Inside-Out: Measuring Generalization in Vision Transformers Through Inner Workings

Yunxiang Peng; Mengmeng Ma; Ziyu Yao; Xi Peng

cs.LGApr 9, 2026

Inside-Out: Measuring Generalization in Vision Transformers Through Inner Workings

Authors: Yunxiang Peng, Mengmeng Ma, Ziyu Yao, Xi Peng

Organizations: University of Delaware · George Mason University

Abstract

Reliable generalization metrics are fundamental to the evaluation of machine learning models. Especially in high-stakes applications where labeled target data are scarce, evaluation of models' generalization performance under distribution shift is a pressing need. We focus on two practical scenarios: (1) Before deployment, how to select the best model for unlabeled target data? (2) After deployment, how to monitor model performance under distribution shift? The central need in both cases is a reliable and label-free proxy metric. Yet existing proxy metrics, such as model confidence or accuracy-on-the-line, are often unreliable as they only assess model output while ignoring the internal mechanisms that produce them. We address this limitation by introducing a new perspective: using the inner workings of a model, i.e., circuits, as a predictive metric of generalization performance. Leveraging circuit discovery, we extract the causal interactions between internal representations as a circuit, from which we derive two metrics tailored to the two practical scenarios. (1) Before deployment, we introduce Dependency Depth Bias, which measures different models' generalization capability on target data. (2) After deployment, we propose Circuit Shift Score, which predicts a model's generalization under different distribution shifts. Across various tasks, both metrics demonstrate significantly improved correlation with generalization performance, outperforming existing proxies by an average of 13.4% and 34.1%, respectively. Our code is available at https://github.com/deep-real/GenCircuit.

Figures & tables

Figure 1: We address two key challenges: (1) Before deployment, how to select models? (2) After deployment, how to monitor performance under distribution shifts? Existing metrics exhibit underspecification and overconfidence issues. Our metrics, based on models’ inner workings, mitigate these issues, yielding significantly stronger correlations with generalization performance.

Figure 2: Our observations from visualizing the circuits in the pre- and post-deployment scenarios. The circuits are obtained via Eq. 1 and visualized by retaining the top-100 edges, following the same pruning procedure as in Hanna et al. [27] . Top: Before Deployment , we observe that models with strong OOD generalization exhibit more deep layer pathways ( $\nabla$ -like shape), while weak models rely on shallow, shortcut connections ( $\Delta$ -like shape). Bottom : After Deployment , we observe that as distribution shifts, a model’s circuit retains overall structure but undergoes intensified rewiring dynamics, with new (red) or removed (blue) edges and nodes.

Figure 3: CCA reveals the Universal Generalization Motif pre-deployment. Left. Universal Generalization Motif obtained by normalizing and averaging $\mathbf{v}_{T}$ (Eq. 3 ) over all generalization tasks. Brighter regions indicate the inter-layer dependencies positively correlated with generalization; darker regions indicate negative correlations. Right. The resulting motif highlights the anti and pro-generalization connections shared across tasks.

Method	PACS (Style Shift)			Camelyon17 (Institution Shift)			Terra Incognita (Geographic Shift)			Average
Method	$\text{R}^{2}$	SRCC	KRCC	$\text{R}^{2}$	SRCC	KRCC	$\text{R}^{2}$	SRCC	KRCC	Average
ID Accuracy [ 49 ]	0.765	0.878	0.720	0.423	0.650	0.480	0.537	0.711	0.528	0.632 $\pm$ 0.047
Sharpness [ 3 ]	0.048	0.075	0.037	0.097	0.204	0.146	0.361	0.576	0.408	0.217 $\pm$ 0.060
AC [ 29 ]	0.646	0.755	0.582	0.535	0.793	0.620	0.367	0.563	0.408	0.585 $\pm$ 0.044
ANE [ 29 ]	0.608	0.728	0.554	0.568	0.781	0.603	0.378	0.590	0.425	0.582 $\pm$ 0.040
MDE [ 54 ]	0.345	0.650	0.478	0.347	0.717	0.502	0.371	0.726	0.541	0.520 $\pm$ 0.048

Table 1: Correlation strength (

R^{2}

, SRCC, and KRCC) for pre-deployment model selection. Experiments are conducted on PACS, Camelyon17, and Terra Incognita with results averaged over all available generalization tasks. The final column reports the mean score and the standard error of the mean (SEM

\downarrow

). The best results are bolded . Our DDB metrics consistently outperform all baselines across datasets.

Figure 4: The training dynamics of OOD accuracy (left y-axis) vs. our

\mathrm{DDB}_{\mathrm{out}}

(right y-axis) on PACS. The plot compares two models: one demonstrating strong generalization (orange line) and the other exhibiting weak generalization (blue line). The strong alignment in the trajectories demonstrates that

\mathrm{DDB}_{\mathrm{out}}

’s dynamic serves as a reliable predictor of a model’s generalization capability throughout the training process.

