Adaptive Gaussian Expansion for On-the-fly Category Discovery
Authors: Chunming Li
Shidong Wang
Haofeng Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Novel Category Discovery; Open Set Recognition
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: On-the-Fly Category Discovery (OCD) aims to address the limitations of transductive learning and closed-set prediction in category discovery tasks by enabling real-time classification of potential future categories using prior knowledge. Existing OCD approaches typically rely on hash-based encodings that map features into low-dimensional hash spaces and directly classify test samples using these encodings. Despite efforts to mitigate the sensitivity of hash functions during testing, these methods still suffer from severe overestimation of the number of categories. In this work, we thoroughly analyze the practical limitations of current OCD methods and formally identify a performance lower bound for the task. Based on this insight, we reformulate OCD into two sub-tasks: Open-Set Recognition and an Fully Novel OCD setting. For all samples, we employ a soft class thresholding strategy to directly detect known classes, which significantly enhances the deployment feasibility of OCD to downstream tasks. For outlier samples, we propose Adaptive Gaussian Expansion (AGE), a dynamic category discovery method that models the Probability Density Functions (PDF) of different classes to uncover potential novel categories in real time. Extensive experiments across multiple datasets demonstrate that our method achieves state-of-the-art performance.

Published as a conference paper at ICLR 2026
ADAPTIVE GAUSSIAN EXPANSION FOR ON-THE-FLY CATEGORY DISCOVERY
Chunming Li', Shidong Wang", Haofeng Zhang"*
Nanjing University of Science and Technology. Nanjing. China
NNewastlle University, Newcastle upon Tyne, United Kingdom
chhnminggi, zhanghf) en justt justtteuuuuuu... edu. "shidong. wang@newcastle..e ac. uk
ABSTRACT
On-the-Fly Category Discovery (OCD) aims to address the limitations of trans- ductive learning and closed-set prediction category discovery tasks by enabling real-time classification of potential future categories using prior knowledge. Ex- isting OCD approaches typically rely on hash-based encodings that map features into low-dimensional hash spaces and directly classify test samples using these en- codings. Despite efforts to mitigate the sensitivity of hash functions during testing, these methods still suffer from severe overestimation of the number of categories. In this work, we thoroughly analyze the practical limitations of current OCD meth- ods and formally identify performance lower bound for the task. Based on this insight, we reformulate OCD into two sub-tasks: Open-Set Recognition and an Fully Novel OCD setting. For samples, we employ a soft class thresholding strategy to directly detect known classes, which significantly enhances the deploy- ment fcasibility of OCD to downstream tasks. For outlier samples, we propose Adaptive Gaussian Expansion (AGE), dynamic category discovery method that models the Probability Density Functions (PDF) of different classes to uncover potential novel categories in real time. Extensive experiments across multiple datasets demonstrate that our method achieves state-of-the-ar performance. Code is available at: https: / /ggthhb.. cwm com/Ashengl//GG
INTRODUCTION
As models continue to scale. many now exhibit recognition capabilities that surpass human performance (He et al., 2016; 2022; Dosovitskiy et al., 2021). While existing models benefit from large-scale datasets to achieve accurate classification known cat- egories, they typically special- ized for closed-set prediction. Con- sequently, when faced with new datasets requiring annotation, these models struggle leverage prior knowledge of known categories to ef- fectively model novel ones. To ad- dress this limitation, researchers have introduced a new task setting known as Category Discovery. Category Discovery commonly divided into Novel Category Discovery (NCD) (Rizve et al., 2022) and Generalized Category Discovery (GCD) (Vaze et al., 2022a: Wen et al., 2023), distinguished by whether the provided new unlabeled dataset includes samples from known categories.
Mackin
06.2
SELL
X Insraciia
Backhang
Esisting
21.7
Knoun
Navel
5p.3
Baokbann
Herbarium (III) Performance
(1i) Our Meehod
Figure I: Overview of our method versus prior approaches. (I) Existing methods predict all samples before category matching, which is impractical. (II) Our method directly classifies known samples and infers novel ones via the AGE framework. (III) Experiments show consistent improve- ments across datasets.
"Coresponding author.

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Published as a conference paper at ICLR 2026
Although the concept of Category Discovery effectively alleviates the constraints of closed-set pre- diction, its reliance on transductive learning paradigms or assumptions of label overlap between training and test sets still distances it from the ideal open-world discovery scenario. Consequently, a more challenging task, On-the-fly Category Discovery (OCD) (Du et al., 2023), has emerged. Un- like GCD and NCD, OCD relaxes the requirements on the training set, demanding models be trained only on a partially labeled dataset. Without assuming predefined categories, the model must lever- age information acquired during training to infer the categories of test samples in real-time, even when test samples include novel categories.
