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This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with…
This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. The algorithm can be used to estimate the error floor of LDPC codes or to be part of the apparatus to design LDPC…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
A basic unanswered question in neural network training is: what is the best learning rate schedule shape for a given workload? The choice of learning rate schedule is a key factor in the success or failure of the training process, but…
Hierarchical classification offers an approach to incorporate the concept of mistake severity by leveraging a structured, labeled hierarchy. However, decoding in such settings frequently relies on heuristic decision rules, which may not…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…
We consider the problem of estimating the trace of a matrix function $f(A)$. In certain situations, in particular if $f(A)$ cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic…
We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ…
This paper investigates the ability of large language models (LLMs) to recognise and solve tasks which have been obfuscated beyond recognition. Focusing on competitive programming and benchmark tasks (LeetCode and MATH), we compare…
Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…
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…
Coded caching scheme, which is an effective technique to increase the transmission efficiency during peak traffic times, has recently become quite popular among the coding community. Generally rate can be measured to the transmission in the…
A human-like chess engine should mimic the style, errors, and consistency of a strong human player rather than maximize playing strength. We show that training from move sequences alone forces a model to learn two capabilities: state…
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error…
We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the…
State-of-the-art deep learning methods achieve human-like performance on many tasks, but make errors nevertheless. Characterizing these errors in easily interpretable terms gives insight into whether a classifier is prone to making…
In extreme classification problems, learning algorithms are required to map instances to labels from an extremely large label set. We build on a recent extreme classification framework with logarithmic time and space, and on a general…
A large class of dense linear algebra operations, such as LU decomposition or inversion of a triangular matrix, are usually performed by blocked algorithms. For one such operation, typically, not only one but many algorithmic variants…