Shared Geometry Is Not Shared Physics: A Layerwise Test of the Platonic Representation Hypothesis in Astronomy

Kshitij Duraphe; Aravind Kannappan; Dun Li Chan; Okiki Famutimi; Yaswant Sai Ejjagiri; Michael J. Smith; John F. Wu

astro-ph.IMOct 2, 2026

Shared Geometry Is Not Shared Physics: A Layerwise Test of the Platonic Representation Hypothesis in Astronomy

Authors: Kshitij Duraphe, Aravind Kannappan, Dun Li Chan, Okiki Famutimi, Yaswant Sai Ejjagiri, Michael J. Smith, John F. Wu

Organizations: UniverseTBD · EleutherAI · INTI International College Penang, Malaysia · Center for Astrophysics, Harvard & Smithsonian ·

Abstract

In this paper we investigate whether geometrically aligned astronomical representations are also scientifically interchangeable. We analyze every layer's representation from 36 pretrained models using cross-matched optical images, infrared images, and spectra. All 139 analyzed model-survey comparisons show significant local-neighborhood alignment somewhere in the network after accounting for the search over depth. However, alignment does not generally increase with network depth and can be stronger for the changes between consecutive computational blocks than for the block outputs themselves. We find that geometry-selected stages under-perform label-selected stages in every image-transfer comparison; moreover, every final HSC-COSMOS-Web model pair is aligned while every redshift transfer has negative R^2. Models can therefore recover a similar cross-survey geometry among astronomical objects without recovering a survey-invariant linear encoding of the physical properties tested here.

Figures & tables

Figure 1: Chance-corrected MKNN (a depth curve ) across normalized depth for saved block outputs and consecutive differences. For each model with

T

valid transitions, transition

r

and its resulting state have depth

d_{r}=(r-1)/(T-1)

; input embeddings and non-block hooks are excluded. Models are interpolated onto a common depth grid and weighted equally. Solid curves: block states, dashed curves: updates (

\Delta Z_{r}=Z_{r+1}-Z_{r}

), bands show standard errors, and markers indicate mean-curve maxima. For image–image comparisons, dashed curves use updates from both views; for DESI, they compare each HSC update with the fixed spectral representation. Vertical scales differ across panels.

Figure 2: Maximum physical prediction versus geometric alignment across 36 models for (a) JWST magnitude, (b) JWST size, (c) Legacy Survey color, and (d) Legacy Survey shape. Circles and triangles indicate HSC-to-survey and reverse transfer, with vertical segments linking directions for each model. Coordinates show maximum valid corrected MKNN and mean held-out linear-probe

R^{2}

across representation stages; colors indicate model family,

\rho

the Spearman correlation, and dashed lines the median maximum MKNN. Shading marks performance below the test-set mean, and JWST panels use a symmetric-log vertical scale. Maxima need not occur at the same stage.

Figure 3: (a) Test-set

R^{2}

loss from selecting a saved representation stage by geometry rather than physical labels. Bars show family-equal mean losses with 95% family-bootstrap intervals; all exclude zero. (b) Empirical CDFs of within- and cross-survey redshift

R^{2}

for 31 aligned final HSC–COSMOS-Web model pairs. All within-survey scores are positive and all cross-survey scores are negative. A broken horizontal axis shows both distributions at readable scales.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

HSC paired with	Released rows	Analyzed rows	Models	Primary use
DESI spectra	20,465	20,321	36	Geometry and common-space retrieval
Legacy Survey images	101,725	101,619	36	Color and shape transfer
JWST images	1,496	929	36	Magnitude and size transfer
COSMOS-Web images	56,322	56,322	31	Layerwise geometry
COSMOS-Web final product	45,000	45,000	31	Five-target final transfer

Appendix

Table 1: Crossmatched datasets used in the experiments. “Released rows” is the size of the representation product; “analyzed rows” is the size after the deterministic filtering described in the text. “Models” counts complete layerwise curves in the first four rows and terminal-representation pairs in the final row.

Family	Model variants
AstroPT	astropt_015M , astropt_095M , astropt_850M
CLIP	clip_base , clip_large
ConvNeXt	convnext_nano , convnext_tiny , convnext_base , convnext_large
DINO	dino_small , dino_base , dino_large , dino_giant
DINOv3	dinov3_vits16 , dinov3_vits16plus , dinov3_vitb16 , dinov3_vitl16 , dinov3_vith16plus , dinov3_vit7b16
I-JEPA	ijepa_huge , ijepa_giant

Appendix

Table 2: The complete model basket. Names follow the released representation files.

