ARCHER: Amortized cross-specimen pose estimation for cryo-electron microscopy

Nhan D. Nguyen; Bao Pham

cs.LGAug 22, 2026

ARCHER: Amortized cross-specimen pose estimation for cryo-electron microscopy

Authors: Nhan D. Nguyen, Bao Pham

Organizations: Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States · Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York 12180, United States

Abstract

Single-particle cryo-electron microscopy (cryo-EM) pose estimation is traditionally solved anew for each dataset, where iterative refinement is done from scratch while the estimator learns to store the molecule in its weights. In this work, we show that pose inference is a generalizable, specimen-agnostic operation when conditioned explicitly on a reference volume. We introduce ARCHER, an amortized contrastive classifier that models the pose posterior over a discrete rotation grid. Trained across a variety of protein structures, it operates zero-shot without retraining per structure. This transferability is grounded in Fourier-space information mechanics, where all specimen dependence is captured by the reference structure's power spectrum and spatial extent. ARCHER achieves a median angular error of 5.0° on 100 held-out test structures and 2.5° on experimental particles, matching dedicated estimators within 0.16 Å in 3D reconstruction. Crucially, downstream conformational signal is preserved. The leading conformational coordinate correlates at 0.97 with deposited benchmarks, faithfully reconstructing free-energy basins and mobile domains. These results overall demonstrate that cryo-EM pose estimation can be generalized across different structures.

Figures & tables

Figure 1: Comparison between ARCHER and typical approaches. ARCHER takes the reference volume as an argument . It is trained once across many structures and then applied to a target it has never seen, whose reference is handed to it at inference time alongside the particles. Refinement is applied afterwards on the estimate it produced, where the particle embeddings it computed support downstream heterogeneity analysis. In other methods, the specimen is absorbed into the weights, so each target requires its own fitted model and its own training run, and nothing learned on one target is transferred to the next.

Figure 2: Overview of ARCHER’s architecture. Pipeline : The reference volume is sliced at every cell of a HEALPix grid on $\mathrm{SO}(3)$ , giving a fixed bank of templates that is embedded once per specimen. Each particle is embedded by a second encoder from a stack of image channels: the recorded particle, its phase-flipped copy, and denoised particles. The transfer function enters the network through the pixels it modulates. The pose $\mathbf{R}$ is the grid cell whose template embedding maximizes a temperature-scaled cosine similarity against the particle embedding. Training : The same forward pass is run on simulated particles whose true rotation is known. That rotation is mapped to its nearest grid cell, and the resulting cosine similarities are trained against a target smoothed over the geodesic neighborhood of that cell. The two encoders share a topology and hold independent weights.

Figure 3: Reconstructions and restorations across specimen. (A) Isosurfaces for four CESPED targets, one row per target and one column per map: the deposited reference, the ARCHER reconstruction, and that reconstruction after cryoFM restoration 94 . Color identifies the specimen; levels enclose a fixed fraction of the mask volume within each row, that is, among maps of the same molecule. (B) Every point is one experimental particle image embedded by principal component analysis, colored by dataset. The four specimens occupy distinguishable regions, and the separation is structural rather than instrumental: repeating the embedding on phase-scrambled particles, which preserves each image’s power spectrum while destroying its structure, collapses the between-specimen separation from $1.06$ to $0.05$ in units of the within-specimen spread. (C) Cosines between restoration displacement vectors in full voxel space. A restorer moves every map it is given in nearly the same direction, whichever estimator produced that map, so restoration acts on the map rather than on the pose estimate that made it. The same reconstructions embedded by method are Fig. S4 .

Figure 4: Error shape governs the map. Reconstructions at matched mean angular error under uniform and heavy-tailed pose perturbation.

Figure 5: ARCHER performance on benchmark datasets used by per-structure estimators (A) Cumulative angular error over the five CESPED targets; lines are the median across specimens, shading their full range. (B) Retained conformational signal on EMPIAR-10409, as the mean canonical correlation over the four latent directions; the dashed line is the shuffled-pose floor. (C) Shell correlation pooled over the four targets of Fig. 3 A, inside the benchmark mask; the abscissa is a fraction of each target’s own Nyquist frequency and the dashed line marks the

0.143

criterion 67 . Scoring conventions, matched particle counts and error bars are given in App. A .

