arXiv subjects

K. V. Rashmi

Publications and source records attributed to K. V. Rashmi.

At least 19 recordsLinked to original sources

arXiv2026

Coral: Cost-Efficient Multi-LLM Serving over Heterogeneous Cloud GPUs

The usage of large language models (LLMs) has grown increasingly fragmented, with no single model dominating. Meanwhile, cloud providers offer a wide range of mid-tier and older-generation GPUs that enjoy better availability and deliver comparable performance per dollar to top-tier hardware. To efficiently harness these heterogeneous resources for serving multiple LLMs concurrently, we introduce Coral, an adaptive heterogeneity-aware multi-LLM serving system. The key idea behind Coral is to jointly optimize resource allocation and the serving strategy of each model replica across all models. To keep pace with shifting throughput demand and resource availability, Coral applies a lossless two-stage decomposition that preserves joint optimality while cutting online solve time from hours to tens of seconds. Our evaluation across 6 models and 20 GPU configurations shows that Coral reduces serving cost by up to 2.79$\times$ over the best baseline, and delivers up to 2.39$\times$ higher goodput under scarce resource availability.

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arXiv2026

Bandwidth Cost of Locally Repairable Convertible Codes in the Global Merge Regime

Recent studies have shown that distributed storage systems can achieve significant space savings by adapting redundancy levels to varying disk failure rates. This adaptation is performed via code conversion, wherein data encoded under an initial code are transformed to data encoded under a final code. While this process is typically resource-intensive, convertible codes are designed to enable these transformations efficiently while preserving desirable decodability constraints such as repair degree, or the number of nodes accessed during node repair. In this work, we focus on the bandwidth cost of conversion, or the total amount of data transferred during the conversion process. We study fundamental limits on the bandwidth cost of conversion between systematic optimal-distance Locally Repairable Codes (LRCs). We restrict our focus to the global merge regime, in which multiple initial codewords are combined to form a single final codeword while preserving information locality. We focus on stable convertible codes, wherein the number of unchanged nodes is maximized during conversion. We generalize an information-theoretic approach for modeling code conversion to the LRC setting, and derive the first non-trivial lower bounds on the bandwidth cost of conversion in this regime. Notably, our bounds do not rely on any linearity assumptions. Consequently, we show that the constructions of Maturana and Rashmi are bandwidth-optimal across a broad range of parameters in the global merge regime.

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arXiv2025

Tight Lower Bounds on the Bandwidth Cost of MDS Convertible Codes in the Split Regime

Recent advances in erasure coding for distributed storage systems have demonstrated that adapting redundancy to varying disk failure rates can lead to substantial storage savings. Such adaptation requires code conversion, wherein data encoded under an initial $[k^I + r^I, k^I]$ code is transformed into data encoded under a final $[k^F + r^F, k^F]$ code - an operation that can be resource-intensive. Convertible codes are a class of codes designed to facilitate this transformation efficiently while preserving desirable properties such as the MDS property. In this work, we investigate the fundamental limits on the bandwidth cost of conversion (total amount of data transferred between the storage nodes during conversion) for systematic MDS convertible codes. Specifically, we study the subclass of conversions known as the split regime (a single initial codeword is converted into multiple final codewords). In this setting, prior to this work, the best known lower bounds on the bandwidth cost of conversion for all parameters were derived by Maturana and Rashmi under certain uniformity assumptions on the number of symbols downloaded from each node. Further, these bounds were shown to be tight for the parameter regime where $r^F \geq k^F$ or $r^I \leq r^F$. In this work, we derive lower bounds on the bandwidth cost of systematic MDS convertible codes for all parameters in the split regime without the uniformity assumption. Moreover, our bounds are tight for the broader parameter regime where $r^F \geq k^F$ or $r^I \leq k^F$. Subsequently, our bounds also partially resolve the conjecture proposed by Maturana and Rashmi. We employ a novel information-theoretic framework, which assumes only that the initial and final codes are systematic and does not rely on any linearity assumptions or the aforementioned uniformity assumptions.

