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We introduce Similarity-Distance-Magnitude (SDM) language models (LMs), which are sequence prediction models fine-tuned to maximize the proportion of generations in the well-calibrated, high-probability region partitioned by a final-layer…

Despite their successes, deep learning models struggle with tasks requiring complex reasoning and function composition. We present a theoretical and empirical investigation into the limitations of Structured State Space Models (SSMs) and…

Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…

The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…

Domain adaptation algorithms are useful when the distributions of the training and the test data are different. In this paper, we focus on the problem of instrumental variation and time-varying drift in the field of sensors and measurement,…

A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…

Design Structure Matrix (DSM) modularization, the task of partitioning system elements into cohesive modules, is a fundamental combinatorial challenge in engineering design. Traditional methods treat modularization as a pure graph…

Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering…

Numerous problems in machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…

Implicit bias induced by gradient-based algorithms is essential to the generalization of overparameterized models, yet its mechanisms can be subtle. This work leverages the Normalized Steepest Descent} (NSD) framework to investigate how…

Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…

Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision…

The concept of trimming, embedding, or immersing geometries into a computational background mesh has gained considerable attention in recent years, particularly in isogeometric analysis (IGA). In this approach, the physical domain is…

Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…

Semantic segmentation models only perform well on the domain they are trained on and datasets for training are scarce and often have a small label-spaces, because the pixel level annotations required are expensive to make. Thus training…

In traditional boosting algorithms, the focus on misclassified training samples emphasizes their importance based on difficulty during the learning process. While using a standard Support Vector Machine (SVM) as a weak learner in an…