arXiv subjects

Netanel Raviv

Publications and source records attributed to Netanel Raviv.

At least 37 records · Page 2Linked to original sources

arXiv2024

Non-Binary Covering Codes for Low-Access Computations

Given a real dataset and a computation family, we wish to encode and store the dataset in a distributed system so that any computation from the family can be performed by accessing a small number of nodes. In this work, we focus on the families of linear computations where the coefficients are restricted to a finite set of real values. For two-valued computations, a recent work presented a scheme that gives good feasible points on the access-redundancy tradeoff. This scheme is based on binary covering codes having a certain closure property. In a follow-up work, this scheme was extended to all finite coefficient sets, using a new additive-combinatorics notion called coefficient complexity. In the present paper, we explore non-binary covering codes and develop schemes that outperform the state-of-the-art for some coefficient sets. We provide a more general coefficient complexity definition and show its applicability to the access-redundancy tradeoff.

cs.IT↗

arXiv2024

Explicit Formula for Partial Information Decomposition

Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion. Specifically, Shannon's mutual information does not capture fine-grained interactions between those three variables, resulting in limited insights in complex systems. To capture these fine-grained interactions, in 2010 Williams and Beer proposed to decompose this mutual information to information atoms, called unique, redundant, and synergistic, and proposed several operational axioms that these atoms must satisfy. In spite of numerous efforts, a general formula which satisfies these axioms has yet to be found. Inspired by Judea Pearl's do-calculus, we resolve this open problem by introducing the do-operation, an operation over the variable system which sets a certain marginal to a desired value, which is distinct from any existing approaches. Using this operation, we provide the first explicit formula for calculating the information atoms so that Williams and Beer's axioms are satisfied, as well as additional properties from subsequent studies in the field.

cs.IT↗

arXiv2024

Linear Codes for Hyperdimensional Computing

Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic computing. One of the long-standing challenges in HDC is factoring a compositional representation to its constituent factors, also known as the recovery problem. In this paper we take a novel approach to solve the recovery problem, and propose the use of random linear codes. These codes are subspaces over the Boolean field, and are a well-studied topic in information theory with various applications in digital communication. We begin by showing that hyperdimensional encoding using random linear codes retains favorable properties of the prevalent (ordinary) random codes, and hence HD representations using the two methods have comparable information storage capabilities. We proceed to show that random linear codes offer a rich subcode structure that can be used to form key-value stores, which encapsulate most use cases of HDC. Most importantly, we show that under the framework we develop, random linear codes admit simple recovery algorithms to factor (either bundled or bound) compositional representations. The former relies on constructing certain linear equation systems over the Boolean field, the solution to which reduces the search space dramatically and strictly outperforms exhaustive search in many cases. The latter employs the subspace structure of these codes to achieve provably correct factorization. Both methods are strictly faster than the state-of-the-art resonator networks, often by an order of magnitude. We implemented our techniques in Python using a benchmark software library, and demonstrated promising experimental results.

cs.IT↗

arXiv2023

Access-Redundancy Tradeoffs in Quantized Linear Computations

Linear real-valued computations over distributed datasets are common in many applications, most notably as part of machine learning inference. In particular, linear computations that are quantized, i.e., where the coefficients are restricted to a predetermined set of values (such as $\pm 1$), have gained increasing interest lately due to their role in efficient, robust, or private machine learning models. Given a dataset to store in a distributed system, we wish to encode it so that all such computations could be conducted by accessing a small number of servers, called the access parameter of the system. Doing so relieves the remaining servers to execute other tasks. Minimizing the access parameter gives rise to an access-redundancy tradeoff, where a smaller access parameter requires more redundancy in the system, and vice versa. In this paper, we study this tradeoff and provide several explicit low-access schemes for $\{\pm1\}$ quantized linear computations based on covering codes in a novel way. While the connection to covering codes has been observed in the past, our results strictly outperform the state-of-the-art for two-valued linear computations. We further show that the same storage scheme can be used to retrieve any linear combination with two distinct coefficients -- regardless of what those coefficients are -- with the same access parameter. This universality result is then extended to all possible quantizations with any number of values; while the storage remains identical, the access parameter increases according to a new additive-combinatorics property we call coefficient complexity. We then turn to study the coefficient complexity -- we characterize the complexity of small sets of coefficients, provide bounds, and identify coefficient sets having the highest and lowest complexity.

