Tent: Fully Test-Time Adaptation by Entropy Minimization
Authors: Dequan Wang
Evan Shelhamer
Shaoteng Liu
Bruno Olshausen
Trevor Darrell
Venue: ICLR 2021 Spotlight (2021)
Keywords: deep learning
unsupervised learning
domain adaptation
self-supervision
robustness

Abstract: A model must adapt itself to generalize to new and different data during testing. In this setting of fully test-time adaptation the model has only the test data and its own parameters. We propose to adapt by test entropy minimization (tent): we optimize the model for confidence as measured by the entropy of its predictions. Our method estimates normalization statistics and optimizes channel-wise affine transformations to update online on each batch. Tent reduces generalization error for image classification on corrupted ImageNet and CIFAR-10/100 and reaches a new state-of-the-art error on ImageNet-C. Tent handles source-free domain adaptation on digit recognition from SVHN to MNIST/MNIST-M/USPS, on semantic segmentation from GTA to Cityscapes, and on the VisDA-C benchmark. These results are achieved in one epoch of test-time optimization without altering training.

Published as a conference paper at ICLR 2021
TENT: FULLY TEST-TIME ADAPTATION BY ENTROPY MINIMIZATION
Dequan Wang': Evan Shelhamer Shaoteng Liu', Bruno Olshausen', Trevor Darrell' dqwangêes berkeley........ edu, theihamer@@oogii com
UC Berkeley' Adobe Research²
ABSTRACT
A model must adapt itself generalize to new and different data during testing. In this setting of fully test-time adaptation the model has only the test data and its own parameters. We propose to adapt by test entropy minimization (tent) : we optimize the model for confidence as measured by the entropy of its predictions. Our method estimates normalization statistics and optimizes channel-wise affine transformations to update online on each batch. Tent reduces generalization error for image classification on corrupted ImageNet and CIFAR- 10/100 and reaches a new state-of-the-art error on ImageNet-C. Tent handles source-free domain adapta- tion on digit recognition from SVHN to UIISS//NIIT-M/USSS on semantic segmentation from GTA to Cityscapes, and on the VisDA-C benchmark. These results are achieved in one epoch test-time optimization without altering training.
INTRODUCTION
Deep networks can achieve high accuracy on training and testing data from the same distribution. as evidenced by tremendous benchmark progress (Krizhevsky al., 2012; [Sioonyan & Zisserman 2015; He et al. 2016). However, generalization to new and different data is limited (Hendrycks & Dietterich| 2019 Recht et al. 2019 Geirhos et al.) 2018). Accuracy suffers when the training (source) data differ from the testing (target) data, a condition known as dataset shift Stuionero-Candel et al., 2009). Models can be sensitive to shifts during testing that were not known during training, whether natural variations or corruptions, such as unexpected weather or sensor degradation. Nevertheless, it can be necessary to deploy a model on different data distributions, so adaptation is needed.
During testing, the model must adapt given only its parameters and the target data. This fully test-time adaptation setting cannot rely on source data or supervision. Neither is practical when the model first encounters new testing data, before it can be collected and annotated, inference must go on. Real-world usage motivates fully test-time adaptation by data, computation, and task needs:
1. Availability, A model might be distributed without source data for bandwidth, privacy, or profit.
2. Efficiency. It might not be computationally practical (re-)process source data during testing.
3. Accuracy. A model might be too inaccurate without adaptation to serve its purpose.
To adapt during testing we minimize the entropy of model predictions. We call this objective the test entropy and name our method tent after it. We choose entropy for its connections error and shift. Entropy is related to error, as more confident predictions are all-in-all more correct (Figure I Entropy is related to shifts due to corruption, as more corruption results in more entropy, with a strong rank correlation to the loss for image classification as the level of corruption increases (Figure 2
To minimize entropy, tent normalizes and transforms inference on target data by estimating statistics and optimizing affine parameters batch-by-bate batchh. This choice of low- dimenssiiinnll channel-wist feature modulation is efficient to adapt during testing, even for online updates. Tent does not restrict or alter model training: it is independent of the source data given the model parameters. If the model can be run, it can be adapted. Most importantly, tent effectively reduces not just entropy but error.
"Equal contribution. Work done at Adobe Rescarch; the author is now at DeepMind. Please see the project page httpthtt:///// thw.iittubbbccoo http://hhhhh..ocm/o//oaaaaaaaaaa for the code and more.

---

Published as a conference paper at ICLR 2021
1.2 original
80
noise
blur
Erro (%)
0.8
digital
co..e level
60
0.4
20
p= 0.61
Entropy
Entropy
Figure 1: Predictions with lower entropy have lower error rates on corrupted CIFAR-100-C. Certainty can serve supervision during testing.
More corruption causes more loss and entropy on CIFAR-100-C. Entropy can estimate the degree of shift without training data or labels.
Figure 2:
Our results evaluate generalization to corruptions for image classification, to domain shift for digit recognition, and to simulation-tor -o-real shift for semantic segmentation. For context with more data and optimization, we evaluate methods for robust training, domain adaptation, and self-supervised learning given the labeled source data. Tent can achieve less emror given only the target data, and it improves on the state-of-the-ar for the ImageNet-C benchmark. Analysis experiments support our entropy objective, check sensitivity to the amount of data and the choice of parameters for adaptation, and back the generality tent across architectures.
Our contributions
We highlight the setting of fully test-time adaptation with only target data and no source data. To emphasize practical adaptation during inference benchmark with offline and online updates.
We examine entropy as adaptation objective and propose tent: test-time entropy minimization scheme to reduce generalization error by reducing the entropy of model predictions on test data.
For robustness corruptions, tent reaches 44.0% error on ImageNet-C, better than the state-of- the-art for robust training (50.2%) and the strong baseline of test-time normalization (49.9%).
For domain adaptation, tent is capable of online and source-free fruree-free adaptation for digit classification and semantic segmentation, and can even rival methods that use source data and more optimization.
2 SETTING: FULLY TEST-TIME ADAPTATION
Adaptation addresses generalization from source to target. A model fa(x) with parameters 0 trained on source data and labels x² y may not generalize when tested on shifted target data xf. Table summarizes adaptation settings, their required data, and types of losses. Our fully test-ting timttime adaptation setting uniquely requires only the model fo and unlabeled target data x' for adaptation during inference.
Existing adaptation settings extend training given more data and supervision. Transfer learning by fine-tuning (Donahue et al., 2014 Yosinski al. (0144 needs target labels (re-)train with supervised loss L(x" Without target labels, our setting denies this supervised training. Domain
adaptation (DA) Quionero-Candela al. 2009 Saenko al. 2010 Ganin & Lempitsky 2015
Tzeng et al. 2015) needs both the source and target data to train with cross-domain loss L(x" ,x' Test-time training (TTT) (Sun al. 2019b) adapts during testing but first alters training to jointly optimize its supervised loss L(x", y and self- superviedd loss L(x=). Without source, our setting denies joint training across domains (DA) or losses (TTT). Existing settings have their purposes, but do not cover all practical cases when source, target, supervision not simultaneously available.
Unexpected target data during testing requires test-time adaptation. TTT and our setting adapt the model by optimizing unsupervised loss during testing L(x²), During training, TTT jointly optimizes this same loss on source data L(x") with a supervised loss L(x", " y²), to ensure the parameters are shared across losses for compatibility with adaptation by L(x"). Fully test-time adaptation is independent of the training data and training loss given the parameters 6. By not changing training, setting has the potential require less data and computation for adaptation.
2

