Predictive Multiplicity in Cell-Fate Assignment: Label-Free Rashomon Sets and the Limits of Per-Cell Certification

Arjun Bhupatiraju; Abhiram Bhupatiraju

cs.LGOct 8, 2026

Predictive Multiplicity in Cell-Fate Assignment: Label-Free Rashomon Sets and the Limits of Per-Cell Certification

Authors: Arjun Bhupatiraju, Abhiram Bhupatiraju

Organizations: McNeil High School, Austin, Texas

Abstract

Single-cell trajectory inference maps transcriptomic measurements onto developmental continua, yet configurations that fit the data equally well can assign conflicting cell fates. FateMultiplicity is a label-free framework that constructs a statistically admissible model set, or Rashomon set, without lineage labels, by evaluating model discrepancy on cross-fitted held-out genes under non-inferiority testing calibrated against random-seed variation. Multiplicity is large and depends more on the diversity of the model space than its size: twelve configurations of a second algorithm expose 20.0% of cells where twenty-four of the first expose 3.8%. Whether the per-cell certified fate margin FM yields more reliable assignments than the fitted model already provides is then tested, and it does not. On simulation ground truth, on the same cells, FM discriminates misassignment at AUC 0.682, against 0.965 for the baseline configuration's own decision margin (p = 0.003) and 0.854 for a seed-dispersion baseline. Informativeness is governed by the breadth of the admitted set, not its cardinality: at cardinality four, seed refits give 0.933 and hyperparameter-perturbed sets 0.701. Relaxing the infimum to a q-quantile recovers discrimination but converges toward the single model's own confidence; the supremum reaches 0.973 because theta*'s membership bounds it from below, while the infimum is unanchored. Multiplicity in trajectory inference is worth measuring and reporting, but per-cell certification over a label-free Rashomon set is not a route to more reliable fate calls. Two constructions survive: a margin-erosion ratio separates real from spurious branch points in simulation (AUC 0.890, untested on real data), and against clonally observed fate, uncertified cells disagree with their clone's outcome 16.4 percentage points more often than certified cells (p < 0.001).

Figures & tables

Symbol	Definition
$\Theta$	Total hyperparameter search space
$\theta$ , $\theta^{*}$	Candidate and baseline configuration
$p_{i,k}(\theta)$	Probability of cell $i$ committing to fate $k$
$k^{*}$	Primary baseline terminal fate assignment
$G_{1}^{(k)}$ , $G_{2}^{(k)}$	Training and held-out gene sets, fold $k$
$K$	Total cross-fitting folds ( $K=3$ )

TABLE I: Summary of Formal Mathematical Notation

Configuration	Predicted	Exclusion mechanism
Scrambled pseudotime	Excluded	Failed acceptance test ( $p\leq 10^{-4}$ , stat $+0.0148$ )
3 nearest neighbors	Excluded	Well-formedness (99.1% uniform)
2 principal components	Excluded	Well-formedness (54.4% uniform)
50 variable genes	Excluded	Pipeline convergence failure
Baseline, seed modified	Admitted	Passed acceptance test ( $p=0.236$ )

TABLE II: Prespecified Control Configurations and Gate Outcomes

Fig. 1: Reported confidence varies 483-fold across reconstructions the data cannot distinguish. (A) Distribution of the per-cell decision margin under each admitted configuration, sorted by median. Each row is one configuration, shade gives the share of its 6,000 cells in each margin bin, and the tick marks the median, with the baseline in blue. (B) Median margin against argmax agreement with the baseline. Configurations differ far more in the confidence they report than in the assignment itself.

Fig. 2: Multiplicity is concentrated in the acute injury response. (A) $\mathrm{FM}$ across the microglial manifold, embedded by uniform manifold approximation and projection [ 24 ] from the baseline representation. (B) The 235 cells whose assignment is overturned within $\mathcal{R}(\alpha)$ ; they cluster rather than scatter. (C) Fraction overturned by injury timepoint, split by dissociation protocol; uninjured cord was profiled under one protocol only.

Fig. 3: Multiplicity depends more on the diversity of the model space than on its size. (A) Fraction of cells overturned against the number of admitted configurations, resampled at each size with bands at $\pm 1$ SD; the three curves are the pooled two-algorithm set and each algorithm alone. (B) Excess multiplicity attributable to the second algorithm at matched candidate-space size, rising monotonically with set size. Each bar compares two sets of equal size, so the increase is not an artifact of counting more models.

