arXiv subjects

Jin Sima

Publications and source records attributed to Jin Sima.

At least 19 recordsLinked to original sources

arXiv2026

Correcting Contextual Deletions in DNA Nanopore Readouts

The problem of designing codes for deletion-correction and synchronization has received renewed interest due to applications in DNA-based data storage systems that use nanopore sequencers as readout platforms. In almost all instances, deletions are assumed to be imposed independently of each other and of the sequence context. These assumptions are not valid in practice, since nanopore errors tend to occur within specific contexts. We study contextual nanopore deletion-errors through the example setting of deterministic single deletions following (complete) runlengths of length at least $k$. The model critically depends on the runlength threshold $k$, and we examine two regimes for $k$: a) $k=C\log n$ for a constant $C\in(0,1)$; in this case, we study error-correcting codes that can protect from a constant number $t$ of contextual deletions, and show that the minimum redundancy (ignoring lower-order terms) is between $(1-C)t\log n$ and $2(1-C)t\log n$, meaning that it is a ($1-C$)-fraction of that of arbitrary $t$-deletion-correcting codes. To complement our non-constructive redundancy upper bound, we design efficiently and encodable and decodable codes for any constant $t$. In particular, for $t=1$ and $C>1/2$ we construct efficient codes with redundancy that essentially matches our non-constructive upper bound; b) $k$ equal a constant; in this case we consider the extremal problem where the number of deletions is not bounded and a deletion is imposed after every run of length at least $k$, which we call the extremal contextual deletion channel. This combinatorial setting arises naturally by considering a probabilistic channel that introduces contextual deletions after each run of length at least $k$ with probability $p$ and taking the limit $p\to 1$. We obtain sharp bounds on the maximum achievable rate under the extremal contextual deletion channel for arbitrary constant $k$.

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arXiv2025

DNA Tails for Molecular Flash Memory

DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards system, which introduces nicks (cuts) in the DNA backbone, encodes only one bit per nicking site, limiting density. We propose \emph{DNA Tails,} a storage paradigm that encodes nonbinary symbols at nicking sites by growing enzymatically synthesized single-stranded DNA of varied lengths. The average tail lengths encode multiple information bits and are controlled via a staggered nicking-tail extension process. We demonstrate the feasibility of this encoding approach experimentally and identify common sources of errors, such as calibration errors and stumped tail growth errors. To mitigate calibration errors, we use rank modulation proposed for flash memory. To correct stumped tail growth errors, we introduce a new family of rank modulation codes that can correct ``stuck-at'' errors. Our analytical results include constructions for order-optimal-redundancy permutation codes and accompanying encoding and decoding algorithms.

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arXiv2025

Generalized Orthogonal de Bruijn and Kautz Sequences

A de Bruijn sequence of order $k$ over a finite alphabet is a cyclic sequence with the property that it contains every possible $k$-sequence as a substring exactly once. Orthogonal de Bruijn sequences are collections of de Bruijn sequences of the same order, $k$, satisfying the joint constraint that every $(k+1)$-sequence appears as a substring in at most one of the sequences in the collection. Both de Bruijn and orthogonal de Bruijn sequences have found numerous applications in synthetic biology, although the latter remain largely unexplored in the coding theory literature. Here we study three relevant practical generalizations of orthogonal de Bruijn sequences where we relax either the constraint that every $(k+1)$-sequence appears exactly once, or that the sequences themselves are de Bruijn rather than balanced de Bruijn sequences. We also provide lower and upper bounds on the number of fixed-weight orthogonal de Bruijn sequences. The paper concludes with parallel results for orthogonal nonbinary Kautz sequences, which satisfy similar constraints as de Bruijn sequences except for only being required to cover all subsequences of length $k$ whose maximum runlength equals to one.

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arXiv2024

Reducing Data Fragmentation in Data Deduplication Systems via Partial Repetition and Coding

Data deduplication, one of the key features of modern Big Data storage devices, is the process of removing replicas of data chunks stored by different users. Despite the importance of deduplication, several drawbacks of the method, such as storage robustness and file fragmentation, have not been previously analyzed from a theoretical point of view. Storage robustness pertains to ensuring that deduplicated data can be used to reconstruct the original files without service disruptions and data loss. Fragmentation pertains to the problems of placing deduplicated data chunks of different user files in a proximity-preserving linear order, since neighboring chunks of the same file may be stored in sectors far apart on the server. This work proposes a new theoretical model for data fragmentation and introduces novel graph- and coding-theoretic approaches for reducing fragmentation via limited duplication (repetition coding) and coded deduplication (e.g., linear coding). In addition to alleviating issues with fragmentation, limited duplication and coded deduplication can also serve the dual purpose of increasing the robusteness of the system design. The contributions of our work are three-fold. First, we describe a new model for file structures in the form of self-avoiding (simple) paths in specialized graphs. Second, we introduce several new metrics for measuring the fragmentation level in deduplication systems on graph-structured files, including the stretch metric that captures the worst-case "spread" of adjacent data chunks within a file when deduplicated and placed on the server; and, the jump metric that captures the worst-case number of times during the reconstruction process of a file that one has to change the readout location on the server. For the stretch metric, we establish a connection between the level of fragmentation and the bandwidth of the file-graph. In particular, ...

