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Energy Ring: Stabilizing Feature Energy for Reliable Test-Time Discovery
Tianle Liu, Fan Lyu, Tingliang Feng, Chenggong Ni, Tianqi Wang, Zhang Zhang, Fuyuan Hu, Rui Yao, Tao Zhou
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%
Last extracted: 10/14/2026, 10:06:54 AM
Summary
The paper introduces Energy Ring, a framework for Test-Time Discovery (TTD) that stabilizes the energy gap between known and unknown classes. It uses a lightweight adapter to anchor known classes on a high-energy ring and unknown classes on a low-energy ring, employing perturbation consistency for clustering. During testing, energy-guided confidence weighting and stability-based rectification improve prediction accuracy and adaptability.
Entities (6)
Relation Signals (4)
Energy Ring → solves → Test-Time Discovery
confidence 95% · In this paper, we therefore propose Energy Ring, a TTD framework that can anchor known classes on a high-energy ring and unknown classes on a low-energy ring.
Energy Ring → improvesupon → Test-Time Discovery
confidence 92% · Experimental results show that Energy Ring significantly improves TTD performance against existing TTD methods.
Energy Ring Adapter → partof → Energy Ring
confidence 90% · we introduce a lightweight energy ring adapter that enlarges separation while preserving feature directions of known classes
Energy Ring → outperforms → DAA
confidence 88% · Our method improves agreement performance by 3.33% compared to DAA (Liu et al., 2025).
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Abstract
Abstract:Test-Time Discovery (TTD) aims to recognize known classes and detect novel ones while the model is already deployed, operating directly on a continual unlabeled test-time stream. Existing TTD methods are overly conservative, making known and unknown features collapse together and difficult to separate during test-time adaptation. In this paper, we revisit TTD from an energy perspective and find that the natural energy gap between known and unknown classes is unstable and easily collapses. We therefore propose Energy Ring to stabilize this gap by anchoring the two types of classes on separate energy rings. A lightweight adapter enlarges the norm-based gap while preserving known-class directions, and a perturbation consistency module forms compact clusters for unknown classes. During testing, energy-guided confidence weighting improves prediction, and a stability-based rectification mechanism corrects unreliable updates. Experimental results show that Energy Ring significantly improves TTD performance against existing TTD methods.
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- Source: https://arxiv.org/abs/2610.14525v1
- Canonical: https://arxiv.org/abs/2610.14525v1
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Energy Ring: Stabilizing Feature Energy for Reliable Test-Time Discovery Tianle Liu Affiliation: School of Electronics and Information Engineering, Suzhou University of Science and Technology Fan Lyu †thanks: Corresponding authors. Affiliation: Computer Vision Center, Universitat Autònoma de Barcelona Tingliang Feng Affiliation: College of Computer Science, Northwest University Chenggong Ni Affiliation: School of Intelligence Science and Technology, Nanjing University Tianqi Wang Affiliation: School of Electronics and Information Engineering, Suzhou University of Science and Technology Zhang Zhang Affiliation: New Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences Fuyuan Hu Rui Yao Tao Zhou Email: tianleliu@post.usts.edu.cnfanlyu@cvc.uab.cat ˜ fuyuanhu@mail.usts.edu.cn Affiliation: School of Computer Science and Technology, China Unviersity of Mining and Technology Affiliation: School of Computer Science Engineering, North Minzu University Abstract Test-Time Discovery (TTD) aims to recognize known classes and detect novel ones while the model is already deployed, operating directly on a continual unlabeled test-time stream. Existing TTD methods are overly conservative, making known and unknown features collapse together and difficult to separate during test-time adaptation. In this paper, we revisit TTD from an energy perspective and find that the natural energy gap between known and unknown classes is unstable and easily collapses. We therefore propose Energy Ring to stabilize this gap by anchoring the two types of classes on separate energy rings. A lightweight adapter enlarges the norm-based gap while preserving known-class directions, and a perturbation consistency module forms compact clusters for unknown classes. During testing, energy-guided confidence weighting improves prediction, and a stability-based rectification mechanism corrects unreliable updates. Experimental results show that Energy Ring significantly improves TTD performance against existing TTD methods. Our code will is available at