The Inhibition of Return (IOR) task evaluates whether an evolved Dynamic Neural Field (DNF) architecture can exhibit novelty-biased orienting behaviour, a well-established phenomenon in human attention.

The desired behaviour is:

1. An initial cue stimulus is presented at a spatial location.

2. The system forms an internal representation of the cued location.

3. After a delay, two test cues are presented simultaneously:

   • One at the previously cued location
   • One at a novel location

4. The system should preferentially respond to the novel location, inhibiting return to the previously attended position.

This task requires the emergence of a persistent inhibitory trace that biases subsequent selection decisions.

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Unlike the earlier instability tasks, IOR consistently requires additional structure beyond a two-field architecture:

• Fields: 3 (input, memory, output)

• Hidden fields: typically 1–2

• Connections: multiple feedforward and inhibitory couplings

• Dynamics:

  • Input field: stimulus-driven representation of spatial cues
  • Memory field: sustained encoding of the initial cue
  • Output field: competitive selection biased by inhibitory input from memory

ior-phenotype-wbg

The figure above illustrates:

• Storage of the initial cue in a dedicated memory field
• Inhibitory projections suppressing the previously cued location
• Selection of the novel cue in the output field

This architecture mirrors classical Dynamic Field Theory accounts of IOR.

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

• Mean: 76.03
• Median: 57.50
• Std: 54.53

• Mean convergence rate (fitness gain/gen): 0.0151
• Mean fitness improvement/gen: 0.0152

• Hidden fields (mean ± std): 1.19 ± 0.39
• Enabled connections (mean ± std): 3.43 ± 0.96

label	run	value
Highest max fitness	2026年01月20日 17h15m00s	0.989475
Lowest max fitness	2026年01月20日 13h59m51s	0.950067
Fastest to threshold	2026年01月21日 01h44m27s	8.0
Slowest to threshold	2026年01月21日 23h38m17s	193.0
Most hidden fields	2026年01月20日 13h18m36s	2.0
Most enabled connections	2026年01月21日 03h06m50s	7.0

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This section reports detailed statistics from the evolutionary run that produced the highest-fitness solution for the Inhibition of Return task.

Final generation: g = 130

• Best fitness: 0.9787
• Target fitness: 0.950
• Average fitness: 0.5423

Overall run statistics

• Max best fitness: 0.9787 (reached at generation 130)
• Mean best fitness over run (AUC): 0.7462
• Mean average fitness over run (AUC): 0.5896
• Longest stagnation period: 3 generations
• Target fitness first reached: generation 130 (best fitness ≈ 0.9787)

Final generation (g = 130)

• Species: 370
• Active species: 29

Across run

• Total distinct species created: 368
• Species extinct by final generation: 341
• Average species per generation: 176.16
• Average active species per generation: 14.44
• Max active species in a generation: 70 (at g = 69)

Species lifetime & size

• Average species lifespan: 61.70 generations
• Longest-lived species: 0 (lifespan 130)
• Average max members per species: 55.19
• Average offspring per species: 350.54

Final generation (g = 130)

• Avg genome size: 4.56
• Avg field genes: 2.52
• Avg connection genes: 2.04

Growth over run

• Genome size change: +2.56 (≈ +0.020 / gen)
• Field genes change: +0.52 (≈ +0.004 / gen)
• Connection genes change: +2.04 (≈ +0.016 / gen)

Ratios

• Avg connections per field (final gen): 0.81

• Field kernels:

  • Gaussian: 133 143 (49.3%)
  • Mexican-hat: 137 149 (50.7%)

• Interaction kernels:

  • Gaussian: 133 637 (93.8%)
  • Mexican-hat: 8 782 (6.2%)

Generation: 130 Fitness: 0.9787

Field	Role	Kernel type	Field parameters	Kernel parameters
nf 1	Input	Gaussian	h = -13.11, τ = 61.57	A = 11.53, σ = 5.12, A_glob = -0.15
nf 2	Output	Mexican-hat	h = -2.65, τ = 94.45	A_exc = 18.18, σ_exc = 11.17, A_inh = 25.82, σ_inh = 7.18, A_glob = -0.03
nf 3	Hidden	Gaussian	h = -3.96, τ = 165.60	A = 11.53, σ = 5.12, A_glob = -0.15

Interaction gene	From → To	Kernel parameters
gk cg 1-2-0	nf 1 → nf 2	A = 24.69, σ = 2.28, A_glob = -0.10
gk cg 1-3-114	nf 1 → nf 3	A = 8.00, σ = 2.00, A_glob = 0.00
gk cg 3-2-115	nf 3 → nf 2	A = -3.00, σ = 1.17, A_glob = -0.05

ior.mp4

IOR exhibits the deepest and most sustained evolutionary dynamics of all tasks:

• Hundreds of species are explored, with long-lived lineages
• Structural growth is slow but persistent, favoring refinement over expansion
• A dedicated hidden field encodes the inhibitory trace
• Output selection emerges from inhibitory coupling, not explicit control logic

Despite the long evolutionary trajectory, the final solution remains compact, interpretable, and neurocognitively plausible.

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IOR is the most demanding task in the benchmark suite:

• Convergence is slow and highly variable.
• Successful solutions require explicit memory-mediated inhibition.
• Evolution reliably discovers architectures consistent with neuropsychological models of attention.

This task demonstrates that neat-dnfs can evolve functionally interpretable, multi-field cognitive architectures, not just minimal reactive systems.