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arXiv2024

On Low Field Size Constructions of Access-Optimal Convertible Codes

Most large-scale storage systems employ erasure coding to provide resilience against disk failures. Recent work has shown that tuning this redundancy to changes in disk failure rates leads to substantial storage savings. This process requires code conversion, wherein data encoded using an $[n^{I\mskip-2mu},k^{I\mskip-2mu}]$ initial code has to be transformed into data encoded using an $[n^{F\mskip-2mu},k^{F\mskip-2mu}]$ final code, a resource-intensive operation. Convertible codes are a class of codes that enable efficient code conversion while maintaining other desirable properties. In this paper, we focus on the access cost of conversion (total number of code symbols accessed in the conversion process) and on an important subclass of conversions known as the merge regime (combining multiple initial codewords into a single final codeword). In this setting, explicit constructions are known for systematic access-optimal Maximum Distance Separable (MDS) convertible codes for all parameters in the merge regime. However, the existing construction for a key subset of these parameters, which makes use of Vandermonde parity matrices, requires a large field size making it unsuitable for practical applications. In this paper, we provide (1) sharper bounds on the minimum field size requirement for such codes, and (2) explicit constructions for low field sizes for several parameter ranges. In doing so, we provide a proof of super-regularity of specially designed classes of Vandermonde matrices that could be of independent interest.

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arXiv2023

Online Versus Offline Rate in Streaming Codes for Variable-Size Messages

One pervasive challenge in providing a high quality-of-service for live communication is to recover lost packets in real-time. Streaming codes are a class of erasure codes that are designed for such strict, low-latency streaming communication settings. Motivated by applications that transmit messages whose sizes vary over time, such as live video streaming, this paper considers the setting of streaming codes under variable-size messages. In practice, streaming codes operate in an "online" setting where the sizes of the future messages are unknown. "Offline" codes, in contrast, have access to the sizes of all messages, including future ones. This paper introduces the first online rate-optimal streaming codes for communicating over a burst-only packet loss channel for two broad parameter regimes. These two online codes match the rates of optimal offline codes for the two settings despite the apparent advantage of the offline setting. This paper further establishes that online codes cannot attain the optimal rate for offline codes for all remaining parameter settings.

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arXiv2022

Learning-Augmented Streaming Codes are Approximately Optimal for Variable-Size Messages

Real-time streaming communication requires a high quality of service despite contending with packet loss. Streaming codes are a class of codes best suited for this setting. A key challenge for streaming codes is that they operate in an "online" setting in which the amount of data to be transmitted varies over time and is not known in advance. Mitigating the adverse effects of variability requires spreading the data that arrives at a time slot over multiple future packets, and the optimal strategy for spreading depends on the arrival pattern. Algebraic coding techniques alone are therefore insufficient for designing rate-optimal codes. We combine algebraic coding techniques with a learning-augmented algorithm for spreading to design the first approximately rate-optimal streaming codes for a range of parameter regimes that are important for practical applications.

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arXiv2022

Bandwidth Cost of Code Conversions in the Split Regime

Distributed storage systems must store large amounts of data over long periods of time. To avoid data loss due to device failures, an $[n,k]$ erasure code is used to encode $k$ data symbols into a codeword of $n$ symbols that are stored across different devices. However, device failure rates change throughout the life of the data, and tuning $n$ and $k$ according to these changes has been shown to save significant storage space. Code conversion is the process of converting multiple codewords of an initial $[n^I,k^I]$ code into codewords of a final $[n^F,k^F]$ code that decode to the same set of data symbols. In this paper, we study conversion bandwidth, defined as the total amount of data transferred between nodes during conversion. In particular, we consider the case where the initial and final codes are MDS and a single initial codeword is split into several final codewords ($k^I=λ^F k^F$ for integer $λ^F \geq 2$), called the split regime. We derive lower bounds on the conversion bandwidth in the split regime and propose constructions that significantly reduce conversion bandwidth and are optimal for certain parameters.

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arXiv2021

Arithmetic-Intensity-Guided Fault Tolerance for Neural Network Inference on GPUs

Neural networks (NNs) are increasingly employed in safety-critical domains and in environments prone to unreliability (e.g., soft errors), such as on spacecraft. Therefore, it is critical to impart fault tolerance to NN inference. Algorithm-based fault tolerance (ABFT) is emerging as an efficient approach for fault tolerance in NNs. We propose an adaptive approach to ABFT for NN inference that exploits untapped opportunities in emerging deployment scenarios. GPUs have high compute-to-memory-bandwidth ratios, while NN layers have a wide range of arithmetic intensities. This leaves some layers compute bound and others memory-bandwidth bound, but current approaches to ABFT do not consider these differences. We first investigate ABFT schemes best suited for each of these scenarios. We then propose intensity-guided ABFT, an adaptive, arithmetic-intensity-guided approach that selects the most efficient ABFT scheme for each NN layer. Intensity-guided ABFT reduces execution-time overhead by 1.09--5.3$\times$ across many NNs compared to traditional approaches to ABFT.