Figure 6: Error quantification from reconstruction maps. (A) Canonical correlation against latent dimension on EMPIAR-10076: the leading direction is flat while the mean declines, so it is the trailing directions that decorrelate. (B) Median error per cell of the view sphere on EMPIAR-10076. (C) Map resolution against mean angular error, log–log. Circles are manufactured perturbations at matched mean and opposite error shape — at a mean of $20\text{\,}\mathrm{\SIUnitSymbolDegree}$ the same particles give $2.94\text{\,}\mathrm{\text{\AA}}$ under a heavy tail and $14.6\text{\,}\mathrm{\text{\AA}}$ under a uniform blur — and diamonds are the real estimators, which sit far to the right of those controls and far below them.

Figure 7: Map restoration. Shell correlation before and after restoration.

Figure 8: Conformational landscape. (A, B) Deconvolved conformational density over the leading two latent dimensions for the same 91,899 EMPIAR-10076 particles embedded twice, with the deposited poses and with ours, plotted as $-\log p$ in units of $k_{\mathrm{B}}T$ . Both panels use the same deconvolution weight, and each latent axis is normalized by its own bounds; markers are basins. (C) The reconstruction at each basin, colored by the mobility of Eq. ( 18 ) in units of the map’s own standard deviation. Columns pair basins by map correlation: the two latent bases are independent, so basin $i$ of one panel need not be basin $i$ of the other.

Figure 9: Information, selection and scale. (A) Per-shell curvature normalized by the correlation

c_{k}

that shell attains at the true pose, against shell radius, with the

k^{2}

prediction of Eq. ( 6 ). The measured exponent over

k=4

–

32

1.89

, with an ordinary least-squares standard error of

0.037

and an autocorrelation-robust one of

0.042

; the latter is the one to read, since neighboring shells are correlated. (B) Fraction of particles for which a correct pose is present among refined candidates, against the fraction for which the score selects it. (C) The score landscape around the true pose, showing the grid spacing and the curvature scale.

Figure 10: Cross-target reconstruction against the sampling bound. Five CESPED targets (EMPIAR-10166, 10280, 10409, 10648, 11120), each evaluated against the Nyquist limit of of the

64^{3}

box the pose estimate is made in. The y-axis is the ratio of map resolution to that ceiling, before and after hierarchical refinement.

Figure 11: Shell correlation carries its own statistics. All three panels are the ARCHER reconstruction of EMPIAR-10409 scored against the deposited map, at the native

1.47\text{\,}\mathrm{\text{\AA}}

sampling. (A) The reconstruction against the fixed

0.143

criterion and against the

\tfrac{1}{2}

-bit criterion, which scales with the number of samples in the shell 82 ; the two disagree most where samples are fewest. (B) Samples per shell, following

4\pi k^{2}

, and the effective count after masking, which is lower by the mask’s volume fraction (

3.3\%

here). (C) The same reconstruction scored masked and unmasked: masking raises the curve throughout, and here pushes the

0.143

crossing past Nyquist altogether, so the shift in reported resolution is a lower bound of

0.63\text{\,}\mathrm{\text{\AA}}

rather than a measured value. The classical arm and cryoPARES are censored at the same

2.94\text{\,}\mathrm{\text{\AA}}

, so on this target the masked criterion cannot separate the three.

Figure S1: Where the accuracy is gained. Median angular error on EMPIAR-10076 through the refinement ladder: the grid maximum of the learned posterior, re-scoring against a reference rebuilt from those poses, and the curvature step.

Figure S2: Set-size control for the ab-initio comparison. CryoFastAR evaluated on the homogeneous EMPIAR-10028 at the same particle count used for EMPIAR-10076, isolating specimen heterogeneity from set size.

Figure S3: Reference-free and per-specimen baselines on matched particles. (A) Cumulative angular error, median over the five CESPED targets with the full range shaded. (B) Median per target. All arms score the same

8{,}000

particles per target from one seeded selection; cryoPARES is matched to them by particle identity ( rlnImageName ). Chance is drawn per target, since a point group of order

\lvert G\rvert

lets a random pose fall nearer an equivalent copy:

120\text{\,}\mathrm{\SIUnitSymbolDegree}

on the three C 1 targets,

97\text{\,}\mathrm{\SIUnitSymbolDegree}

on the C 2 target,

90\text{\,}\mathrm{\SIUnitSymbolDegree}

on the D 2 target. cryoPARES was trained for four of the five targets and reaches