---

Published as a conference paper at ICLR 2021
Table Adaptation settings differ by their data and therefore losses during training and testing, Of the source and target' data z and labels y, our fully test-time setting only needs the target data x².
setting
source data
target data
train loss
test loss
fine-tuning
x². y
L(a, L(x", .y) + +(x L(x ,1) )²=+ + ((x))
domain adaptation
x., y 2. y
test-time training
L(x') L(x')
fully test-time adaptation
x
2.9
y
fxxx
2 9)
1/"
Loss (V. yy)
x²
(x (+A)
Entropy (g))
(a) training
(b) fully test-time adaptation
Figure 3: Method overview. Tent does not alter training (a), but minimizes the entropy of predictions during testing (b) over a constrained modulation A, given the parameters 0 and target data x².
3 METHOD: TEST ENTROPY MINIMIZATION VIA FEATURE MODULATION
We optimize the model during testing minimize the entropy of its predictions by modulating its features. We call our method tent for test entropy. Tent requires compatible model, an objective to minimize (Section 3.1 and parameters to optimize over (Section 3.2) to fully define the algorithm (Section Section 3.3 Figure 3 outlines our method for fully test-time adaptation.
The model to be adapted must be trained for the supervised task. probabilistic, and differentiable. No supervision is provided during testing, so the model must already be trained. Measuring the entropy of predictions requires distribution over predictions, so the model must be probabilistic. Gradients are required for fast iterative optimization, so the model must be differentiable. Typical deep networks for supervised learning satisfy these model requirements.
3.1 ENTROPY OBJECTIVE
Our test-time objective L(x;) is to minimize the entropy H() of model predictions & = fa(x).. In particular, we measure the Shannon entropy (Shannon 1948). (i) -c p(O.) log p(gc) for the probability De of class c. Note that optimizing a single prediction has a trivial solution: assign all probability the most probable class. We prevent this by jointly optimizing batched predictions parameters that are shared across the batch.
Entropy is unsupervised objective because it only depends on predictions and not annotations. However, as a measure of the predictions it is directly related to the supervised task and model.
In contrast, proxy tasks for self-supervised learning are not directly related to the supervised task. Proxy tasks derive a self-supervised label y' from the input 2, without the task label y. Examples of these proxies include rotation prediction (Gidaris al. 2018), context prediction (Doersch et al.) 2013), and cross-channel auto-encoding (Zhang et al. 2017). Too much progress on a proxy task could interfere with performance on the supervised task, and self-supervised adaptation methods have to limit or mix updates accordingly (Sun et al. 2019b]a) a). As such, care is needed to choose proxy compatible with the domain and task, to design the architecture for the proxy model, and balance optimization between the task and proxy objectives. Our entropy objective does not need such efforts.
3.2 MODULATION PARAMETERS
The model parameters 0 are natural choice for test-time optimization, and these are the choice of prior work for train-time entropy minimization (Grandvalet & Bengio 2005 Dhillon et al.) 2020 Carlucci et al. 2017). However, 0 is the only representation of the wraning/souree data in setting, and altering could cause the model to diverge from its training. Furthermore, f can be nonlinear and O can be high dimensional, making optimization sensitive and inefficient for test-time usage.
3

---

Published as a conference paper at ICLR 2021
P
3
normalization μt + E|z,] + El(A - xx) transformation 7 + 0H / 3 <- 0H /08
IN
OUT
Figure 4: Tent modulates features during testing by estimating normalization statistics μ4, and optimizing transformation parameters 7, 3. Normalization and transformation apply channel-wise scales and shifts to the features. The statistics and parameters are updated on target data without use of source data. In practice, adapting n, B efficient because they make up <1% of model parameters.
For stability and efficiency, we instead only update feature modulations that are linear (scales and shifts), and low-dimensional (channel-wise). Figure shows the two steps of our modulations: normalization by statisties and transformation by parameters. Normalization centers and standardizes the input x into ã = (x p)/a by its mean μ and standard deviation σ. Transformation turns æ into the output x' qa + 8 by affine parameters for scale y and shift B. Note that the statistics p,, estimated from the data while the parameters 7,8 are optimized by the loss.
For implementation, simply repurpose the normalization layers of the source model. We update their normalization statistics and affine parameters for all layers and channels during testing.
3.3 ALGORITHM
Initialization The optimizer collects the affine transformation parameters {y,., B1,b) for each normalization layer I and channel & in the source model. The remaining parameters 9 { (, } are fixed. The normalization statistics {Mi, σ1,x) from the source data are discarded.
Iteration Each step updates the normalization statistics and transformation parameters data. The normalization statistics are estimated for each layer in turn, during the forward pass. The transformation parameters Y, B are updated by the gradient of the prediction entropy V H (T), during the backward pass. Note that the transformation update follows the prediction for the current batch, and it only affects the next batch (unless forward is repeated). This needs just one gradient per point of additional computation, so we use this scheme by default for efficiency.
batch of
Termination For online adaptation, no termination is necessary, and iteration continues as long as there is test data. For offline adaptation, the model is first updated and then inference is repeated. Adaptation may of course continue by updating for multiple epochs.
EXPERIMENTS
We evaluate tent for corruption robustness on CIFAR-IO/CIFAR-100 and ImageNet, and for domain adaptation digit adaptation from SVHN MNIST/MNIST-MMUSSS. Our implementation is in PyTorch (Paszke et al. 2019) with the pycls library (Radosavovic et al. 2019).
Datasets We
image classification datasets for corruption and domain adaptation conditions. For large-scale experiments we choose ImageNet (Russakovsky et al. 2015), with 1,000 classes, training set of 1.2 million, and a validation set of 50,000. For experiments an accessible scale we choose CIFAR- 10/CI---// (Krizhevsky) 2009). with 10/100 classes, training set of 50,000, and a test set of 10,000. For domain adaptation we choose SVHN (Netzer et al. 2011) as source and (Ganin & Lempitsky (2155/USPS (Hull) 1994) as targets,
MNIST (LeCun et al.] (998)/MIIST. with ten classes for the digits 0-9. SVHN has color images of house numbers from street views with a training set of 73,257 and test set of 26,032. MNIST/MNIST- a training sets 50,,000660,0007.00 .291 and test sets of 10,000/100 00000/1,,000/..00 00077.007.
have handwritten digits with
Models For corruption use residual networks (He et al. 2016) with 26 layers (R-26) CIFAR- 10/100 and 50 layers (R-50) on ImageNet. For domain adaptation we use the R-26 architecture. For fair comparison, all methods in each experimental condition share the same architecture
Our networks are equipped with batch normalization [Toffe & Szegedy 2015). For the source model without adaptation, the normalization statistics are estimated during training the source data. For all test-time adaptation methods, we estimate these statistics during testing on the target data, as done
in concurrett work adaptation by normalization (Schneider al. 2020 Nado al. 2020
4