cs.IT↗

arXiv2023

Private Inference in Quantized Models

A typical setup in many machine learning scenarios involves a server that holds a model and a user that possesses data, and the challenge is to perform inference while safeguarding the privacy of both parties. Private Inference has been extensively explored in recent years, mainly from a cryptographic standpoint via techniques like homomorphic encryption and multiparty computation. These approaches often come with high computational overhead and may degrade the accuracy of the model. In our work, we take a different approach inspired by the Private Information Retrieval literature. We view private inference as the task of retrieving inner products of parameter vectors with the data, a fundamental operation in many machine learning models. We introduce schemes that enable such retrieval of inner products for models with quantized (i.e., restricted to a finite set) weights; such models are extensively used in practice due to a wide range of benefits. In addition, our schemes uncover a fundamental tradeoff between user and server privacy. Our information-theoretic approach is applicable to a wide range of problems and robust in privacy guarantees for both the user and the server.

cs.IT↗

arXiv2023

Error Correction for DNA Storage

DNA-based storage is an emerging storage technology that provides high information density and long duration. Due to the physical constraints in the reading and writing processes, error correction in DNA storage poses several interesting coding theoretic challenges, some of which are new. In this paper, we give a brief introduction to some of the coding challenges for DNA-based storage, including deletion/insertion correcting codes, codes over sliced channels, and duplication correcting codes.

cs.IT↗

arXiv2023

Robust Indexing for the Sliced Channel: Almost Optimal Codes for Substitutions and Deletions

Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In this paper, we address this problem and present an order-wise optimal construction of codes that are capable of correcting multiple substitution, deletion, and insertion errors for this channel model. The key ingredient in the code construction is a technique we call robust indexing: simultaneously assigning indices to unordered strings (hence, creating order) and also embedding information in these indices. The encoded indices are resilient to substitution, deletion, and insertion errors, and therefore, so is the entire code.

cs.IT↗

arXiv2023

Transaction Confirmation in Coded Blockchain

As blockchains continue to seek to scale to a larger number of nodes, the communication complexity of protocols has become a significant priority as the network can quickly become overburdened. Several schemes have attempted to address this, one of which uses coded computation to lighten the load. Here we seek to address one issue with all such coded blockchain schemes known to the authors: transaction confirmation. In a coded blockchain, only the leader has access to the uncoded block, while the nodes receive encoded data that makes it effectively impossible for them to identify which transactions were included in the block. As a result, a Byzantine leader might choose not to notify a sender or receiver of a transaction that the transaction went into the block, and even with an honest leader, they would not be able to produce a proof of a transaction's inclusion. To address this, we have constructed a protocol to send the nodes enough information so that a client sending or receiving a transaction is guaranteed to not only be notified but also to receive a proof of that transaction's inclusion in the block. Crucially, we do this without substantially increasing the bit complexity of the original coded blockchain protocol.

cs.IT↗

arXiv2023

A Generalized Covering Algorithm for Chained Codes

The covering radius is a fundamental property of linear codes that characterizes the trade-off between storage and access in linear data-query protocols. The generalized covering radius was recently defined by Elimelech and Schwartz for applications in joint-recovery of linear data-queries. In this work we extend a known bound on the ordinary covering radius to the generalized one for all codes satisfying the chain condition -- a known condition which is satisfied by most known families of codes. Given a generator matrix of a special form, we also provide an algorithm which finds codewords which cover the input vectors within the distance specified by the bound. For the case of Reed-Muller codes we provide efficient construction of such generator matrices, therefore providing a faster alternative to a previous generalized covering algorithm for Reed-Muller codes.

