Adaptive Computation with Conformal Certification

Shehtab Zaman; Aneesh Rangnekar; Nancy Lee; Harini Veeraraghavan

cs.LGOct 13, 2026

Adaptive Computation with Conformal Certification

Authors: Shehtab Zaman, Aneesh Rangnekar, Nancy Lee, Harini Veeraraghavan

Organizations: Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, USA · Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, NY, USA

Abstract

Scientific imaging data involving medical (e.g., 3D radiographic, microscopic images) and astronomical sensors pose different challenges from natural images. One key challenge is that these datasets are often orders of magnitude larger than natural images. Efficient training and inference on such data is challenging due to the increased hardware requirements, often needing bespoke solutions. Moreover, the relevant objects such as tumors and astronomical phenomena are sparsely distributed with respect to the background information. Standard efficiency techniques like quantization and pruning apply uniform scaling of all regions, potentially compromising the precision/fidelity of predictions. Thus, efficient methods that reduce computational requirements without losing resolution for relevant parts of the data and with uncertainty estimates on predictions are essential. We present Conformal Adaptation with risk guarantees for uncertainty-aware sparse computations. Our formalism is general, spanning dense pixel-level classification and regression tasks where hierarchical models predict at low resolution, certify the signal using conformal risk control, and refine the certified predictions. We benchmark our method on multiple tasks such as 3D medical image segmentation, 2D galaxy flux prediction, and 1D calcium spike rate prediction, achieving $2.5$ -- $72\times$ wall-clock speedup across the various tasks, including on commodity CPUs.

Figures & tables

Figure 1: The two-stage process for Conformal Adaptation consists of (1) dense predictions at a spatial scale reduced by a factor $r$ and (2) sparse refinement on the selected set $S$ of coarse cells. The selection is based on thresholds calibrated using CRC, and the operating regime we target is $|S|\ll|\Omega_{\text{coarse}}|$ .

Model	Full	Coarse	Coarse + Refine ( $\alpha=0.1$ )	Cell Miss Rate	FLOPs Speedup
U-Net	$0.63\pm 0.03$	$0.51\pm 0.00$	$0.68\pm 0.01$	$0.10\pm 0.01$	2.70 $\times$
Swin-UNETR	$0.74\pm 0.01$	$0.61\pm 0.01$	$0.70\pm 0.01$	$0.09\pm 0.00$	54.03 $\times$
VISTA3D	$0.74\pm 0.00$	$0.62\pm 0.01$	$0.71\pm 0.00$	$0.08\pm 0.01$	82.10 $\times$

Table 1: Performance comparison on MSD Task01. Values are reported as mean

\pm

standard deviation over three seeds. Columns 2-4 are the DSC for each model arrangement. Capacity-constrained models like U-Net see an improvement in performance due to additional weights. Larger scans require sliding window inference, increasing the FLOPs required for a single sample.

Figure 2: Left: Empirical verification of the CRC calibration quality. Middle: mean DSC of the Full baseline against the Coarse + Refine model at

\alpha=0.1

. Right: Corresponding measured wall-clock speedup over the Full baseline on different devices.

Figure 3: Predicted tumor boundaries on a held-out test scan (Swin-UNETR, $\alpha=0.1$ ). The Coarse + Refine model tracks the boundary as closely as the Full baseline at a fraction of the FLOPs (Table 1 ).

Panel of Figure 4 — Figure 4: (Left) : False negative rates (FNR) can rapidly increase depending on chosen threshold, requiring a principled methods like CRC to choose appropriate $\lambda$ (See Appendix C.3 . (Middle) Tumor cells span a small fraction of the total scanned volume in most scans in the dataset. (Right) Training the coarse model on the aggregated samples and a separate refiner to convergence requires $15\times$ fewer FLOPs. All models are trained until validation loss stops decreasing with a set patience level.

Panel of Figure 5 — Figure 5: (Left) Visualizations of model segmentation with ground truth showing Coarse + Refine models with comparable contours. (Right) A coarse inference reduces per-scan compute cost while a sparse refinement improves prediction quality with little additional expense.

Figure 6: (a) Input signal. (b) Example test window: ground-truth spike rate overlaid with the Full prediction and the Coarse + Refine reconstruction, at a retained fraction of $8.4\%$ .

Figure 7: (Left) Achieved real-world wall-clock speedups on GPUs and CPU thread counts. (Right) Sample selection and comparison between the Full and Coarse + Refine models. The CRC-certified Coarse + Refine predictions have little discrepancy while costing a fraction of the compute and time.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 8 — Figure 8: Selected (refined) region against the calibrated threshold for two held-out test scans (Swin-UNETR, seed 0). ”Full refinement” is the reference at foreground-probability threshold $0$ , i.e. $\lambda=1$ in Eq. 6 (every foreground-probable cell refined); at $\alpha=1\%$ and $2\%$ , CRC’s calibrated threshold is itself $0$ ( $\hat{\lambda}=1$ ) for this architecture/seed. As $\alpha$ relaxes, the selected region shrinks toward the tumor boundary and the measured cell miss rate rises toward its target.

System	GTVp	GTVn	Mean	Speedup
nnU-Net (250 ep)	0.7938	0.7271	0.7604	–
Full	0.7755	0.6957	0.7356	1.0 $\times$
Coarse	0.7487 $\pm$ 0.0117	0.5660 $\pm$ 0.0307	0.6573 $\pm$ 0.0145	68.3 $\times$
Coarse + Refine ( $\alpha{=}0.1$ )	0.7810 $\pm$ 0.0005	0.6646 $\pm$ 0.0068	0.7228 $\pm$ 0.0034	68.1 $\times$

Appendix

Table 2: DSC and FLOPs speedup across models. All rows except nnU-Net are Swin-UNETR. Mean DSC is the unweighted average of GTVp and GTVn; speedup is the ratio of Full-model FLOPs to pipeline FLOPs.

