Related papers: Absdet-Pseudo-Codewords and Perm-Pseudo-Codewords:…
The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks.…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…
The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free…
A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…
Over the last years, word and sentence embeddings have established as text preprocessing for all kinds of NLP tasks and improved the performances significantly. Unfortunately, it has also been shown that these embeddings inherit various…
By introducing a small set of additional parameters, a probe learns to solve specific linguistic tasks (e.g., dependency parsing) in a supervised manner using feature representations (e.g., contextualized embeddings). The effectiveness of…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
A program is usually represented as a word chain. It is exactly a word chain that appears as the lexical analyzer output and is parsed. The work shows that a program can be syntactically represented as an oriented word tree, that is a…
Binary code analysis plays a pivotal role in the field of software security and is widely used in tasks such as software maintenance, malware detection, software vulnerability discovery, patch analysis, etc. However, unlike source code,…
Error-correcting codes (ECC) are used to reduce multiclass classification tasks to multiple binary classification subproblems. In ECC, classes are represented by the rows of a binary matrix, corresponding to codewords in a codebook.…
Pre-trained models of code built on the transformer architecture have performed well on software engineering (SE) tasks such as predictive code generation, code summarization, among others. However, whether the vector representations from…