https://github.com/LeTianL-T/ER-for-TTD. 1 Introduction Novel Class Discovery (NCD) (Pu et al., 2023; Wu et al., 2023) aims to identify new categories from unlabeled data using knowledge from known classes. However, it separates the testing and discovery phases, assuming a fixed unlabeled set available in advance. Such a static setting is unsupported in open environments, where new classes appear continuously after deployment. Recently, Test-Time Discovery (TTD) (Lyu et al., 2025b) was proposed to detect and learn novel classes while the model is already deployed. Unlike traditional NCD, TTD operates in a continual, unlabeled stream where both known and unknown samples arrive sequentially under test-time constraints, while discovering and testing in real time. This capability is essential for real-world applications where new concepts may emerge unexpectedly after model deployment (Tan et al., 2026a; Lyu et al., 2026a; Lyu et al., 2026b). Existing TTD methods usually take a conservative strategy to avoid false discovery of new classes and to protect performance on known ones. As shown in Fig. 1, HM (Lyu et al., 2025b) freezes the backbone so that pretrained features stay fixed. This prevents drift on known classes but also blocks useful updates for new classes. DAA (Liu et al., 2025) adds a learnable adapter that allows updates, yet forces all feature vectors to have the same norm. This improves stability but removes a key source of variation, which may lead to crowding and confusion across unknown and known classes. In this paper, we revisit the TTD problem from an energy view. Prior studies (Sodano et al., 2024; Gu et al., 2025; Park et al., 2023; Ding et al., 2026) suggest that feature energy, measured by the norm of a feature, reflects class-specific information. In many cases, known classes have higher energy and unknown classes have lower energy. This natural gap can be used as a cue to separate old and new classes at test time, reducing interference and improving discovery. However, the energy of unknown classes is easy to turn chaotic, and the boundary between high and low energy erodes, yielding the unreliability of the whole system. Motivated by this, we aim to amplify and stabilize the energy difference between known and unknown classes. Features are expected to be distributed at varying heights during TTD just like concentric rings, with each category forming distinct clusters, thereby facilitating easier discrimination and discovery. In this paper, we therefore propose Energy Ring, a TTD framework that can anchor known classes on a high-energy ring and unknown classes on a low-energy ring. Specifically, we introduce a lightweight energy ring adapter that enlarges separation while preserving feature directions of known classes to retain prior knowledge. In addition, we enforce consistent perturbations to encourage compact and stable clustering of unknown samples along the energy ring. During testing, the learned energy-ring structure enables query classification via energy-weighted confidence, while a high-perturbation priority rectification mechanism identifies unstable predictions and corrects them, further improving the accuracy and stability of the energy rings. Our method improves agreement performance by 3.33% compared to DAA (Liu et al., 2025). In summary, our contributions are: Figure 1: Energy comparisons among existing TTD methods and our method. HM keeps the backbone frozen and classifies based on fixed spatial energy. DAA collapses the original energy intensity onto a single hypersphere. Energy Ring compresses known and unknown classes onto different energy rings, yielding spatial-energy difference and retaining separability. (1) We propose Energy Ring, a TTD framework that stabilizes the inherently fragile energy gap by anchoring known and unknown classes on separate energy rings. (2) We design a lightweight energy ring adapter and a perturbation-consistency module that jointly enlarge the energy gap, preserve known-class directions, and produce compact, stable clusters for unknown classes. (3) Extensive experiments demonstrate the effectiveness of Energy Ring, showing clear improvements over prior TTD methods. 