Decentralized Erasure Codes for Distributed Networked Storage

We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We want a data collector, who can appear anywhere in the network, to query any k storage nodes and be able to retrieve the data. We introduce Decentralized Erasure Codes, which are linear codes with a specific randomized structure inspired by network coding on random bipartite graphs. We show that decentralized erasure codes are optimally sparse, and lead to reduced communication, storage and computation cost over random linear coding.Comment: to appear in IEEE Transactions on Information Theory, Special Issue: Networking and Information Theor

Sympiler: Transforming Sparse Matrix Codes by Decoupling Symbolic Analysis

Sympiler is a domain-specific code generator that optimizes sparse matrix computations by decoupling the symbolic analysis phase from the numerical manipulation stage in sparse codes. The computation patterns in sparse numerical methods are guided by the input sparsity structure and the sparse algorithm itself. In many real-world simulations, the sparsity pattern changes little or not at all. Sympiler takes advantage of these properties to symbolically analyze sparse codes at compile-time and to apply inspector-guided transformations that enable applying low-level transformations to sparse codes. As a result, the Sympiler-generated code outperforms highly-optimized matrix factorization codes from commonly-used specialized libraries, obtaining average speedups over Eigen and CHOLMOD of 3.8X and 1.5X respectively.Comment: 12 page

Sparse neural networks with large learning diversity

Coded recurrent neural networks with three levels of sparsity are introduced. The first level is related to the size of messages, much smaller than the number of available neurons. The second one is provided by a particular coding rule, acting as a local constraint in the neural activity. The third one is a characteristic of the low final connection density of the network after the learning phase. Though the proposed network is very simple since it is based on binary neurons and binary connections, it is able to learn a large number of messages and recall them, even in presence of strong erasures. The performance of the network is assessed as a classifier and as an associative memory

Distributed memory compiler methods for irregular problems: Data copy reuse and runtime partitioning

Outlined here are two methods which we believe will play an important role in any distributed memory compiler able to handle sparse and unstructured problems. We describe how to link runtime partitioners to distributed memory compilers. In our scheme, programmers can implicitly specify how data and loop iterations are to be distributed between processors. This insulates users from having to deal explicitly with potentially complex algorithms that carry out work and data partitioning. We also describe a viable mechanism for tracking and reusing copies of off-processor data. In many programs, several loops access the same off-processor memory locations. As long as it can be verified that the values assigned to off-processor memory locations remain unmodified, we show that we can effectively reuse stored off-processor data. We present experimental data from a 3-D unstructured Euler solver run on iPSC/860 to demonstrate the usefulness of our methods

Binding and Normalization of Binary Sparse Distributed Representations by Context-Dependent Thinning

Distributed representations were often criticized as inappropriate for encoding of data with a complex structure. However Plate's Holographic Reduced Representations and Kanerva's Binary Spatter Codes are recent schemes that allow on-the-fly encoding of nested compositional structures by real-valued or dense binary vectors of fixed dimensionality. In this paper we consider procedures of the Context-Dependent Thinning which were developed for representation of complex hierarchical items in the architecture of Associative-Projective Neural Networks. These procedures provide binding of items represented by sparse binary codevectors (with low probability of 1s). Such an encoding is biologically plausible and allows a high storage capacity of distributed associative memory where the codevectors may be stored. In contrast to known binding procedures, Context-Dependent Thinning preserves the same low density (or sparseness) of the bound codevector for varied number of component codevectors. Besides, a bound codevector is not only similar to another one with similar component codevectors (as in other schemes), but it is also similar to the component codevectors themselves. This allows the similarity of structures to be estimated just by the overlap of their codevectors, without retrieval of the component codevectors. This also allows an easy retrieval of the component codevectors. Examples of algorithmic and neural-network implementations of the thinning procedures are considered. We also present representation examples for various types of nested structured data (propositions using role-filler and predicate-arguments representation schemes, trees, directed acyclic graphs) using sparse codevectors of fixed dimension. Such representations may provide a fruitful alternative to the symbolic representations of traditional AI, as well as to the localist and microfeature-based connectionist representations