cs.IT↗

arXiv2023

Approximate Private Inference in Quantized Models

Private inference refers to a two-party setting in which one has a model (e.g., a linear classifier), the other has data, and the model is to be applied over the data while safeguarding the privacy of both parties. In particular, models in which the weights are quantized (e.g., to 1 or -1) gained increasing attention lately, due to their benefits in efficient, private, or robust computations. Traditionally, private inference has been studied from a cryptographic standpoint, which suffers from high complexity and degraded accuracy. More recently, Raviv et al. showed that in quantized models, an information theoretic tradeoff exists between the privacy of the parties, and a scheme based on a combination of Boolean and real-valued algebra was presented which attains that tradeoff. Both the scheme and the respective bound required the computation to be done exactly. In this work we show that by relaxing the requirement for exact computation, one can break the information theoretic privacy barrier of Raviv et al., and provide better privacy at the same communication costs. We provide a scheme for such approximate computation, bound its error, show its improved privacy, and devise a respective lower bound for some parameter regimes.

cs.IT↗

arXiv2022

All-to-All Encode in Synchronous Systems

We define all-to-all encode, a collective communication operation serving as a primitive in decentralized computation and storage systems. Consider a scenario where every processor initially has a data packet and requires a linear combination of all data packets; the linear combinations are distinct from one processor to another, and are specified by a generator matrix of an error correcting code. We use a linear network model, in which processors transmit linear combinations of their data and previously received packets, and adopt a standard synchronous system setting to analyze its communication cost. We provide a universal algorithm which computes any matrix in this model by only varying intermediate coefficients, and prove its optimality. When the generator matrix is of the Vandermonde or Lagrange type, we further optimize the communication efficiency of the proposed algorithm.

cs.DC↗

arXiv2022

Multivariate Public Key Cryptosystem from Sidon Spaces

A Sidon space is a subspace of an extension field over a base field in which the product of any two elements can be factored uniquely, up to constants. This paper proposes a new public-key cryptosystem of the multivariate type which is based on Sidon spaces, and has the potential to remain secure even if quantum supremacy is attained. This system, whose security relies on the hardness of the well-known MinRank problem, is shown to be resilient to several straightforward algebraic attacks. In particular, it is proved that the two popular attacks on the MinRank problem, the kernel attack, and the minor attack, succeed only with exponentially small probability. The system is implemented in software, and its hardness is demonstrated experimentally.

cs.CR↗

arXiv2022

Breaking Blockchain's Communication Barrier with Coded Computation

Although blockchain, the supporting technology of various cryptocurrencies, has offered a potentially effective framework for numerous decentralized trust management systems, its performance is still sub-optimal in real-world networks. With limited bandwidth, the communication complexity for nodes to process a block scales with the growing network size and hence becomes the limiting factor of blockchain's performance. In this paper, we suggest a re-design of existing blockchain systems, which addresses the issue of the communication burden. First, by employing techniques from Coded Computation, our scheme guarantees correct verification of transactions while reducing the bit complexity dramatically such that it grows logarithmically with the number of nodes. Second, with the adoption of techniques from Information Dispersal and State Machine Replication, the system is resilient to Byzantine faults and achieves linear message complexity. Third, we propose a novel 2-dimensional sharding strategy, which inherently supports cross-shard transactions, alleviating the need for complicated communication protocols between shards, while keeping the computation and storage benefits of sharding.

cs.DC↗

arXiv2021

Enhancing Robustness of Neural Networks through Fourier Stabilization

Despite the considerable success of neural networks in security settings such as malware detection, such models have proved vulnerable to evasion attacks, in which attackers make slight changes to inputs (e.g., malware) to bypass detection. We propose a novel approach, \emph{Fourier stabilization}, for designing evasion-robust neural networks with binary inputs. This approach, which is complementary to other forms of defense, replaces the weights of individual neurons with robust analogs derived using Fourier analytic tools. The choice of which neurons to stabilize in a neural network is then a combinatorial optimization problem, and we propose several methods for approximately solving it. We provide a formal bound on the per-neuron drop in accuracy due to Fourier stabilization, and experimentally demonstrate the effectiveness of the proposed approach in boosting robustness of neural networks in several detection settings. Moreover, we show that our approach effectively composes with adversarial training.