A common strategy involves decomposing sample feature embeddings into sign and magnitude components, using the sign as a proxy for category identity. However, this approach suffers from a critical limitation in its high sensitivity, as the way the model defines a category can differ signifi- cantly from human semantic understanding, potentially relying on irrelevant features to identify new categories. Moreover, hash-based encoding OCD poses significant challenge for downstream tasks. Even for well-established categories with ample training data, the model continues to depend on mash-based detection to identify the most likely cluster corresponding to an old class, rather than directly and accurately recognizing the known category.
According to the OCD evaluation metric based Hungarian matching, which ex- plores all possible assignments to find the maximum performance across all classes, we argue that model performance has a lower bound. Given trained closed- set classifier, assuming no novel cate- gories exist, the model can already achieve respectable performance under the OCD metric (see Table Close-set I). If we as- sume that novel categories do exist and performance is maximized through the matching process, an unintuitive result emerges: relying solely the closed-set classifier can yield performance comparable to state-of-the-art methods (see Table 1 Close-set II). We therefore define this performance as a lower bound for OCD models.
Table I: Performance with close-set elassifier.
ImageNNet-100
CUR-200
Herbarium19
Method
All
Old
New
All
Old
New
All
Old
New
SLC
32.9
86.6
5.2
28.6
44.0
20.9
14.9
27.4
8.1
MLDG
30.6
29.5
48.4
20.1
36.7
12.3
RankStat
31.1
73.3
9.8
21.2
26.9
18.4
13.8
20.6
10.2
WTA
30.8
72.9
9.7
21.9
26.9
19.4
14.6
21.2
11.1
SMILE
33.8
13.5
22.9
39.3
14.1
PHR
34.1
80.6
10.8
36.4
55.8
27.0
22.5
38.5
14.0
Close-set
32.0
96.1
0
28.5
85,6
0
22.2
66.5
0
Close-set
38.7
15.3
35.5
52.2
27.1
26.1
52.7
11.2
Given this identified lower bound, argue that existing methods do not fully effectively ploit the information in the labeled data, highlighting the need for more robust approaches to novel category identification. Under the established evaluation criteria, hash encoding proves ineffective for accurately classifying seen categories and is therefore not a robust method for real-time novel category detection. In this paper, we propose to reframe the OCD task as combination of Open-Set Recognition and real-time novel category identification. Given that different labeled datasets may impose different criteria for defining novelty, we further decompose the real-time identification task according to the granularity of the available labeled data.
Inspired by the Chinese Restaurant Process (CRP) in Dirichlet Process Gaussian Mixture Model (DPGMM) (Blei & Jordan, 2006), we propose an online incremental clustering and classification method called Adaptive Gaussian Expansion (AGE), which simultaneously addresses known cate- gory recognition and novel category discovery. Specifically, all sample features are first projected into a lower-dimensional space to climinate redundancy, reduce collinearity, and improve computa- tional efficiency. Then, a stable covariance matrix is estimated for each known class subset using the Ledoit-Wolf shrinkage estimator (Ledoit & Wolf, 2004), and global covariance matrix is con- structed as prior. During inference, since test samples are entirely unknown, we adopt a greedy strategy that makes locally optimal decisions based on the available information. Each new sample is matched against existing clusters using the Mahalanobis distance (De Maesschalck et al., 2000) and Gaussian Probability Density Function (PDF). If its maximum posterior probability falls within an existing cluster, the mean and covariance of that cluster are incrementally updated according to the Dirichlet process concentration parameter; otherwise, the sample is treated as the seed of new cluster, and its parameters are initialized accordingly. This greedy, posterior-based cluster assign- ment rule adaptively forms new clusters during streaming inference without requiring a predefined number of categories. Experimental results demonstrate that our method achieves state-of the-art art performance across multiple datasets, with an average accuracy improvement of 10% over all cate- gories.
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Published as a conference paper at ICLR 2026
Our contributions can be summarized as follows:
We establish theoretical lower bound for OCD performance, revealing inherent limitations of prior approaches and motivating a reformulation of the task.
We reformulate the OCD task as a dual subproblem, enabling explicit disentanglement of known and novel class inference via a statistically grounded, class-specific thresholding mechanism.
We propose AGE for OCD, achieving state-of-the art results across benchmarks.
2
RELATED WORKS
2.1 OPEN SET RECOGNITION
Open Set Recognition (OSR) aims to address the challenge of encountering unknown classes during testing that were present in the training phase. Unlike traditional closed-set classification, which assumes that all test samples belong to known categories, OSR explicitly models the uncertainty and incompleteness of the training data. OSR methods are generally divided into two main approaches: generative models (Ge et al., 2017; Jo et al., 2018; Neal et al., 2018) and discriminative models (Bendale Boult, 2016; Chen et al., 2020; Guo et al., 2021). While generative models aim to model the underlying data distribution, discriminative models focus on learning decision boundaries between known classes. Recent work (Kasarla al., 2022) highlights that enforcing prior that encourages well-separated embeddings remains essential for achieving strong performance in open- set recognition. Open Set Recognition (OSR) focuses on identifying unknown classes during the testing phase, while OCD goes step further by attempting to subdivide these unknown classes into distinct and meaningful categories.
