Related papers: A* Based Algorithm for Reduced Complexity ML Decod…
The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free…
Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional data. A well-known method for TR decomposition is the alternating…
In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial…
Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for…
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in…
The process of turbo-code decoding starts with the formation of a posteriori probabilities (APPs) for each data bit, which is followed by choosing the data-bit value that corresponds to the maximum a posteriori (MAP) probability for that…
Integrating textual graphs into Large Language Models (LLMs) is promising for complex graph-based QA. However, a key bottleneck is retrieving informative yet compact subgraphs that fit the LLM context. Existing retrievers often struggle,…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…
Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients,…
Algebraic codes that achieve list decoding capacity were recently constructed by a careful ``folding'' of the Reed-Solomon code. The ``low-degree'' nature of this folding operation was crucial to the list decoding algorithm. We show how…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
Beam search is the go-to method for decoding auto-regressive machine translation models. While it yields consistent improvements in terms of BLEU, it is only concerned with finding outputs with high model likelihood, and is thus agnostic to…
Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate…
Over the past decade, various improvements have been made to Tardos' collusion-resistant fingerprinting scheme [Tardos, STOC 2003], ultimately resulting in a good understanding of what is the minimum code length required to achieve…
This paper presents an incremental replanning algorithm, dubbed LTL-D*, for temporal-logic-based task planning in a dynamically changing environment. Unexpected changes in the environment may lead to failures in satisfying a task…
Length-control summarization aims to condense long texts into a short one within a certain length limit. Previous approaches often use autoregressive (AR) models and treat the length requirement as a soft constraint, which may not always be…
Constrained decoding with lookahead heuristics (CDLH) is a highly effective method for aligning LLM generations to human preferences. However, the extensive lookahead roll-out operations for each generated token makes CDLH prohibitively…
Hierarchical problem abstraction, when applicable, may offer exponential reductions in computational complexity. Previous work on coarse-to-fine dynamic programming (CFDP) has demonstrated this possibility using state abstraction to speed…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…