Related papers: An Efficiently Generated Family of Binary de Bruij…

Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…

Linear recurrent neural networks, such as State Space Models (SSMs) and Linear Recurrent Units (LRUs), have recently shown state-of-the-art performance on long sequence modelling benchmarks. Despite their success, their empirical…

Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive…

Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

Deep neural networks have significantly improved performance on a range of tasks with the increasing demand for computational resources, leaving deployment on low-resource devices (with limited memory and battery power) infeasible. Binary…

We introduce RecurrentGemma, a family of open language models which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state,…

The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and an additive static output feedback is applied. The first step is to consider the so called…

We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…

Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…

Generation and prediction of time series is analyzed for the case of a Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output…

We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…

The discrepancy of a binary string is the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. In this note we determine the minimal discrepancy that a…

We present a dynamic prediction framework for binary sequences that is based on a Bernoulli generalization of the auto-regressive process. Our approach lends itself easily to variants of the standard link prediction problem for a sequence…

Relation classification is an important semantic processing task in the field of natural language processing (NLP). In this paper, we present a novel model, Structure Regularized Bidirectional Recurrent Convolutional Neural…

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body…

Motivated by the constructions of pseudorandom sequences over the cyclic elliptic function fields by Hu \textit{et al.} in \text{[IEEE Trans. Inf. Theory, 53(7), 2007]} and the constructions of low-correlation, large linear span binary…

While biological vision systems rely heavily on feedback connections to iteratively refine perception, most artificial neural networks remain purely feedforward, processing input in a single static pass. In this work, we propose a…

In this paper, we construct four binary linear codes closely connected with certain exponential sums over the finite field F_q and F_q-{0,1}. Here q is a power of two. Then we obtain four recursive formulas for the power moments of…

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…