---

Published as a conference paper at ICLR 2021
Table Corruption benchmark on CIFAR-IO- and CIFAR- 1-FAR-100-C for the highest severity. Tent has least error, with less optimization than domain adaptation (RG, UDA-SS) and test-time training (TTT), and improves on test-time norm (BN).
59.5%
49.9%
tent 44.0%
ANT
Error (96)
Method
Source
Target
C10-C
Error (%)
C100-C
original
gausg
shot
impulse
defocus
glass
motion
zom
snow
frost
fog
bright
contract elastic pi kel jadl
Source
train
40.8
67.2
RG
train
train
18.3
38.9
UDA-SS
train
train
16.7
47.0
Figure 5: Corruption benchmark on ImageNet-C:
TTT
train
test
17.5
45.0
error for each type averaged over severity levels.
BN
test
17.3
42.6
Tent improves on the prior state-of-the-art, adver- sarial noise training (Rusak et al. (020), by fully test-time adaptation without altering training.
PL
test
15.7
41.2
Tent (ours)
test
14.3
37.3
Optimization We optimize the modulation parameters 7, 3 following the training hyperparameters for the source model with few changes, On ImageNet we optimize by SGD with momentum; on other datasets we optimize by Adam (Kingma & Ba 2015). We lower the batch size (BS) to reduce memory usage for inference, then lower the learning rate (LR) by the same factor to compensate (Goyal et al. 2017). On ImageNet, we set BS = 64 and LR = 0.00025, and on other datasets we set BS 128 and LR 0.001.We control for ordering by shuffling and sharing the order across methods.
Baselines We compare to domain adaptation, superviier,,,,,, normalization, and pseudo-labeling:
source applies the trained classifier to the test data without adaptation,
adversarial domain adaptation (RG) reverses the gradients of a domain classifier on source and
target optimize for a comainninvarrin representation (Ganin & Lempitsky 2015).
self-supervised domain adaptation (UDA-SS) jointly trains self-supervised rotation and position
tasks on source and target optimize for a shared representation (Sun al. 2019a),
test-time training (TTT) jointly trains for supervised and self-supervised tasks on source, then
keeps training the self-supervised task on target during testing (Sun et al.) (2019b),
rest-time normalization (BN) updates batch normalization statistics (loffe & Szegedy 2015 on
the target data during testing (Schneider et al., 2020, Nado et al. 2020).
pseudo-labeling (PI.) tunes a confidence threshold, assigns predictions over the threshold as labels, and then optimizes the model to these pscudo-labels before testing (Lee 2013).
Only test-time normalization (BN), pseudo-labeling (PL), and tent (ours) are fully test- fest-time adaptation methods. See Section 2 for an explanation and contrast with domain adaptation and test- cest-time training.
4.1 ROBUSTNESS TO CORRUPTIONS
To benchmark robustness corruption, we make of common image corruptions (see Appendix A for examples). The CIFAR- 10/10000000000 and ImageNet datasets are turned into the CIFAR- 10/1000C and ImageNet-C corruption benchmarks by duplicating their test/validation sets and applying 15 types of corruptions at five severity levels (Hendrycks & Dietterich 2019).
Tent improves more with less data and computation. Table 2 reports errors averaged over corrup- tion types at the severest level of corruption. On CIFAR- 100AA-1001100- we compare all methods, including those that require joint training across domains or losses, given the convenient sizes of these datasets. Adaptation is offline for fair comparison with offline baselines. Tent improves on the fully test-time adaptation baselines (BN, PI.) but also the domain adaptation (RG, UDA-SS) and test-time training (TTT) methods that need several epochs of optimization on source and target.
Tent consistently improves across corruption types. F the error for each corruption type averaged over corruption levels on ImageNet-C. We compare the most efficient methods-souree normalization, and tent tent-given the large scale of the source data (>1 million images) needed by other methods and the 75 target combinations of corruption types and levels. Tent and BN adapt online to rival the efficiency of inference without adaptation. Tent reaches the least error for most corruption types without increasing the emrrr on the original data.
5

