A Computational Cognitive Model for Processing Repetitions of Hierarchical Relations

TL;DR

The paper addresses how humans detect abstract repeats arising from hierarchical relations in sequences by introducing a Template programming language that foregrounds repetition combinators. It couples this language with a weighted deduction algorithm guided by Minimum Description Length to infer the smallest, most compressor-friendly template that explains observed sequences. Demonstrations in action planning and music show that minimal templates reveal meaningful relational repeats, including recursive and duplicated computations, suggesting a cognitively plausible mechanism for pattern recognition. The framework provides a versatile tool for exploring cognitive representations of structure and offers avenues for neuroscientific and psychological investigations into how people infer underlying generative patterns.

Abstract

Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within sequential data, and develop a candidate computational model of how humans detect and understand such structural repeats. Based on a weighted deduction system, our model infers the minimal generative process of a given sequence in the form of a Template program, a formalism that enriches the context-free grammar with repetition combinators. Such representation efficiently encodes the repetition of sub-computations in a recursive manner. As a proof of concept, we demonstrate the expressiveness of our model on short sequences from music and action planning. The proposed model offers broader insights into the mental representations and cognitive mechanisms underlying human pattern recognition.

Figures (4)

• Figure 1: Three examples of structural repetition across domains demonstrates the kinds of computation involved in structural repeat. (\ref{['fig:poetry']}) An excerpt from the Tang poetry "山居秋暝" written by Wang Wei (699–761), translated by Xu Yuanchong, exhibits parallel syntactic structure (repetition of complete computation). (\ref{['fig:music']}) A melodic reduction of the opening theme in K331 (mm. 1-4) shows mm. 1-3 share the same underlying generative process up to a certain point (repetition of suspended computation). (\ref{['fig:coffee']}) The hierarchical action planning involved in making coffee reveals polymorphic relations as the basis of structural repeats.
• Figure 2: Visual illustration on how hierarchical relations compose. $R$ has arity 3, $R_1$ has arity 2, $R_2$ has arity 0, $R_3$ has arity 1, and the composed relation $R \circ (R_1 \otimes R_2 \otimes R_3)$ has arity $2+0+1=3$.
• Figure 3: A visual illustration of the inference rule Complete-rep, showing mergeT (composition of the colored shapes) and mergeR (composition of the surface segments). Relation trees are represented by triangles potentially containing holes. This example is a special case where $t$ has two holes (arity = 2) while $t_1$ and $t_2$ each has one hole (arity = 1).
• Figure 4: Results for inferring the minimal template program in two contrasting domains: action planning and music. Fig. (\ref{['coffeehisto']} and \ref{['chordhisto']}) shows the template size distribution for the coffee action planning and jazz chord progression. Fig. (\ref{['fig:coffeeResult']} and \ref{['fig:chordResult']}) The inferred minimal template program for action planning in making coffee reveals hidden yet cognitively plausible relational repeat within the sequential data.