Neural-network fitting as a structure sensor

Can the fitting process of a plain autoencoder act as a sensor for hidden structure in single-cell data — recovering a biological axis it was never shown?

Honest negative result Pre-registered · A∧B∧C∧D GSE233321 · immune lifespan prototype, confirmed 2 seeds × d{16,32}

An undercomplete autoencoder is trained only to reconstruct gene expression — it never sees donor age. If age nonetheless surfaces in its compressed code, the fit itself would be a usable sensor. Calibrated on the age axis as ground truth, the method fails its own pre-committed bar — and the way it fails is informative.

Headline. The autoencoder never beats a linear baseline (PCA) at recovering age, across two seeds and both latent dimensions. Worse, training erodes the signal: age is most decodable at initialisation and declines over 100 epochs. A synthetic positive control shows the instrument can beat linear methods — but only in a geometric regime that single-cell data does not occupy. The negative is a property of the data geometry, not a fluke or a biased test.

167

donors (effective n) · CD4 T cells

0 / 2

configs where the latent beats matched PCA

p = 0.001

latent ↔ perceptome eigenspace (CCA)

pre-registered amendments, decided before looking

The design

One autoencoder architecture, three matched data conditions, and a pre-committed pass/fail rule fixed before any result was seen.

Ground truth. Donor age is a donor-level variable, so every probe uses leave-donors-out cross-validation (effective n = 167 donors, not cells). A cell-level split would measure donor leakage, not an age law.
Three conditions. REAL (untouched) · GENE-PERMUTED (co-expression destroyed, marginals kept — an artifact floor) · age-shuffled (a within-source permutation null for the probe).
Verdict A∧B∧C∧D, locked in advance: A age beats the within-source null · B the effect does not reproduce on gene-permuted data · C the latent beats a matched linear PCA · D the signal survives a data-source (batch) control.
Independent cross-check against the perceptome 9-PC eigenspace — a biology-curated coordinate system built from 154 cell types.

What the fit reveals

The sensor signal is not the reconstruction loss. It is read three ways, each against a matched null.

Effective dimensionality: REAL vs gene-permuted — **Structure is present.** Participation ratio of the latent covariance is far lower for real data than for the gene-permuted floor (6.2 vs 14.4 at d=16) — the autoencoder is compressing genuine co-expression, not noise. So the question is not *whether* there is structure, but whether the fit exposes *age* better than a linear method.

Age recovery: autoencoder latent vs matched linear baselines — **The autoencoder loses to linear PCA (criterion C fails).** Leave-donors-out age recovery for the latent vs matched PCA-d, PCA-50, raw HVG, and the shuffled-age null. The latent (0.85) sits *below* every linear baseline on the lifespan axis, and below them again on the harder adult-aging axis. A from-scratch neural compression adds nothing over ordinary linear statistics — the lesson the Arc Virtual Cell Challenge taught at scale, reproduced here.

Learning order: age and cell-type decodability decline over training — **Training erodes the signal.** Both age (blue, leave-donors-out) and cell type (pink) are maximally decodable at epoch 1 — when the untrained network is essentially a random projection that preserves linear structure — and decline monotonically as the bottleneck specialises for reconstruction. The fit moves *away* from the target it was hoped to expose. Confirmed across two seeds and both latent dimensions.

The instrument is sound — but narrowly

Could a linear probe be hiding a nonlinear success? A synthetic positive control settles it.

Nonlinear positive control across three synthetic regimes — **The autoencoder beats matched PCA only in one regime.** Three synthetic targets through the same pipeline. On a high-linear-rank, low-intrinsic-dimension manifold (CURVE), the d=2 autoencoder beats matched PCA-2 (criterion C *can* fire — the test is fair). On a linear target or a low-rank manifold (ROLL), it cannot. And in every case, giving PCA a few more components ties or wins. Real scRNA-seq has low effective rank (≈50 PCs) and a linearly-dominated age axis — outside the firing window.

