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Twisted Reed-Solomon (TRS) codes are a family of codes that contains a large number of maximum distance separable codes that are non-equivalent to Reed--Solomon codes. TRS codes were recently proposed as an alternative to Goppa codes for…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein.…
Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…
Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
Both horizontal interleaving as well as the sum-rank metric are currently attractive topics in the field of code-based cryptography, as they could mitigate the problem of large key sizes. In contrast to vertical interleaving, where…
Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources…
Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first…
Decoding algorithms for Reed--Solomon (RS) codes are of great interest for both practical and theoretical reasons. In this paper, an efficient algorithm, called the modular approach (MA), is devised for solving the Welch--Berlekamp (WB) key…
Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to $t$ links, erase up to $\rho$ packets, and wire-tap up…
We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
Decision Trees are prominent prediction models for interpretable Machine Learning. They have been thoroughly researched, mostly in the batch setting with a fixed labelled dataset, leading to popular algorithms such as C4.5, ID3 and CART.…
The two primary decoding algorithms for Reed-Solomon codes are the Berlekamp-Massey algorithm and the Sugiyama et al. adaptation of the Euclidean algorithm, both designed to solve a key equation. In this article an alternative version of…
The growing scale of Large Language Models (LLMs) has exacerbated inference latency and computational costs. Speculative decoding methods, which aim to mitigate these issues, often face inefficiencies in the construction of token trees and…
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Speculative decoding is a technique to leverage hardware concurrency in order to enable multiple steps of token generation in a single forward pass, thus improving the efficiency of large-scale autoregressive (AR) Transformer models.…