MIRA: Mutual Information guided calibration for Reliable Test-Time Adaptation

MIRA pipeline: cache backbone features once, probe Gaussian classifier samples at candidate radii, select a radius using mutual information and top-1 agreement, then adapt using detached reliability weights and a stochastic entropy objective. — **MIRA probes reliability at the classifier.** A single backbone forward pass supplies features for repeated probes; mutual information and confidence guide each sample’s contribution to adaptation.

Abstract

Well-calibrated confidence estimates are important for reliable decision-making when models encounter distribution shift. However, entropy-based test-time adaptation can reinforce confident errors even when accuracy improves, without necessarily yielding well-calibrated predictions.

We propose MIRA, Mutual Information guided calibration for Reliable Test-Time Adaptation, a source-free online method that probes prediction reliability with Gaussian perturbations of the final classifier. MIRA computes backbone features once per target batch and reuses them across classifier samples and candidate perturbation scales. A mutual-information (MI) criterion and a prediction-agreement constraint select a batch-specific probing radius without target labels or posterior fitting. The resulting local disagreement and confidence define detached sample weights for a stochastic entropy objective.

The stochastic objective supplies the adaptation signal, while reliability weighting reduces the influence of perturbation-sensitive samples. Experiments with CNNs, a vision transformer, and CLIP show improvements in the accuracy–calibration trade-off. Further evaluations cover continual and dynamic adaptation, stronger representation shifts, and computational time constraints. MIRA provides a reliability module whose accuracy gains depend on the base adaptation method; its MI is an operational stability signal, rather than calibrated Bayesian posterior uncertainty.

Accuracy and confidence under adaptation

Confidence can be too high or too low under distribution shift. The goal is to improve prediction quality and calibration together.

Online TENT and TENT+MIRA accuracy and confidence on ImageNet-C fog: overconfident ResNet-34 and underconfident EfficientNet-B0. Shading and bars show the absolute accuracy–confidence gap. — Online accuracy and confidence. Shading and bars show the absolute accuracy–confidence gap.

How MIRA works

Cache features and probe the classifier

Compute the backbone features once, then reuse them for Gaussian weight and bias perturbations of the final classifier. The same noise draws are shared across candidate radii within a batch.
Select an informative probing radius

Use normalized MI to find a non-trivial response and top-1 agreement to limit prediction changes. The finite-grid implementation includes a fallback when both conditions cannot be met.
Adapt with detached reliability weights

Combine local disagreement and confidence into unit-mean sample weights. Keep those weights detached while minimizing the stochastic entropy objective and updating the base method’s adaptation parameters.

MI = HE − EHℒ = mean_i [w_i (HE_i + γ EH_i)]

HE: entropy of the mean prediction. EH: mean predictive entropy.

Accuracy and calibration

TENT with and without MIRA.

Confidence–accuracy plots: (a) Source, TENT, and MIRA across architectures; (b) attaching MIRA to four base TTA methods; (c) entropy coefficient gamma variants on ImageNet-C and ResNet-50. The diagonal denotes perfect confidence–accuracy alignment. — Figure 3. Confidence–accuracy plane; the diagonal marks confidence = accuracy. (a) Architectures, (b) MIRA on base TTA methods, (c) γ variants of MIRA_TENT on ImageNet-C / ResNet-50.

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Mean ± standard deviation.
Method	Accuracy (%) ↑	MMC	ECE ↓	NLL ↓
CIFAR-100-C / ResNeXt AugMix
TENT	67.844 ± 0.052	0.7461 ± 0.0007	0.0693 ± 0.0004	1.2547 ± 0.0021
TENT + MIRA	68.692 ± 0.153	0.7305 ± 0.0012	0.0452 ± 0.0007	1.1940 ± 0.0111
ImageNet-C / ResNet-50
TENT	36.618 ± 0.120	0.4089 ± 0.0014	0.0478 ± 0.0018	3.2549 ± 0.0075
TENT + MIRA	39.448 ± 0.141	0.4053 ± 0.0014	0.0361 ± 0.0022	3.0205 ± 0.0020

What changes when gradient norms are matched?

The stochastic objective accounts for much of the adaptation gain. The incremental effect of reliability weighting depends on the protocol. In a separate control with the global L2 norm of the adaptation gradient fixed to 1, full MIRA improves CIFAR accuracy relative to TENT, but falls below TENT on ImageNet-C. This control changes the update scale and is evaluated separately from the main comparison above.

Gradient-norm control (global L2 norm = 1).
Method	Accuracy (%) ↑	ECE ↓	NLL ↓
CIFAR-10-C / WRN AugMix
TENT	87.787 ± 0.046	0.0635 ± 0.0006	0.4462 ± 0.0025
TENT + MIRA	88.416 ± 0.067	0.0396 ± 0.0011	0.3808 ± 0.0023
CIFAR-100-C / ResNeXt AugMix
TENT	65.972 ± 0.106	0.0586 ± 0.0005	1.3250 ± 0.0029
TENT + MIRA	66.180 ± 0.106	0.0322 ± 0.0009	1.2937 ± 0.0025
ImageNet-C / ResNet-50
TENT	32.336 ± 0.121	0.0298 ± 0.0001	3.5997 ± 0.0040
TENT + MIRA	32.132 ± 0.132	0.0324 ± 0.0014	3.6162 ± 0.0036

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