2 Related Work Novel Category Discovery (NCD) (Han et al., 2020; Zhang et al., 2023; Zhong et al., 2021) tackles the problem of recognizing classes that never appear in the training labels. Standard NCD pipelines first learn a transferable representation from the labelled data, then cluster the unlabelled stream to reveal new groups. DTC (Han et al., 2019) exploits semantic anchors from related classes to reduce clustering ambiguity; GCD (Vaze et al., 2022) and PromptCCD (Cendra et al., 2024) replace the traditional k-means stage with contrastive learning prompting for purer prototypes. On-the-fly Category Discovery (OCD) (Du et al., 2023; Zheng et al., 2024) pushes NCD toward real-time operation by hashing incoming images and assigning them to the nearest Hamming bucket. OCD, however, is designed only for discovery whose backbone remains frozen, no fine-tuning on the new classes is performed. NCD methods treat discovery and adaptation as two separate stages. Test-Time Training (T) (Liang et al., 2023; Sun et al., 2020; Tan et al., 2026b; Lyu et al., 2025a) is a paradigm that adapts a pre-trained model to distribution shifts while the model is already deployed. Instead of relying on a frozen model, T injects self-supervised objectives and uses the test stream itself to update the backbone on the fly. Representative methods such as T++ (Liu et al., 2021b) and T-MAE (Gandelsman et al., 2022) show that this on-line alignment significantly improves accuracy under covariate shift (Lin et al., 2023; Mei et al., 2026; Tan et al., 2026c). Yet the vast majority of T work assumes the model is only asked to preserve performance on the known classes, leaving it blind to categories that emerge after deployment. Test-Time Discovery (TTD) unifies the two desiderata: retain accuracy on old classes while instantly detecting and learning new ones during inference. The first TTD implementation, pioneered by Lyu et al. (Lyu et al., 2025b), keeps the network frozen and instead maintains an external memory built with Locality-Sensitive Hashing. By avoiding any gradient update, the method sidesteps catastrophic forgetting, but it also forfeits the possibility of refining the feature space when old and new classes overlap. DAA retains the adaptation spirit of T while embracing the discovery mandate of NCD: it updates only a small set of adapters in real time, thereby sharpening the decision boundary between known and emerging classes without erasing previous knowledge. 3 Methods 3.1 TTD Definition and Energy-based Discovery As shown in Fig. 2, TTD aims to recognize known classes and discover unknown ones in a continuous unlabeled stream after model deployment. Formally, let train=(xi,yi)i=1ND_train=\(x_i,y_i)\_i=1^N denote the training set, where xi∈x_i is input image and yi∈kny_i _kn is its label from the known class set knY_kn. During testing, the model encounters a test stream test=kn∪unD_test=D_kn _un, where unD_un may contain unknown classes that were never seen during training. TTD requires model to satisfy two objectives simultaneously. First, novel class discovery and learning, where inputs x∈testunx _test^un must be identified as belonging to unseen classes and assigned new labels to distinguish them from known-class samples. Second, unified classification, where all inputs x∈testx _test are accurately classified into either a known class y∈kny _kn or a novel class y∈seeny _seen, with seenY_seen denoting the set of dynamically discovered novel classes. Figure 2: Task setting of TTD. In TTD, a model is pretrained on data containing only known classes. During deployment, the test data may include both known and unknown classes, requiring the model to predict known classes and discover novel ones. Figure 3: Comparison of norm and angular prediction for test samples. Our method further expands the differences of energy in both intensity and direction. In this paper, we study TTD from an energy view. During testing, the model receives a mixture of known and unknown samples and must make decisions based on the learned representation z=F(x)z=F(x). For known classes, the supervised objective explicitly optimizes the dependency between visual features and their corresponding class identifiers. In contrast, unknown classes are absent from training and their visual information is not explicitly organized or aligned with the learned class-discriminative space. This distinction often manifests in the magnitude of learned representations. Discriminative training tends to amplify feature responses along directions that are useful for separating known classes, producing more confident and higher-energy representations for in-distribution samples. This motivation is consistent with prior OOD detection and novelty discovery studies showing that known samples often exhibit stronger activation energy, while unknown samples tend to produce lower feature responses (Gu et al., 2025; Sodano et al., 2024; Park et al., 2023; Ni et al., 2025). Thus, we use the feature norm ‖z‖2\|z\|_2 as a soft indicator of representation confidence, rather than as a strict separation criterion between known and unknown classes. This preliminary creates a natural difference in energy, reflected in both the norm and direction of features. As illustrated in Fig. 3, known classes usually appear with higher energy and unknown ones with lower energy. Simulated features have lower average norms and therefore provide an appropriate low-energy initialization cue. However, this separation is unstable as their purpose is to expose ERA