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arXiv2021

ECRM: Efficient Fault Tolerance for Recommendation Model Training via Erasure Coding

Deep-learning-based recommendation models (DLRMs) are widely deployed to serve personalized content to users. DLRMs are large in size due to their use of large embedding tables, and are trained by distributing the model across the memory of tens or hundreds of servers. Server failures are common in such large distributed systems and must be mitigated to enable training to progress. Checkpointing is the primary approach used for fault tolerance in these systems, but incurs significant training-time overhead both during normal operation and when recovering from failures. As these overheads increase with DLRM size, checkpointing is slated to become an even larger overhead for future DLRMs, which are expected to grow in size. This calls for rethinking fault tolerance in DLRM training. We present ECRM, a DLRM training system that achieves efficient fault tolerance using erasure coding. ECRM chooses which DLRM parameters to encode, correctly and efficiently updates parities, and enables training to proceed without any pauses, while maintaining consistency of the recovered parameters. We implement ECRM atop XDL, an open-source, industrial-scale DLRM training system. Compared to checkpointing, ECRM reduces training-time overhead for large DLRMs by up to 88%, recovers from failures up to 10.3$\times$ faster, and allows training to proceed during recovery. These results show the promise of erasure coding in imparting efficient fault tolerance to training current and future DLRMs.

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arXiv2021

PACEMAKER: Avoiding HeART attacks in storage clusters with disk-adaptive redundancy

Data redundancy provides resilience in large-scale storage clusters, but imposes significant cost overhead. Substantial space-savings can be realized by tuning redundancy schemes to observed disk failure rates. However, prior design proposals for such tuning are unusable in real-world clusters, because the IO load of transitions between schemes overwhelms the storage infrastructure (termed transition overload). This paper analyzes traces for millions of disks from production systems at Google, NetApp, and Backblaze to expose and understand transition overload as a roadblock to disk-adaptive redundancy: transition IO under existing approaches can consume 100% cluster IO continuously for several weeks. Building on the insights drawn, we present PACEMAKER, a low-overhead disk-adaptive redundancy orchestrator. PACEMAKER mitigates transition overload by (1) proactively organizing data layouts to make future transitions efficient, and (2) initiating transitions proactively in a manner that avoids urgency while not compromising on space-savings. Evaluation of PACEMAKER with traces from four large (110K-450K disks) production clusters show that the transition IO requirement decreases to never needing more than 5% cluster IO bandwidth (0.2-0.4% on average). PACEMAKER achieves this while providing overall space-savings of 14-20% and never leaving data under-protected. We also describe and experiment with an integration of PACEMAKER into HDFS.

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arXiv2020

Bandwidth Cost of Code Conversions in Distributed Storage: Fundamental Limits and Optimal Constructions

Erasure codes have become an integral part of distributed storage systems as a tool for providing data reliability and durability under the constant threat of device failures. In such systems, an $[n, k]$ code over a finite field $\mathbb{F}_q$ encodes $k$ message symbols into $n$ codeword symbols from $\mathbb{F}_q$ which are then stored on $n$ different nodes in the system. Recent work has shown that significant savings in storage space can be obtained by tuning $n$ and $k$ to variations in device failure rates. Such a tuning necessitates code conversion: the process of converting already encoded data under an initial $[n^I, k^I]$ code to its equivalent under a final $[n^F, k^F]$ code. The default approach to conversion is to reencode data, which places significant burden on system resources. Convertible codes are a recently proposed class of codes for enabling resource-efficient conversions. Existing work on convertible codes has focused on minimizing access cost, i.e., the number of code symbols accessed during conversion. Bandwidth, which corresponds to the amount of data read and transferred, is another important resource to optimize. In this paper, we initiate the study on the fundamental limits on bandwidth used during code conversion and present constructions for bandwidth-optimal convertible codes. First, we model the code conversion problem using network information flow graphs with variable capacity edges. Second, focusing on MDS codes and an important parameter regime called the merge regime, we derive tight lower bounds on the bandwidth cost of conversion. The derived bounds show that bandwidth cost can be significantly reduced even in regimes where access cost cannot be reduced as compared to the default approach. Third, we present a new construction for MDS convertible codes which matches the proposed lower bound and is thus bandwidth-optimal during conversion.