ID	Question
E1	Is local alignment significant anywhere along each complete depth curve?
E2	Does alignment increase from early to late saved stages?
E3	Does label-free geometric selection identify scientifically useful saved stages?
E4	Does an explicitly fitted common space improve image–spectrum retrieval?
E5	Which consecutive block updates write the shared geometry?
E6	Do model scale, architecture, or training objective explain alignment?

Appendix

Table 3: List of experiments.

Survey	Target	Transfer	$Q_{25}$	Median $\Delta$	$Q_{75}$	Median $\|\Delta\|$	Range
Legacy Survey	Color	HSC $\rightarrow$ Legacy	$-0.380$	$-0.042$	$0.117$	$0.237$	$[-0.912,\ 0.400]$
Legacy Survey	Color	Legacy $\rightarrow$ HSC	$-0.295$	$0.127$	$0.322$	$0.322$	$[-0.877,\ 0.731]$
Legacy Survey	Shape	HSC $\rightarrow$ Legacy	$0.029$	$0.160$	$0.599$	$0.240$	$[-0.857,\ 0.848]$
Legacy Survey	Shape	Legacy $\rightarrow$ HSC	$-0.180$	$0.286$	$0.614$	$0.523$	$[-0.882,\ 0.857]$
JWST	Magnitude	HSC $\rightarrow$ JWST	$-0.300$	$-0.140$	$0.034$	$0.237$	$[-0.594,\ 0.800]$
JWST	Magnitude	JWST $\rightarrow$ HSC	$-0.267$	$-0.098$	$0.281$	$0.269$	$[-0.800,\ 0.690]$

Appendix

Table 4: Distribution of the normalized saved-stage difference

\Delta=s_{\mathrm{label}}-s_{\mathrm{geometry}}

. Each row contains 36 model-level values after averaging the five folds.

Q_{25}

and

Q_{75}

are the first and third quartiles.

	Legacy Survey				JWST
Family	Color H $\to$ L	Color L $\to$ H	Shape H $\to$ L	Shape L $\to$ H	Magnitude H $\to$ J	Magnitude J $\to$ H	Size H $\to$ J	Size J $\to$ H
AstroPT	0.084	0.040	0.375	0.692	4.665	4.120	3.618	0.598
CLIP	0.041	0.055	1.001	0.931	1.400	0.365	1.828	0.843
ConvNeXt	0.015	0.190	1.605	1.099	0.931	0.433	2.818	0.445
DINO	0.045	0.093	0.745	1.003	1.361	0.402	0.674	0.262
DINOv3	0.097	0.088	0.269	0.408	1.679	0.152	0.265	0.275

Appendix

Table 5: Mean held-out

R^{2}

lost by selecting a saved representation stage using geometry rather than physical labels, reported separately by model family. H, L, and J denote HSC, Legacy Survey, and JWST.

Panel of Figure 4 — Figure 4: Saved-stage Legacy Survey color prediction and geometric alignment for all 36 models. The upper panel transfers a color predictor from HSC to the Legacy Survey; the lower panel transfers in the reverse direction. In each panel, the left map shows held-out $R^{2}$ and the right map shows corrected MKNN. Each model column is scaled from its own minimum to maximum so that depth structure remains visible; the scatter plots above retain the actual model-level maxima, and white triangles locate them along the normalized saved-stage index.

Panel of Figure 5 — Figure 5: Saved-stage Legacy Survey shape prediction and geometric alignment for all 36 models. The upper panel transfers from HSC to the Legacy Survey and the lower panel transfers in the reverse direction. Plotting conventions follow Figure 4 .

Panel of Figure 6 — Figure 6: Saved-stage JWST magnitude prediction and geometric alignment for all 36 models. The upper panel transfers from HSC to JWST and the lower panel transfers in the reverse direction. Plotting conventions follow Figure 4 .

Panel of Figure 7 — Figure 7: Saved-stage JWST size prediction and geometric alignment for all 36 models. The upper panel transfers from HSC to JWST and the lower panel transfers in the reverse direction. Plotting conventions follow Figure 4 .

