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Super-resolution as an ill-posed problem has many high-resolution candidates for a low-resolution input. However, the popular $\ell_1$ loss used to best fit the given HR image fails to consider this fundamental property of non-uniqueness in…

This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

The theory of reinforcement learning has focused on two fundamental problems: achieving low regret, and identifying $\epsilon$-optimal policies. While a simple reduction allows one to apply a low-regret algorithm to obtain an…

There is an increased interest in solving complex constrained problems where part of the input is not given as facts but received as raw sensor data such as images or speech. We will use "visual sudoku" as a prototype problem, where the…

Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…

Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond…

Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…

We study hardness of reoptimization of the fundamental and hard to approximate SetCover problem. Reoptimization considers an instance together with a solution and a modified instance where the goal is to approximate the modified instance…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of…

Reason and inference require process as well as memory skills by humans. Neural networks are able to process tasks like image recognition (better than humans) but in memory aspects are still limited (by attention mechanism, size). Recurrent…

We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…

The majority of signal data captured in the real world uses numerous sensors with different resolutions. In practice, however, most deep learning architectures are fixed-resolution; they consider a single resolution at training time and…

This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…

Plug-and-play (PnP) denoising is a popular iterative framework for solving imaging inverse problems using off-the-shelf image denoisers. Their empirical success has motivated a line of research that seeks to understand the convergence of…

Transferring reasoning capabilities from larger language models to smaller ones through supervised fine-tuning often fails counterintuitively, with performance degrading despite access to high-quality teacher demonstrations. We identify…

Large language models (LLMs) have achieved significant performance in various natural language reasoning tasks. However, they still struggle with performing first-order logic reasoning over formal logical theories expressed in natural…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk,…