to ambiguous boundary regions rather than to imitate the semantics of future categories. The norms of different classes overlap, the angular differences are weak, and as more novel classes arrive, these patterns may drift and cause confusion between old and new categories. These observations motivate us to design a method that enlarges and stabilizes the energy difference so that known and unknown classes remain distinguishable during test-time discovery. We therefore explicitly construct two non-overlapping energy rings, keeping known classes at higher energy ring and unknown classes at lower energy ring. We introduce a lightweight Energy Ring Adapter (ERA) and (i) construct energy rings through warm up after training the backbone model to achieve the effect of expanding the energy difference among known and unknown classes while maintaining the energy direction of the learned old classes; (i) enhance the stability of the unknown classes energy ring through perturbations and prepare for rectification. During testing, we (i) utilize the constructed energy rings for energy weighted prediction to improve the accuracy of discovery and classification and (iv) conduct test-time training to correct and optimize the energy rings based on the predicted results and high-perturbation priority rectification mechanism. Figure 4: Method Schema. ERA projects features onto concentric energy rings: high-energy ring for known classes and low-energy ring for unknowns, together with perturbation-consistency during training. During testing, we conduct energy-weighted prediction, while selectively rectifying high-perturbation samples to refresh memory queues and update ERA to rectify energy rings. 3.2 Preconstruct Energy Rings through Warm-up Following DAA (Liu et al., 2025), we also adopt a warm-up strategy to enlarge the gap between known and unknown classes before testing. Unlike DAA, which collapses all features onto a single hypersphere and removes energy differences, our goal is to preserve and further widen the natural gap observed earlier. Since known and unknown classes already show different energy scales, warm-up encourages them to lie on different energy levels, making later discovery more reliable. To achieve this, we introduce an adapter ERA inserted into the pre-trained backbone, which transforms the original feature (x)=f(x)r(x)=f(x) into an adapted representation =ERA((x))z=ERA(r(x)). Specifically, we simulate unknown samples during warm-up by mixing pairs of features with a coefficient λ drawn from a Beta distribution and adding Gaussian noise, forming a synthetic feature ~(x)=λ(x)+(1−λ)(x′)+ r(x)= (x)+(1-λ)r(x )+n. These mixed features serve as proxies for unknown classes (Liu et al., 2025; Zhang et al., 2018) and help stabilize and enlarge the energy separation before test-time discovery. Below, we construct the energy rings during warm-up through three aspects: 1) constraining known and unknown classes onto different energy tracks (norm constraint), 2) maintaining separability for known classes (direction constraint), and 3) enhancing the stability of the energy rings under perturbation. First, we enforce a norm constraint that pushes known samples onto an outer ring and unknown samples onto an inner ring, creating a clear spatial gap between them: ℒ||(x)=(‖ERA((x))‖2−(kn(x)rkn+un(x)run))2,L_||(x)= (\|ERA(r(x))\|_2-(1_kn(x)\,r_kn+1_un(x)\,r_un) )^2, (1) where (x)1(x) is an indicator function, if x is a known class, kn=1,un=01_kn=1,1_un=0 and vice versa. rknr_kn and runr_un denote known and unknown classes energy ring. Second, to preserve previously learned knowledge, ERA must not alter the semantic direction of known-class features. We maintain feature direction by maximizing cosine similarity between the original and adapted features: ℒ∠(x)=1−cos((x),ERA((x))).L_ (x)=1- (r(x),\,ERA(r(x)) ). (2) Third, even with spatial separation and direction preservation, the simulated unknown samples generated by mixup and noise remain random and unstable. To enhance the consistency of unknown classes, we introduce a perturbation-based constraint. For each adapted unknown feature ~=ERA(~(x)) z=ERA( r(x)), we create K norm-preserving perturbations by sampling random directions ∼(0,) δ (0,I), projecting them onto the tangent space of ~ z, and scaling them to an angular radius ε . The perturbed features therefore remain on the same energy ring: b=~+ε−(⊤~)~/‖~‖2‖−(⊤~)~/‖~‖2‖.z_b= z+ \, δ- ( δ^\! z ) z/\| z\|^2 \| δ- ( δ^\! z ) z/\| z\|^2 \|. (3) We treat the K perturbations of the same feature as soft positives b=b(i)∣i=1,…,KP_b=\z_b^(i) i=1,...,K\ and perturbations from different features as soft negatives b=b′(i)∣b′≠b,i=1,…,KN_b=\z_b ^(i) b ≠ b,\;i=1,...,K\. This encourages perturbations of the same unknown sample to stay close, while pushing those from different samples apart, improving the stability and separability of unknown classes without altering norm information: ℒ§=1K∑bmax(0,‖b(0)−¯b‖−‖b(0)−¯b‖).L_ @sectionsign= 1K _b \! (0,\,\|z_b^(0)\!