Objective-function experiment: MSE vs negative-binomial vs information-bottleneck — **The objective explains the erosion — but not the failure.** Holding everything fixed and varying only the training loss: a count-appropriate negative-binomial likelihood (unsupervised) *removes* the learning-order decay (slope flips negative → positive), confirming that MSE-on-counts was eroding the signal. But it only reaches parity with PCA, never a decisive win. An aligned objective fixes the dynamics; the data geometry still caps the utility.

The independent cross-check

Perceptome cross-check: CCA and inflammaging alignment — **The latent re-derives the perceptome eigenspace, but not its aging axis.** Cross-validated CCA between the autoencoder latent and the 9-PC perceptome coordinates gives three significant shared axes (0.95 / 0.56 / 0.74, all permutation p = 0.001) — the data-driven factorisation independently recovers the biology-curated one. Yet the latent's age direction is *orthogonal* to the reference inflammaging direction (cosine −0.78 / −0.50, not significant), consistent with the prior that perceptome axes are pathology-specific, not healthy-aging.

What was found

(Negative.) The autoencoder does not beat matched linear PCA at recovering age — 0/2 across seeds × dims (lifespan latent 0.86–0.89 vs PCA 0.90–0.93; adult 0.35–0.40 vs 0.44–0.48). More capacity (d=32) does not rescue it, so the bottleneck is the data geometry, not the network size.
Training erodes the signal under MSE. Age decodability is highest at initialisation (≈ random projection) and declines over 100 epochs; the unsupervised fit specialises for reconstruction and overwrites the linearly-accessible age axis.
Naive adult-aging recovery is partly a batch artifact. The latent predicts dataset-of-origin at 0.94 balanced accuracy (chance 0.33); within a single source the adult signal collapses to ρ ≈ 0.14 (n.s.). The pre-registered source control (D) catches exactly this.
The latent independently re-derives the perceptome eigenspace (CCA 0.95 / 0.56 / 0.74, p = 0.001) but not its aging axis (cosine to inflammaging −0.78 / −0.50, n.s.) — perceptome axes look pathology-specific.
The instrument is sound but the regime is wrong. A positive control confirms the autoencoder can beat matched PCA — only when intrinsic-dim < bottleneck < linear-rank. Single-cell data (low effective rank, linear age) is outside that window; no objective changes that.

Target	A · beats null	B · not on permuted	C · beats PCA	D · source-robust	Verdict
Lifespan (167 donors)	✅	✅	❌	✅	FAIL
Adult-aging (85 donors)	✅	✅	❌	❌	FAIL

What this means

The result is a clean, mechanistically dissected negative. Autoencoder-fitting-as-a-sensor beats linear baselines only on data whose structure is nonlinearly entangled — high linear rank, low intrinsic dimension. Standard single-cell expression, after the usual preprocessing, is well-approximated by ~50 linear components and carries a linearly-dominated age axis; there is simply no nonlinear advantage for the bottleneck to find that a generous linear method does not already capture. The training objective controls whether the fit erodes the signal (it does under MSE; a count-appropriate loss does not), but it cannot manufacture an advantage the geometry does not offer.

A positive by-product: the unsupervised latent independently re-derives the hand-built perceptome eigenspace — evidence that the curated coordinate system is real structure in the data — while declining to align with its aging direction, exactly as a pathology-specific framework should.

The honest conclusion for the method: it needs a nonlinearly-encoded target to be worth the machinery. Immune age is the wrong target — and now we know precisely why.

Reproducibility

The full pipeline is pre-registered (three locked amendments), leave-donors-out throughout, fixed seeds, and packaged as a one-click notebook (data download → QC → train ×{real, gene-permuted} → A∧B∧C∧D verdict → learning-order → perceptome cross-check → figures). Every headline number is reported with its matched control and with variance across seeds and folds. Dataset: GSE233321 (healthy human immune system across the lifespan, 167 donors). Code, pre-registration, and the full report — repository in preparation under github.com/mool32.

Part of the perceptome program · methodological negative result · pre-registration discipline per the AI-collaborative research methodology. Theodor Spiro · ORCID 0009-0004-5382-9346 · tspiro@vaika.org