---

Published as a conference paper at ICLR 2021
Table 3: Digit domain adaptation from SVHN MNIST/MNIST-MICUSSS. Source-free adaptation is not only feasible, but more efficient. Tent always improves normalization (BN), and in 2/3 cases achieves less error than domain adaptation (RG, UDA-SS) without joint training on source & target.
Epochs
Error ( (%)
Method
Source
Target
Source Target
MNIST
MNIST-M
USPS
Source
train
18.2
39.7
19.3
RG
train
train train
10 10
15.0
33.4
18.9
UDA-SS
train
10 10
11.1
22.2
18.4
BN
test
0+ 1
15.7
39.7
18.0
Tent (ours)
test
0+
10.0
37.0
16.3
Tent (ours)
test
0+ 10
8.2
36.8
14.4
Tent reaches new state-of-the-art without altering training. The state-of-the-art methods for robustness extend training with adversarial noise (ANT) (Rusak et al. 2020) for 50.2% error or mixtures of data augmentations (AugMix) (Hendrycks et al. 2020) for 51.7% error. Combined with stylization from external images (SIN) (Geirhos et al. 2019). ANT+SIN reaches 47.4%. Tent reaches a new state-of-the-an of 44.0% by online adaptation and 42.3% by offline adaptation. It improves on ANT for all types except noise, on which ANT is trained. This requires just one gradient per test point, without more optimization on the training set (ANT, AugMix) or use of external images (SIN), Among fully test-time adaptation methods, tent reduces the error beyond test-time normalization for 18% relative improvement. In concurrent work. Schneider et al. (2020) report 49.3% error for test-time normalization, for which tent still gives 14% relative improvement.
4.2 SOURCE-FREE DOMAIN ADAPTATION
We benchmark digit adaptation (Gannn & Lempitsky 2015 Zzng et al., 2017) Shu et al. (0188) for shifts from SVHN to MNISTMMISTTMMUSEE makes use the labeled source data and unlabeled target data, while our fully test-time adaptation setting denies use of source data. Adaptation is offline for fair comparison with offline baselines.
Recall that unsupervised domain adaptation
Tent adapts to target without source. Table 3 reports the target errors for domain adaptation and fully test-time adaptation methods. Test-time normalization (BN) marginally improves, while adversarial domain adaptation (RG) and supervudee domain adaptation (UDA-SS) improve more by joint training on source and target. Tent always has lower error than the source model and BN, and it achieves the lowest error in 2/3 cases, even in just epoch and without of source data.
While encouraging for fully test-time adaptation, unsupervised domain adaptation remains necessary for the highest accuracy and harder shifts. For SVHN-to-MNIST DIRT-T (Shu et al., 2018) achieves a remarkable 0.6% error For MNIST-10-SVHN, a difficult shift with source-only error of 71.3%, DIRT-T reaches 45.5% and UDA-SS reaches 38.7%. Tent fails on this shift and increases error to 79.8%. In this case success presently requires joint optimization over source and target.
Tent needs less computation, but still improves with more. Tent adapts efficiently on target data alone with just one gradient per point. RG & UDA-SS also use the source data (SVHN train). which ~>x the size of the target data (MNIST test). and optimize for 10 epochs. Tent adapts with ~-80 less computation. With more updates, tent reaches 8.2% error in 10 epochs and 6.5% in 100 epochs. With online updates, tent reaches 12.5% error in one epoch and 8.4% error in epochs.
Tent scales to semantic segmentation. To show scalability to large models and inputs, we evaluate semantic segmentation (pixel-wise classification) on domain shift from simulated source to a real target. The source is GTA (Richter et al. 2017). video game in urban environment, and the target Cityscapes (Cordts et al. 2016), an urban autonomous driving dataset. The model is HRNet- 18, fully convolutional network (Shelhamer et al., 2017) with high-resolution architecture (Wang et al.) 2020). The target pneerscction-over-nee tent 35.8% with offline optimization by Adam. For adaptation to a single image, tent reaches 36.4% in 10 iterations with episodic optimization. See the appendix for qualitative example (Appendix [B)
scores (higher is better) are source 28.8%, BN 31.4%, and
We exclude DIRT-T from our experiments because of incomparable differences in architecture and model selection. DIRT-T tunes with labeled target data, but do not. Please refer to Shu et al. (2018) for detail.

---

Published as a conference paper at ICLR 2021
1.0
0.5
Source
(b) BN
0.0
-0.5
p= 0.22
-1.0
-1.0
-0.5
0.0
0.5
1.0
(c) Tent
(d) Oracle
AH
Figure 6: Tent reduces the entropy and loss. We plot changes in entropy AH and loss AL for all of LEFAR-100-C. Change in entropy rank-correlates with change in loss: note the dark diagonal and the rank correlation coefficient of 0.22.
Figure 7: Adapted features on CIFAR-100-C
with Gaussian noise (front) and reference features without corruption (back). Corruption shifts fea- tures away from the reference, but BN reduces the shifts. Tent instead shifts features more, and closer oracle that optimizes target labels.
Tent scales to the VisDA-C challenge. To show adaptation on a more difficult benchmark, we evaluate the VisDA-C challenge (Peng et al. (0177.. The task is object recognition for 12 classes where the source data is synthesized by rendering 3D models and the target data is collected from real scenes. The validation error for our source model (ResNet-50, pretrained on ImageNet) is 56. 56.1%. while tent reaches 45.6%, and improves to 39.6% by updating all layers except for the final classifier as done by Liang et al. (2020). Although offline source-free free adaptation by model adaptation (Li et al.) 2020) or SHOT (Liang et al. 2020) can reach lower error with more computation and tuning, tent can adapt online during testing.
4.3 ANALYSIS
Tent reduces entropy and error. Figure verifies tent does indeed reduce the entropy and the task loss (softmax cross-entropy). We plot changes in entropy and loss on CIFAR- 100-C for all 75 corruption type/level combinations. Both axes are normalized by the maximum entropy of prediction (log 100) and clipped to +1. Most points have lower entropy and error after adaptation.
Tent needs feature modulation. We ablate the normalization and transformation steps of feature modulation. Not updating normalization increases errors, and can fail to improve over BN and PL. Not updating transformation parameters reduces the method test-time normalization. Updating only the last layer of the model can improve but then degrades with further optimization. Updating the full model parameters 9 never improves over the unadapted source model.
Tent generalizes across target data. Adaptation could be limited to the points used for updates. We check that adaptation generalizes across points by adapting on target train and not target test. Test errors drop: CIFAR- 100-C error goes from 37.3% to 34.2% and SVHN-to-MNIST error goes from 8.2% to 6.5%. (Train larger than test; when subsampling to the same size errors differ by <%.1%. Therefore the adapted modulation is not point specific but general.
Tent modulation difffer from normalization. Modulation normalizes and transforms features. We examine the combined effect. 7 contrasts adapted features corrupted data against reference features on uncorrupted data. We plot features from the source model, normalization, tent, and an oracle that optimizes but tent does not. Instead, tent makes features more like the oracle. This suggests a different and task-specific effect. See the appendix for visualizations of more layers (Appendix C
the target labels. Normalization makes features more like the reference,
7