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arXiv2024

Federated Aggregation of Mallows Rankings: A Comparative Analysis of Borda and Lehmer Coding

Rank aggregation combines multiple ranked lists into a consensus ranking. In fields like biomedical data sharing, rankings may be distributed and require privacy. This motivates the need for federated rank aggregation protocols, which support distributed, private, and communication-efficient learning across multiple clients with local data. We present the first known federated rank aggregation methods using Borda scoring and Lehmer codes, focusing on the sample complexity for federated algorithms on Mallows distributions with a known scaling factor $\phi$ and an unknown centroid permutation $\sigma_0$. Federated Borda approach involves local client scoring, nontrivial quantization, and privacy-preserving protocols. We show that for $\phi \in [0,1)$, and arbitrary $\sigma_0$ of length $N$, it suffices for each of the $L$ clients to locally aggregate $\max\{C_1(\phi), C_2(\phi)\frac{1}{L}\log \frac{N}{\delta}\}$ rankings, where $C_1(\phi)$ and $C_2(\phi)$ are constants, quantize the result, and send it to the server who can then recover $\sigma_0$ with probability $\geq 1-\delta$. Communication complexity scales as $NL \log N$. Our results represent the first rigorous analysis of Borda's method in centralized and distributed settings under the Mallows model. Federated Lehmer coding approach creates a local Lehmer code for each client, using a coordinate-majority aggregation approach with specialized quantization methods for efficiency and privacy. We show that for $\phi+\phi^2<1+\phi^N$, and arbitrary $\sigma_0$ of length $N$, it suffices for each of the $L$ clients to locally aggregate $\max\{C_3(\phi), C_4(\phi)\frac{1}{L}\log \frac{N}{\delta}\}$ rankings, where $C_3(\phi)$ and $C_4(\phi)$ are constants. Clients send truncated Lehmer coordinate histograms to the server, which can recover $\sigma_0$ with probability $\geq 1-\delta$. Communication complexity is $\sim O(N\log NL\log L)$.

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arXiv2024

Perturbation-Resilient Trades for Dynamic Service Balancing

A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in [1] for exchanging blocks of data chunks stored on distributed storage systems in an access- and load-balanced manner. More precisely, data chunks in the trades of interest are labeled by popularity ranks and the blocks are required to have both balanced overall popularity and stability properties with respect to swaps in chunk popularities. The original construction of such trades relied on computer search and paired balanced sets obtained through iterative combining of smaller sets that have provable stability guarantees. To reduce the substantial gap between the results of prior approaches and the known theoretical lower bound, we present new analytical upper and lower bounds on the minimal disbalance of blocks introduced by limited-magnitude popularity ranking swaps. Our constructive and near-optimal approach relies on pairs of graphs whose vertices are two balanced sets with edges/arcs that capture the balance and potential balance changes induced by limited-magnitude popularity swaps. In particular, we show that if we start with carefully selected balanced trades and limit the magnitude of rank swaps to one, the new upper and lower bound on the maximum block disbalance caused by a swap only differ by a factor of $1.07$. We also extend these results for larger popularity swap magnitudes.

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arXiv2024

Nearest Neighbor Representations of Neurons

The Nearest Neighbor (NN) Representation is an emerging computational model that is inspired by the brain. We study the complexity of representing a neuron (threshold function) using the NN representations. It is known that two anchors (the points to which NN is computed) are sufficient for a NN representation of a threshold function, however, the resolution (the maximum number of bits required for the entries of an anchor) is $O(n\log{n})$. In this work, the trade-off between the number of anchors and the resolution of a NN representation of threshold functions is investigated. We prove that the well-known threshold functions EQUALITY, COMPARISON, and ODD-MAX-BIT, which require 2 or 3 anchors and resolution of $O(n)$, can be represented by polynomially large number of anchors in $n$ and $O(\log{n})$ resolution. We conjecture that for all threshold functions, there are NN representations with polynomially large size and logarithmic resolution in $n$.

