Related papers: An Algorithm for Constructing a Smallest Register …

In this paper, we consider recovering $n$ dimensional signals from $m$ binary measurements corrupted by noises and sign flips under the assumption that the target signals have low generative intrinsic dimension, i.e., the target signals can…

The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…

ReLU neural networks define piecewise linear functions of their inputs. However, initializing and training a neural network is very different from fitting a linear spline. In this paper, we expand empirically upon previous theoretical work…

A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…

Effective text generation and chat interfaces for low-resource languages (LRLs) remain a challenge for state-of-the-art large language models (LLMs) to support. This is mainly due to the difficulty of curating high-quality instruction…

This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in…

Data augmentation is a widely used technique in machine learning to improve model performance. However, existing data augmentation techniques in natural language understanding (NLU) may not fully capture the complexity of natural language…

We put forward new general criteria to design successor rules that generate binary de Bruijn sequences. Prior fast algorithms based on successor rules in the literature are then shown to be special instances. We implemented the criteria to…

In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this…

Incremental processing allows interactive systems to respond based on partial inputs, which is a desirable property e.g. in dialogue agents. The currently popular Transformer architecture inherently processes sequences as a whole,…

Neurons, modeled as linear threshold unit (LTU), can in theory compute all thresh- old functions. In practice, however, some of these functions require synaptic weights of arbitrary large precision. We show here that dendrites can alleviate…

We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly…

The potential number of drug like small molecules is estimated to be between 10^23 and 10^60 while current databases of known compounds are orders of magnitude smaller with approximately 10^8 compounds. This discrepancy has led to an…

Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…

Recurrent neural networks (RNNs) are widely used to model sequential data but their non-linear dependencies between sequence elements prevent parallelizing training over sequence length. We show the training of RNNs with only linear…

The size $b$ of the smallest bidirectional macro scheme, which is arguably the most general copy-paste scheme to generate a given sequence, is considered to be the strictest reachable measure of repetitiveness. It is strictly lower-bounded…

Linear-feedback shift register (LFSR) based pseudo-random number generator (PRNG) has applications in a plethora of fields. The issue of being linear is generally circumvented by introducing non-linearities as per the required applications,…

Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate…

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal…

Many natural language processing applications use language models to generate text. These models are typically trained to predict the next word in a sequence, given the previous words and some context such as an image. However, at test time…