---

Published as a conference paper at ICLR 2021
Tent adapts alternative architectures. Tent is architecture agnostic in principle. To gauge its generality in practice, we evaluate new architectures based on self-attention (SAN) (Zhao et al. 2020) and equilibrium solving (MDEQ) (Bai et al. 2020) for corruption robustness CIFAR- 100-C. Table 4 shows that tent reduces emror with the same settings as convolutional residual networks.
Table 4: Tent adapts alternative architectures on CIFAR-100-C without tuning. Results are error (%).
SAN-10 (pair)
SAN-10 (patch)
MDEQ (large)
Source
BN
Tent
Source
BN
Tent
Source
BN
Tent
55.3
39.7
36.7
48.0
31.8
29.2
53.3
44.9
41.7
RELATED WORK
We relate tent to existing adaptation, entropy minimization, and feature modulation methods.
Train-Tine Time Adaptation Domain adaptation jointly optimizes source and target by cross-domain
losses L(x .x) to mitigate shift. These losses optimize feature aligmment (Gretton et al. 2009 Sun
et al. 2017). adversarial invariance (Ganin & Lempitsky 2013 Zzng al. [2017]
shared proxy
tasks (Sun et al., 2019a). Transduction (Gammerman et al. 1998 Joachims] 1999] Zhou et al. 2004)
jointly optimizes train and test to better fit specific test instances. While effective in their settings, neither applies when joint use of source/train and target/test is denied. Tent adapts on target alone.
Recent "source-free" methods (Li al. 2020; Kundu et al. 2020 Liang al. 2020) also adapt without source data. [i et al. 2020); Kundu el al. (2020) rely on generative modeling and optimize multiple models with multiple losses. Kundu et al. 2220 Liang et al. (2020) also alter training. Tent does not need generative modeling, nor does it alter training, and so it can deployed more generally to adapt online with much more computational efficiency. SHOT (Liang et al. 2020) adapts by informa- tion maximization (entropy minimization and diversity regularization), but differs in its other losses and its parameterization. These source-free methods optimize offline with multiple losses for multiple epochs, which requires more tuning and computation than tent, but may achieve more accuracy with more computation. Tent optimizes online with just one loss and an efficient parameterization of modulation to emphasize fully test-time adaptation during inference. We encourage examination of each of these works on the frontier of adaptation without source data.
Chidlovski et al. (2016) are the first to motivate adaptation without source data for legal, commercial, or technical concerns. They adapt predictions by applying denoising auto-encoders while we adapt models by entropy minimization. We share their motivations, but the methods and experiments differ.
Test-Time Adaptation Tent adapts by test-time optimization and normalization to update the model. Test-time adaptation of predictions, through which harder and uncertain cases are adjusted based on easier and certain cases (Jain & Learned-Miller 2011), provides inspiration for certainty-based model adaptation schemes like our own.
Test-time training (TTT) (Sun et al.) 2019b) also optimizes during testing, but differs in its loss and must alter training. TTT relies on proxy task, such recognizing rotations of an image, and so its loss depends on the choice of proxy. (Indeed, its authors caution that the proxy must be "both well-defined and non-trivial in the new domain")). TTT alters training to optimize this proxy loss on source before adapting to target. Tent adapts without proxy tasks and without altering training.
Normalizing feature statisties is common for domain adaptation (Gretton al.) 2009 Sun al.) 2017). For batch normalization [i et al. (2017): Carlucci et al. (2017) separate source and target statistics during training. (Schneider et al. (2020): Nado et al. (2020) estimate target statistics during testing to improve generalization. Tent builds on test-time normalization to further reduce generalization error.
Entropy Minimization Entropy minimization is key regularizer for domain adaptation (Carlucci et al. 2017 Shu et al.] 2018, Saito et al. [2019] Roy et al. 2019), semi-supervised learning (Grandvalet & Bengio 2005] Lee, 2013] Berthelot et al. 2019). and few-shot learning (Dhillon et al., 2020). Regularizing entropy penalizes decisions at high densities in the data distribution to improve accuracy for distinct classes (Grandvalet & Bengio 2005). These methods regularize entropy during training in concert with other supervised and unsupervised losses on additional data. Tent is the first minimize
8

---

Published as a conference paper at ICLR 2021
entropy during testing, for adaptation to dataset shifts, without other losses data. Entropic losses are common; our contribution is to exhibit entropy as the sole loss for fully test-time adaptation.
Feature Modulation Modulation makes model vary with its input. We optimize modulations that are simpler than the full model for stable and efficient adaptation. We modulate channel-wiss affine transformations, for their effectiveness in tandem with normalization (loffe & Szegedy [2015] Wu & He 2018). and for their flexibility in conditioning for different tasks (Perez et al.) (2018). These normalization and conditioning methods optimize the modulation during training by supervised loss, but keep it fixed during testing. We optimize the modulation during testing by an unsupervised loss, so that can adapt to different target data.
DISCUSSION
Tent reduces generalization error on shifted data by test-time entropy minimization. In minimizing entropy, the model adapts itself to feedback from its own predictions. This is truly self-supervvsed self-improvement. Self-supprvision of this sort is totally defined by the supervised task, unlike proxy tasks designed to extract more supervision from the data, and yet it remarkably still reduces error. Nevertheless, errors due to corruption and other shifts remain, and therefore more adaptation is needed. Next steps should pursue test-time adaptation more and harder types of shift, over more general parameters, and by more effective and efficient losses.
Shifts Tent reduces error for a variety of shifts including image corruptions, simple changes in appearance for digits, and simulation-to-reat discrepancies. These shifts are popular as standardized benchmarks, but other real-world shifts exist. For instance, the CIFAR 10.1 and ImageNetV2 test sets (Recht et al. 2018 2019). made by reproducing the dataset collection procedures, entail natural but unknown shifts. Although error is higher both sets, indicating the presence of shift, tent does not improve generalization. Adversarial shifts (Szegedy et al. 2014) also threaten real-world usage, and attackers keep adapting to defenses. While adversarial training (Madry et al., 2018 makes difference, test-time adaptation could help counter such test-time attacks.
Parameters Tent modulates the model by normalization and transformation, but much of the model stays fixed. Test-time adaptation could update more of the model, but the issue is to identify parameters that are both expressive and reliable, and this may interact with the choice of loss. TTT adapts multiple layers of features shared by supervised and self-supervised models and SHOT adapts all but the last layer(s) of the model. These choices depend on the model architecture, the loss, and tuning. For tent modulation is reliable, but the larger shift on VisDA is better addressed by the SHOT parameterization. Jointly adapting the input could be a more general alternative. If a model can adapt itself on target, then perhaps its input gradients might optimize spatial transformations image translations to reduce shift without source data.
Losses Tent minimizes entropy. For more adaptation, is there an effective loss for general but episodic test-time optimization? Entropy is general across tasks but limited in scope. It needs batches for optimization, and cannot update episodically on point at time. TTT can do so, but only with the right proxy task. For less computation, is there an efficient loss for more local optimization? Tent and TTT both require full (re-)computation of the model for updates because they depend on its predictions. If the loss were instead defined on the representation. then updates would require less forward and backward computation. Returning entropy specifically, this loss may interact with calibration (Guo et al. 2017). as better uncertainty estimation could drive better adaptation.
We hope that the fully test-time adaptation setting can promote new methods for equipping a model to adapt itself, just as tent yields new model with every update.
ACKNOWLEDGMENTS
We thank Eric Tzeng for discussions on domain adaptation, Bill Freeman for comments on the experiments, Yu Sun for consultations test-time training, and Kelsey Allen for feedback on the exposition. We thank the anonymous reviewers of ICLR 2021 for their feedback, which certainly improved the latest adaptation of the paper.

