Related papers: Efficient linear feedback shift registers with max…

This paper develops methods for analyzing periodic orbits of states of linear feedback shift registers with periodic coefficients and estimating their lengths. These shift registers are among the simplest nonlinear feedback shift registers…

Feedback shift registers(FSRs) are a fundamental component in electronics and secure communication. An FSR $f$ is said to be reducible if all the output sequences of another FSR $g$ can also be generated by $f$ and the FSR $g$ has less…

We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed.

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

We present Adaptive Soft Rolling KV Freeze with Entropy-Guided Recovery (ASR-KF-EGR), a training-free inference-time framework for efficient large language model generation. Our method introduces a reversible soft-freeze mechanism that…

We show how to solve a generalised version of the Multi-sequence Linear Feedback Shift-Register (MLFSR) problem using minimisation of free modules over $\mathbb F[x]$. We show how two existing algorithms for minimising such modules run…

This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…

This paper solves the sparsest feedback selection problem for linear time invariant structured systems, a long-standing open problem in structured systems. We consider structurally cyclic systems with dedicated inputs and outputs. We prove…

Large language models frequently commit unrecoverable reasoning errors mid-generation: once a wrong step is taken, subsequent tokens compound the mistake rather than correct it. We introduce $\textbf{Latent Phase-Shift Rollback}$ (LPSR): at…

Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequence. In this…

The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated…

Linear feedback shift registers (LFSRs) are used to generate secret keys in stream cipher cryptosystems. There are different kinds of key-stream generators like filter generators, combination generators, clock-controlled generators, etc.…

Sequence-based deep learning recommendation models (DLRMs) are an emerging class of DLRMs showing great improvements over their prior sum-pooling based counterparts at capturing users' long term interests. These improvements come at immense…

Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Learned Sparse Retrieval (LSR) is an effective IR approach that exploits pre-trained language models for encoding text into a learned bag of words. Several efforts in the literature have shown that sparsity is key to enabling a good…

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods…

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with feedback function $f(x_0, x_1, \ldots, x_{n-1}) = x_0 + x_1 + x_{n-1}$ for $n \geq 3$, using the cycle joining…

The emergence of deep learning has yielded noteworthy advancements in time series forecasting (TSF). Transformer architectures, in particular, have witnessed broad utilization and adoption in TSF tasks. Transformers have proven to be the…