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arXiv2020

Access-optimal Linear MDS Convertible Codes for All Parameters

In large-scale distributed storage systems, erasure codes are used to achieve fault tolerance in the face of node failures. Tuning code parameters to observed failure rates has been shown to significantly reduce storage cost. Such tuning of redundancy requires "code conversion", i.e., a change in code dimension and length on already encoded data. Convertible codes are a new class of codes designed to perform such conversions efficiently. The access cost of conversion is the number of nodes accessed during conversion. Existing literature has characterized the access cost of conversion of linear MDS convertible codes only for a specific and small subset of parameters. In this paper, we present lower bounds on the access cost of conversion of linear MDS codes for all valid parameters. Furthermore, we show that these lower bounds are tight by presenting an explicit construction for access-optimal linear MDS convertible codes for all valid parameters. En route, we show that, one of the degrees-of-freedom in the design of convertible codes that was inconsequential in the previously studied parameter regimes, turns out to be crucial when going beyond these regimes and adds to the challenge in the analysis and code construction.

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arXiv2020

A locality-based approach for coded computation

Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple solution of replicating computation entails significant resource overhead. Coded computation has emerged as a resource-efficient alternative, wherein multiple units of data are encoded to create parity units and the function to be computed is applied to each of these units on distinct servers. A decoder can use the available function outputs to decode the unavailable ones. Existing coded computation approaches are resource efficient only for simple variants of linear functions such as multilinear, with even the class of low degree polynomials requiring the same multiplicative overhead as replication for practically relevant straggler tolerance. In this paper, we present a new approach to model coded computation via the lens of locality of codes. We introduce a generalized notion of locality, denoted computational locality, building upon the locality of an appropriately defined code. We show that computational locality is equivalent to the required number of workers for coded computation and leverage results from the well-studied locality of codes to design coded computation schemes. We show that recent results on coded computation of multivariate polynomials can be derived using local recovering schemes for Reed-Muller codes. We present coded computation schemes for multivariate polynomials that adaptively exploit locality properties of input data-- an inadmissible technique under existing frameworks. These schemes require fewer workers than the lower bound under existing coded computation frameworks, showing that the existing multiplicative overhead on the number of servers is not fundamental for coded computation of nonlinear functions.

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arXiv2019

Parity Models: A General Framework for Coding-Based Resilience in ML Inference

Machine learning models are becoming the primary workhorses for many applications. Production services deploy models through prediction serving systems that take in queries and return predictions by performing inference on machine learning models. In order to scale to high query rates, prediction serving systems are run on many machines in cluster settings, and thus are prone to slowdowns and failures that inflate tail latency and cause violations of strict latency targets. Current approaches to reducing tail latency are inadequate for the latency targets of prediction serving, incur high resource overhead, or are inapplicable to the computations performed during inference. We present ParM, a novel, general framework for making use of ideas from erasure coding and machine learning to achieve low-latency, resource-efficient resilience to slowdowns and failures in prediction serving systems. ParM encodes multiple queries together into a single parity query and performs inference on the parity query using a parity model. A decoder uses the output of a parity model to reconstruct approximations of unavailable predictions. ParM uses neural networks to learn parity models that enable simple, fast encoders and decoders to reconstruct unavailable predictions for a variety of inference tasks such as image classification, speech recognition, and object localization. We build ParM atop an open-source prediction serving system and through extensive evaluation show that ParM improves overall accuracy in the face of unavailability with low latency while using 2-4$\times$ less additional resources than replication-based approaches. ParM reduces the gap between 99.9th percentile and median latency by up to $3.5\times$ compared to approaches that use an equal amount of resources, while maintaining the same median.