Control	Matched reference	MKNN	CKA	Procrustes	MRR
Shuffle correspondence	Raw	$0.027\%$	$0.075\%$	$7.325\%$	$10.116\%$
Matched Gaussian data	Raw	$0.022\%$	$10.133\%$	$33.896\%$	$10.008\%$
Random projection to 32 dimensions	Raw	$50.987\%$	$80.656\%$	$89.378\%$	$47.879\%$
Random projection to 64 dimensions	Raw	$70.577\%$	$91.299\%$	$93.243\%$	$64.616\%$
Remove first five principal components	Raw held-out	$128.367\%$	$37.341\%$	$67.705\%$	$478.818\%$
Regress magnitude, color, and redshift	Raw complete-case held-out	$96.887\%$	$70.858\%$	$87.771\%$	$315.826\%$

Appendix

Table 6: Alignment retained after each control, expressed as a percentage of the corresponding unmodified mean metric. PC removal is compared with raw held-out representations, and catalog regression with raw complete-case held-out representations; the other controls use the full-sample raw representations. Values above

100\%

indicate that the intervention increases the metric.

Figure 8: Block-state and block-update alignment over normalized computational depth for the three image–image comparisons. Input embeddings, normalization-only hooks, pooling outputs, projections, and output heads are excluded so that depth zero consistently denotes the first computational block. For

B

retained block states, state

j

is placed at

j/(B-1)

and update

j\!\rightarrow\!j+1

at its midpoint

(j+1/2)/(B-1)

. Solid dark curves show block states; dashed colored curves show consecutive block updates, with circles and triangles marking their respective mean-curve maxima. Each curve averages models with valid first and final block representations after placing them on a common block-depth grid; bands show one standard error across models. Figure 1 instead assigns an update and the state it produces to the same transition coordinate so that their trajectories can be compared directly. Vertical scales differ between panels.

Figure 9: Cross-block alignment for the three image–image comparisons. Input embeddings and non-block hooks are excluded, and every remaining HSC block is compared with every block in the paired survey. Each model’s map is placed on a common normalized block-depth grid and divided by its own maximum before models are averaged, preventing models with larger metric baselines from dominating the timing pattern. Rows denote surveys and columns denote alignment measures. Dashed lines mark equal block depth and stars mark the maxima of the averaged relative maps.

Outcome	$\beta_{\log\mathrm{parameters}}$	Permutation $p$	Family 95% interval	$\beta_{\log\mathrm{width}}$
Maximum alignment	$-0.0028$	$0.0875$	$[-0.0322,\ 0.0123]$	$0.0234$
Final-stage alignment	$-0.0069$	$0.0027$	$[-0.0441,\ 0.0279]$	$0.0215$
Area under depth curve	$-0.0025$	$0.0773$	$[-0.0217,\ 0.0102]$	$0.0201$
Peak saved-stage index	$0.0336$	$0.6146$	$[-0.2838,\ 0.2223]$	$-0.3170$
Final minus early alignment	$-0.0094$	$0.0014$	$[-0.0529,\ 0.0185]$	$0.0189$
Maximum update alignment	$0.0028$	$0.0654$	$[-0.0281,\ 0.0215]$	$0.0046$

Appendix

Table 7: Model-property summaries after excluding SDSS. (a) Coefficients from regressions containing log parameter count, log representation width, survey indicators, parameter-count-by-survey interactions, and architecture-family indicators. Inference was prespecified for the log-parameter coefficient; width is shown descriptively. (b) Family-equal differences in maximum MKNN for broad training categories relative to all other families.

Figure 10: Held-out HSC–DESI retrieval after fitting the rank-64 PCA–CCA common space. Points show the 11 architecture-family means; the diamond and interval show their family-equal mean and 95% family-bootstrap interval. The dashed line marks the fold-averaged random-ranking expectation.

Physical target	Alignment coefficient	Family 95% interval	Permutation $p$	Secondary $q$
HSC $g-r$ color	$-95.33$	$[-860.36,\ 906.19]$	$0.6225$	$0.6868$
Magnitude	$-172.92$	$[-603.43,\ 201.39]$	$0.3622$	$0.6868$
Stellar mass	$-118.73$	$[-320.25,\ 36.50]$	$0.0369$	$0.1476$
Redshift (primary)	$-349.24$	$[-1624.34,\ 113.66]$	$0.2943$	—
Specific star-formation rate	$-90.29$	$[-395.73,\ 69.96]$	$0.6868$	$0.6868$

Appendix

Table 8: Coefficient of corrected MKNN when predicting cross-survey physical-transfer

R^{2}

. Every regression also contains parameter count, representation width, within-survey performance, and architecture-family indicators. The redshift test is primary;

q

is the Benjamini–Hochberg value across the four secondary targets.