---

Published as a conference paper at ICLR 2021
REFERENCES
Shaojie Bai, Vladlen Koltun, and Zico Kolter. Multiscale deep equilibrium models. arXiv preprint arXiv:2006.0866 2020.
David Berthelot, Nicholas Carlini, lan Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning, In NeurIPS, 2019.
Fabio Maria Carlucci, Lorenzo Porzi, Barbara Caputo, Elisa Ricci, and Samuel Rota Bulo. Autodial: Automatic domain alignment layers. In 2017 IEEE International Conference Computer Vision (ICCV), pp. 5077-5085. IEEE, 2017.
Boris Chidlovskii. Stephane Clinchant, and Gabriela Csurka. Domain adaptation the absence of source domain data. In SIGKDD, pp. 451 460, 2016.
Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schielc. The cityscapes dataset for semantic urban scene understanding. In CVPR, 2016.
Guncet Singh Dhillon, Pratik Chaudhari, Avinash Ravichandran, and Stefano Soatto. A baseline for few-shot image classification. ICLR, 2020.
Carl Doersch, Abhinav Gupta, and Alexei Efros. Unsupervised visual representation learning by context prediction. ICCV, 2015.
J. Donahue, Y. Jia, O. Vinyals, J. Hoffman, N. Zhang, E. Tzeng, and Darrell. Decaf: A deep convolutional activation feature for generic visual recognition. In ICML, 2014.
A Gammerman, V Vovk, and V Vapnik. Learning by transduction. In UAI. 1998.
Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by backpropagation. In ICML, 2015.
Robert Geirhos, Carlos RM Temme, Jonas Rauber, Heiko H Schütt, Matthias Bethge, and Felix A Wichmann. Generalisation in humans and deep neural networks. In NeurIPS, 2018
Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. Imagenet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In International Conference on Learning Representations, 2019.
Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by predicting image rotations. In ICLR, 2018.
Priya Goyal, Piotr Dollár, Ross Girshick, Pieter Noordhuis, Lukasz Wesolowski, Aapo Kyrola, Andrew Tulloch, Yangqing Jia, and Kaiming He. Accurate, large minibatch sgd: training imagenet in I hour. arXiv preprint arXiv:1706.0200 2017.
Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. NeurlPS, 2005.
A. Gretton, AJ. Smola, Huang, M. Schmittfull, KM. Borgwardt, and B. Schölkopf. Covariate shift and local learning by distribution matching. In Dataset Shift in Machine Learning, pp. 131-160. MIT Press, Cambridge, MA. USA, 2009.
Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger. On calibration of modern neural networks. In ICML, 2017.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, June 2016.
Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corruptions and perturbations. In JCLR, 2019.
Dan Hendrycks, Norman Mu, Ekin D Cubuk, Barret Zoph, Justin Gilmer, and Balaji Lakshminarayanan. Augmix: A simple data processing method to improve robusiness and uncertainty. In ICLR, 2020.
Jonathan J. Hull. A database for handwritten text recognition research. TPAMI, 1994.
Sergey Toffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In ICML, 2015.
10

---

Published as a conference paper at ICLR 2021
Vidit Jain and Erik Learned-Miller. Online domain adaptation of pre-trained cascade of classifiers. In CVPR, 2011.
Thorsten Joachims. Transductive inference for text classification using support vector machines. In ICMI., 1999.
Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In /CLR, 2015.
A. Krizhevsky, 1. Sutskever, and G. Hinton. Imagenet classification with deep convolutional neural networks. NeurIPS, 25, 2012.
Alex Krizhevsky. Learning multiple layers of features from tiny images. Technical report, University of Toronto, 2009.
Jogendra Nath Kundu, Naveen Venkat, R Venkatesh Babu, et al. Universal source-free domain adaptation. In CVPR, pp. 4544-4553, 2020.
Y. LeCun, L. Bottou, Y. Bengio, and Haffner. mradient-based learinng applied to document recognition. Proceedings of the IEEE, 86(11):2278 2324, 1998.
Dong- Hyun Lec. Pscudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In ICML Workshop on challenges in representation learning, 2013.
Rui Li, Qianfen Jiao, Wenming Cao, Hau-San Wong, and Wu. Model adaptation: Unsupervised domain adaptation without source data. In CVPR, June 2020.
Yanghao Li, Naiyan Wang. Jianping Shi, Jiaying Liu, and Xiaodi Hou. Revisiting batch normalization for practical domain adaptation. In /CLRW, 2017.
Jian Liang, Dapeng Hu, and Jiashi Feng. Do we really need to access source data? source hypothesis transfer for unsupervised domain adaptation. In /CML, 2020.
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018.
Zachary Nado, Shreyas Padhy, D Sculloy, Alexander D' Amour, Balaji Lakshminarayanan, and Jasper Snoek. Evaluating prediction-time batch normalization for robustness under covariate shift. arXiv preprint arXiv:2006. 2020.
Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading digits in natural images with unsupervised feature learning. NeurIPS Workshop on Deep Learning and Unsupervised Feature Learning, 2011.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library. In NeurlPS, 2019.
Xingchao Peng, Ben Usman, Neela Kaushik, Judy Hoffman, Dequan Wang, and Kate Saenko. VisDA: The visual domain adaptation challenge. arXiv preprint 17X1v:1710.06924. 2017.
Ethan Perez, Florian Strub, Harm De Vries, Vincent Dumoulin, and Aaron Courville. Film: Visual reasoning with a general conditioning layer. In AAAI, 2018.
Joaquin Ciionero-Candela Masashi Sugiyama. Anton Schwaighofer, and Neil D Lawrence. Dataset shift in machine learning. MIT Press, Cambridge, MA, USA, 2009.
Ilija Radosavovic, Justin Johnson, Saining Xie, Wan- Lo, and Piotr Dollár, On network design spaces for visual recognition. In ICCV, 2019.
Benjamin Recht, Rebecca Roclofs, Ludwig Schmidt, and Vaishaal Shankar. Do cifar- classifiers generalize cifar-10? arXiv preprint 100v:1880600055/ 2018.
Benjamin Recht, Rebecca Roelofs, Ludwig Schmidt, and Vaishaal Shankar. Do ImageNet classifiers generalize to ImageNet? In ICMI. 2019.
Stephan Richter, Zeeshan Hayder, and Vladlen Koltun. Playing for benchmarks. In ICCV, 2017.
Subhankar Roy, Aliaksandr Siarohin, Enver Sangineto, Samuel Rota Bulo, Nicu Sebe, and Elisa Ricci. Unsuper- vised domain adaptation using whiteing and consensus loss. In CVPR, 2019.
11

