History, Adaptation, and Hidden Gain: Two Prospective Tests of Learned Predictive Control in a Synthetic Neural Population

Mahesh Reddy Pagadala

cs.LGOct 9, 2026

History, Adaptation, and Hidden Gain: Two Prospective Tests of Learned Predictive Control in a Synthetic Neural Population

Authors: Mahesh Reddy Pagadala

Organizations: Aston University, Birmingham, UK

Abstract

We study learned one-step predictive control of a synthetic population of 64 leaky integrate-and-fire neurons whose light sensitivity is scaled by a hidden factor s, using two prospective confirmations on plants simulated only after the analysis was frozen. In the first (50 plants, 11 conditions), removing the 200-ms input-output history substantially worsened a parameter-count-matched neural predictor at low and moderate gain (s = 0.6, 0.8; RMSE rose by 2.47 Hz at s = 0.6, 97.5% CI 2.43-2.51). In secondary comparisons, recursively adapted ARX had the lowest mean error of the deployable controllers in 10 of 11 conditions, tuned PI with anti-windup matched or beat the network for s >= 0.7, and training for 10,000 rather than 900 epochs lowered prediction error but worsened control. Development work suggested the network's learned action sensitivity did not track the hidden gain. A second protocol (50 new plants, 9 sensitivities, 2 noise levels) confirmed three pre-specified predictions at the primary noise level. Re-estimating a single multiplicative input gain recovered 87% (95% CI 86-88%) of the benefit of full adaptive ARX. Supplying that online estimate to the network as an extra input reduced high-gain tracking error by 1.84 Hz [1.81, 1.88]. Longer training worsened the plain network by 1.09 Hz but improved the gain-input network by 1.07 Hz, a differential of 2.16 Hz [2.13, 2.20]. Under high process noise (sigma = 2.0) the effects shrank to about 0.04 Hz or less and gain-only adaptation recovered only 24% of the adaptive-ARX benefit. In this synthetic plant, at the primary noise level, one-parameter online gain estimation accounts for most of the gap between a history-based network and full adaptive ARX, and for its prediction-control mismatch.

Figures & tables

Arm	Definition	Protocol
PI tuned	positional PI, $K_{p}=0.02$ , $K_{i}=0.20$ , integrator clip $\pm 10$ (development grid of 400 gain pairs)	v3, v4
PI tuned + AW	as above with back-calculation anti-windup, $K_{p}=0.02$ , $K_{i}=0.25$ , $k_{t}=0.5$	v3, v4
PI sens. ref.	best PI of the family when $s$ is known; not deployable, reference only	v3
ARX fixed	least-squares prior, no online update	v3, v4
ARX + RLS	all ten coefficients adapted by RLS, $P_{0}=10^{9}\,\Sigma_{0}$ , $\lambda=0.98$	v3, v4
ARX- $g$	one-parameter gain RLS (Section 3.4 ), $P_{0}=1000$ , $\lambda=0.98$	v4

Table 1: Controllers. Network arms have five initialisations each, averaged within plant. Every gain, epoch and checkpoint was fixed on training, validation or development plants before the corresponding confirmation.

Protocol	ID	Contrast	Level / decision
v3	P1	Mem-141 $-$ H4-10k at $s=0.6,0.8$	97.5% each; both lower bounds $>0$
v3	P2	ARX fixed $-$ H4-10k at $s=0.6$	95%; interval within $\pm 0.25$ Hz
v3	B1	PI tuned (+AW) $-$ H4-10k, 11 conditions	99.77% each; no direction
v3	S1, S3–S5	RLS effect, chronology shuffle, ARX+RLS $-$ H4-10k, H4-900 $-$ H4-10k	97.5–99.55%; exploratory
v4	Q1	gain fraction, $\sigma=0.5$	95%; lower bound $\geq 0.70$
v4	Q3	H4-10k $-$ I2, mean over $\mathcal{H}$ , $\sigma=0.5$	95%; lower bound $>0$

Table 2: Pre-specified tests. Secondary results do not change primary decisions. Development values for v4 came from plants 5200–5249.