cs.LG↗

arXiv2020

Low Latency Cross-Shard Transactions in Coded Blockchain

Although blockchain, the supporting technology of Bitcoin and various cryptocurrencies, has offered a potentially effective framework for numerous applications, it still suffers from the adverse affects of the impossibility triangle. Performance, security, and decentralization of blockchains normally do not scale simultaneously with the number of participants in the network. The recent introduction of error correcting codes in sharded blockchain by Li et al. partially settles this trilemma, boosting throughput without compromising security and decentralization. In this paper, we improve the coded sharding scheme in three ways. First, we propose a novel 2-Dimensional Sharding strategy, which inherently supports cross-shard transactions, alleviating the need for complicated inter-shard communication protocols. Second, we employ distributed storage techniques in the propagation of blocks, improving latency under restricted bandwidth. Finally, we incorporate polynomial cryptographic primitives of low degree, which brings coded blockchain techniques into the realm of feasible real-world parameters.

cs.CR↗

arXiv2020

What is the Value of Data? On Mathematical Methods for Data Quality Estimation

Data is one of the most important assets of the information age, and its societal impact is undisputed. Yet, rigorous methods of assessing the quality of data are lacking. In this paper, we propose a formal definition for the quality of a given dataset. We assess a dataset's quality by a quantity we call the expected diameter, which measures the expected disagreement between two randomly chosen hypotheses that explain it, and has recently found applications in active learning. We focus on Boolean hyperplanes, and utilize a collection of Fourier analytic, algebraic, and probabilistic methods to come up with theoretical guarantees and practical solutions for the computation of the expected diameter. We also study the behaviour of the expected diameter on algebraically structured datasets, conduct experiments that validate this notion of quality, and demonstrate the feasibility of our techniques.

cs.LG↗

arXiv2020

CodNN -- Robust Neural Networks From Coded Classification

Deep Neural Networks (DNNs) are a revolutionary force in the ongoing information revolution, and yet their intrinsic properties remain a mystery. In particular, it is widely known that DNNs are highly sensitive to noise, whether adversarial or random. This poses a fundamental challenge for hardware implementations of DNNs, and for their deployment in critical applications such as autonomous driving. In this paper we construct robust DNNs via error correcting codes. By our approach, either the data or internal layers of the DNN are coded with error correcting codes, and successful computation under noise is guaranteed. Since DNNs can be seen as a layered concatenation of classification tasks, our research begins with the core task of classifying noisy coded inputs, and progresses towards robust DNNs. We focus on binary data and linear codes. Our main result is that the prevalent parity code can guarantee robustness for a large family of DNNs, which includes the recently popularized binarized neural networks. Further, we show that the coded classification problem has a deep connection to Fourier analysis of Boolean functions. In contrast to existing solutions in the literature, our results do not rely on altering the training process of the DNN, and provide mathematically rigorous guarantees rather than experimental evidence.

cs.LG↗

arXiv2020

Support Constrained Generator Matrices of Gabidulin Codes in Characteristic Zero

Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic. In parallel, the interest in sparse generator matrices of Reed-Solomon and Gabidulin codes has increased lately, due to applications in distributed computations. In particular, a certain condition pertaining the intersection of zero entries at different rows, was shown to be necessary and sufficient for the existence of the sparsest possible generator matrix of Gabidulin codes over finite fields. In this paper we complete the picture by showing that the same condition is also necessary and sufficient for Gabidulin codes over fields of characteristic zero. Our proof builds upon and extends tools from the finite field case, combines them with a variant of the Schwartz-Zippel lemma over automorphisms, and provides a simple randomized construction algorithm whose probability of success can be arbitrarily close to one. In addition, potential applications for low-rank matrix recovery are discussed.

cs.IT↗