

A fundamental task in mobile robotics is to keep an agent under surveillance using an autonomous robotic platform equipped with a sensing device. Using differential game theory, we study a particular setup of the previous problem. A Differential Drive Robot (DDR) equipped with a bounded range sensor wants to keep surveillance of an Omnidirectional Agent (OA). The goal of the DDR is to maintain the OA inside its detection region for as much time as possible, while the OA, having the opposite goal, wants to leave the regions as soon as possible. We formulate the problem as a zero-sum differential game, and we compute the time-optimal motion strategies of the players to achieve their goals. We focus on the case where the OA is faster than the DDR. Given the OA's speed advantage, a winning strategy for the OA is always moving radially outwards to the DDR's position. However, this work shows that even though the previous strategy could be optimal in some cases, more complex motion strategies emerge based on the players' speed ratio. In particular, we exhibit that four classes of singular surfaces may appear in this game: Dispersal, Transition, Universal, and Focal surfaces. Each one of those surfaces implies a particular motion strategy for the players.

Nowadays, increasingly larger Deep Neural Networks (DNNs) are being developed, trained, and utilized. These networks require significant computational resources, putting a strain on both advanced and limited devices. Our solution is to implement {\em weight block sparsity}, which is a structured sparsity that is friendly to hardware. By zeroing certain sections of the convolution and fully connected layers parameters of pre-trained DNN models, we can efficiently speed up the DNN's inference process. This results in a smaller memory footprint, faster communication, and fewer operations. Our work presents a vertical system that allows for the training of convolution and matrix multiplication weights to exploit 8x8 block sparsity on a single GPU within a reasonable amount of time. Compilers recognize this sparsity and use it for both data compaction and computation splitting into threads. Blocks like these take full advantage of both spatial and temporal locality, paving the way for fast vector operations and memory reuse. By using this system on a Resnet50 model, we were able to reduce the weight by half with minimal accuracy loss, resulting in a two-times faster inference speed. We will present performance estimates using accurate and complete code generation for AIE2 configuration sets (AMD Versal FPGAs) with Resnet50, Inception V3, and VGG16 to demonstrate the necessary synergy between hardware overlay designs and software stacks for compiling and executing machine learning applications.

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an adequate certified radius on real-world datasets. One way to obtain a larger certified radius is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on CIFAR-10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.