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arXiv2019

Convertible Codes: Efficient Conversion of Coded Data in Distributed Storage

Large-scale distributed storage systems typically use erasure codes to provide durability of data in the face of failures. A set of $k$ blocks to be stored is encoded using an $[n, k]$ code to generate $n$ blocks that are then stored on different storage nodes. The redundancy configuration is chosen based on the failure rates of storage devices, and is typically kept constant. However, a recent work by Kadekodi et al. shows that the failure rate of storage devices vary significantly over time, and that adapting the redundancy configuration in response to such variations provides significant benefits. Converting the redundancy configuration of already encoded data by re-encoding requires significant overhead on resources such as accesses, device IO, network bandwidth, and compute cycles. In this work, we first present a framework to formalize the notion of code conversion: the process of converting data encoded with an $[n^I, k^I]$ code into data encoded with an $[n^F, k^F]$ code while maintaining desired decodability properties, such as the maximum-distance-separable (MDS) property. We then introduce convertible codes, a new class of codes that allow for code conversions in a resource-efficient manner. For an important parameter regime (which we call the merge regime) along with the linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit low-field-size constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to re-encoding.

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arXiv2018

Learning a Code: Machine Learning for Approximate Non-Linear Coded Computation

Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic tools called "codes" is an emerging technique to alleviate the adverse effects of such unavailabilities. A code consists of an encoding function that proactively introduces redundant computation and a decoding function that reconstructs unavailable outputs using the available ones. Past work focuses on using codes to provide resilience for linear computations and specific iterative optimization algorithms. However, computations performed for a variety of applications including inference on state-of-the-art machine learning algorithms, such as neural networks, typically fall outside this realm. In this paper, we propose taking a learning-based approach to designing codes that can handle non-linear computations. We present carefully designed neural network architectures and a training methodology for learning encoding and decoding functions that produce approximate reconstructions of unavailable computation results. We present extensive experimental results demonstrating the effectiveness of the proposed approach: we show that the our learned codes can accurately reconstruct $64 - 98\%$ of the unavailable predictions from neural-network based image classifiers on the MNIST, Fashion-MNIST, and CIFAR-10 datasets. To the best of our knowledge, this work proposes the first learning-based approach for designing codes, and also presents the first coding-theoretic solution that can provide resilience for any non-linear (differentiable) computation. Our results show that learning can be an effective technique for designing codes, and that learned codes are a highly promising approach for bringing the benefits of coding to non-linear computations.

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arXiv2015

Optimal Systematic Distributed Storage Codes with Fast Encoding

Erasure codes are being increasingly used in distributed-storage systems in place of data-replication, since they provide the same level of reliability with much lower storage overhead. We consider the problem of constructing explicit erasure codes for distributed storage with the following desirable properties motivated by practice: (i) Maximum-Distance-Separable (MDS): to provide maximal reliability at minimum storage overhead, (ii) Optimal repair-bandwidth: to minimize the amount of data needed to be transferred to repair a failed node from remaining ones, (iii) Flexibility in repair: to allow maximal flexibility in selecting subset of nodes to use for repair, which includes not requiring that all surviving nodes be used for repair, (iv) Systematic Form: to ensure that the original data exists in uncoded form, and (v) Fast encoding: to minimize the cost of generating encoded data (enabled by a sparse generator matrix). This paper presents the first explicit code construction which theoretically guarantees all the five desired properties simultaneously. Our construction builds on a powerful class of codes called Product-Matrix (PM) codes. PM codes satisfy properties (i)-(iii), and either (iv) or (v), but not both simultaneously. Indeed, native PM codes have inherent structure that leads to sparsity, but this structure is destroyed when the codes are made systematic. We first present an analytical framework for understanding the interaction between the design of PM codes and the systematic property. Using this framework, we provide an explicit code construction that simultaneously achieves all the above desired properties. We also present general ways of transforming existing storage and repair optimal codes to enable fast encoding through sparsity. In practice, such sparse codes result in encoding speedup by a factor of about 4 for typical parameters.

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arXiv2015

Information-theoretically Secure Erasure Codes for Distributed Storage

Repair operations in distributed storage systems potentially expose the data to malicious acts of passive eavesdroppers or active adversaries, which can be detrimental to the security of the system. This paper presents erasure codes and repair algorithms that ensure security of the data in the presence of passive eavesdroppers and active adversaries, while maintaining high availability, reliability and efficiency in the system. Our codes are optimal in that they meet previously proposed lower bounds on the storage, network-bandwidth, and reliability requirements for a wide range of system parameters. Our results thus establish the capacity of such systems. Our codes for security from active adversaries provide an additional appealing feature of `on-demand security' where the desired level of security can be chosen separately for each instance of repair, and our algorithms remain optimal simultaneously for all possible levels. The paper also provides necessary and sufficient conditions governing the transformation of any (non-secure) code into one providing on-demand security.

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