Emergent Intelligence: Resonant Oscillators Produce Proactive Adaptive Behavior

Alex Fedosov; Maxim Yakimenko; Sander Stepanov

cs.NESep 18, 2026

Emergent Intelligence: Resonant Oscillators Produce Proactive Adaptive Behavior

Authors: Alex Fedosov, Maxim Yakimenko, Sander Stepanov

Organizations: FoundAItion Inc · FoundAItion Inc.

Abstract

Most artificial neural systems are built to map given inputs to outputs. Adaptive agents face a prior problem: they must act without enough evidence, seek encounters with the world, and revise behavior when evidence appears. We propose another starting point for intelligent neural networks: proactive search without signals, curiosity at its most basic. We ask whether it can come from a minimal untrained circuit. The spiking unit studied here inverts its response to input: with no signal in its window it fires faster; once signals arrive it switches to a slower, inverted regime. Search needs three or more such oscillators in counter-phase, each reading the same input in a different time window. With no training, supervision, parameter tuning, or controller, the composite switches on its own between exploratory spiral search and exploitative tracking, finding both first-degree symmetry and second-degree groups. The switch comes from temporal disagreement between its fast and slow readings of the same signal. We view the circuit as evolutionarily trained: its abilities come from structure, not experience. Ablation over 63 configurations and 63,000 trials shows the switch needs both temporal staggering and counter-phase opposition, neither enough alone: the behavior is emergent, not programmed. The spiral persists at zero rotational diffusion, so it is structural, and degrades gently under perturbation. More oscillators improve spiral regularity but cut resource capture, so the smallest sufficient circuit wins. We propose that this principle underlies search in simple organisms, navigation and decisions in complex ones, and, being so simple and common, goes unnoticed unless you strip the logic bare. Eventually, networks of such proactive primitives may offer another foundation for AI architectures that explore our world rather than merely predict the next symbol in a sequence.

Figures & tables

Parameter	Role
$C_{1}$	Decision window length; Left output period in active (HIGH) state
$C_{2}$	Left output period in suppressed (LOW) state
$C_{3}$	Right output period in active (HIGH) state
$C_{4}$	Right output period in suppressed (LOW) state

Table 1: Inverter period parameters

Panel of Figure 1 — Figure 1: Composite wiring topology for an N ${\times}$ 1 ${\times}$ 2 counter-phase circuit. Blue: normal wiring ( $f_{1}$ ). Red: counter-phase wiring ( $f_{2}$ through $f_{N}$ ).

ID	Config	Opposition	Staggering	Prediction
H2a	Stochastic agent	–	–	Random walk, no spiral
H2b	1 inverter	–	–	Stable circle
H2c	2-inv (N + C)	Yes	Yes	Wider arc, no spiral (insufficient inverters)
H2d	2-inv (N + N)	No	Yes	Faster circle
H2e	3-inv, all same $C_{1}$	Yes	No	Reversed circle (opposition without staggering)
H2f	3-inv, all normal	No	Yes	Accelerating circle (staggering without opposition)

Table 2: H2 ablation configurations

ID	Agent	Environment	Prediction
H3a	Composite (4-inv)	Dense band	Spiral $\to$ tracking transition
H3b	Composite (4-inv)	Small circle	Spiral $\to$ tracking transition
H3c	Single inverter	Dense band	Tracking only (control)
H3d	Single inverter	Small circle	Tracking only (control)

Table 3: H3 mode-switching configurations

ID	Inverters	$C_{1}$ Values (s)	Prediction
H6a1	3	0.15, 0.75, 1.5	Most food
H6a2	4	0.15, 0.5, 1.0, 2.0	Slightly less food
H6a3	5	0.15, 0.5, 1.0, 2.0, 4.0	Less food
H6a4	6	0.15, 0.5, 1.0, 2.0, 4.0, 8.0	Less food still
H6a5	7	0.15, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0	Least food

Table 4: H6 complexity-scaling configurations

ID	Inverters	$C_{1}$ Values (s)	Prediction
H8a1	3	0.15, 0.75, 1.5	Lowest spiral quality
H8a2	4	0.15, 0.5, 1.0, 2.0	Higher quality
H8a3	5	0.15, 0.5, 1.0, 2.0, 4.0	Higher quality
H8a4	6	0.15, 0.5, 1.0, 2.0, 4.0, 8.0	Higher quality
H8a5	7	0.15, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0	Highest quality

Table 5: H8 reconciliation configurations

Hypothesis	Configs	Trials/Config	Total Trials
H0: Baseline	7	1,000	7,000
H1: Emergence	3	1,000	3,000
H2: Specificity	7	1,000	7,000
H3: Exploitation	4	1,000	4,000
H4a: Opposition Balance	7	1,000	7,000
H4b: Robustness	4	1,000	4,000

Table 6: Experimental design summary

Config	Opposition	Staggering	Spiral Quality [95% CI]	Area Visited
H2a (stochastic)	–	–	0.038 [0.032, 0.044]	38.3
H2b (1 inverter)	–	–	0.067 [0.062, 0.073]	21.3
H2c (2-inv N+C)	Yes	Yes	0.127 [0.118, 0.137]	49.4
H2d (2-inv N+N)	No	Yes	0.060 [0.055, 0.065]	16.1
H2e (same $C_{1}$ )	Yes	No	0.073 [0.067, 0.079]	120.0
H2f (all normal)	No	Yes	0.088 [0.082, 0.095]	15.0

Table 7: H2 ablation results

Figure 2: H2 ablation results. Mean spiral quality across N = 1,000 trials per configuration. All six conditions lacking either opposition or staggering fall below the 0.20 spiral quality threshold. The positive control (H2g, both present) exceeds the best ablation by $3.1{\times}$ .

