Related papers: Fundamental Bounds and Approaches to Sequence Reco…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

After decades, the theoretical study of core-collapse supernova explosions is moving from parameterized, spherically symmetric models to increasingly realistic multi-dimensional simulations. Obtaining nucleosynthesis yields based on such…

Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…

The errors occurring in DNA-based storage are correlated in nature, which is a direct consequence of the synthesis and sequencing processes. In this paper, we consider the memory-$k$ nanopore channel model recently introduced by Hamoum et…

Single image super-resolution traditionally assumes spatially-invariant degradation models, yet real-world imaging systems exhibit complex distance-dependent effects including atmospheric scattering, depth-of-field variations, and…

We present the Insertion Transformer, an iterative, partially autoregressive model for sequence generation based on insertion operations. Unlike typical autoregressive models which rely on a fixed, often left-to-right ordering of the…

The study of functional genomics--particularly in non-model organisms has been dramatically improved over the last few years by use of transcriptomes and RNAseq. While these studies are potentially extremely powerful, a computationally…

Designing protein sequences that fold into a target 3D structure, known as protein inverse folding, is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering…

While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances…

DNA is a leading candidate as the next archival storage media due to its density, durability and sustainability. To read (and write) data DNA storage exploits technology that has been developed over decades to sequence naturally occurring…

In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary…

This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…

A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…

Reverse engineering can be used to derive a 3D model of an existing physical part when such a model is not readily available. For parts that will be fabricated with subtractive and formative manufacturing processes, existing reverse…

Deep generative models have been successfully used to learn representations for high-dimensional discrete spaces by representing discrete objects as sequences and employing powerful sequence-based deep models. Unfortunately, these…

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

DNA-based storage offers unprecedented density and durability, but its scalability is fundamentally limited by the efficiency of parallel strand synthesis. Existing methods either allow unconstrained nucleotide additions to individual…

DNA sequence encoding is fundamental to gene function prediction, protein synthesis, and diverse downstream biological tasks. Despite the substantial progress achieved by large-scale DNA sequence pretraining, existing studies have…

In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost…

We propose the Insertion-Deletion Transformer, a novel transformer-based neural architecture and training method for sequence generation. The model consists of two phases that are executed iteratively, 1) an insertion phase and 2) a…