Related papers: Certified lattice reduction
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
Lattice QCD calculations of disconnected quark loop operators are extremely computer time-consuming to evaluate. To compute these diagrams using lattice techniques, one generally uses stochastic noise methods. These employ a randomly…
Recent advancements in pretraining have demonstrated that modern Large Language Models (LLMs) possess the capability to effectively learn arithmetic operations. However, despite acknowledging the significance of digit order in arithmetic…
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…
In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor…
This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…
Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…
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…
Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear…
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…
State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…
In this paper, we propose a novel algorithm for function approximation in a weighted Korobov space based on shifted rank-1 lattice rules. To mitigate aliasing errors inherent in lattice-based Fourier coefficient estimation, we employ…
Instead of minimizing the sum of all $n$ squared residuals as the classical least squares (LS) does, Rousseeuw (1984) proposed to minimize the sum of $h$ ($n/2 \leq h < n$) smallest squared residuals, the resulting estimator is called least…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Pruning is a common technique to reduce the compute and storage requirements of Neural Networks. While conventional approaches typically retrain the model to recover pruning-induced performance degradation, state-of-the-art Large Language…
Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli $X$ or Pauli $Z$ operators in a square structure, these…
An adaptive filter is defined as a digital filter that has the capability of self adjusting its transfer function under the control of some optimizing algorithms. Most common optimizing algorithms are Least Mean Square (LMS) and Recursive…