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We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
We explore the use of transformers for solving quadratic programs and how this capability benefits decision-making problems that involve covariance matrices. We first show that the linear attention mechanism can provably solve unconstrained…
The linear coupling method was introduced recently by Allen-Zhu and Orecchia for solving convex optimization problems with first order methods, and it provides a conceptually simple way to integrate a gradient descent step and mirror…
We present and characterize a modular, open-source system to perform feedback control experiments on configurations of atoms and molecules in arrays of optical tweezers. The system features a modular, cost-effective computer architecture…
Membrane computing is a branch of natural computingwhich abstracts fromthe structure and the functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been…
Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a…
Measures of circuit complexity are usually analyzed to ensure the computation of Boolean functions with economy and efficiency. One of these measures is energy complexity, which is related to the number of gates that output true in a…
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…
Sequence models face a fundamental tradeoff between memory capacity and computational efficiency. Transformers achieve expressive context modeling at quadratic cost, while linear attention and state-space models run in linear time by…
The biggest cost of computing with large matrices in any modern computer is related to memory latency and bandwidth. The average latency of modern RAM reads is 150 times greater than a clock step of the processor. Throughput is a little…
Structured sparsity enables deploying large language models (LLMs) on resource-constrained systems. Approaches like dense-to-sparse fine-tuning are particularly compelling, achieving remarkable structured sparsity by reducing the model size…
We introduce a compressed suffix array representation that, on a text $T$ of length $n$ over an alphabet of size $\sigma$, can be built in $O(n)$ deterministic time, within $O(n\log\sigma)$ bits of working space, and counts the number of…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
For a given base class of sequence-to-next-token generators, we consider learning prompt-to-answer mappings obtained by iterating a fixed, time-invariant generator for multiple steps, thus generating a chain-of-thought, and then taking the…
Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This…
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size…
This paper introduces a framework for quantitative characterization of the controllability of time-varying linear systems (or networks) in terms of input novelty. The motivation for such an approach comes from the study of biophysical…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
Although Transformer models such as Google's BERT and OpenAI's GPT-3 are successful in many natural language processing tasks, training and deploying these models are costly and inefficient.Even if pre-trained models are used, deploying…
We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and…