Dataset	Algorithm	$\|\mathcal{R}\|$	$\bar{d}_{\text{seed}}$	$\bar{d}_{\text{space}}$	$\Pi$	Mult.	AUC
Microglia	Abs. walk	24	0.003972	0.008595	2.16	0.038	—
Haematop.	Abs. walk	15	0.1198	0.1223	1.02	0.457	0.568
Haematop.	Palantir	16	0.2441	0.2791	1.14	0.847	0.615
Reprogram.	Abs. walk	16	0.2949	0.2437	0.83	0.743	—

TABLE III: Certification power across four dataset–algorithm arms.

\bar{d}_{\text{space}}

is mean pairwise fate-assignment disagreement between admitted configurations;

\bar{d}_{\text{seed}}

is the within-algorithm seed floor. “Mult.” is the fraction of cells with

\mathrm{FM}\leq 0

. AUC is of

-\mathrm{FM}

against clonally observed fate, which only the barcoded object supplies; the microglial and reprogramming arms carry no lineage labels and contribute

\Pi

and multiplicity only.

\mathrm{FM}

’s AUC against simulation truth is 0.682 (Section III-L ) and is not comparable to these, being measured against a different reference standard on a different cohort.

Fig. 4: Certification power. (A) $\Pi$ for each of the four dataset–algorithm arms, with the area under the curve for $-\mathrm{FM}$ predicting clonally observed misassignment annotated on the two arms that carry lineage labels. Only the microglial arm exceeds $\Pi=1$ appreciably. (B) The two components of $\Pi$ per arm, model-space disagreement against the within-algorithm seed floor, on a logarithmic axis; an arm on the diagonal has $\Pi=1$ and certifies nothing beyond seed stability.

Fig. 5: Simulation validation on the corrected cohort. (A) Misassignment against $\mathrm{FM}$ quintile; error falls from 31% in the lowest quintile to 0% in the highest, so the sign and coarse ordering of $\mathrm{FM}$ do carry information. (B) Per-object misassignment either side of $\mathrm{FM}=0$ , one line per object and the mean in black, over the 43 objects with cells on both sides. (C) Fraction certified by scenario. The two containing no true fork, in red, certify at roughly 0.97—far above the 0.55 to 0.59 of the three that do contain one, which is the inversion Section III-M addresses.

Fig. 6: Per-cell certification is limited by its aggregator, not by the quantity being aggregated. Every panel reports mean per-object AUC for discriminating misassignment against simulation truth over the 28 scorable forking objects; the solid grey line is the baseline configuration’s own decision margin (0.965) and the dashed line the seed-dispersion baseline (0.854). (A) Replacing the infimum over $\mathcal{R}(\alpha)$ with the $q$ -quantile of the same per-model margins. $q=0$ is $\mathrm{FM}$ as defined. Discrimination rises monotonically in $q$ but converges toward the single model’s own confidence from below rather than exceeding it. The breadth-matched series restricts the set to four configurations carrying hyperparameter perturbations. (B) At fixed cardinality $|\mathcal{R}|=4$ , four seed refits and four hyperparameter-perturbed configurations differ by 0.232. Breadth, not count, is the governing variable. (C) Discrimination against the size of randomly drawn admitted subsets, shaded by standard error, falling monotonically over the seven sizes (Spearman $\rho=-1.000$ , slope $-0.034$ per configuration). The barcoded arm is not drawn: its AUC is measured against clonally observed fate rather than simulation truth, and the two are not comparable (Table III ).

Predictor	AUC	vs. $\theta^{*}$
Margin at $\theta^{*}$ (single model)	0.965	—
$q=0.50$ margin over $\mathcal{R}(\alpha)$	0.973	$p=0.221$
$q=0.25$ margin over $\mathcal{R}(\alpha)$	0.893	$p=0.367$
Mean margin over $\mathcal{R}(\alpha)$	0.883	$p=0.374$
$\bar{m}$ , the supremum over $\mathcal{R}(\alpha)$	0.973	$p=0.494$
Seed dispersion (no acceptance region)	0.854	$p<0.001$

TABLE IV: Discrimination of Misassignment Against Simulation Truth, Every Statistic Computed on the Same Cells

Fig. 7: The baseline comparison per object, over the 28 forking objects passing all scoring filters. Table IV gives the means; this gives the distributions behind them. (A) Per-object AUC for each predictor; the dotted line marks chance. The margin at $\theta^{*}$ , the $q=0.50$ margin and the supremum $\bar{m}$ sit tight against the ceiling, while $\mathrm{FM}$ and bootstrap stability spread down to near zero on individual objects. (B) Each predictor’s AUC difference from the margin at $\theta^{*}$ , one grey point per object, mean as a diamond. Points left of zero are objects where the predictor is worse than the single fitted model.

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