-\! P_b\|-\|z_b^(0)\!-\! N_b\| ). (4) The final warm-up loss combines all three terms: ℒwarmup=ℒ||+ℒ∠+ℒ§.L_warmup=L_||+L_ +L_ @sectionsign. (5) 3.3 Energy Ring Guided Prediction and Discovery Warm-up establishes the initial energy rings for known and unknown classes. We now move to the testing phase and describe how these energy rings guide prediction and discovery. To provide energy information, similar to DAA, we maintain memory queues for both known and undiscovered classes. For a test image x, its ERA representation =ERA((x))z=ERA(r(x)). We first compute an energy coefficient ρ based on its position between the two energy rings: ρ=‖2−runrkn−run∈[0,1].ρ= \|z\|_2-r_unr_kn-r_un∈[0,1]. (6) Let c μ_c be the prototype of class c. Features closer to the outer ring should receive slightly higher similarity toward known classes. Given a small amplitude α∈(0,1)α∈(0,1), we adjust cosine similarities within a narrow range [1−α, 1+α][1-α,\,1+α], so the energy prior nudges but does not dominate the prediction: s~c=cos(,c)⋅[1+α(2ρ−1)],c∈kncos(,c)⋅[1−α(2ρ−1)],c∈seen. s_c= cases (z, μ_c)·[1+α(2ρ-1)],&c _kn\\ (z, μ_c)·[1-α(2ρ-1)],&c _seen. cases (7) This weighting increases confidence for known classes on the outer ring and decreases confidence for unknown classes on the inner ring. We then use a confidence threshold γ to decide whether a test sample belongs to an existing class or a new one: y^=arg maxc∈(kn∪seen)(s~c),if maxcs~c>γ,new discovered class,otherwise. y= casesarg max_c∈(Y_kn _seen)( s_c),&if _c s_c>γ,\\ new discovered class,&otherwise. cases (8) To ensure the reliability of an unknown prediction, we adopt a stability recheck strategy. For a sample predicted as an unknown class, we reuse the perturbation mechanism used in warm-up. We draw k random directions k∼(0,) δ_k (0,I), project them at the feature y^z_ y, and form perturbed features (k)=+kz^(k)=z+ δ_k. For each perturbed feature we recompute the similarity scores s~c(k) s_c^(k) and obtain a new prediction. The stability of the original prediction is then measured by S=1k∑i=1k[argmaxcs~c(i)=y^]S= 1k _i=1^k1 [ _c s_c^(i)= y ] (9) where (⋅)1(·) is the indicator function. For each unknown-class sample, we store the tuple (xci,Si)(x_c^i,S^i) in the queue. Samples with the lowest stability are selected for rectification and added to the test-time training, helping reduce prototype drift and improving the accuracy of class representations. And the model will treat this sample as the first instance of this new seen class. The image feature z will be used as the initial prototype for this class, denoted as y μ_ y. Subsequent samples will be compared to all known and seen prototypes, including this new y μ_ y. 3.4 Test-Time Training to Stabilize Energy Rings During testing phase, ERA not only produces energy-aware features but also continues to learn from the streaming batch. The process requires real-time updating of the adapter, strengthening the dual ring spatial structure, while preventing the forgetting of old knowledge, and performing memory correction to selectively update the most unstable unknown samples to refine the class margin. For known classes, we continue to use lower energy ring loss and direction-preservation loss, which penalizes deviations between the original and adapted features and constrains known class features on the larger energy ring to ensure that the ERA does not alter the feature representations significantly. Contrary to known classes, stable unknown classes that have been evaluated are processed using larger energy ring loss and contrastive loss, which encourages ERA to better adapt to new knowledge of unknown classes. Specifically, given a test batch data ℬB, the test-time training with ERA can be represented by two kinds of loss functions. The first kind of loss is the self-supervised learning loss via the pseudo labels: ℒkn(x)=y^∈kn[ℒ||(x∣y^)+ℒ∠(x∣y^)],ℒun(x)=y^∈unS>κ[ℒ||(x|y^,S)+ℒcont(x|y^,S)], array[]lL_kn(x)=E_ subarrayc y _kn subarray [\,L_||(x y)+L_ (x y) ],\;L_un(x)=E_ subarrayc y _un\\ S>κ subarray~ [L_||(x| y,S)+L_cont(x| y,S) ], array (10) where ℒcontL_cont represents Contrastive Loss (Mao et al., 2023). The second kind represents the replay for known and the renewal for seen classes via retrain samples in memory. Specifically, for every discovered class p we retrieve the samples with the lowest SpiS_p^i (highest instability) regularly, and these samples would be reprocessed, re-evaluated, and update ERA again: ℒknreplay(x)=ℒ||(x)+ℒ∠(x),ℒunrenewal(x)=ℒ||(x)+ℒcont(x). array[]cL_kn^replay(x)=E~L_||(x)+L_ (x), _un^renewal(x)=E~L_||(x)+L_cont(x). array (11) The overall testing phase loss is shown below: ℒtest(x)=λ1⋅y^∈kn(ℒkn(x|y^)+ℒknreplay(x))+λ2⋅y^∈seen(ℒun(x|y^)+ℒunrenewal(x|y^)), array[]cL_test(x)= _1·E_ y _kn (L_kn(x| y)+L_kn^replay(x) )+ _2·E_ y _seen (L_un(x| y)+L_un^renewal(x| y) ), array (12) where λ1 _1 and λ2 _2 are hyperparameters that balance the contributions of each loss term. 4 Experiment 4.1 Experimental Details Datasets. We conduct our experiments based on four benchmark datasets. CIFAR100 (C100) (Krizhevsky et al., 2009) is a commonly used classic dataset. Tiny ImageNet (Le & Yang, 2015) is a subset of ImageNet (Deng et al., 2009). Caltech-UCSD Birds-200-2011 (CUB) (Wah et al., 2011) and FGVC-Aircraft (Maji et al., 2013) are complex fine-grained datasets. All these datasets are split into known and unknown classes (7:3). The model is trained on the known training set and tested on the mixture of known and unknown test sets. Because the dataset is used for discovery, we follow the names of four transformed datasets from HM (Lyu et al., 2025b): CIFAR100D, CUB-200D, Tiny-ImageNetD, and AircraftD. Implementation details. In our implementation, we build our method on the prompt-based method L2P (Wang et al., 2022b), which employs a ViT-B/16 backbone (Khan et al., 2022) following the pretraining procedure of NCD and GMP work. We employed the contrastive loss of the GCD literature when we fine-tune the pretrained model on the known classes, using SGD optimizer and cosine decay learning rate scheduler with an initial learning rate of 0.1 and minimum learning rate of 0.0001, and weight decay of 0.00005. All input images are resized to 224 × 224 and augmented to match the pretrained backbone settings. Table 1: Comparisons on four datasets. Real-time evaluation reflects the accumulated performance across all test batches, while post evaluation reassesses all test samples after testing. Bold and underlining denote the best and second-best results. Method Real-time Evaluation Post Evaluation KA↑ TA↑ CA↑ KA↑ TA↑ CA↑ KF↓ CIFAR100D L2P (Wang et al., 2022b) 59.93±2.15 8.57±2.49 43.10±4.30 50.53±7.25 9.60±1.50 27.39±2.11 27.85±7.21 DP (Wang et al., 2022a) 66.09±1.01 8.80±1.69 48.34±6.78 56.19±2.00 8.68±2.06 28.93±2.25 29.06±1.99 GMP (Cendra et al., 2024) 72.77±1.20 7.37±0.88 42.26±4.54 67.21±2.53 13.04±2.59 27.10±1.77 17.69±2.53 PHE (Zheng et al., 2024) 72.35±1.12 16.74±1.05 37.34±1.31 70.12±1.07 14.55±1.01 24.65±1.35 2.12±0.92 HM (Lyu et al., 2025b) 79.17±0.13 21.13±0.62 56.37±1.42 80.73±1.59 31.03±1.24 34.81±1.22 3.41±1.49 DAA (Liu et al., 2025) 80.81±0.44 31.94±0.98 45.38±0.88 80.27±0.60 35.63±1.11 37.31±1.20 4.10±0.60 Ours 81.79±0.42 33.31±0.77 47.42±1.04 80.40±0.66 37.23±1.18 38.25±1.34 4.00±0.50 CUB200D L2P (Wang et al., 2022b) 46.22±1.53 9.01±0.87 55.37±7.79 31.97±3.35 4.75±0.73 24.48±1.65 42.29±3.14 DP (Wang et al., 2022a) 53.69±1.24 43.68±2.20 45.68±5.88 63.37±3.27 45.94±0.91 7.92±1.10 5.85±3.11 GMP (Cendra et al., 2024) 62.97±1.33 46.44±1.87 47.99±4.34 58.11±3.00 48.02±1.20 10.31±1.45 5.46±2.77 PHE (Zheng et al., 2024) 57.29±1.23 32.68±1.66 57.22±2.75 54.77±1.75 27.92±0.43 21.36±1.36 2.18±0.71 HM (Lyu et al., 2025b) 66.20±0.55 58.30±2.37 43.33±6.10 64.42±0.65 65.28±1.78 37.25±4.90 4.07±0.47 DAA (Liu et al., 2025) 68.09±0.33 54.49±1.03 58.34±1.35 66.26±0.39 64.13±2.23 44.65±0.88 3.60±0.39 Ours 67.10±1.48 57.63±0.47 58.19±1.42 67.38±1.82 64.23±1.78 45.53±1.05 3.00±0.52 T-ImageNetD L2P (Wang et al., 2022b) 46.25±1.41 7.79±2.92 53.55±6.47 29.50±3.77 10.38±2.42 23.28±0.79 47.97±3.77 DP (Wang et al., 2022a) 46.51±0.58 6.41±0.93 58.27±6.10 28.53±3.33 9.63±2.10 26.80±1.38 47.57±3.32 GMP (Cendra et al., 2024) 62.47±1.40 6.25±1.72 58.02±4.29 63.95±2.04 15.64±2.63 26.31±2.33 16.86±2.04 PHE (Zheng et al., 2024) 63.28±1.29 13.54±1.20 70.33±3.80 58.39±1.14 12.80±1.05 19.42±1.45 1.88±0.35 HM (Lyu et al., 2025b) 75.31±1.31 16.04±0.76 73.81±2.67 74.94±2.20 16.23±1.24 37.43±1.30 1.15±2.18 DAA (Liu et al., 2025) 76.38±0.82 24.10±0.80 71.70±2.02 75.50±1.96 23.17±1.35 36.41±1.12 2.39±1.56 Ours 76.72±1.25 25.23±0.71 72.60±1.43 75.28±1.98 24.33±1.38 37.93±1.49 1.50±0.95 AircraftD L2P (Wang et al., 2022b) 43.21±1.08 20.11±1.20 35.52±1.93 40.17±2.34 21.00±1.21 27.21±1.33 15.04±2.10 DP (Wang et al., 2022a) 40.18±1.10 21.88±1.23 34.80±1.79 42.53±1.46 20.22±0.96 28.15±1.74 12.68±1.74 GMP (Cendra et al., 2024) 41.26±1.04 21.12±0.67 35.10±2.50 32.56±1.75 21.25±1.02 26.34±1.48 22.65±2.25 PHE (Zheng et al., 2024) 45.82±1.02 22.56±1.05 41.72±2.13 47.28±2.88 25.09±1.76 24.38±1.67 7.93±1.13 HM (Lyu et al., 2025b) 50.35±1.08 28.01±0.85 40.23±2.22 49.77±1.94 29.80±1.25 28.74±1.53 5.44±1.56 DAA (Liu et al., 2025) 49.37±1.46 27.79±0.31 40.51±1.05 48.87±1.73 28.37±1.69 28.99±1.69 5.61±1.04 Ours 50.88±1.42 28.49±0.76 41.90±1.91 49.42±1.66 29.79±1.50 30.79±1.55 5.20±0.96 Evaluation metrics. Following HM, we use the following metrics. For unknown classes, we use two agreement metrics: (1) True-label Agreement ratio (TA). This metric measures the maximum proportion of samples from a given true class that are predicted