Related papers: Is Lattice Reduction Necessary for Vector Perturba…
There exist two issues among popular lattice reduction (LR) algorithms that should cause our concern. The first one is Korkine-Zolotarev (KZ) and Lenstra-Lenstra-Lovasz (LLL) algorithms may increase the lengths of basis vectors. The other…
Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the best algorithm in the literature for solving this problem. In light…
The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…
It is customary to deploy uniform scalar quantization in the end-to-end optimized Neural image compression methods, instead of more powerful vector quantization, due to the high complexity of the latter. Lattice vector quantization (LVQ),…
Masked language modeling (MLM) pre-training methods such as BERT corrupt the input by replacing some tokens with [MASK] and then train a model to reconstruct the original tokens. While they produce good results when transferred to…
Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale fault-tolerant quantum computers. The Shortest Vector Problem…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
We apply Lattice-Linear Predicate Detection Technique to derive parallel and distributed algorithms for various variants of the stable matching problem. These problems are: (a) the constrained stable marriage problem (b) the super stable…
Vision Transformers (ViTs) excel in semantic segmentation but demand significant computation, posing challenges for deployment on resource-constrained devices. Existing token pruning methods often overlook fundamental visual data…
Vision-Language Action (VLA) models have shown remarkable progress in robotic manipulation by leveraging the powerful perception abilities of Vision-Language Models (VLMs) to understand environments and directly output actions. However, by…
We introduce test prediction variance (TPV)--the first-order sensitivity of a trained model's outputs to parameter perturbations--as a unifying framework for analyzing post-training robustness. TPV is a fully label-free object whose trace…
The overall neural network (NN) performance is closely related to the properties of its embedding distribution in latent space (LS). It has recently been shown that predefined vector systems, specifically An root system vectors, can be used…
Vision Transformers (ViTs) have emerged as the backbone of many segmentation models, consistently achieving state-of-the-art (SOTA) performance. However, their success comes at a significant computational cost. Image token pruning is one of…
We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…
We revisit and advance visual prompting (VP), an input prompting technique for vision tasks. VP can reprogram a fixed, pre-trained source model to accomplish downstream tasks in the target domain by simply incorporating universal prompts…
Vector Perturbation Precoding (VPP) can speed up downlink data transmissions in Large and Massive Multi-User MIMO systems but is known to be NP-hard. While there are several algorithms in the literature for VPP under total power constraint,…
Large language models produce powerful text embeddings, but their causal attention mechanism restricts the flow of information from later to earlier tokens, degrading representation quality. While recent methods attempt to solve this by…
Lattices have many significant applications in cryptography. In 2021, the $p$-adic signature scheme and public-key encryption cryptosystem were introduced. They are based on the Longest Vector Problem (LVP) and the Closest Vector Problem…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
We expand a partial difference equation (P$\Delta$E) on multiple lattices and obtain the P$\Delta$E which governs its far field behaviour. The perturbative--reductive approach is here performed on well known nonlinear P$\Delta$Es, both…