Analysis	Outcome	Families improved	Mean MSE ratio
E6	Maximum alignment	$11/11$	$0.088$
E6	Final-stage alignment	$11/11$	$0.086$
E6	Area under depth curve	$11/11$	$0.064$
E6	Maximum update alignment	$11/11$	$0.079$
E6	Final minus early alignment	$6/11$	$0.930$
E6	Peak saved-stage index	$6/11$	$0.939$

Appendix

Table 9: Leave-one-family-out stability. “Families improved” counts held-out families for which the fitted model has lower squared error than the training-mean baseline. The MSE ratio is the mean fitted-model MSE divided by the mean baseline MSE; values below one favor the fitted model. E8 leave-family-out evaluation was prespecified for redshift.

Computing Resource	Usage
Shared GPU infrastructure	GPU-based embedding extraction and analysis
8 $\times$ NVIDIA A100 node	GPU-based embedding extraction and analysis
128 CPU cores / 1 TB RAM	CPU-intensive downstream analyses
Local workstation	Supplementary experiments and analysis
Estimated total GPU usage	$\approx 1{,}500$ GPU-hours

Appendix

Table 10: Summary of computing resources used in the experiments.

Platonic Representation Hypothesis

Platonic Representation Hypothesis asks whether independently trained models converge on shared internal structures that reflect the world.

See all 18 papers

The Platonic Universe: Do Foundation Models See the Same Sky?
Sep 23, 2025UniverseTBD, :, Trinidad Borrell +11Cross-Modal Alignment Multimodal Model Evaluation
Independent Researcher · AstroAI · Harvard-Smithsonian CfA +4
Gestalt: a meta-foundation model for astronomy
Sep 29, 2026Michael J. Smith, Shashwat SouravEnsemble Learning AI-Assisted Scientific Research
AstroAI · Center for Astrophysics | Harvard & Smithsonian · UniverseTBD +1
Native Geometry vs. Linear Recoverability: How Alignment Changes Platonic Scaling
Oct 15, 2026Angus Hoy, Austin Lutterbach, Jasper Chong +2Neural Representation Geometry Latent Space Geometry
EleutherAI SOAR · UniverseTBD · University of Queensland +4

Sep 23, 2025J/K move · Enter open · S save

The Platonic Universe: Do Foundation Models See the Same Sky?

UniverseTBD, :, Trinidad Borrell, Steven Dillmann+10

Independent Researcher · AstroAI · Harvard-Smithsonian CfA+4

Cross-Modal Alignment Multimodal Model Evaluation Representation Alignment Platonic Representation Hypothesis

Open paper AskPDF arXiv

We investigate when foundation models converge towards shared representations, and how this convergence depends on model capacity, training regime, and model architecture. We take a `science-for-AI' approach, using astronomy as an experimental instrument to test the Platonic Representation Hypothesis and its Aristotelian refinement against an external physical reference. The historical success of astrophysics is evidence that a compact, modality-invariant description of galaxy observables exists, and so representation convergence toward reality should be measurable against the physical parameters astronomers already use. Given this framework, we evaluate eleven foundation model families (spanning classification, self-distillation, joint-embedding prediction, autoencoding, vision-language pre-training, and astro-specific architectures from

\mathcal{O}

(10M)

{\to}\mathcal{O}

(10B) parameters) on crossmatched JWST, HSC, and Legacy imagery, and DESI spectroscopy. All models are evaluated frozen, with no astronomy-specific fine-tuning. We probe redshift, stellar mass, and sSFR via linear probes, and local (MKNN) and global (CKA) embedding geometry within families, between modalities, and across architectures. We find that physics performance scales predictably with capacity; probe directions align consistently with expected astrophysical correlations and selection effects; and local (not global) embedding alignment tracks physics performance, including between DESI spectra and HSC imagery---modalities that share essentially no low-level statistics. Our results support the ARH over the strict PRH, demonstrate astronomy's value as an experimental framework for neural representation learning, and suggest that astro-foundation models can build on general-purpose pre-trained architectures, capitalizing on the broader open machine learning community's already-spent computational investment.

Abstract

Platonic Representation Hypothesis

Explore similar work

The Platonic Universe: Do Foundation Models See the Same Sky?

Gestalt: a meta-foundation model for astronomy

Native Geometry vs. Linear Recoverability: How Alignment Changes Platonic Scaling