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arXiv2024

Nearest Neighbor Representations of Neural Circuits

Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer correspondence between NN representations and neural networks. Although it was known how to represent a single neuron using NN representations, there were no results even for small depth neural networks. Specifically, for depth-2 threshold circuits, we provide explicit constructions for their NN representation with an explicit bound on the number of bits to represent it. Example functions include NN representations of convex polytopes (AND of threshold gates), IP2, OR of threshold gates, and linear or exact decision lists.

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arXiv2024

Online Distribution Learning with Local Private Constraints

We study the problem of online conditional distribution estimation with \emph{unbounded} label sets under local differential privacy. Let $\mathcal{F}$ be a distribution-valued function class with unbounded label set. We aim at estimating an \emph{unknown} function $f\in \mathcal{F}$ in an online fashion so that at time $t$ when the context $\boldsymbol{x}_t$ is provided we can generate an estimate of $f(\boldsymbol{x}_t)$ under KL-divergence knowing only a privatized version of the true labels sampling from $f(\boldsymbol{x}_t)$. The ultimate objective is to minimize the cumulative KL-risk of a finite horizon $T$. We show that under $(\epsilon,0)$-local differential privacy of the privatized labels, the KL-risk grows as $\tilde{\Theta}(\frac{1}{\epsilon}\sqrt{KT})$ upto poly-logarithmic factors where $K=|\mathcal{F}|$. This is in stark contrast to the $\tilde{\Theta}(\sqrt{T\log K})$ bound demonstrated by Wu et al. (2023a) for bounded label sets. As a byproduct, our results recover a nearly tight upper bound for the hypothesis selection problem of gopi et al. (2020) established only for the batch setting.

cs.LG↗

arXiv2024

Oracle-Efficient Hybrid Online Learning with Unknown Distribution

We study the problem of oracle-efficient hybrid online learning when the features are generated by an unknown i.i.d. process and the labels are generated adversarially. Assuming access to an (offline) ERM oracle, we show that there exists a computationally efficient online predictor that achieves a regret upper bounded by $\tilde{O}(T^{\frac{3}{4}})$ for a finite-VC class, and upper bounded by $\tilde{O}(T^{\frac{p+1}{p+2}})$ for a class with $\alpha$ fat-shattering dimension $\alpha^{-p}$. This provides the first known oracle-efficient sublinear regret bounds for hybrid online learning with an unknown feature generation process. In particular, it confirms a conjecture of Lazaric and Munos (JCSS 2012). We then extend our result to the scenario of shifting distributions with $K$ changes, yielding a regret of order $\tilde{O}(T^{\frac{4}{5}}K^{\frac{1}{5}})$. Finally, we establish a regret of $\tilde{O}((K^{\frac{2}{3}}(\log|\mathcal{H}|)^{\frac{1}{3}}+K)\cdot T^{\frac{4}{5}})$ for the contextual $K$-armed bandits with a finite policy set $\mathcal{H}$, i.i.d. generated contexts from an unknown distribution, and adversarially generated costs.

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arXiv2023

Break-Resilient Codes

We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up to~$t$ arbitrary positions. We establish lower bounds on the redundancy of any $(n, t)$-BRC and present code constructions that meet these bounds up to asymptotically negligible terms. Interestingly, this problem shares similarities with the recently studied torn paper channel, which has emerged in the context of DNA data storage.

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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.

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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.

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arXiv2023

Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hulls

Hierarchical and tree-like data sets arise in many applications, including language processing, graph data mining, phylogeny and genomics. It is known that tree-like data cannot be embedded into Euclidean spaces of finite dimension with small distortion. This problem can be mitigated through the use of hyperbolic spaces. When such data also has to be processed in a distributed and privatized setting, it becomes necessary to work with new federated learning methods tailored to hyperbolic spaces. As an initial step towards the development of the field of federated learning in hyperbolic spaces, we propose the first known approach to federated classification in hyperbolic spaces. Our contributions are as follows. First, we develop distributed versions of convex SVM classifiers for Poincar\'e discs. In this setting, the information conveyed from clients to the global classifier are convex hulls of clusters present in individual client data. Second, to avoid label switching issues, we introduce a number-theoretic approach for label recovery based on the so-called integer $B_h$ sequences. Third, we compute the complexity of the convex hulls in hyperbolic spaces to assess the extent of data leakage; at the same time, in order to limit communication cost for the hulls, we propose a new quantization method for the Poincar\'e disc coupled with Reed-Solomon-like encoding. Fourth, at the server level, we introduce a new approach for aggregating convex hulls of the clients based on balanced graph partitioning. We test our method on a collection of diverse data sets, including hierarchical single-cell RNA-seq data from different patients distributed across different repositories that have stringent privacy constraints. The classification accuracy of our method is up to $\sim 11\%$ better than its Euclidean counterpart, demonstrating the importance of privacy-preserving learning in hyperbolic spaces.

