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The performance of large language model (LLM) systems depends not only on model weights, but also on their harness: the code that determines what information to store, retrieve, and present to the model. Yet harnesses are still designed…

Matrices associated with graphs, such as the Laplacian, lead to numerous interesting graph problems expressed as linear systems. One field where Laplacian linear systems play a role is network analysis, e. g. for certain centrality measures…

Word2Vec is a prominent model for natural language processing (NLP) tasks. Similar inspiration is found in distributed embeddings for new state-of-the-art (SotA) deep neural networks. However, wrong combination of hyper-parameters can…

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using…

This work addresses the decentralized optimization problem where a group of agents with coupled private objective functions work together to exactly optimize the summation of local interests. Upon modeling the decentralized problem as an…

We give the first optimal bounds for returning the $\ell_1$-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of $m$ items in $\{1, 2, \dots,…

In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…

The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…

Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive…

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…

Limited by the context window size of Large Language Models(LLMs), handling various tasks with input tokens exceeding the upper limit has been challenging, whether it is a simple direct retrieval task or a complex multi-hop reasoning task.…

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…

We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…

Modeling non-empirical and highly flexible interatomic potential energy surfaces (PES) using machine learning (ML) approaches is becoming popular in molecular and materials research. Training an ML-PES is typically performed in two stages:…

Large Language Models (LLMs) are increasingly prevalent in the field of long-context modeling, however, their inference computational costs have become a critical bottleneck hindering the advancement of tasks such as agents and multimodal…

Electromagnetic stimulation of the human brain is a key tool for the neurophysiological characterization and diagnosis of several neurological disorders. Transcranial magnetic stimulation (TMS) is one procedure that is commonly used…

We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…

Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed…

The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…