2.2 CATEGORY DISCOVERY
Novel Category Discovery (NCD) aims identify novel classes from unlabeled data with limited labeled examples, unlike semi-supervised learning which assumes shared class space. This task was first formally introduced by Deep Transfer Clustering (DTC) (Han al., 2019), which combines unsupervised clustering (DEC) with protolype-basee classification. Autonovel (Han al., 2020) adopts self-supervised pretraining along with a ranking strategy to generate pseudo-labels, enabling joint training with labeled samples. NCL (Zhong al., 2021) leverages contrastive learning to hance feature discriminability, while UNO (Fini et al., 2021) presents a unified architecture that simultaneously learns from both labeled and novel categories. For example, DCCL (Pu et al., 2023) employs an alternating optimization strategy to extract visual concepts and learn their representa- tions; PromptCAL. (Zhang al., 2023) introduces prompt-based learning: SimGCD (Wen et al., 2023) integrates contrastive objectives with parametric classification; and SPTNet (Wang et al., 2024) proposes a two-stage iterative framework that incorporates spatial prompt tuning. More re- cently, to address the constraint in NCD that all class data must be seen during training, OCD (Du al.. 2023) has been introduced. OCD removes the dependency on training-see set access, enabling real-time, streaming inference on entirely unseen, unlabeled data. Recently PHE (Zheng et al., 2024) distinguishes known and unknown classes via prototype hypersphere estimation, while Diff- GRE (Liu et al., 2025) leverages multimodal and generative models for unknown class discovery.
3 METHODOLOGY
3.1 SETTING
In OCD tasks, the data typically consist of two sets: a labeled support set Ds = {( 9:) N
S
X x Ys. containing a subset of labeled samples, and an unlabeled query set DQ = {(,,, vi) H S
X' x J'Q encountered during inference, where the label space satisfies 3/s C Vo. We define the set of novel classes as VN = =YQ \ Vs. In traditional supervised learning, V/v = 0. whereas in OCD
tasks, VN F 0 and typically contains multiple unseen classes. During the training phase, only the support set D& is available. Unlike most existing approaches, we further split Dş into a validation set Dv.
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Published as a conference paper at ICLR 2026
Precess of Knows Featury
Precee of Teature
Meae
Precess of Comtnn Franar
San Pastare
Leloli-Woff
Dy
PDF
Kuvva Feature
Solt Covoriance
UiR?
Pg
Initialize
Novel
Backiront
Create
Figure 2: Overview of the AGE framework. Incoming features are first classified by a closed-set module; now-confieence samples enter the AGE module, which uses adaptive covariance estimates to update existing class distributions or create new components for novel category discovery.
During the testing phase, the model processes incoming samples in streaming fashion and receives ground-truth labels in real-time.
3.2 МЕТHОО OVERVIEW
We decompose our model into an encoder E, an MLP projection head H. and a parameterized classi- fier C = [ ). |'sl] where each classifier weight vector o; is fz-normalized and and does not include a bias term. As outlined the introduction, the core challenge of the OCD problem lies in effectively distinguishing between known-class samples and anomalous instances within DQ. Within the pro- posed framework, the model initially trained on the support set. During inference, spec-sce thresholds are estimated using held-out validation set. For each incoming query sample, the model first conducts closed-set classification via a normalized classifier and then determines whether sample is anomalous based on the corresponding threshold. Samples identified anomalies subsequently handled by our proposed AGE, which enables flexible and incremental discovery of new classes.
3.3 TRAINING
Unlike existing methods such as SMILE and PHE, which typically decouple features into sign and magnitude components and assign the sign as unique hash code, our approach performs discrim- inative analysis directly in the feature space. Consequently, we do not employ feature-decoupled projection head. Instead, we train the model on the support set Ds using a combination of cross- entropy loss and supervised contrastive learning.
Formally, given mini-batch of samples Bs {x H:) the supervised contrastive loss is com- puted as:
Cuu
Σ By
1
Σ
log exp(2: zp/T) Egen exp(z. za/T)"
Bsl
P())
PEP(()
where z; = H(E(x:)) E Rd is the fg-normalized projection of sample x; and P; indexes images that hold the same label as n, Bs.
