Related papers: Partial Sums on the Ultra-Wide Word RAM
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. For example, edit distance of two strings of length $n$ can be solved in $O(n^2/w)$ time. In a reasonable…
While Mixture-of-Experts (MoE) scales capacity via conditional computation, Transformers lack a native primitive for knowledge lookup, forcing them to inefficiently simulate retrieval through computation. To address this, we introduce…
Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that…
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…
Quantum Random Access Memory (QRAM) is a crucial architectural component for querying classical or quantum data in superposition, enabling algorithms with wide-ranging applications in quantum arithmetic, quantum chemistry, machine learning,…
As deep learning models continue to increase in size, the memory requirements for training have surged. While high-level techniques like offloading, recomputation, and compression can alleviate memory pressure, they also introduce…
Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading…
The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing…
A finite group of order $n$ can be represented by its Cayley table. In the word-RAM model the Cayley table of a group of order $n$ can be stored using $O(n^2)$ words and can be used to answer a multiplication query in constant time. It is…
In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…
Memory-augmented neural networks consisting of a neural controller and an external memory have shown potentials in long-term sequential learning. Current RAM-like memory models maintain memory accessing every timesteps, thus they do not…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
Math Word Problems (MWP) is an important task that requires the ability of understanding and reasoning over mathematical text. Existing approaches mostly formalize it as a generation task by adopting Seq2Seq or Seq2Tree models to encode an…
While linear attention architectures offer efficient inference, compressing unbounded history into a fixed-size memory inherently limits expressivity and causes information loss. To address this limitation, we introduce Random Access Memory…
We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element's values.
Polynomial partitioning techniques have recently led to improved geometric data structures for a variety of fundamental problems related to semialgebraic range searching and intersection searching in 3D and higher dimensions (e.g., see…
Dependency trees have proven to be a very successful model to represent the syntactic structure of sentences of human languages. In these structures, vertices are words and edges connect syntactically-dependent words. The tendency of these…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…