One pool, many targets: a conservation layer and what archival data can identify

Zahra Khodagholi; Niloofar Yousefi

cs.LGSep 30, 2026

One pool, many targets: a conservation layer and what archival data can identify

Authors: Zahra Khodagholi, Niloofar Yousefi

Organizations: Department of Industrial Engineering University of Central Florida

Abstract

Pairwise guide--transcript scores do not enforce conservation of a finite guide-loaded RISC pool when they are interpreted independently as occupancies. We formulate a differentiable scalar equilibrium layer: one conservation equation with a unique positive root and exact implicit gradients. It yields a redistribution theorem, a qualified high-resource limit, an analysis of the retrieval approximation, and a conditional rank-invariance result: within one construct at one dose, rankings by fractional occupancy cannot distinguish equilibrium from independent scoring. We therefore audit the two experiments that proposition leaves open, dose and cross-context, on archival off-target data. Corrected thermodynamic affinities associate weakly with measured repression in the direction a working predictor requires, but a paired permutation test and a construct-cluster bootstrap do not establish added predictive value from the coupling: what survives their differing permutation-null baselines is \GapNet{}, a descriptive \GapNetOverSE{} of the equilibrium association's cluster standard error. The dose fits are heterogeneous and frequently violate the model-implied exponent constraint, which is superlinear rather than sublinear, so these data do not identify the competition parameter. A saturable compression of the competitor set holds both accuracy targets on held-out guide families but is not faster at the size measured. The contribution is a reusable conservation operator and the experimental information needed to test it. The code for this study is available at https://github.com/shadi97kh/One-Pool-Many-Targets.

Figures & tables

Figure 1: Does the shared-pool coupling add anything over independent scoring? GSE5814, 24 constructs, 34,676 pooled construct–transcript pairs. (a) Pooled Spearman against measured log ratio, each scoring net of its own within-construct permutation null (1000 draws); bands are 2000 construct-cluster 95% intervals. Repression is negative, so below zero is the working direction. (b) Their difference. The raw gap is reliably nonzero, its cluster interval excluding zero at 5 of 6 values of

\rho

, yet under a paired null (one shuffle applied to both models) what survives is at most 0.27 of one cluster standard error (§ 5 ).

Figure 2: Compressing the competitor set: 54 held-out cases, 7 guide families disjoint from the 8 used to fix the configuration. (a) Relative error against the full retrieved reference at

R=100{}

, one point per case, three treatments of the omitted transcripts; dotted lines are the 1% targets, so only the lower-left quadrant passes both. (b) Two error measures for the same solutions, each divided by

\max(M,1)

; median and quartiles. (c) Median forward time (ms) over 4,919 competitors, single-threaded float64; bin construction is part of preparation.

Figure 3: Fitted dose exponent

\mathrm{d}\log(\text{pool})/\mathrm{d}\log(\text{dose})

per construct on GSE28786, both estimators, 95% bootstrap intervals, 5 constructs. Conservation makes the pool convex in the loaded amount, so under proportional loading the exponent cannot fall below

1

: the shaded region indicts that combined specification rather than equilibrium alone. The constructs are variants of one another, so the audit cannot separate mechanism from assumption (§ J ).

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: The full pipeline, shown at page width because the panel text is part of the content. Archival expression datasets, canonical 3 ′ UTR sequences, computed thermodynamic affinities, and stated literature ranges are combined in a differentiable shared-pool equilibrium model. At fixed construct and dose, equilibrium and independent fractional-occupancy scores induce identical transcript rankings under the one-effective- $K$ model. Pool effects instead remain testable across doses or transcriptomic contexts. Intracellular loading proportional to transfected dose is an explicit modelling assumption rather than a direct measurement. Boxes name the archival accessions, the affinity construction of § M , the conservation equation ( 1 ) of the main text, and which experiments each part licenses.

Figure 5: Model calculation on measured inputs (abundances from the GSE5814 mock channel, structure from GENCODE v50 3’UTRs; MAPK14-193 parent). Total bound transcript against the loaded pool, with the over-allocation ratio on the right axis: the independent counterfactual exceeds the budget by up to 1,491-fold more complexes, but only at pools far below one complex per cell, while equilibrium is constrained to the budget by construction. Green triangles are published Argonaute copy numbers, total Ago1–4 in the HeLa case; the grey band is the swept loaded fraction. Redistribution and the high-resource limit are shown in § C .

Figure 6: Model calculation on measured GSE5814 HeLa abundances. Kendall

\tau

between the two scorings’ candidate rankings against

\rho

, with the band covering the swept

H_{K}

. The

\tau=0.9

contour lies inside the 4.1-decade scenario range, so the calculation cannot say which side a real cell falls on: the identifiability problem § 6 does not close.

