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The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Model reduction is essential for real-time simulation of deformable objects. Linear techniques such as PCA provide structured and predictable behavior, but their limited expressiveness restricts accuracy under large or nonlinear…
The distribution of the computational cost of linear-programming (LP) relaxation for vertex cover problems on Erdos-Renyi random graphs is evaluated by using the rare-event sampling method. As a large-deviation property, differences of the…
Determining the exact decoding error probability of linear block codes is an interesting problem. For binary BCH codes, McEliece derived methods to estimate the error probability of a simple bounded distance decoding (BDD) for BCH codes.…
We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing…
Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple…
Locally decodable codes (LDCs) are error correcting codes that allow for decoding of a single message bit using a small number of queries to a corrupted encoding. Despite decades of study, the optimal trade-off between query complexity and…
Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating expectation thresholds comes from the fractional relaxation of…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
Many models for complex phenomena use a model for strongly-interacting elements on a small scale to generate larger-scale simulations of some aspects of experimental realizations. These models may be agent-based (as in the case of discrete…
The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variable-length codes has already been determined. On the…
The problem of the order of the fluctuation of the Longest Common Subsequence (LCS) of two independent sequences has been open for decades. There exist contradicting conjectures on the topic, due to Chvatal - Sankoff in 1975 and Waterman in…
This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known…
In this paper, we introduce an achievability bound on the frame error rate of random tree code ensembles under a sequential decoding algorithm with a hard computational limit and consider the optimization of the random tree code ensembles…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Analog error-correcting codes (Analog ECCs) for approximate vector-matrix multiplication have been extensively studied as means to achieve fault-tolerant in-memory computation. The theoretical foundations for such coding schemes,…