1.29

5.59

and

2.44\text{\,}\mathrm{\SIUnitSymbolDegree}

on the matched particles. EMPIAR-11120 carries no cryoPARES bar because no model exists for it; EMPIAR-10409 carries none in this panel alone, where the name-matched subset was not computed, and its model reaches

5.42\text{\,}\mathrm{\SIUnitSymbolDegree}

on the unmatched

8{,}000

(Tables S14 , S15 , S16 ). The two reference-free methods solve a harder problem — no reference and no translations — and ran at their default settings, each additionally given a solved global rotation and a choice of handedness beyond the point-group quotient every arm receives. Those allowances can only help them, and a random-pose control through the identical alignment stays at

119.6\text{\,}\mathrm{\SIUnitSymbolDegree}

, so the alignment manufactures no accuracy. Particle count decides cryoDRGN. At

8{,}000

particles it sits at chance on every target; at

100{,}000

it reaches

1.96

5.32

and

17.09\text{\,}\mathrm{\SIUnitSymbolDegree}

on the three C 1 targets, ahead of our network on all three, breaking from chance only near epoch

14

30

. It reaches

35.49

(C 2 ) and

21.53\text{\,}\mathrm{\SIUnitSymbolDegree}

(D 2 ) on the symmetric targets, well above chance but far behind the other arms, as abinit_homo exposes no symmetry option. None of these transfers: each is a separate optimization costing

2.6

–

5.3

GPU-hours. CryoFastAR does not improve with count over the same range.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S4: Reconstructions of EMPIAR-10409, by method. Each arm’s map of that one specimen, embedded in the same principal-component space as the projections of Fig. 3 B; one point is one map. Restored maps group by restorer rather than by the estimator that produced the input, which is the conclusion the displacement cosines of Fig. 3 C reach numerically.

	3-channel	2-channel	leads
Median error	5.07 ∘	5.22 ∘	122/150
Within $5^{\circ}$	0.493	0.474	121/150
Within $15^{\circ}$	0.755	0.753	85/150

Appendix

Table S2: The denoised channel, step-matched. Both arms share every setting and differ only in the added third channel. Means over the last

150

step-matched held-out evaluations, spanning steps

600{,}000

–

1{,}345{,}000

; the lead column counts evaluations at which the

3

-channel arm is ahead. Consecutive evaluations of one run are correlated, so those counts describe the trajectory and are not independence tests. The accuracy figures reported in the main text are the

2

-channel model.

Figure	Where	Grid	SNR	part.	prot.	sym.
Held-out synthetic proteins
median $5.0^{\circ}$ ; $<15^{\circ}$ $0.77$ ; top-1 $0.41$	§ IV.1	3 ( $36{,}864$ )	$0.02$ – $0.30$	768	100	no
$<15^{\circ}$ $0.6807$ ; median $10.07^{\circ}$	Table S4 , S5	2 ( $4{,}608$ )	$0.02$ – $0.30$	960	100	no
hard-noise $<15^{\circ}$ $0.4047$	Table S4	2 ( $4{,}608$ )	hard	960	100	no
$<15^{\circ}$ $0.5463$ ; sym-aware $0.6180$	Table S12	2 ( $4{,}608$ )	$0.02$ – $0.30$	192	100	both
classical $<15^{\circ}$ $0.6412$ – $0.9161$	Table S9	2 ( $4{,}608$ )	swept	192	30	no

Appendix

Table S3: Every reported accuracy figure and the configuration that produced it. Grid is the HEALPix order and the resulting cell count; SNR is the evaluation noise range, pinned explicitly whenever checkpoints are compared; sym. is whether the geodesic is minimized over the point group. The order-2 rows are training-choice sweeps, not the reported model.

Stage	mean SNR	legacy $<15^{\circ}$	median	hard-noise $<15^{\circ}$
Warm start (167.5k)	1.60	0.4688	16.8 ∘	—
6	0.206	0.5042	14.7 ∘	0.1719
7	0.137	0.5573	12.9 ∘	0.2255
8	0.091	0.5979	11.7 ∘	0.2766
9	0.060	0.6141	11.4 ∘	0.3135
10 (target, plateau)	0.040	0.6130	11.4 ∘	0.3260

Appendix

Table S4: Re-annealing to the calibrated endpoint. The legacy metric is held at the pinned

(0.02,0.30)

range in every row, so the rows are directly comparable. Stages are numbered along the geometric anneal (ratio

\approx 0.665

per stage); the warm start enters at stage 6. The stage-10 row is a plateau median over the 12 evaluations of that stage (steps 350k–377.5k). The cycle-2 row continues the stage-10 arm through a learning-rate restart rather than standing beside it, so it is set below the rule; that row is the reported model .