Score	$\tau$
Score	0.1	0.2	0.3	0.4	0.5
$R^{2}$	0.744	0.772	0.798	0.801	0.772
SRCC	0.743	0.843	0.862	0.849	0.838
KRCC	0.562	0.653	0.684	0.671	0.673

Table 2: Ablation on

\mathrm{DDB}_{\mathrm{out}}

’s hyperparameter

\tau

. The results consistently show that

\tau=0.3

yields the strongest correlation .

Figure 5: Generalization Motifs post-deployment shows contradictory patterns. Left. The GM on PACS, most inter-layer dependencies are positively correlated with performance. Right. The GM on FMoW shows mostly negative correlation. Inter-layer topology no longer provides a consistent signal of generalization.

Method	PACS (Style Shift)			FMoW (Temporal Shift)			Camelyon17 (Institution Shift)			ImageNet (Adversarial + Style)			Average
Method	$\text{R}^{2}$	SRCC	KRCC	$\text{R}^{2}$	SRCC	KRCC	$\text{R}^{2}$	SRCC	KRCC	$R^{2}$	SRCC	KRCC	Average
AC [ 29 ]	0.031	0.117	0.111	0.314	0.700	0.556	0.035	0.058	0.055	0.928	0.943	0.839	0.391 $\pm$ 0.104
ANE [ 29 ]	0.105	0.200	0.222	0.315	0.767	0.611	0.038	0.033	0.034	0.921	0.942	0.833	0.418 $\pm$ 0.102
MDE [ 54 ]	0.002	0.217	0.222	0.428	0.717	0.611	0.036	0.273	0.187	0.829	0.897	0.754	0.431 $\pm$ 0.088
RANKME [ 20 ]	0.100	0.600	0.500	0.322	0.383	0.333	0.020	0.193	0.152	0.666	0.901	0.729	0.408 $\pm$ 0.076
$\alpha$ -ReQ [ 2 ]	0.325	0.650	0.500	0.306	0.433	0.333	0.024	0.132	0.087	0.419	0.714	0.547	0.373 $\pm$ 0.060

Table 3: Correlation strength (

R^{2}

, SRCC, and KRCC) for post-deployment performance monitoring. We bold the best results. Our proposed CSS metric consistently achieves the strongest correlation across all datasets .

Figure 6: Alarm F1 score on the Camelyon17 dataset. Circuit Shift Score consistently outperform other baseline metrics in a clinical acceptable performance range

0.8\text{--}0.9

[ 64 , 17 ] .

Figure 7: Visualization of circuit rank changes across domains on FMoW and Camelyon17. Each pixel in the heatmap shows the absolute change in edge rank between the ID and OOD circuits, averaged across edges from source layer (y-axis) to target layer (x-axis). Subplots are annotated with the domain name and corresponding F1 score. Notably, different dataset exhibit distinct circuit shift patterns: FMoW exhibits widespread cross-layer changes, while Camelyon17 shows concentrated changes at deeper layers .

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Shift type	Domain
PACS [ 38 ]	style shift	art_painting cartoon photo sketch
Camelyon17 [ 34 ]	institution shift	ID Hospitals hospital1 hospital2
Terra Incognita [ 4 ]	geographic shift	location 38 location 43 location 46 location 100

Appendix

Table 4: Overview over datasets in pre-deployment setting and their associated domains, along with a shift type for each dataset

Dataset	ID domain	OOD domain
PACS [ 38 ]	Sketch	art_painting subset 1-3 cartoon subset 1-3 photo subset 1-3
Camelyon17 [ 34 ]	hospital 0 slide 0-7 hospital 1 slide 10-17	hospital 0 slide 8-9 hospital 1 slide 18-19 hospital 2 slide 20-29 hospital 3 slide 30-39 hospital 4 slide 40-49
FMoW [ 34 ]	Official ID split	time 1 region 0-4 time 2 region 0-4
ImageNet [ 12 ]	ImageNet Validation	ImageNet-Sketch ImageNet-v2 motion blur 0-4 defocus blur 0-4 zoom blur 0-4 snow 0-4 frost 0-4

Appendix

Table 5: Overview over datasets in post-deployment setting and their associated ID and OOD domains, along with a shift type for each dataset. The hospital id and slide id in Camelyon17 domains as well as the region id in FMoW domains follows the indexing in original dataset metadata. The time id correspondence in FMoW dataset is: time 1

\to

val split and time 2

\to

test split in the original dataset split

Model	Timm model name
random init ViT OPENAI CLIP LAION2b CLIP ImageNet 21k ImageNet 1k MAE	N/A vit_base_patch16_clip_224.openai vit_base_patch16_clip_224.laion2b vit_base_patch16_224_in21k vit_base_patch16_224.orig_in21k_ft_in1k vit_base_patch16_224.mae

Appendix

Table 6: The list of ViTs used in our study. Pretrained weights are sourced from the PyTorch Image Models (timm) library [ 74 ] , using the model names listed

Learning Rate	Batch Size	Weight Decay	Fine-tune
3e-2 1e-2 3e-3	128 256	0 1e-2	Only head Whole model

Appendix

Table 7: Hyperparameter sweep grid for constructing the model zoo for the PACS and Terra Incognita pre-deployment experiment

