相关论文: Still Simpler Static Level Ancestors

Latent reasoning compresses the chain-of-thought (CoT) into continuous hidden states, yet existing methods rely on dense latent transitions that remain difficult to interpret and control. Meanwhile, sparse representation models uncover…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…

The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic…

We consider symbolic tree automata (sta) and symbolic tree transducers (stt). We characterize s-recognizable tree languages (which are the tree languages recognizable by sta) in terms of (classical) recognizable tree languages and…

A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case…

Background. The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set $L$ is known to be solvable in linear time.…

Large language models (LLMs) have emerged as powerful tools for natural language table reasoning, where there are two main categories of methods. Prompt-based approaches rely on language-only inference or one-pass program generation without…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

Table reasoning with large language models (LLMs) plays a critical role in building intelligent systems capable of understanding and analyzing tabular data. Despite recent progress, existing methods still face key limitations: their…

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell…

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence.…

Understanding how the time-complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived…

We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…

Given a rooted tree $T$ with leaves $v_1,v_2,\ldots,v_n$, we define the ancestral matrix $C(T)$ of $T$ to be the $n \times n$ matrix for which the entry in the $i$-th row, $j$-th column is the level (distance from the root) of the first…

Stochastic differential equations, especially the one called Langevin equation, play an important role in many fields of modern science. In this paper, we use the bicolour rooted tree method, which is based on the stochastic Taylor…

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

We present a new exact algorithm for the Steiner tree problem in edge-weighted graphs. Our algorithm improves the classical dynamic programming approach by Dreyfus and Wagner. We achieve a significantly better practical performance via…

Backtracking line search is foundational in numerical optimization. The basic idea is to adjust the step-size of an algorithm by a constant factor until some chosen criterion (e.g. Armijo, Descent Lemma) is satisfied. We propose a novel way…

We consider two closely related problems of text indexing in a sub-linear working space. The first problem is the Sparse Suffix Tree (SST) construction of a set of suffixes $B$ using only $O(|B|)$ words of space. The second problem is the…