相关论文: Generating functions for generating trees

We model the recursive production property of context-free grammars for natural and synthetic languages. To this end, we present a dynamic programming algorithm that marginalises over latent binary tree structures with $N$ leaves, allowing…

Neural codes appear efficient. Naturally, neuroscientists contend that an efficient process is responsible for generating efficient codes. They argue that natural selection is the efficient process that generates those codes. Although…

We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…

We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

The meaning of a sentence is a function of the relations that hold between its words. We instantiate this relational view of semantics in a series of neural models based on variants of relation networks (RNs) which represent a set of…

A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…

Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…

Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

"A generator is a parser of randomness." This perspective on generators for random data structures is well established as folklore in the programming languages community, but it has apparently never been formalized, nor have its…

We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant extension known as '$\Gamma$-species' which incorporates data about 'structural' group actions). This culminates…

We explore the relationship between polynomial functors and (rooted) trees. In the first part we use polynomial functors to derive a new convenient formalism for trees, and obtain a natural and conceptual construction of the category…

Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up, are a popular architecture. But there have not been rigorous evaluations showing for exactly which tasks this syntax-based method is…

Entailment trees have been proposed to simulate the human reasoning process of explanation generation in the context of open--domain textual question answering. However, in practice, manually constructing these explanation trees proves a…

To any rooted tree, we associate a sequence of numbers that we call the logarithmic factorials of the tree. This provides a generalization of Bhargava's factorials to a natural combinatorial setting suitable for studying questions around…

In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we…

Predictions using a combination of decision trees are known to be effective in machine learning. Typical ideas for constructing a combination of decision trees for prediction are bagging and boosting. Bagging independently constructs…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…