Condition	PI	PI+AW	ARX	ARX+RLS	H4-10k	H4-900	Mem-141	PI ref. †
$s=0.50$	4.316	2.844	2.873	2.769	2.784	2.794	5.572	2.664
$s=0.60$	1.870	1.670	1.692	1.567	1.642	1.627	4.111	1.471
$s=0.70$	1.504	1.311	1.394	1.273	1.412	1.359	3.119	1.226
$s=0.80$	1.264	1.128	1.278	1.080	1.384	1.218	2.425	1.124
$s=0.90$	1.126	1.069	1.353	1.002	1.542	1.206	1.966	1.070
$s=1.00$	1.084	1.075	1.707	0.971	1.886	1.305	1.748	1.075

Table 3: Protocol v3: mean tracking RMSE (Hz) over 50 confirmation plants (7000–7049). Lowest of the deployable arms shown in bold. † Uses knowledge of

s

; excluded from bold. A legacy PI with phase-1 gains (

K_{i}=0.15

, not shown) was 0.004 Hz lower than ARX+RLS at

s=1.4

and higher elsewhere.

Figure 1: Protocol v3: mean tracking RMSE against hidden sensitivity at

\sigma=0.5

. The memoryless network (1.7–5.6 Hz) is omitted for scale; all values are in Table 3 .

Condition	PI tuned $-$ H4-10k	PI + AW $-$ H4-10k
$s=0.50$	+1.532 [+1.485, +1.569]	+0.060 [+0.045, +0.076]
$s=0.60$	+0.228 [+0.209, +0.248]	+0.028 [+0.008, +0.046]
$s=0.70$	+0.092 [+0.070, +0.110]	$-$ 0.101 [ $-$ 0.122, $-$ 0.082]
$s=0.80$	$-$ 0.119 [ $-$ 0.146, $-$ 0.097]	$-$ 0.256 [ $-$ 0.285, $-$ 0.233]
$s=0.90$	$-$ 0.416 [ $-$ 0.456, $-$ 0.379]	$-$ 0.473 [ $-$ 0.511, $-$ 0.431]
$s=1.00$	$-$ 0.801 [ $-$ 0.851, $-$ 0.759]	$-$ 0.810 [ $-$ 0.860, $-$ 0.762]

Table 4: Protocol v3: PI minus H4-10k RMSE (Hz) with simultaneous 95% intervals (99.77% each). Negative values favour PI.

ID	Criterion	Development	$\sigma=0.5$	Decision	$\sigma=2.0$
Q1	lower bound $\geq 0.70$	0.86	0.871 [0.863, 0.878]	supported	0.24 [0.17, 0.32]
Q3	lower bound $>0$	+1.84 Hz	+1.84 [1.81, 1.88]	supported	+0.042 [0.033, 0.054]
Q4	lower bound $>0$	+1.0 to +3.8 Hz ∗	+2.16 [2.13, 2.20]	supported	+0.018 [0.008, 0.027]

Table 5: Protocol v4 primary decisions at

\sigma=0.5

(plants 8000–8049; 95% BCa intervals) and the same statistics at

\sigma=2.0

(98.3% intervals; robustness, not decisions). ∗ Development values at

s=1.0

and

1.4

; no high-gain-set mean was recorded.

$\sigma=0.5$ (primary)
$s$	PI+AW	ARX	ARX+RLS	ARX- $g$	H4-10k	H4-900	I1	I3	I2
0.50	2.872	2.901	2.806	2.857	2.822	2.825	2.851	2.808	2.792
0.60	1.668	1.696	1.608	1.691	1.638	1.627	1.647	1.595	1.571
0.70	1.317	1.400	1.290	1.421	1.421	1.362	1.362	1.321	1.269
0.80	1.131	1.261	1.088	1.271	1.397	1.225	1.206	1.179	1.095
0.90	1.062	1.367	0.985	1.206	1.549	1.210	1.158	1.160	1.037

Table 6: Protocol v4: mean tracking RMSE (Hz) over 50 plants. ARX-

g

: one-parameter gain RLS; I1–I3: interventions. Lowest in each row in bold. H4 and I2 at fixed epochs are in Figure 4 .

Figure 2: Protocol v4: mean tracking RMSE against hidden sensitivity for six arms. Shading marks the pre-specified high-gain set. All arms are in Table 6 .

