Topology Evolution Roadmap

This document outlines the planned integration of full TWEANN (Topology and Weight Evolving Artificial Neural Networks) capabilities into macula_neuroevolution, and how the Liquid Conglomerate meta-learning architecture will control topology evolution.

Current State

Currently, macula_neuroevolution uses fixed-topology networks where:

• Network structure is defined at initialization: {InputSize, HiddenLayers, OutputSize}
• Only weights are evolved through crossover and mutation
• All individuals in the population have identical topology

The underlying macula_tweann library already supports full topology evolution operators:

NEAT-Inspired Topology Evolution

The planned topology evolution follows the NEAT (NeuroEvolution of Augmenting Topologies) approach by Stanley and Miikkulainen (2002):

Core Principles

1. Start Minimal - Networks begin with minimal structure (direct input-output connections)
2. Complexify Gradually - Structure grows through mutations over generations
3. Protect Innovation - New structures need time to optimize their weights
4. Speciation - Similar topologies compete primarily with each other

Innovation Numbers

Each structural change (new connection, new node) receives a unique innovation number:

Connection Gene: {from: 1, to: 4, weight: 0.5, enabled: true, innovation: 42}

Innovation numbers enable:

• Alignment during crossover (match genes by innovation)
• Distance calculation for speciation
• Historical tracking of structural changes

Liquid Conglomerate Integration

The Liquid Conglomerate meta-controller will extend to control topology evolution parameters dynamically.

Extended Meta-Controller Outputs

Current outputs (weight evolution):

• mutation_rate - Probability of weight mutation
• mutation_strength - Magnitude of weight perturbation
• selection_ratio - Survival ratio per generation

New outputs (topology evolution):

• topology_mutation_rate - Probability of structural mutation
• add_neuron_rate - Relative probability of adding neurons
• add_connection_rate - Relative probability of adding connections
• remove_connection_rate - Relative probability of removing connections
• complexity_penalty - Fitness penalty per structural element

Extended Meta-Controller Inputs

Current inputs (population metrics):

• Best/average/worst fitness
• Fitness improvement rate
• Population diversity
• Stagnation count

New inputs (topology metrics):

• Average network complexity (neuron count, connection count)
• Complexity variance across population
• Topology diversity (unique structures)
• Innovation frequency
• Species count and health

Adaptive Topology Control

The meta-controller learns when to:

1. Encourage Complexification

   • Fitness plateaus but hasn't peaked
   • High diversity in weights but not structure
   • Problem appears to need more representational capacity

2. Discourage Complexification

   • Networks growing without fitness improvement
   • Over-fitting indicators (train/test divergence)
   • Computational budget concerns

3. Encourage Simplification

   • Prune unused connections
   • Remove redundant neurons
   • Regularize toward minimal effective complexity

Speciation with Liquid Conglomerate

Species as Sub-Populations

Each species maintains its own population dynamics:

Meta-Controller Per Species

The Liquid Conglomerate hierarchy could extend to species-level control:

This enables different evolutionary strategies for different topological niches.

Crossover with Variable Topology

When crossing individuals with different topologies:

Gene Alignment

Compatibility Distance

compatibility_distance(Genome1, Genome2, Config) ->
    {Excess, Disjoint, WeightDiff} = compare_genomes(Genome1, Genome2),
    N = max(genome_size(Genome1), genome_size(Genome2)),

    Config#compat_config.c1 * Excess / N +
    Config#compat_config.c2 * Disjoint / N +
    Config#compat_config.c3 * WeightDiff.

Implementation Phases

Phase 1: Foundation

• Add innovation number tracking to networks
• Implement gene-based genome representation
• Add compatibility distance calculation
• Basic speciation without meta-control

Phase 2: Topology Operators

• Integrate add_neuron, add_outlink, add_inlink operators
• Implement connection enable/disable
• Add crossover for variable topologies
• Implement speciation dynamics

Phase 3: Meta-Controller Extension

• Extend meta-controller inputs (complexity metrics)
• Add topology evolution outputs
• Train meta-controller on topology-aware reward signal
• Implement adaptive complexity penalties

Phase 4: Species-Level Meta-Control

• Per-species meta-controllers
• Inter-species resource allocation
• Hierarchical Liquid Conglomerate for species

Expected Benefits

From Topology Evolution

1. Automatic Architecture Discovery - No manual network design needed
2. Minimal Complexity Bias - Solutions grow only as complex as needed
3. Diverse Strategies - Different topologies for different sub-problems
4. Incremental Building - Complex solutions built on simpler precursors

From Liquid Conglomerate Control

1. Adaptive Complexification - Grow structure when needed, not randomly
2. Phase-Appropriate Strategies - Explore structure early, refine late
3. Automatic Regularization - Meta-learned complexity penalties
4. Transfer of Meta-Knowledge - Learn "how to evolve topology" across domains

Relation to DXNN2

This roadmap draws heavily from Gene Sher's DXNN2 architecture (described in "Handbook of Neuroevolution Through Erlang"). Key concepts from DXNN2:

• Morphology-based sensor/actuator specification
• Constraint records for controlling mutation operators
• Substrate encoding for hypercube geometry
• Exoself architecture for agent lifecycle

The Liquid Conglomerate extends DXNN2's concepts by adding:

• Hierarchical meta-learning at multiple timescales
• LTC neurons for continuous temporal dynamics
• Adaptive tau for timescale self-organization
• Species-level meta-control

References

• Stanley, K.O. & Miikkulainen, R. (2002). Evolving Neural Networks through Augmenting Topologies. Evolutionary Computation, 10(2), 99-127.

• Sher, G.I. (2013). Handbook of Neuroevolution Through Erlang. Springer.

• Hasani, R. et al. (2021). Liquid Time-constant Networks. AAAI.

Next Steps

See The Liquid Conglomerate for the full meta-learning theory, or LTC Meta-Controller for current implementation details.