---

Published as a conference paper at ICLR 2021
Evgenia Rusak, Lukas Schott, Roland S Zimmermann, Julian Bitterwolf, Oliver Bringmann, Matthias Bethge, and Wieland Brendel. simple way make neural networks robust against diverse image corruptions. In ECCV, 2020.
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh. Sean Ma. Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bersstein, al. ImageNet large scale visual recognition challenge. IJCV, 2015.
Kate Saenko, Brian Kulis, Mario Fritz, and Trevor Darrell. Adapting visual category models to new domains. In European conference on computer vision, pp. 213-226. Springer, 2010.
Kuniaki Saito, Donghyun Kim, Stan Sclaroff, Trevor Darrell, and Kate Saenko. suprr-suee domain adaptation via minimax entropy. In /CCV, 2019.
Steffen Schneider, Evgenia Rusak, Luisa Eck, Oliver Bringmann, Wieland Brendel, and Matthias Bethge. Improv- ing robustness against common corruptions by covariate shift adaptation. arXiv preprint arXiv:2006.1697 2020.
C.E. Shannon. A mathematical theory of communication. Bell system technical journal, 27, 1948.
Evan Shelhamer, Jonathan Long, and Trevor Darrell. Fully convolutional networks for semantic segmentation. PAMI, 2017.
Rui Shu, Hung H Bui, Hirokazu Narui, and Stefano Ermon. A dirt-t approach to unsupervised domain adaptation. In ICLR, 2018.
Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In ICLR, 2015.
Baochen Sun, Jiashi Feng, and Kate Saenko. Correlation alignment for unsupervised domain adaptation. In Domain Adaptation in Computer Vision Applications. pp. 153-171. Springer. 2017.
Yu Sun, Eric Tzeng, Trevor Darell,, and Alexei A Efros. Unsupervised domain adaptation through self- supervision. arXiv preprint 4rXiv:1909.11822 2019a.
Yu Sun, Xiaolong Wang. Zhuang Liu, John Miller, Alexei A Efros, and Moritz Hardt. Test-time training for out-of-distribution generalization. arXiv preprint arXiv:1909, 13231, 2019b.
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. 2014.
Eric Tzeng, Judy Hoffman, Trevor Darrell, and Kate Saenko. Simultaneous deep transfer across domains and tasks. In ICCV, 2015.
Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell, Adversarial discriminative domain adaptation. In CVPR, 2017.
Jingdong Wang, Ke Sun, Tianheng Cheng, Borui Jiang, Chaorui Deng, Yang Zhao, Dong Liu, Yadong Mu, Mingkui Tan, Xinggang Wang, al. Deep high-resolution representation learning for visual recognition. PAMI, 2020.
Yuxin Wu and Kaiming He. Group normalization. In ECCV, 2018.
Jason Yosinski, Jeff Clune, Yoshua Bengio, and Hod Lipson. How transferable are features in deep neural networks? In NeurlPS, 2014.
Richard Zhang, Phillip Isola, and Alexci A Efros. Split-brain autocncoders: Unsupervised learning by cross- channel prediction. In CVPR, 2017.
Hengshuang Zhao, Jiaya Jia, and Vladlen Koltun. Exploring self-attention for image recognition. In CVPR, 2020.
Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston, and Bernhard Schölkopf. Learning with local and global consistency. NeurlPS, 2004.
12

---

Published as a conference paper at ICLR 2021
APPENDIX
This supplement summarizes the image comuptiinss used in experiments, highlights qualitative example of instance-wist wisn adaptation semantic segmentation, and visualizes feature shifts across more layers.
A ROBUSTNESS CORRUPTIONS
In Section 4.] we evaluate methods on a common image corruptions benchmark. Table reports errors on the most severe level of corruption, level 5, and Figure reppots errors for each corruption type averaged across each of the levels 1-5. We summarize these corruptions types by example in Figure
Gaussian Noise
Shot Noise
Impulse Noise
Defocus Blur Frosted Glass Blur
Motion Blur
Zoom Blur
Snow
Frost
Fog
Brightness
Contrast
Elastic
Pixelate
JPEG
Figure 8: Examples of each corruption type the image corruptions benchmark. While synthetic, this set of corruptions aims to represent natural factors of variation like noise, blur, weather, and digital imaging effects. This figure is reproduced from Hendrycks & Dietterich (2019)
B SOURCE-FREE ADAPTATION FOR SEMANTIC SEGMENTATION
qualitative result on source fource-free adaptation for semantic segmentation (pixel-wise classification) with simulation-tor -orrrattio--to-aaal (sim-to-real) shift.
For this sim-to-real condition, the source data is simulated while the target data real. Our data is GTA sooualll-sophstictteed video game set in urban environment, our target data Cityscapes Cordts et al. (2016), an urban autonomous driving dataset. The supervised model is HRnet-VV W a fully convolutional network Shellhamer et al. (2017) in the high-resolution network family Wang et al. (2020). For this qualitative example, run tent single image for multiple iterations, because image in effect a batch of pixels. This demonstrates adaptation target instance, without any further domain through usage of multiple images from the target distribution.
Richter et al. (2017).
the target
13

---

Published as a conference paper at ICLR 2021
image
tent, iteration
label
tent, iteration 5
source-only
tent, iteration 10
Figure 9: Adaptation for semantic segmentation with simulation- ianullttionto-reall shift from GTA Richter et al. (2017) to Cityscapes Cordts et al. (2016). Tent only uses the target data, and optimizes over single image as dataset of pixel-wise predictions. This episodic optimization in effect fits a custom model each image of the target domain. In only 10 iterations method suppresses noise (see the completion the street segment, in purple) and recovers missing classes (see the motorcycle and rider, center).
14

---

Published as a conference paper at ICLR 2021
C
FEATURE SHIFTS ACROSS LAYERS AND METHODS
(a) Source
(b) BN
(c) Tent
(d) Oracle
Layer
Layer 5
Layer 8
Layer 11
Layer 14
A
Layer 18
Layer 20
Layer
Layer 26
Figure 10: Adapted features on CIFAR-100 100-C with Gaussian noise (front) and reference features
without corruption (back). Corruption shifts the source features from the reference. BN shifts the features back to be more like the reference. Tent shifts features to be less like the reference, and more like oracle that optimizes on target labels.
15