Learning Rate	Batch Size	Weight Decay	Fine-tune
3e-2 1e-2 3e-3	128 256	0	Only head Whole model

Appendix

Table 8: Hyperparameter sweep grid for constructing the model zoo for the Camelyon17 pre-deployment experiment

Model	Benchmark	ID accuracy	OOD accuracy	OOD-ID Gap
random init	PACS	0.477 $\pm$ 0.018	0.201 $\pm$ 0.010	0.276 $\pm$ 0.156
	Camelyon17	0.934 $\pm$ 0.009	0.686 $\pm$ 0.014	0.248 $\pm$ 0.006
	Terra Incognita	0.565 $\pm$ 0.014	0.221 $\pm$ 0.011	0.344 $\pm$ 0.023
	FMoW	0.547 $\pm$ 0.020	0.497 $\pm$ 0.009	0.051 $\pm$ 0.003
ViT-B MAE pretrained	PACS	0.580 $\pm$ 0.017	0.242 $\pm$ 0.012	0.338 $\pm$ 0.011
	Camelyon17	0.912 $\pm$ 0.021	0.836 $\pm$ 0.018	0.076 $\pm$ 0.005

Appendix

Table 9: Model generalization comparison. Columns show averaged ID, OOD accuracy and OOD-ID Gap of each model over all domains within the dataset.

Figure 8: All pre-deployment metrics’ scatter plots for all 12 (ID $\to$ OOD) generalization tasks in PACS. Each blue dot represents one trained network. Each row represent one generalization task, and the name is shown in the y-axis label. Each column represent one pre-deployment metric. Y-axis shows models’ performance on the OOD domain, and x-axis shows value of the corresponding metric. All raws share the same y-axis.

Figure 9: All pre-deployment metrics’ scatter plots for the 2 (ID

\to

OOD) generalization tasks in the Camelyon17 dataset.

Figure 10: All pre-deployment metrics’ scatter plots for all 12 (ID $\to$ OOD) generalization tasks in the Terra Incognita dataset.

Figure 11: All post-deployment metrics’ scatter plot. In each plot, the yellow triangles represent OOD domains in the dataset, Y-axis shows models’ GT performance on the OOD domain, and x-axis shows value of the corresponding metric. All rows share the same y-axis.

Method	Color-MNIST		Waterbirds	ImageNet
Method	small-ViT	ViT-B/16	ViT-B/16	ViT-B/16
Random	0.555	0.748	0.754	0.732
EActP	0.466	0.095	0.271	0.360
EAP	0.332	0.103	0.299	0.376
EAP-IG-inp	0.567	0.063	0.242	0.325
EAP-IG-act	0.452	0.076	0.327	0.381

Appendix

Table 10: CMD(

\downarrow

) scores across circuit discovery methods. All evaluations were performed using mean ablations. We bold and underline the best and second-best methods per column, respectively.

Method	Color-MNIST		Waterbirds	ImageNet
Method	small-ViT	ViT-B/16	ViT-B/16	ViT-B/16
Random	0.263	0.274	0.260	0.299
EActP	1.679	0.732	0.698	0.804
EAP	1.658	0.712	0.570	0.655
EAP-IG-inp	2.033	0.902	0.706	0.813
EAP-IG-act	1.658	0.858	0.656	0.810

Appendix

Table 11: CPR(

\uparrow

) scores across circuit discovery methods. All evaluations were performed using mean ablations. We bold and underline the best and second-best methods per column, respectively.

Figure 12: The training dynamics of OOD performance (left y-axis) vs. our

\mathrm{DDB}_{\mathrm{out}}

metric (right y-axis) on PACS, Camelyon17 and Terra Incognita. Across all datasets, DDB closely follows the trajectory of OOD accuracy throughout training, confirming that it captures the evolving generalization behavior of the model.

Score	$\tau$
Score	0.1	0.2	0.3	0.4	0.5
$R^{2}$	0.441	0.467	0.750	0.491	0.433
SRCC	0.780	0.788	0.853	0.743	0.630
KRCC	0.592	0.609	0.681	0.565	0.478

Appendix

Table 12: Ablation on

\mathrm{DDB}_{\mathrm{deep}}

’s hyperparameter

\tau

. The results consistently show that

\tau=0.3

yields the strongest correlation scores.

Score	$\tau$
Score	0.1	0.2	0.3	0.4	0.5
$R^{2}$	0.683	0.516	0.541	0.500	0.447
SRCC	0.786	0.653	0.655	0.606	0.553
KRCC	0.620	0.514	0.519	0.478	0.433

Appendix

Table 13: Ablation on

\mathrm{DDB}_{\mathrm{global}}

’s hyperparameter

\tau

. The results consistently show that

\tau=0.1

yields the strongest correlation scores.

Figure 13: Pre-deployment Generalization Motifs $\mathbf{v}_{T}$ (Eq.3) of all tasks. Brighter regions indicate the inter-layer dependencies positively correlated with OOD generalization; darker regions indicate negative correlations.

Figure 14: Circuit discovery runtime profile for a single batch (size 32). Backward pass is the major bottleneck, and replacing EAP-IG with EAP yields approximately 5

\times

speedup.

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