as the same class; and (2) Cluster Agreement ratio (CA). This metric measures the maximum proportion of samples from a given predicted cluster that have the same true label. We also provide some clustering metrics that traditional NCD methods use, including Hungarian Cluster Accuracy (HCA) (Meilă, 2003), Adjusted Rand Index (ARI) (Rand, 1971), Normalized Mutual Information (NMI) (McDaid et al., 2011) and V-Measure (Rosenberg & Hirschberg, 2007). For known classes, we also employ two key metrics to comprehensively assess the model’s performance: Known Accuracy (KA) and Known Forgetting (KF). KA measures the traditional classification accuracy of the model on known classes while KF quantifies the degree of performance degradation on known classes over time. 4.2 Major Comparisons In this paper, we first compare our methods with naive thresholding-based training-free methods. When exceeding the threshold, the naive method will be considered to have discovered a new class. And we compare with some training-required methods including L2P (Wang et al., 2022b), DP (Wang et al., 2022a), and GMP (Cendra et al., 2024) as these methods update prompts like TTA and CL methods. We also compare with the recent PHE (Zheng et al., 2024) method for OCD and HM (Lyu et al., 2025b), DAA (Liu et al., 2025) for TTD. Comparisons on TA & CA. The analysis of our experimental results, as illustrated in Table 1, offers key insights into the performance of various methods in the context of Test-Time Discovery (TTD). Training-based methods, which update model parameters upon encountering new classes, tend to suffer from performance degradation. This decline is largely due to their immediate adaptation to novel classes, resulting in lower TA and CA, as well as an increased risk of catastrophic forgetting. On the other hand, training-free methods, such as HM, avoid parameter updates but has restricted capacity to refine its representations in response to novel data. While DAA incorporates a lightweight module that can be updated which only focuses on energy direction and the amplification of inter-class differences remains limited. Our proposed method strikes a more balanced effectiveness among these challenges, achieving more consistent performance across all four datasets. These results demonstrate that our approach enhances the network’s adaptability in discovering novel classes without compromising the retention of previously acquired knowledge. Comparison of compatibility metrics. TA and CA directly reflect online discovery quality and class consistency as the primary metrics, while the four clustering metrics mainly serve compatibility with post-hoc NCD evaluation. The results in Table 2 demonstrate that our method also has better clustering performance on post evaluation. Balance of TA & CA. TA and CA are two complementary indicators, and a high individual indicator does not necessarily indicate a good overall classification performance. Therefore, higher values of both metrics, along with greater balance between them, indicate better classification performance. We compared the balance in Fig. 5 and found that some methods have higher values but deviate far from the Perfect Balance line. And our method is more balanced and effective (larger red areas) on different datasets. Table 2: Comparisons of clustering metrics of post evaluation on four datasets. Method CIFAR100D CUB200D T-ImageNetD AircraftD HCA ARI NMI VM HCA ARI NMI VM HCA ARI NMI VM HCA ARI NMI VM HM (Lyu et al., 2025b) 63.69 48.35 73.08 73.08 50.46 27.81 70.25 70.25 56.64 40.35 72.70 72.70 33.30 21.33 46.46 46.46 DAA (Liu et al., 2025) 65.62 53.96 75.20 75.21 58.19 32.43 75.29 75.29 58.91 42.50 73.53 73.53 32.08 21.20 46.44 46.44 Ours 66.38 53.54 75.36 75.36 58.34 33.70 75.53 75.53 58.25 43.26 73.36 73.36 33.21 22.13 47.02 47.02 Figure 5: Comparison on balance of Real-time TA and CA. Perfect Balance represents the most balanced TA and CA (TA = CA). 4.3 Analysis on Energy ring Comparison on norm and confidence. Fig. 3 shows that there is indeed a certain norm difference between the features of known and unknown classes obtained by the backbone network, as stated in (Sodano et al., 2024; Lyu et al., 2025b). The average norm of unknown classes is slightly lower than that of known classes. Our method trains simulated classes as unknown classes and significantly reduce the norm of the simulation classes, which successfully simulate unknown classes to a certain extent, thus reducing the norm of the unknown classes. And our strategy makes their average confidence differences larger, which means that unknown classes are easier to be discovered. Table 3: Different energy weight during testing. Energy weight Real-time Eval Post Eval α TA CA T+C TA CA T+C KF 0 (No norm) 31.81 44.59 76.40 35.25 36.99 72.24 4.30 0.01 32.56 45.58 78.14 36.42 37.43 73.85 4.07 0.05 33.52 47.66 