Reviews:
[{"review_id": "o_XB55lOHYq", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary: This paper tackles an interesting problem setting — fully test-time adaptation with only target data. The proposed method is to minimize the test-time entropy, and the loss is used to update the feature modulation layer only. The proposed method compares favorably with the state of the arts, on the ImageNet-C benchmark and unsupervised domain adaptation tasks.\n\nStrength:\n+ The problem setting is interesting and meaningful\n+ The proposed method is simple, efficient, network-agnostic, and generally applicable to many tasks\n+ The proposed method achieves competitive performance on the ImageNet-C benchmark and unsupervised domain adaptation tasks\n\nWeakness:\n- When comparing with UDA methods (i.e., RG and UDA-SS), I am not sure if the current setting is fair or not. I think they can use the target test set instead of the target training set during training? In this case, it should be a fair comparison with the offline adaptation. \n- I wonder if the improvement comes from modulating the features to the target domain distribution, or because the network is optimized specifically on the test data. Run online/offline adaptation on the target training set, and then directly apply this model on the target test set without optimization might be interesting.\n- Figure 6 is a bit not intuitive to me. Are the authors trying to convey that “entropy reduction is correlated with classification loss reduction”? Probably a better visualization is needed.\n- In Section 4.3 “Tent needs feature modulation”, I wonder where are the exact numbers that I can refer to.\n- What is the message the authors try to convey in Figure 7? What does “BN brings them back” mean? I think this study is interesting and important, more discussions and insights are appreciated.\n\nOther comments:\n* I wonder when this method will fail. I guess if the target test set is very small, the proposed method might not improve over the source model too much?\n* Neural networks sometimes tend to output overconfident (but wrong) predictions even when given out-of-distribution data as input. In this case, I wonder if test entropy is still a good supervision signal to use.\n\n---- Post-rebuttal comments----\n\nThanks for the response. The rebuttal addresses all my concerns. I am willing to increase my score to 8 and recommend acceptance.", "extra_scores": {}, "extra_text": {}}, {"review_id": "jn_gK58GubU", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "$Paper$ $Summary$\n\nThis paper proposes a method to adapt a pre-trained model to a target domain, without the need to access samples from the source domain - on which the model was originally trained. The idea is to adapt layer normalization parameters at test time, by learning affine transformations. This is applied in tandem with the re-collection of the domain statistics.\n\n$Pros$\n\n- The paper is very well written: it is easy to understand the core idea and its applicability in the context of the broader literature. Figures and Tables are also well designed and placed.\n\n- The method is reasonable and simple, and results are strong. As the Authors claim, it is true that the proposed approach has significantly wider applicability than UDA methods and TTT.\n\n$Cons$\n\n- While interesting, I believe Section 4.2 ('Target-only Domain Adaptation') would require additional experiments to properly assess how competitive the proposed approach is with respect to the state of the art of UDA. For instance, several better performing methods could be included in Table 3 (different papers from CVPR/ICLR/etc 2018-2020 achieve significantly higher results on the SVHN -> MNIST split, basically closing the gap with target models - see for example  \"A DIRT-T Approach to Unsupervised Domain Adaptation\" [Shu et al. ICLR 2018]). The better performing methods still need more data to train (source + target), so higher numbers for the competitors would not undermine the proposed method, but they would provide the reader with a more realistic perspective. \n\n- Results associated with more challenging splits should be provided; for instance, can the proposed method handle MNIST -> SVHN adaptation? This would also clarify one concern I have, which is <how good the source model should be for the method to be effective>. The MNIST -> SVHN split would help clarifying this point, since MNIST models are severely under-performing on SVHN (typically accuracy is ~30%).  \n\n- One important baseline that is missing is \"Domain Adaptation in the Absence of Source Data\", [Chidlovskii et al. SIGKDD 2016]. Can the authors comment on this? It seems to me that some of the Algorithms proposed in this related work could be applied here. \n\n$Minor$ $points$/$suggestions$\n\n- Is the performance of UDA-SS in Table 3 correct? The error is larger than the Source model. I am also checking at the original paper.\n\n- The paper \"On Calibration of Modern Neural Networks\" [Guo et al. ICML 2017] shows that deep neural networks are poorly calibrated, as over-confident on samples they are wrong about. Since high-confidence generally implies low-entropy, their results are not aligned with Figure 1, that seems to suggest proper calibration. It would be nice to comment on this in the manuscript.  \n\n$Review$ $summary$\n\nI believe this is a strong paper, proposing a simple method with large applicability - hence I recommend acceptance. Still, it presents some weaknesses at this stage: I would be happy to read the Author response on these points and iterate the discussion.\n\n---- Post-rebuttal comments----\n\nThe rebuttal and the paper revision address my concerns. I fully recommend acceptance.", "extra_scores": {}, "extra_text": {}}, {"review_id": "UuMHWoFssoQ", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "\nPresents Test-time Entropy (TENT) minimization, an algorithm for adapting deep models at test time to distributionally shifted data, without requiring access to source training data. At test time, the algorithm updates batch-norm parameters (that control channel-wise normalization and transformation) to minimize predictive entropy over target data. This simple approach is found to lead to state of the art performance on various corruption benchmarks for image classification, and competitive performance on simple DIGITS recognition-based domain adaptation shifts. \n\nStrengths\n\n– The approach appears very simple to implement and seems to work well, particularly on adapting to corruptions\n\n– The paper is well-written, clearly motivated, and very easy to follow. In particular, the source free-assumption is a compelling feature of the method.\n\n– The analysis on rank-correlation b/w change in entropy and loss, and applicability to different architectures, strengthen the claims of the paper\n\nWeaknesses\n\n– While it’s clear that entropy minimization is correlated with correctness, the motivation beyond updating (only) batch-norm parameters to minimize it is unclear to me. Sec 3.2 states that the reason is “stability and efficiency”, but I think a more comprehensive ablation study would validate this choice better. \n\n– I appreciate the fact that the method is benchmarked on multiple tasks – visual corruptions and DA. However the DA experiments/comparisons appear quite cursory. DIGITS is an easy benchmark, and the DA point of comparison (RevGrad) is not competitive with the current SoTA. Without results on other more challenging benchmarks (VisDA, DomainNet, OfficeHome, etc.) I’m not convinced of the usefulness of this method as a DA technique. \nTo be clear, it would be completely fine if the method *does not* outperform prior work that uses source data or additional computation, but I think it is important to at least benchmark its performance to understand whether it is a viable DA strategy. The qualitative results on semantic segmentation in supplementary appears promising but a quantitative comparison would have been more convincing.\n\nAdditional questions / suggestions\n\n– In Fig. 5, how is source performance measured for TENT? Is this performance on source data after applying TENT, with the updated batch-norm parameters? If so, how does TENT achieve identical performance on the source test set?\n\n– It would be interesting to benchmark the performance of TENT for online DA – beyond not requiring source data, being able to also adapt (even reasonably well) online could be very useful.\n\n– A more descriptive caption for Figure 2 would be helpful. Does opacity correspond to the severity of corruption?\n\n– In Fig. 5, it would be good to break down performance of ANT by corruption type as is done for other methods\n\n– Sec 4.2: “Tent needs less computation, but still improves with more”: Does this hold indefinitely? Does performance degrade after a certain number of epochs, or does it remain stable?\n\nOverall comments\n\nInteresting paper on test-time-adaptation that proposes a simple entropy-minimization based objective to update batch norm parameters, and works well on robustness benchmarks. I have concerns around the motivation behind the algorithm’s design, and its viability as a DA method, but would be willing to reevaluate based on the author response.\n\n---- Post-rebuttal comments----\n\nThe author rebuttal + revised draft adequately addresses most of my concerns – in particular, the experiments on online adaptation and semantic segmentation are strong, and the additional context on the DA results is helpful. I would still have liked to see DA results on more challenging benchmarks but nevertheless think that the paper proposes an interesting approach and is worth accepting.\n", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper is proposing a test time adaptation method without modifying the training. The proposed idea is simple and effective, adapting the normalization layers using the entropy of the model predictions as a loss function. The paper presents an extensive empirical study. Paper received unanimously accept scores. It also has potential to be impactful as it is easy to apply without any strong assumption/requirement. A clear accept!
Decision: Accept (Spotlight)