Figure 3: Gain estimate

g

(mean of the last 60 steps of ARX-

g

) against

s

for each of the 50 v4 plants (thin lines) and their mean,

\sigma=0.5

$s$	H4-10k $-$ I2 (Hz)	plants $>0$
1.00	+0.89 [+0.85, +0.93]	100%
1.10	+1.36 [+1.32, +1.41]	100%
1.20	+1.90 [+1.84, +1.97]	100%
1.40	+3.21 [+3.15, +3.28]	100%

Table 7: H4-10k

-

I2 at each high-gain setting (

\sigma=0.5

; 98.75% intervals) and the share of plants with a positive difference.

Figure 4: Matched-epoch comparison at

\sigma=0.5

: plain DR-H4 and gain-input I2 at 900 (dashed) and 6000 (solid) epochs. Shading marks the high-gain set.

$s$	I2 $-$ ARX+RLS	I2 $-$ PI+AW	H4-10k $-$ I1	H4-10k $-$ I3
0.50	$-$ 0.015 [ $-$ 0.040, +0.007]	$-$ 0.081 [ $-$ 0.096, $-$ 0.067]	$-$ 0.030 [ $-$ 0.038, $-$ 0.021]	+0.014 [+0.006, +0.022]
0.60	$-$ 0.037 [ $-$ 0.080, $-$ 0.009]	$-$ 0.097 [ $-$ 0.113, $-$ 0.078]	$-$ 0.009 [ $-$ 0.023, +0.006]	+0.043 [+0.031, +0.056]
0.70	$-$ 0.021 [ $-$ 0.056, +0.004]	$-$ 0.048 [ $-$ 0.065, $-$ 0.031]	+0.058 [+0.044, +0.070]	+0.099 [+0.085, +0.112]
0.80	+0.008 [ $-$ 0.012, +0.028]	$-$ 0.036 [ $-$ 0.051, $-$ 0.021]	+0.191 [+0.171, +0.214]	+0.218 [+0.202, +0.236]
0.90	+0.052 [+0.025, +0.076]	$-$ 0.025 [ $-$ 0.047, $-$ 0.003]	+0.391 [+0.364, +0.431]	+0.389 [+0.360, +0.423]
1.00	+0.043 [+0.009, +0.066]	$-$ 0.038 [ $-$ 0.055, $-$ 0.020]	+0.712 [+0.675, +0.748]	+0.657 [+0.622, +0.690]

Table 8: Protocol v4 secondary contrasts at

\sigma=0.5

(Hz; 99.44% intervals). For I2

-

X, negative favours I2; for H4-10k

-

X, positive favours X.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Stage	Plants	Outcome
v0.1–v0.6 (exploratory)	0–69, 1000–1049, 1400–1649	learned controller brittle to gain shift; history helps
C0 confirmation	3000–3049	chronology effect +2.1 / +5.4 Hz
Experiment A	4000–4049	matched history ablation +2.76 Hz at $s=0.6$
Experiment B	6000–6049	linear equivalence at $s=0.6$ ; PI later found under-tuned, RLS inactive
Phase-2 development	5000–5149	PI search, adaptive RLS, 10 000-epoch retraining, rehearsal
v3 confirmation	7000–7049	Section 4

Appendix

Table 13

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When Does Feedback Help? Auditing Learned Voltage-Clamp Experimental Design

Rayan Nyaupane, Abhiram Bhupatiraju

The University of Texas at Austin

Active Experimental Design Feedback Control Policy Learning

Open paper AskPDF arXiv

A learned scientific controller can outperform a misspecified planner without benefiting from feedback. We audit two synthetic voltage-clamp tasks with a training-selected fixed protocol, current masking, a Bayesian reference, and an excluded target. Five recurrent policies repeat one fixed protocol in all 1,200 off-grid rollouts; masking current changes no decision. In a crossed four-hypothesis task, a fixed diagnostic pulse is followed by one learned choice. Policies then use the first current, but tie a correctly specified Bayesian controller, and a fitted threshold reproduces the learned actions without being that controller. The excluded-target prediction gain is

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Abstract

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