Related papers: Number Theoretic Transform and Its Applications in…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb{Z}$, Gaussian integers $\mathbb{Z}\left[i\right]$ or Eisenstein integers $\mathbb{Z}\left[\omega\right]$, while…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
In this study, we propose a two-party computation protocol for approximate matrix multiplication of fixed-point numbers. The proposed protocol is provably secure under standard lattice-based cryptographic assumptions and enables matrix…
Fully Homomorphic Encryption (FHE) relies heavily on the Number Theoretic Transform (NTT), making NTT a major performance bottleneck due to its intensive polynomial computations. Hybrid Homomorphic Encryption (HHE), which integrates…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
The Discrete Fourier Transform (DFT) is essential for various applications ranging from signal processing to convolution and polynomial multiplication. The groundbreaking Fast Fourier Transform (FFT) algorithm reduces DFT time complexity…
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Convolutional neural networks have become increasingly deep and complex, leading to higher computational costs. While tropical convolutional neural networks (TCNNs) reduce multiplications, they underperform compared to standard CNNs. To…
Modern FFT/NTT analytics, coded computation, and privacy-preserving ML interface routinely move polynomial frames across NICs, storage, and accelerators. However, even rare silent data corruption (SDC) can flip a few ring coefficients and…
Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
We show how to improve the efficiency of the computation of fast Fourier transforms over F_p where p is a word-sized prime. Our main technique is optimisation of the basic arithmetic, in effect decreasing the total number of reductions…