81.18 37.74 38.92 76.66 3.65 0.10 29.25 48.23 77.48 34.92 40.95 75.87 3.83 0.50 25.70 49.48 75.18 27.25 36.51 63.76 8.49 (Norm-based) 12.87 27.16 40.03 20.92 24.79 45.71 12.90 Table 4: Ablation study. T: Test-time Training, W: Energy-weighted prediction, P: Perturbation rectification, T+C: TA+CA. T W P Real-time Eval Post Eval TA CA T+C TA CA T+C KF 30.81 42.13 72.94 34.91 38.53 73.44 2.27 ✓ 24.68 53.74 78.42 24.89 42.68 67.57 6.84 ✓ 29.61 45.54 75.15 32.44 36.45 68.89 3.05 ✓ ✓ 31.60 44.99 76.59 34.52 36.52 71.04 4.22 ✓ ✓ ✓ 33.52 47.66 81.18 37.74 38.92 76.66 3.65 Energy weight. We exploit the spatial variation in feature responses to re-weight categorical similarity, using a norm-based modulation that remains deliberately light (Sec.3.3). The feature-to-category similarities already lie in [0, 1] and the overlap zone clusters around 0.7. Consequently, as Table 4 shows, only a small modulation factor is required, once the exponent becomes large, the relative reliabilities are overturned and the norm effectively seizes control of the decision; in the limiting case of a purely norm-governed weight, the accuracy collapses. Ablation study. Table 4 summarizes the ablation results. Test-time Training (T) alone lifts CA from 42.13 to 53.74, but results in larger KF and lowers post-TA, revealing instability. Energy-weighted prediction (W) without T already outperforms the fixed model, pushing real-time TA+CA from 72.94 to 75.15, confirming the effectiveness of energy-weight assistance. Injecting perturbation consistency rectification (P) into the full pipeline helps rectify unstable samples, attaining the best overall trade-off (TA+CA 81.18 real-time and 76.66 post). These results demonstrate that W and P can effectively enable positive test-time update without catastrophic forgetting. Different Perturbation. We mainly enhance the stability among unknown classes through perturbations, and during testing, we make corrections based on the results of perturbations. In Fig. 7, insufficient perturbations makes the judgment of stability reckless and coincidental changes or no changes can be considered unstable or very stable, so the effect cannot be effectively improved, while excessive perturbations does not significantly improve the effect and introduces greater time cost. Energy rings during warm-up. We treat the energy ring rknr_kn and runr_un as a coupled hyper-parameter pair that determines the spatial energy layout of feature. Fig. 7 shows when runr_un is too small the inner ring is pushed close to the origin with a large gap between rknr_kn, making classification difficult and yielding unstable clusters. The experiment of Fig 3 finds that the norm of backbone features for known classes centers around 70. Therefore, we fix the known class feature norm at 70 and handle unknown classes for better results. Figure 6: Different perturbations k during testing. Figure 7: Different rknr_kn & runr_un during Warm-Up. Post visualization using T-SNE. In Fig. 8, we employ t-SNE (Van der Maaten & Hinton, 2008) to visualize the distribution of test samples. Methods that directly update the base model parameters often risk disrupting the model’s existing structure, leading to destructive confusion between classes. In contrast, HM methods cannot update the model, leaving the feature distribution static. Meanwhile, DAA dismisses the spatial difference of feature, limiting its angular amplification effect. In contrast, our method strikes a balance by not only distinguishing features based on angles but also accounting for the energy intensity between the inner and outer energy rings, and by learning updates that separate features across different classes and maintain clearer spatial boundaries than other methods. Figure 8: T-SNE visualization in angular space on CIFAR100D with 5 known and 5 unknown classes. Comparison of unknown class label matching. Fig. 9 shows the matching between predictions and ground truth, where the base-model updating method easily leads to chaotic predictions and misclassification. In the fixed-energy method like HM, lots of old samples are classified into unknown clusters. DAA has improved its ability to discover new classes, but there are still some categories that fail to be discovered. Our method can discover a larger number of new classes and make the matching more balanced while classifying fewer known classes as unknown. Figure 9: Matching comparison between unknown class predictions and ground truth across methods on CIFAR-100D (90+10). Black rectangles indicate old class samples misclassified as unknowns. 5 Conclusion In this paper, we introduced the Energy Ring framework to address the challenging Test-Time Discovery task. Our method enables instant recognition of unknown classes while safeguarding the accuracy of previously learned ones. 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