Figure 7: Model calculation on measured GSE5814 abundances and GENCODE v50 structure. (a) Redistribution: raising one transcript’s

K_{t}

lowers its own occupancy and raises every other’s, monotonically. (b) The relative gap between the two scorings decays with exponent

-2.00\pm 0.002

against a predicted

-2

, over 9 decades.

	linear	saturable bins, $B=$
$R$	(no bins)	1	2	5	10	50	200
25	91.1	74.6	72.5	64.6	27.1	1.13	0.0548
100	26.7	8.21	7.88	6.13	3.06	0.153	0.0137
500	0.0233	0.00155	0.000502	9.22e-05	2.25e-05	2.24e-06	1.32e-06

Appendix

Table 1: Maximum relative error in on-target occupancy against the full 952-transcript reference, in per cent, over

\rho\in\{0.01,0.5,10\}

, quantile bins. The first column is the linear affinity-weighted rule, which uses no bins at all. The columns to its right are

B

saturable bins, so the

B{=}1

column is one saturable bin: a different object, which errs differently. Forcing a saturable bin to its linear limit does reproduce the linear column exactly, to a maximum relative difference of 0, but that is a regression check on the implementation and not a row of this table.

Figure 8: Detail behind Figure 2 . (a) Development selection surface: 90th-percentile focal occupancy error over the 8 development families for every configuration on the frozen grid; the circled point is the selected one, fixed before any held-out family was scored. (b) The two residual definitions on the 54 held-out cases, each divided by

\max(M,1)

. (c) Median forward cost at matched outputs, preparation and cached solve stacked, against the full reference end to end. (d) Analytic gradients against central differences over 17 coordinates including omitted competitors; the dotted line is equality.

Figure 9: Measured repression by seed site class over 24 GSE5814 constructs under both site-assignment rules, bootstrap 95% intervals on the median, pair counts above each pair. The two 7mer classes are exchanged relative to the canonical order under both rules, which is the observation this section is about.

construct	cells	doses	$n$ thermo.	$n$ class	exponent	95% CI	$M$ slope
HK2-3581	Hep3B	3	4,633	17,317	0.21	[0.13, 0.27]	0.10
HK2-3581M	Hep3B	3	4,633	17,317	1.09	[0.87, 1.41]	0.80
HK2-4031	Hep3B	2 †	5,625	17,317	7.99	[3.70, 18.00]	4.79
STAT3-1676	MCF7	3	5,091	17,317	0.63	[0.47, 0.86]	0.37
STAT3-1676M	MCF7	3	5,091	17,317	0.60	[0.37, 0.86]	0.32

Appendix

Table 2: Dose series, per construct. Exponent is

\mathrm{d}\log(\text{pool})/\mathrm{d}\log(\text{dose})

under the site-class estimator with a bootstrap interval over transcripts;

1

is the independent-scoring prediction and below

1

is incompatible with the combined model under proportional loading. The sample sizes belong to different estimators:

n

thermo. is the retrieved subset,

n

class every measured gene.

M

slope must be

1

if proportional loading holds.

\dagger

: two dose points, zero residual df.

Figure 10: Approximation error on data-derived inputs. Relative error in on-target occupancy against the full 952-transcript reference when the competitor set is truncated to the top

R

, under the affinity-weighted calibration rule and the abundance-mass control, at three values of the competition parameter. The dotted line is 1% error.

Panel of Figure 11 — Figure 11: Left: the two-dimensional form of Figure 6 , kept for completeness; the $\tau=0.9$ contour runs near-vertical, which is why the main text shows a one-dimensional curve with an envelope. Right: the dose fit with each construct’s pool normalised to its own lowest dose, under both affinity models.

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Representable but Unlearned: Encoding Rank and the Interaction-Prediction Floor

Zahra Khodagholi, Niloofar Yousefi

University of Central Florida Orlando, Florida, USA

Ranking Encoders Floor

Open paper AskPDF arXiv

Input encodings can restrict which measured contrasts a predictor can jointly reproduce, even when no single contrast is forced to vanish. We compute the attainable contrast space from an encoder's equivalence classes and a fixed contrast design, without labels, loss, or a fitted model; projecting the recorded contrasts onto that space gives an empirical error floor for any unrestricted decoder on those classes. On a 140-rectangle siRNA interaction panel, a graph neural network's training-only feature mask merges 165 endpoint states into 90 classes and cuts the rank of the 140 interaction contrasts to 72. The resulting floor is 0.009980, which is 14.6% of the fitted model's interaction squared error; the fitted model reaches 0.068335, slightly worse than a control predicting no interaction at all. A minimum of three restored chemistry columns recovers full rank. Refitting without the mask removes the floor entirely, yet interaction MSE improves by only 0.000017 under the reported protocol, and the restored columns remain absent from every training input. On a released RNA-splicing predictor, whose encoding is injective on the measured states, the same computation returns the full design rank of 1,986 and a floor of exactly zero. These results separate what an encoding permits from what a fitted model achieves; they do not identify what limits the remaining error. The rank check needs no fits and bounds what any amount of training under a fixed encoding can recover. The project repository is available at https://github.com/shadi97kh/REPRESENTABLE-BUT-UNLEARNED.

Abstract

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