	B (scratch)	C (warm)	A (warm)
	calibrated	calibrated	legacy
Legacy $<15^{\circ}$	0.6542	0.6130	0.5922
Legacy $<30^{\circ}$	0.7219	0.6849	0.6781
Median error	10.5 ∘	11.4 ∘	12.0 ∘
Hard-noise $<15^{\circ}$	0.3760	0.3260	0.2651
Total steps	462.5k	377.5k	397.5k

Appendix

Table S5: Endpoint arms at their own plateau criteria. Arm B is a from-scratch replication at the calibrated endpoint; Arm C is warm-started at the same endpoint; Arm A is warm-started at the legacy endpoint. Bold marks the best of the three. The reported model continues Arm C through a learning-rate restart and exceeds all of them (Table S4 , last row).

Endpoint	legacy $<15^{\circ}$	hard-noise $<15^{\circ}$
Control, legacy $(0.02,0.30)$	0.5156	0.1677
Calibrated $(0.005,0.075)$	0.5573	0.2255
Difference	$+$ 0.0417	$+$ 0.0578

Appendix

Table S6: The controlled endpoint comparison. Both arms resume the same checkpoint with the same stage count, caps, plateau window, patience, learning-rate schedule and plateau metric; the only difference is the SNR bounds. Medians over the last 10 matched-step evaluations, from 32 matched steps spanning 170k–247.5k. The calibrated arm leads at 32 of 32 matched steps on both metrics. Consecutive evaluations of one run are correlated, so that count is reported as a description of the trajectory and not as an independence test.

Arm	$\rho^{2}$	true-pose $z$	rank	$<15^{\circ}$	median
Real (independent half)	28.84	$+$ 4.233	0	0.8217	8.1 ∘
Real (shuffled poses)	3.22	$+$ 0.068	2159	0.0063	129.0 ∘
Synthetic, SNR 0.03	40.85	$+$ 4.955	0	0.9527	7.8 ∘
Synthetic, SNR 0.01	13.76	$+$ 3.341	2	0.5303	13.2 ∘
Synthetic, SNR 0.003	4.14	$+$ 1.962	115	0.0850	120.9 ∘

Appendix

Table S7: Whitened matched-filter detectability, CESPED EMPIAR-10409 at

L=64

(

3.128\,\text{\AA}

/px, Nyquist

6.26\,\text{\AA}

) against a reconstructed reference. rank is the rank of the true pose among

M=4{,}608

candidates for the median particle. The real-particle row is the anchor the noise calibration targets; the synthetic rows bracket it. Real particles are rlnRandomSubset == 2 scored against the half-1 map, so none contributed to the reference; the partly-overlapping variant gives

0.8380

\rho^{2}=29.44

, a 2% difference.

Junk class	AUROC
Phase scramble (matched spectrum)	0.9626
Pure noise	0.9690
Off-center pick	0.9630

Appendix

Table S8: Junk rejection on EMPIAR-10409,

2{,}000

particles at

L=64

against a half-1 reference, for the reported model. AUROC of the pose confidence, real versus each junk class;

0.5

is no separation. Median confidence is

0.364

on real particles against

0.16

–

0.18

on junk. The phase-scrambled row is the strongest control, since it matches the real amplitude spectrum shell for shell.

Synthetic SNR	all proteins	non-symmetric	symmetric
0.30	0.7094	0.9161	0.2490
0.08	0.6905	0.8960	0.2317
0.04	0.6412	0.8222	0.2141
0.02	0.5115	0.6361	0.1700

Appendix

Table S9: Classical

<15^{\circ}

against synthetic SNR, split by whether the protein admits indistinguishable poses. The all-proteins column saturates at the ceiling implied by ambiguity alone; the non-symmetric column crosses the real-data anchor of

0.8217

at SNR

0.04

. Bold marks that row, the calibrated endpoint adopted throughout; it is the operating point, not the largest entry.

Statistic (30-protein sweep set)	Value
Mean fraction of poses that are ambiguous	0.3000
Proteins with $>50\%$ ambiguous poses	9 of 30
corr(ambiguous fraction, classical accuracy)	$-$ 0.8431
corr(voxel size, classical accuracy)	$+$ 0.2922
Ceiling implied by ambiguity alone	0.7000
Classical accuracy actually observed	0.6985

Appendix

Table S10: Pose ambiguity measured from the volumes alone — no particles, no noise, no scorer.

