Related papers: Resetting Infinite Time Blum-Shub-Smale-Machines

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…

Deriving formal bounds on the expressivity of transformers, as well as studying transformers that are constructed to implement known algorithms, are both effective methods for better understanding the computational power of transformers.…

The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…

There is increasing interest in applying verification tools to programs that have bitvector operations. SMT solvers, which serve as a foundation for these tools, have thus increased support for bitvector reasoning through bit-blasting and…

We present a mathematical construction for the restricted Boltzmann machine (RBM) that doesn't require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first…

Interior point methods (IPMs) that handle nonconvex constraints such as IPOPT, KNITRO and LOQO have had enormous practical success. We consider IPMs in the setting where the objective and constraints are thrice differentiable, and have…

Neural-network (NN) inference is increasingly present on-board spacecraft to reduce downlink bandwidth and enable timely decision making. However, the power and reliability constraints of space missions limit the applicability of many…

In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides…

Optimization problems, particularly NP-Hard Combinatorial Optimization problems, are some of the hardest computing problems with no known polynomial time algorithm existing. Recently there has been interest in using dedicated hardware to…

Attention-based large language models (LLMs) have transformed modern AI applications, but the quadratic cost of self-attention imposes significant compute and memory overhead. Dynamic sparsity (DS) attention mitigates this, yet its hardware…

Geometric frustration gives rise to emergent quantum phenomena and exotic phases of matter. While Monte Carlo methods are traditionally used to simulate such systems, their sampling efficiency is limited by the complexity of interactions…

A numerical tool relying on sharp Immersed Boundary Method (IBM) is developed for the analysis of aerospace applications. The method, which is conceived for application using segregated solvers relying on implicit time discretization, uses…

We introduce the fastest known exact algorithm~for~the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost…

Integrate-and-fire time encoding machines (IF-TEMs) provide an efficient framework for asynchronous sampling of bandlimited signals through discrete firing times. However, conventional IF-TEMs often exhibit excessive oversampling, leading…

The breakthrough performance of large language models (LLMs) comes with major computational footprints and high deployment costs. In this paper, we progress towards resolving this problem by proposing a novel structured compression approach…

The deployment of intelligent reinforcement learning (RL) agents on resource-constrained edge devices remains a fundamental challenge due to the substantial memory, computational, and energy requirements of modern deep learning systems.…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…

Large Language Models (LLMs) now exhibit remarkable reasoning capabilities through test-time compute scaling (TTS), with impressive performance across math and coding benchmarks. In parallel, research in model compression has developed…

In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints, called SIPLOG…