Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Recombinant dynamical systems

Saul Kato

TL;DR

The paper introduces a memory-based, recombination-based framework for problem solving where remembered solutions exist as runnable dynamical constructs (BNMs) and can be recombined to tackle new tasks. It formalizes BNMs and their composition, defines the ESG problem for efficient sequence generation, and provides empirical evidence suggesting ESG is hard for random search and hill climbing. A simple recombine-and-test procedure—gluing BNMs via a minimal rule—consistently yields efficient 2BNMs in polynomial time on tested instances, offering a potential path toward compositional, experience-based problem solving. However, the authors acknowledge significant caveats (scalability, potential triviality, and generality) and call for exploring richer problem classes and broader applications, including string compression and extrapolative BNMs. The accompanying code enables replication and further exploration of recombinant dynamical systems.

Abstract

We describe a connectionist model that attempts to capture a notion of experience-based problem solving or task learning, whereby solutions to newly encountered problems are composed from remembered solutions to prior problems. We apply this model to the computational problem of \emph{efficient sequence generation}, a problem for which there is no obvious gradient descent procedure, and for which not all posable problem instances are solvable. Empirical tests show promising evidence of utility.

Recombinant dynamical systems

TL;DR

The paper introduces a memory-based, recombination-based framework for problem solving where remembered solutions exist as runnable dynamical constructs (BNMs) and can be recombined to tackle new tasks. It formalizes BNMs and their composition, defines the ESG problem for efficient sequence generation, and provides empirical evidence suggesting ESG is hard for random search and hill climbing. A simple recombine-and-test procedure—gluing BNMs via a minimal rule—consistently yields efficient 2BNMs in polynomial time on tested instances, offering a potential path toward compositional, experience-based problem solving. However, the authors acknowledge significant caveats (scalability, potential triviality, and generality) and call for exploring richer problem classes and broader applications, including string compression and extrapolative BNMs. The accompanying code enables replication and further exploration of recombinant dynamical systems.

Abstract

We describe a connectionist model that attempts to capture a notion of experience-based problem solving or task learning, whereby solutions to newly encountered problems are composed from remembered solutions to prior problems. We apply this model to the computational problem of \emph{efficient sequence generation}, a problem for which there is no obvious gradient descent procedure, and for which not all posable problem instances are solvable. Empirical tests show promising evidence of utility.
Paper Structure (7 sections, 4 figures)

This paper contains 7 sections, 4 figures.

Table of Contents

  1. Introduction
  2. Definitions
  3. The problem
  4. Empirical evidence for ESG being a hard problem
  5. THE RECOMBINATION PROCEDURE
  6. DISCUSSION
  7. Code

Figures (4)

  • Figure 1: A ZISO-2BNM (or simply 2BNM here) of size 4 with output $\textbf{110}$. Each node's boolean function is represented as a truth table. Asterisks denote irrelevant inputs.
  • Figure 2: A bag of BNMs and a gluing rule: glue the output of $X_1$ to one randomly selected input of a node in $X_2$
  • Figure 3: Output lengths of 10 million randomly chosen 2BNMs of size 3, 6, and 9 appear to follow a power law.
  • Figure 4: In blue, the distribution of output lengths of 1 million randomly generated 2BNMs of size 6 by gluing randomly selected 2BNMs of size 3 with output length 6 and 7. For comparison, the distribution of output lengths of 1 million randomly generated 2BNMs of size 6 is shown in orange.