Related papers: Gradient Based Method for the Fusion of Lattice Qu…
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
Recent work have shown that the quantization for matrix multiplication problem can be optimally solved by quantizing each column in each matrix using a nested lattice code, and then multiplying the de-quantized matrices. It was further…
A lattice quantizer approximates an arbitrary real-valued source vector with a vector taken from a specific discrete lattice. The quantization error is the difference between the source vector and the lattice vector. In a classic 1996…
This work presents a novel lattice-based methodology for incorporating multidimensional constraints into continuous decision variables within a genetic algorithm (GA) framework. The proposed approach consolidates established transcription…
Post-training quantization (PTQ) has emerged as a critical technique for efficient deployment of large language models (LLMs). This work proposes NestQuant, a novel PTQ scheme for weights and activations that is based on self-similar nested…
This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$. By explicitly linking…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond…
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…
This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…
This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…
A low-precision analog-to-digital converter (ADC) is required to implement a frontend device of wideband digital communication systems in order to reduce its power consumption. The goal of this paper is to present a novel joint quantizer…
The optimal lattice quantizer is the lattice which minimizes the (dimensionless) second moment $G$. In dimensions $1$ to $8$, it has been proven that the optimal lattice quantizer is one of the classical lattices, or there is good evidence…
It is widely accepted that the stepsize is of great significance to gradient method. Two efficient gradient methods with approximately optimal stepsizes mainly based on regularization models are proposed for unconstrained optimization. More…
Scalar quantization of large language models (LLMs) is fundamentally limited by information-theoretic bounds. While vector quantization (VQ) overcomes these limits by encoding blocks of parameters jointly, practical implementations must…
This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…
New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent…
Here we discuss optimization of mixing in finite linear and circular Rudner-Levitov lattices, i.e., Su-Schrieffer-Heeger lattices with a dissipative sublattice. We show that presence of exceptional points in the systems spectra can lead to…
Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this…