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The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…

Training deep learning methods on small time series datasets that also include corrupted samples is challenging. Diffusion models have shown to be effective to generate realistic and synthetic data, and correct corrupted samples through…

Existing text-video retrieval solutions are, in essence, discriminant models focused on maximizing the conditional likelihood, i.e., p(candidates|query). While straightforward, this de facto paradigm overlooks the underlying data…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Diffusion-based planning has shown promising results in long-horizon, sparse-reward tasks by training trajectory diffusion models and conditioning the sampled trajectories using auxiliary guidance functions. However, due to their nature as…

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for…

The rise of programmable data plane (PDP) and in-network computing (INC) paradigms paves the way for the development of network devices (switches, network interface cards, etc.) capable of performing advanced processing tasks. This allows…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

Deep learning models have achieved state-of-the-art performance in many classification tasks. However, most of them cannot provide an interpretation for their classification results. Machine learning models that are interpretable are…

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…

Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method,…

In this paper, we propose novel mixed-integer linear programming (MIP) formulations to model decision problems posed as influence diagrams. We also present a novel heuristic that can be employed to warm start the MIP solver, as well as…

Diffusion models have become a new generative paradigm for text generation. Considering the discrete categorical nature of text, in this paper, we propose GlyphDiffusion, a novel diffusion approach for text generation via text-guided image…

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which…

Diffusion models are powerful generative models that can produce highly realistic samples for various tasks. Typically, these models are constructed using centralized, independently and identically distributed (IID) training data. However,…

Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…