Config	Agent	Environment	Pre-food Spiral [95% CI]	Food Eaten	Revisitation
H3a	Composite	Dense band	0.413 [0.397, 0.430]	283.9	0.964
H3b	Composite	Small circle	0.472 [0.456, 0.487]	144.6	0.962
H3c	Inverter	Dense band	0.056 [0.045, 0.067]	88.2	0.945
H3d	Inverter	Small circle	0.069 [0.057, 0.080]	48.3	0.946

Table 8: H3 mode-switching results

Figure 3: H3 mode switching. Representative single-trial trajectory (selected as the trial closest to the median food_eaten). A composite agent spawns in void (center), develops an outward spiral, encounters a dense food band, and transitions autonomously to sinusoidal tracking along the food source.

Config	Inverters	Food Eaten [95% CI]	Area Visited	Mean Speed (px/s)	Revisitation
H6a1	3	749.0 [737.0, 760.9]	165.2	181.5	0.909
H6a2	4	733.8 [722.7, 744.9]	165.1	209.3	0.909
H6a3	5	654.7 [646.0, 663.5]	140.5	208.3	0.923
H6a4	6	593.1 [585.4, 600.9]	117.6	198.0	0.935
H6a5	7	530.2 [522.2, 538.3]	96.6	193.5	0.947

Table 9: H6 complexity-scaling results

Config	Inverters	Spiral Quality	Detection Rate	Area Visited	Mean Speed (px/s)
H8a1	3	0.270 [0.255, 0.286]	0.650	164.5	268.0
H8a2	4	0.310 [0.293, 0.327]	0.679	190.5	325.0
H8a3	5	0.383 [0.366, 0.400]	0.778	188.7	326.1
H8a4	6	0.538 [0.522, 0.555]	0.934	177.1	303.3
H8a5	7	0.720 [0.709, 0.730]	0.998	146.0	277.6

Table 10: H8 reconciliation results

Figure 4: Quality-efficiency dissociation. Mean values across N = 1,000 trials per configuration. (a) H6: more inverters catch less food in a foraging environment, declining 41% from 3 to 7 inverters. (b) H8: the same configurations produce better spirals in void, increasing $2.66{\times}$ . The optimal foraging agent is the minimal circuit.

Figure 5: Baseline single-inverter dynamics. Mean values across N = 1,000 trials per configuration. (a) Circle radius tightens monotonically with L/R frequency ratio. (b) Speed scales linearly with absolute frequency; radius remains constant.

Config	Net Diff	Food Eaten [95% CI]	Area Visited	Mean Speed (px/s)	Revisitation
H5a1 (tight)	+1.89	456.3 [448.4, 464.2]	48.9	156.9	0.973
H5a2 (medium)	+0.89	559.6 [552.6, 566.5]	78.3	150.3	0.957
H5a3 (wide)	+0.45	636.5 [628.2, 644.8]	128.3	147.7	0.929
H5a4 (open)	+0.22	746.6 [734.8, 758.4]	165.2	181.2	0.909

Table 11: H5 exploitation geometry results

Panel of Figure 6 — Figure 6: H5 exploitation geometry: tight vs. open spiral trajectories in the dense-bands environment.

Agent	Food Eaten [mean $\pm$ std]	Area Visited	Spiral Quality	Speed (px/s)
NNN (3-inv)	483 $\pm$ 76	71	0.07	62
NNN (7-inv)	385 $\pm$ 131	51	0.13	83
Log spiral	228 $\pm$ 32	131	0.46	97
Levy walk	127 $\pm$ 98	111	0.06	126
ARS	126 $\pm$ 73	81	0.18	99
CRW	105 $\pm$ 79	114	0.06	131

Table 12: External baseline comparison (dense-bands, 1,000 trials each)

Agent	Spiral Quality [mean $\pm$ std]	Area Visited	Speed (px/s)
NNN (7-inv)	0.67 $\pm$ 0.20	150	138
Log spiral	0.33 $\pm$ 0.42	131	89
NNN (3-inv)	0.25 $\pm$ 0.24	167	133
Stochastic	0.08 $\pm$ 0.11	57	61
CRW	0.07 $\pm$ 0.09	114	128
Levy	0.07 $\pm$ 0.09	110	124

Table 13: External baseline comparison (void, 1,000 trials each)

Hypothesis	Checks	Result	Key Finding
H0: Baseline	14/14	PASS	Single inverter = circles; speed and radius scale as predicted
H1: Emergence	8/8	PASS	3+ inverters $\to$ spiral; quality increases with inverter count
H2: Specificity	11/11	PASS	Both opposition and staggering required; $3.1{\times}$ gap
H3: Exploitation	9/9	PASS	Spiral $\to$ tracking transition; composite eats $3.2{\times}$ more
H4a: Opposition	12/12	PASS	Near-balance = peak quality; balance = max area
H4b: Robustness	5/5	PASS	Graceful degradation; detectable at 30% jitter

Table 14: Hypothesis validation summary

Panel of Figure 7 — Figure 7: H5 performance traces: tight spiral (single band) vs. open spiral (both bands).

Panel of Figure 8 — Figure 8: Proposed translation of the composite behavioral model into a neural network. Neurons 1 through N oscillate at different intrinsic periods ( $\delta t_{1}$ through $\delta t_{n}$ ) via self-excitatory feedback loops. All receive the same shared input signal. Their outputs converge on a summarizing neuron S, which fires only when all input signals coincide. The inhibitory input (blue minus) from the shared signal resets the counting cycle on each input event.

Panel of Figure 9 — Figure 9: The $2{\times}2$ associative inverter. Two input signals (black arrows) are evaluated within the same decision window but offset by $\Delta$ . Two output signals (grey arrows) are produced. The function f determines the output periods based on the joint input state.

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