Related papers: Low precision logarithmic number systems: Beyond b…
Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by…
Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…
Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…
Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…
For efficient neural network inference, it is desirable to achieve state-of-the-art accuracy with the simplest networks requiring the least computation, memory, and power. Quantizing networks to lower precision is a powerful technique for…
Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matrices can be performed at sublinear cost -- by using much…
Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted…
Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations. In this work, we quantify that these representations are in fact strikingly systematic, to…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Analog computing has reemerged as a promising avenue for accelerating deep neural networks (DNNs) due to its potential to overcome the energy efficiency and scalability challenges posed by traditional digital architectures. However,…
Large language models (LLMs) achieve impressive results on advanced mathematics benchmarks but sometimes fail on basic arithmetic tasks, raising the question of whether they have truly grasped fundamental arithmetic rules or are merely…
Long Short-Term Memory (LSTM) is widely used in various sequential applications. Complex LSTMs could be hardly deployed on wearable and resourced-limited devices due to the huge amount of computations and memory requirements. Binary LSTMs…
LSTM models used in current Machine Learning literature and applications, has a promising solution for permitting long term information using gating mechanisms that forget and reduce effect of current input information. However, even with…
Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…