The Selection Instability task evaluates whether an evolved Dynamic Neural Field (DNF) architecture can perform decision-making through competitive dynamics.

The desired behaviour is:

1. Multiple external stimuli are presented simultaneously, inducing multiple peaks in the input field.
2. The input field maintains a multi-peak representation during stimulus presentation.
3. Activity is transmitted to the output field.
4. The output field resolves competition via winner-take-all dynamics, stabilizing a single dominant peak.
5. After stimulus offset, both fields relax back to baseline.

This task tests the emergence of selection and decision-making as a dynamical property, rather than as an explicit symbolic operation.

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The highest-fitness solutions typically converge to a near-minimal topology, though with greater variability than detection or memory:

• Fields: 2 (input → output)

• Hidden fields: usually 0, occasionally 1–2

• Connections: typically 1 feedforward coupling, with optional additional connections

• Dynamics:

  • Input field: Mexican-hat kernel supporting stable multi-peak activation
  • Output field: Gaussian kernel enabling competitive suppression and selection

phenotype-selection-wbg

The figure above shows:

• Blue: activity during stimulus presentation
• Red: activity after stimulus removal

The output field selects a single stimulus location while suppressing competitors, implementing winner-take-all behavior.

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Analysed 100 runs; 100 reached the fitness threshold (100.0% success, threshold = 0.950)

• Mean: 13.00
• Median: 9.00
• Std: 12.26

• Mean convergence rate (fitness gain/gen): 0.0347
• Mean fitness improvement/gen: 0.0357

• Hidden fields (mean ± std): 0.27 ± 0.56
• Enabled connections (mean ± std): 1.45 ± 1.07

label	run	value
Highest max fitness	2026年01月24日 19h08m33s	0.981938
Lowest max fitness	2026年01月24日 18h55m02s	0.950192
Fastest to threshold	2026年01月24日 23h07m48s	1.0
Slowest to threshold	2026年01月24日 20h15m51s	73.0
Most hidden fields	2026年01月24日 19h08m33s	2.0
Most enabled connections	2026年01月24日 19h54m56s	7.0

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This section reports detailed statistics from the evolutionary run that produced the highest-fitness solution for the Selection Instability task.

Final generation: g = 11

• Best fitness: 0.9803
• Target fitness: 0.950
• Average fitness: 0.7336

Overall run statistics

• Max best fitness: 0.9803 (reached at generation 11)
• Mean best fitness over run (AUC): 0.7756
• Mean average fitness over run (AUC): 0.7020
• Longest stagnation period: 2 generations
• Target fitness first reached: generation 11 (best fitness ≈ 0.9803)

Final generation (g = 11)

• Species: 118
• Active species: 93

Across run

• Total distinct species created: 63
• Species extinct by final generation: 2
• Average species per generation: 26.25
• Average active species per generation: 23.67
• Max active species in a generation: 93 (at g = 11)

Species lifetime & size

• Average species lifespan: 3.13 generations
• Longest-lived species: 0 (lifespan 11)
• Average max members per species: 42.65
• Average offspring per species: 158.73

Final generation (g = 11)

• Avg genome size: 7.22
• Avg field genes: 3.36
• Avg connection genes: 3.86

Growth over run

• Genome size change: +5.22 (≈ +0.475 / gen)
• Field genes change: +1.36 (≈ +0.124 / gen)
• Connection genes change: +3.86 (≈ +0.351 / gen)

Ratios

• Avg connections per field (final gen): 1.15

• Field kernels:

  • Gaussian: 22 497 (89.4%)
  • Mexican-hat: 2 674 (10.6%)

• Interaction kernels:

  • Gaussian: 11 241 (97.9%)
  • Mexican-hat: 240 (2.1%)

Generation: 11 Fitness: 0.9803

Field	Role	Kernel type	Field parameters	Kernel parameters
nf 1	Input	Mexican-hat	h = -4.20, τ = 55.66	A_exc = 17.34, σ_exc = 5.00, A_inh = 28.55, σ_inh = 5.88, A_glob = -0.08
nf 2	Output	Gaussian	h = -3.42, τ = 31.69	A = 3.00, σ = 1.55, A_glob = -0.13

Interaction gene	From → To	Kernel parameters
gk cg 1-2-1	nf 1 → nf 2	A = 3.00, σ = 2.09, A_glob = 0.00

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selection.mp4

• Winner-take-all behavior emerges from strong inhibitory Mexican-hat dynamics in the input field

Despite the population exploring highly complex genomes, the best solution collapses back to a compact, interpretable architecture, reinforcing neat-dnfs’ bias toward minimal sufficiency.

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Selection Instability is substantially more demanding than detection or memory:

• Convergence is slower and more variable.
• Some (very little) runs require additional structure beyond the minimal two-field topology.
• Nevertheless, winner-take-all decision-making reliably emerges from continuous DNF dynamics.

This task marks the transition from representation to choice.