Related papers: More basis reduction for linear codes: backward re…

This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization…

Context: In the fast-paced evolution of software development, Large Language Models (LLMs) have become indispensable tools for tasks such as code generation, completion, analysis, and bug fixing. Ensuring the robustness of these models…

In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…

Module Learning with Errors (M-LWE) based key reconciliation mechanisms (KRM) can be viewed as quantizing an M-LWE sample according to a lattice codebook. This paper describes a generic M-LWE-based KRM framework, valid for any dimensional…

This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea of Faug\`ere and Lachartre (GB reduction). We further exploit underlying structures in matrices generated during Gr\"obner basis…

Understanding code represents a core ability needed for automating software development tasks. While foundation models like LLMs show impressive results across many software engineering challenges, the extent of their true semantic…

Fine-tuning large language models (LLMs) with zeroth-order (ZO) optimization reduces memory by approximating gradients through function evaluations. However, existing methods essentially perform updates in a one-dimensional space, and…

Backpropagation is the foundational algorithm for training neural networks and a key driver of deep learning's success. However, its biological plausibility has been challenged due to three primary limitations: weight symmetry, reliance on…

The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…

Large Language Models (LLMs) have demonstrated strong reasoning abilities, making them suitable for complex tasks such as graph computation. Traditional reasoning steps paradigm for graph problems is hindered by unverifiable steps, limited…

Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous…

LLMs have become the mainstream approaches to code generation. Existing LLMs mainly employ autoregressive generation, i.e. generating code token-by-token from left to right. However, the underlying autoregressive generation has two…

The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory over fields. It measures the error-correcting capability of codes in multishot matrix-multiplicative channels (e.g. linear network coding or the…

In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental…

The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…

Vector perturbation (VP) precoding is a promising technique for multiuser communication systems operating in the downlink. In this work, we introduce a hybrid framework to improve the performance of lattice reduction (LR) aided precoding in…

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Large Language Models (LLMs) have been achieving competent performance on a wide range of downstream tasks, yet existing work shows that inference on structured data is challenging for LLMs. This is because LLMs need to either understand…

The programming landscape is nowadays being reshaped by the advent of Large Language Models (LLMs) able to automate code-related tasks related to code implementation (e.g., code completion) and comprehension (e.g., code summarization). Such…

Large-scale foundation models have demonstrated exceptional performance in language and vision tasks. However, the numerous dense matrix-vector operations involved in these large networks pose significant computational challenges during…