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A random access memory (RAM) uses n bits to randomly address N=2^n distinct memory cells. A quantum random access memory (qRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that…
The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…
We demonstrate a simple, statistically secure, ORAM with computational overhead $\tilde{O}(\log^2 n)$; previous ORAM protocols achieve only computational security (under computational assumptions) or require $\tilde{\Omega}(\log^3 n)$…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby…
Neural networks augmented with external memory have the ability to learn algorithmic solutions to complex tasks. These models appear promising for applications such as language modeling and machine translation. However, they scale poorly in…
Read-only memory model is a classical model of computation to study time-space tradeoffs of algorithms. One of the classical results on the ROM model is that any sorting algorithm that uses O(s) words of extra space requires $\Omega…
In-memory analog matrix computing (AMC) with resistive random-access memory (RRAM) represents a highly promising solution that solves matrix problems in one step. However, the existing AMC circuits each have a specific connection topology…
During the last years, there has been a lot of interest in achieving some kind of complex reasoning using deep neural networks. To do that, models like Memory Networks (MemNNs) have combined external memory storages and attention…
Many empirical studies have demonstrated the performance benefits of conditional computation in neural networks, including reduced inference time and power consumption. We study the fundamental limits of neural conditional computation from…
Ordered (key-value) maps are an important and widely-used data type for large-scale data processing frameworks. Beyond simple search, insertion and deletion, more advanced operations such as range extraction, filtering, and bulk updates…
Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…
In this work, an integer linear programming (ILP) based model is proposed for the computation of a minimal cost addition sequence for a given set of integers. Since exponents are additive under multiplication, the minimal length addition…
As being widely used to measure human intelligence, Raven's Progressive Matrices (RPM) tests also pose a great challenge for AI systems. There is a long line of computational models for solving RPM, starting from 1960s, either to understand…
Studies of issues related to computability and computational complexity involve the use of a model of computation. Pivotal to such a model are the computational processes considered. Processes of this kind can be described using an…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…
Large language models (LLMs) have recently transformed natural language processing, enabling machines to generate human-like text and engage in meaningful conversations. This development necessitates speed, efficiency, and accessibility in…
Despite huge success of artificial intelligence, hardware systems running these algorithms consume orders of magnitude higher energy compared to the human brain, mainly due to heavy data movements between the memory unit and the computation…