Indistinguishable alternatives	Proteins	Implied $\|G\|$	Point group
1	10	2	C2
3	12	4	C4 / D2
6	1	7	C7
7	3	8	C8 / D4

Appendix

Table S11: Independent verification of the ambiguity measurement by point-group quantization. A point group of order

|G|

predicts exactly

|G|-1

indistinguishable alternatives per pose.

Subset	$n$	$<15^{\circ}$	symmetry-aware $<15^{\circ}$
All held-out proteins	100	0.4223 $\to$ 0.5463	0.4771 $\to$ 0.6180
Non-symmetric only	74	0.5255 $\to$ 0.6779	0.5393 $\to$ 0.6892
Symmetric only	26	0.1284 $\to$ 0.1719	0.3001 $\to$ 0.4155

Appendix

Table S12: Re-scoring both checkpoints with symmetry separated out. All 100 held-out proteins, 192 particles each, both checkpoints scored at the same pinned

(0.02,0.30)

range. Arrows run from the 167.5k checkpoint to the plateaued calibrated checkpoint. The non-symmetric row is the control confirming the symmetry-aware correction is not simply inflationary: it moves almost nothing there.

Median angular error (degrees)
	EMPIAR-10166	EMPIAR-10280	EMPIAR-10409	EMPIAR-10648
$n$ scored	1269	4562	4079	1190
Network (grid argmax)	6.28	12.48	9.91	9.04
ARCHER pipeline	2.97	10.14	7.06	7.90
Classical matched filter	2.63	8.13	5.54	7.60
cryoPARES	1.46	5.79	5.69	2.61

Appendix

Table S13: Per-target accuracy on the particles cryoPARES did not train on. All four arms are scored on the same particles of each target — the intersection of our seeded

8{,}000

with the complement of that target’s cryoPARES training split,

n

below — with the same symmetry-aware geodesic, so the columns are directly comparable. Bold marks the best arm per target. cryoPARES holds the best median on three of the four targets while the classical filter holds the largest fraction within

15\text{\,}\mathrm{\SIUnitSymbolDegree}

on two of them: the two statistics rank the arms differently, which is why both are reported. EMPIAR-10409 is the clearest case: cryoPARES leads on neither statistic there, taking a median within

0.15\text{\,}\mathrm{\SIUnitSymbolDegree}

of the classical filter while placing

0.179

fewer particles within

15\text{\,}\mathrm{\SIUnitSymbolDegree}

— a tail close to that of our unrefined grid argmax.

Target	GPU-hours
EMPIAR-10166	13.2
EMPIAR-10280	22.8
EMPIAR-10409	23.3
EMPIAR-10648	31.2
Total, four targets	90.5

Appendix

Table S14: Training cost of the per-specimen comparison. cryoPARES 68 is supervised on the target it is applied to, so each entry is a separate optimization; times are single-GPU wall clock for the completed run on each dataset at the scope used here (

200{,}000

particles,

40

epochs). ARCHER is trained once across

3{,}330

structures and applied to every target without retraining, so its cost does not recur per specimen — for a new target it is an inference pass.

	particles per half		resolution ( Å )
Target	ours	cryoPARES	ours	classical	cryoPARES	cP at our count
EMPIAR-10166	60,000	100,000	5.97	5.91	3.86	4.35
EMPIAR-10280	60,000	100,000	6.30	6.14	4.24	4.61
EMPIAR-10409	203,000	100,000	3.63	3.62	3.48	—
EMPIAR-10648	117,478	100,000	4.27	4.56	4.05	—

Appendix

Table S15: Reconstruction quality per target against the deposited map, as the unmasked

0.143

crossing. Unmasked is reported because the masked curve does not cross before Nyquist on EMPIAR-10409 and 10648, so a masked number there is a floor rather than a measurement (Fig. 11 C). Our poses were predicted for

60{,}000

particles per half on EMPIAR-10166 and 10280 against cryoPARES’s

100{,}000

, so on those two we also rebuilt cryoPARES from the same

60{,}000

(last column). Matching the count recovers

0.49

and

0.37\text{\,}\mathrm{\text{\AA}}

of the gap and cryoPARES still leads by

1.62

and

1.69\text{\,}\mathrm{\text{\AA}}

, so the deficit there is mostly pose quality and not set size. The reverse control — rebuilding cryoPARES at the larger counts we used on EMPIAR-10409 and 10648 — was not run, hence the two dashes; it would widen the gap on those targets rather than narrow it. Entries are rounded to two decimals, which is coarser than the differences discussed in the main text: on EMPIAR-10409 the three values are