	GTVp			GTVn
System	Recall	Prec.	DSC	Recall	Prec.	DSC
nnU-Net (250 ep)	0.766	0.572	0.819	0.615	0.378	0.773
Full	0.685	0.625	0.822	0.553	0.526	0.772
Coarse	0.599	0.628	0.799	0.339	0.471	0.745
Coarse + Refine ( $\alpha{=}0.1$ )	0.680	0.638	0.814	0.465	0.475	0.732

Appendix

Table 3: Lesion-specific results for our HNC models. All rows except nnU-Net are Swin-UNETR. Unlike the volumetric DSC, we perform post-processing to detect lesions from predicted volumes to calculate lesion detection metrics.

Panel of Figure 9 — Figure 9: Grid of HECKTOR predictions. From top to bottom: nnU-Net, Swin-UNETR native resolution, Swin-UNETR Coarse, and Swin-UNETR Coarse + Refine.

		FNR at fixed $\lambda$			FNR with CRC ( $\alpha=0.1$ )
Dataset	Model	$\lambda=0.5$	$\lambda=0.1$	$\lambda=0.01$	Calib.	Test
Brain Tumor	UNet	0.17 $\pm$ 0.01	0.072 $\pm$ 0.008	0.021 $\pm$ 0.003	0.085 $\pm$ $<$ 0.001	0.097 $\pm$ 0.006
	Swin-UNETR	0.11 $\pm$ 0.02	0.07 $\pm$ 0.01	0.031 $\pm$ 0.006	0.086 $\pm$ $<$ 0.001	0.091 $\pm$ 0.001
	VISTA3D	0.11 $\pm$ 0.01	0.07 $\pm$ 0.01	0.04 $\pm$ 0.01	0.086 $\pm$ 0.001	0.084 $\pm$ 0.004
HECKTOR	Swin-UNETR	0.86 $\pm$ 0.02	0.25 $\pm$ 0.02	0.13 $\pm$ 0.01	0.092 $\pm$ 0.001	0.072 $\pm$ 0.009

Appendix

Table 4: A naively chosen like threshold can result in high FNR as the predicted scores are non-linear compared to the selection. CRC

Model	Role	Params	FLOPs (window $=$ 1024)
FineUNet1D	Full baseline ( $\mathcal{F}_{\Omega_{\text{fine}}}$ )	10,475,204	2,668,494,848
FineOnLowRes	Coarse ( $\mathcal{F}_{\Omega_{\text{coarse}}}$ )	10,475,204 (same)	333,561,856 (8.0 $\times$ fewer)
LocalRefinerUNet1D	Refiner (count head)	158,721	–

Appendix

Table 5: CASCADE model architectures, parameter counts, and analytic FLOPs. The total FLOPs for the refiner depends on the number of selected windows and is therefore omitted.

$\alpha$	Retained fraction	FLOPs speedup	Reconstructed MAE ( $\Delta$ )
0.01	1.00	0.89 $\times$	0.30 ( $+0.05$ )
0.05	0.48	1.65 $\times$	0.34 ( $+0.09$ )
0.10	0.08	4.77 $\times$	0.32 ( $+0.06$ )
0.20	0.07	5.21 $\times$	0.35 ( $+0.10$ )

Appendix

Table 6: Reconstructed MAE is reported in Hz, with the gap to the full-resolution baseline (

0.250

Hz) in parentheses.

Model	Role	Params	FLOPs
2D U-Net, base width 64	Full baseline	31,389,764	$1.78\times 10^{12}$
Same U-Net, $8\times$ -downsampled input	Coarse	31,389,764 (same)	$2.78\times 10^{10}$ ( $64\times$ fewer)
Local refinement operator	Refiner	17,809	$3.05\times 10^{6}$ per cell

Appendix

Table 7: Galaxy flux field model sizes and analytic floating-point operation counts, per

1024^{2}

field for the full-resolution baseline and the coarse model, and per certified cell for the refiner.

Panel of Figure 10 — Figure 10: Grid of galaxy flux field predictions.

Adaptive Computation

Adaptive computation allocates model depth, tokens, attention, or sensing effort according to input difficulty and resource constraints.

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VLM Adaptation Conformal Prediction

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Conformal prediction provides set-valued predictions with distribution-free coverage guarantees, making it attractive for high-stakes image classification. However, split conformal prediction is data-inefficient, while full conformal prediction (FCP), despite its stronger statistical efficiency, is computationally prohibitive at scale because it requires candidate-specific model refits at test time. We address this limitation by leveraging zero-shot vision-language models (VLMs) to guide scalable FCP in large label spaces. We introduce Targeted Full Conformal Prediction (T-FCP), which uses a lightweight inductive conformal predictor to prune unlikely labels and applies FCP only to the remaining candidates, reducing computation while retaining the formal guarantee of the combined conformal procedure. We further propose Stabilized Online LDA (SO-LDA), an efficient VLM adaptation solver based on rank-one inverse-covariance updates. Across multiple benchmarks, including ImageNet, T-FCP enables practical full-conformal image classification with modest test-time overhead, yielding efficient prediction sets and more stable empirical coverage than split conformal alternatives.

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