Related papers: Correctable Erasure Patterns in Product Topologies
Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to…
We develop a compositional framework for generalized reversible computing using copy-discard categories and resource theories. We introduce partitioned matrices between partitioned sets as subdistribution matrices which preserve the…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
We present a locality preserving loss (LPL) that improves the alignment between vector space embeddings while separating uncorrelated representations. Given two pretrained embedding manifolds, LPL optimizes a model to project an embedding…
A common approach for sequence tagging tasks based on contextual word representations is to train a machine learning classifier directly on these embedding vectors. This approach has two shortcomings. First, such methods consider single…
To recover simultaneous multiple failures in erasure coded storage systems, Patrick Lee et al introduce concurrent repair based minimal storage regenerating codes to reduce repair traffic. The architecture of this approach is simpler and…
Classical erasure codes, e.g. Reed-Solomon codes, have been acknowledged as an efficient alternative to plain replication to reduce the storage overhead in reliable distributed storage systems. Yet, such codes experience high overhead…
The {\em repair locality} of a distributed storage code is the maximum number of nodes that ever needs to be contacted during the repair of a failed node. Having small repair locality is desirable, since it is proportional to the number of…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Despite its empirical success, less is known about the…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
In cloud computing, storage area networks, remote backup storage, and similar settings, stored data is modified with updates from new versions. Representing information and modifying the representation are both expensive. Therefore it is…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…