3.634

(ours),

3.625

(classical) and

3.477\text{\,}\mathrm{\text{\AA}}

(cryoPARES), a spread of

0.157\text{\,}\mathrm{\text{\AA}}

. The classical arm, reconstructed from the same particles as ours with no learned component, lands within

0.3\text{\,}\mathrm{\text{\AA}}

of our pipeline on every target: the gap to cryoPARES is therefore a property of reference-conditioned refinement at this working resolution and not of the network. On the two targets where we supply more particles than cryoPARES the gap is

0.16\text{\,}\mathrm{\text{\AA}}

and

0.22\text{\,}\mathrm{\text{\AA}}

; the former is the agreement quoted in the main text.

	particles from
model trained on	10166	10280	10409	10648
10166	3.9	104.0	124.6	83.6
10280	133.2	7.8	132.1	86.0
10409	134.9	107.3	8.8	80.2
10648	129.5	97.2	134.7	5.4
chance	120	97	120	90

Appendix

Table S16: cryoPARES transfer. Each row is a model trained on one target; each column the particles it is applied to. Values are median angular error in degrees on the same

8{,}000

particles per target, symmetry-aware, using the network stage alone — the local-refinement stage projects the training target’s own reference volume and cannot be run across specimens. The diagonal (bold) is the same-specimen setting every other cryoPARES number in this work reports. Chance is

120\text{\,}\mathrm{\SIUnitSymbolDegree}

for the C 1 targets 10166 and 10409,

97\text{\,}\mathrm{\SIUnitSymbolDegree}

for C 2 10280 and

90\text{\,}\mathrm{\SIUnitSymbolDegree}

for D 2 10648, so every off-diagonal entry is at chance.

Check	Result
Checkerboard $\equiv$ fftshift	max abs diff $0.00\mathrm{e}{+}00$
In-plane composition identity	centered $+0.9888$ vs uncentered $+0.0535$
CTF sign vs reference implementation	phase-flip sign agreement $1.0000$
Slicer/backprojector round trip	true $0.9857$ vs shuffled $0.1168$
Real particles at deposited poses	$6.3\,\text{\AA}$ , FSC $0.9325$ vs shuffled $0.0947$

Appendix

Table S17: Geometric and CTF conventions checked against external references; all five agree. Real particles backprojected at their deposited poses reconstruct to the

L=64

Nyquist limit with mean FSC

0.9325

over shells 3–20 against a shuffled-pose floor of

0.0947

; the external anchor is an independent codebase’s reconstructor at

4.17\,\text{\AA}

from the same poses and particles.

Corpus and splits
Setting	Value
Training structures	3,330 EMDB entries
Held-out structures	100, split by structure ID
Split granularity	structure, never particle
Voxel-size range	median 4.7 Å /px; 90% within 3.1–6.9 Å /px
Box size	$L=64$

Appendix

Table S18: Settings for the reported model and its evaluation.

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Understanding biomolecular function requires characterizing three-dimensional structure and conformational variability, for which cryogenic electron microscopy (cryo-EM) is a powerful tool. Cryo-EM produces noisy two-dimensional particle images in which molecular structure, particle pose, and imaging conditions are jointly encoded. Recovering biological information from these observations spans inverse problems including pose estimation, heterogeneity analysis, and reconstruction. These tasks are usually addressed independently despite shared protein structure and image formation, motivating a common representation across inverse problems. Since biologically meaningful differences may be spatially localized, we study self-distillation with complementary global and masked patch objectives. Because experimental dataset discrimination can reflect acquisition-specific cues, we develop controlled synthetic and experimental evaluations and find that structural discrimination benefits from dense spatial features. We introduce the EMber family of vision transformers, pre-trained on >50 million experimental particle images from 214 EMPIAR datasets together with simulated projections from 268,000 molecular assemblies. EMber improves upon existing methods at conformational and compositional discrimination by 14.85 and 14.26 percentage points, estimates conformational populations to within 1.59pp error with a linear probe, and produces particle assignments yielding reference-quality reconstructions in fewer epochs. We demonstrate how to learn representations that capture biological information for use across multiple cryo-EM inverse problems.

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