cs.LG↗

arXiv2023

Machine Unlearning of Federated Clusters

Federated clustering (FC) is an unsupervised learning problem that arises in a number of practical applications, including personalized recommender and healthcare systems. With the adoption of recent laws ensuring the "right to be forgotten", the problem of machine unlearning for FC methods has become of significant importance. We introduce, for the first time, the problem of machine unlearning for FC, and propose an efficient unlearning mechanism for a customized secure FC framework. Our FC framework utilizes special initialization procedures that we show are well-suited for unlearning. To protect client data privacy, we develop the secure compressed multiset aggregation (SCMA) framework that addresses sparse secure federated learning (FL) problems encountered during clustering as well as more general problems. To simultaneously facilitate low communication complexity and secret sharing protocols, we integrate Reed-Solomon encoding with special evaluation points into our SCMA pipeline, and prove that the client communication cost is logarithmic in the vector dimension. Additionally, to demonstrate the benefits of our unlearning mechanism over complete retraining, we provide a theoretical analysis for the unlearning performance of our approach. Simulation results show that the new FC framework exhibits superior clustering performance compared to previously reported FC baselines when the cluster sizes are highly imbalanced. Compared to completely retraining K-means++ locally and globally for each removal request, our unlearning procedure offers an average speed-up of roughly 84x across seven datasets. Our implementation for the proposed method is available at https://github.com/thupchnsky/mufc.

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arXiv2023

On the Information Capacity of Nearest Neighbor Representations

The $\textit{von Neumann Computer Architecture}$ has a distinction between computation and memory. In contrast, the brain has an integrated architecture where computation and memory are indistinguishable. Motivated by the architecture of the brain, we propose a model of $\textit{associative computation}$ where memory is defined by a set of vectors in $\mathbb{R}^n$ (that we call $\textit{anchors}$), computation is performed by convergence from an input vector to a nearest neighbor anchor, and the output is a label associated with an anchor. Specifically, in this paper, we study the representation of Boolean functions in the associative computation model, where the inputs are binary vectors and the corresponding outputs are the labels ($0$ or $1$) of the nearest neighbor anchors. The information capacity of a Boolean function in this model is associated with two quantities: $\textit{(i)}$ the number of anchors (called $\textit{Nearest Neighbor (NN) Complexity}$) and $\textit{(ii)}$ the maximal number of bits representing entries of anchors (called $\textit{Resolution}$). We study symmetric Boolean functions and present constructions that have optimal NN complexity and resolution.

cs.CC↗

arXiv2023

Finding a Burst of Positives via Nonadaptive Semiquantitative Group Testing

Motivated by testing for pathogenic diseases we consider a new nonadaptive group testing problem for which: (1) positives occur within a burst, capturing the fact that infected test subjects often come in clusters, and (2) that the test outcomes arise from semiquantitative measurements that provide coarse information about the number of positives in any tested group. Our model generalizes prior work on detecting a single burst of positives with classical group testing[1] as well as work on semiquantitative group testing (SQGT)[2]. Specifically, we study the setting where the burst-length $\ell$ is known and the semiquantitative tests provide potentially nonuniform estimates on the number of positives in a test group. The estimates represent the index of a quantization bin containing the (exact) total number of positives, for arbitrary thresholds $η_1,\dots,η_s$. Interestingly, we show that the minimum number of tests needed for burst identification is essentially only a function of the largest threshold $η_s$. In this context, our main result is an order-optimal test scheme that can recover any burst of length $\ell$ using roughly $\frac{\ell}{2η_s}+\log_{s+1}(n)$ measurements. This suggests that a large saturation level $η_s$ is more important than finely quantized information when dealing with bursts. We also provide results for related modeling assumptions and specialized choices of thresholds.

cs.IT↗

arXiv2023

On Constant-Weight Binary $B_2$-Sequences

Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length $n$ with the property that the real-valued sums of all distinct pairs of strings are distinct. In addition to this defining property, constant-weight binary $B_2$-sequences also satisfy the constraint that each string has a fixed, relatively small weight $ω$ that scales linearly with $n$. The constant-weight constraint ensures low-cost synthesis and uniform processing of the data readout via tandem mass spectrometers. Our main results include upper bounds on the size of the codes formulated as entropy-optimization problems and constructive lower bounds based on Sidon sequences.

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