The standard supervised cross-entropy loss is defined as:
Let
yi log P:,
(2)
Bsl
iEBs
where C(2,). The total training objective is the weighted sum of the two losses: =
Lets + Luup-
3.4 INFERENCE
As previously mentioned, in constructed dataset, split portion of the support set to form validation set, which is then used to estimate the threshold for detecting anomalous samples during the testing phase. Unlike global thresholding strategies that compute confidence thresholds based
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Published as a conference paper at ICLR 2026
on the overall distribution of all samples, we propose soft thresholding method. For any sample 2; E Dy, we define its confidence as 7 = max Softmax(p:)) For all samples of class k, we define
the mean and standard deviation of their confidence scores as follows:
MA
1 N
72
(R)
(4)
N₂
ok = 0.8
7
(k)
(5)
N
The final threshold is obtained by averaging these class-wise thresholds:
To 3 * (Me σ.) (1 B)
Yss
Ms
ok.
(6)
kEYss
Here, 3 represents the fusion ratio between class-specific and global thresholds. While global threshold may overlook certain low-confidence classes, class-specific thresholds become exces- sively noisy when the validation set is small.
The proposed method effectively mitigates distortion caused by class imbalance and inter-class variance by modeling intra-class statistical properties. It enhances the discriminative performance on known classes while maintaining strong anomaly detection capabilities. Most existing OOD de- tection methods rely on metrics such as OSCR (Dhamija et al., 2018) and H-score (Fu et al., 2020), requiring manual threshold adjustment based on specific scenarios or validation sets. As a concrete embodiment of anomaly detection in real-world scenarios, the AGE-based OCD task holds signifi- cant value advancing the deployment and practical application of anomaly detection methods.
We apply the predefined threshold to all samples in the query set Do. If sample x; has a confidence score above the threshold, is classified as belonging to a known class. Otherwise, its & no-oormalized feature representation f E(x,) is extracted and fed into the proposed real-time category discovery framework AGE. Ideally, the model should accurately distinguish known-class samples from anomalous ones. This assumption serves as crucial foundation for the validity of the subsequent category discovery process.
Wolf The Ledoit-Wolf shrinkage estimator improves covariance estimation in high- dimensional settings with limited samples by shrinking the empirical covariance matrix toward a more stable target. Given the small validation set and the incremental accumulation of samples from newly discovered classes during inference, we apply this method to enhance the robustness of co- variance estimation. For any set features {f: ) the sample mean and the unbiased estimate of the covariance matrix:
Nr belonging to the same class k. we first compute
f
Σ Edd.
S No 1--1EA
Σ - f( - -f E Rddd A=0
NE
The Ledoit-Woo covariance estimator is defined as
(Sw(S) = (1- X1 F
where F= (tr is the shrinkage target, with I denoting the identity matrix. The coefficient X the optimal shrinkage parameter that balances the contribution between the empirical covariance matrix S and the target matrix F. It computed as:
E
||
>
>
However, since the true covariance matrix Σ is not accessible, Ledoit and Wolf proposed an unbiased estimator. In practice, the optimal shrinkage coefficient computed as:
Σn
(x;
x) x) - x) S
(10)
S
FI?
For simplicity, during real-time inference on Dq. denote the Ledoit Ledoit-Wolf covariance estimate for class & as Eky- In the remainder of the paper, refer Σk simply as "variance".
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Adaptive Gaussian Expansion Assuming we have extracted features Fs UnEv' (lr D from all samples in the validation set, we first compute the mean feature vector and covariance matrix for all features, denoted {ui (42, Mpy'al J and Ean. To mitigate the imbalance caused by long-tailed distributions in covariance estimation, we adopt smoothed covariance strategy to estimate the covariance matrices for different classes:
ΣS (1 a2) Ei + Dg tEl
(11)
where Or:: Na+s denotes soft prior weight, and is introduced to prevent the covariance estima- tion from being excessively biased when the sample size small, which could lead significant performance drop. The term e serves as a numerical stability factor. As & increases, the covari- ance approaches the identity matrix, causing the model to degenerate into Fuclidean distance-based introduce a fixed-size sliding window to prevent memory consumption from growing linearly with the number of samples. The window operates in a first-in, first-out manner, such that once the number of stored samples exceeds a predefined limit, the earliest samples discarded.
model. In practice,
During the inference phase, the model continuously discovers new categories. At any given time, suppose we have set Fp = UrEy, "3 features from different discovered novel cat- egories, along with their corresponding means and covariances, which are computed according to Eq. 11. Here, Np denotes the number of novel categories discovered so far. For any feature fod identified as outlier, initialize covariance Eod Eall
Most conventional methods rely on classifiers to obtain the logit of a sample, which only reflects its relative proximity to known classes and fails capture the intra-class distribution characteristics. In contrast, classification using a multivariate Gaussian PDF explicitly estimates the mean vector and covariance matrix for each class, enabling direct computation of the generative likelihood of the sample under that class. This allows for more precise characterization of the known class distributions, thereby significantly enhancing the generalization ability and the quality of uncertainty estimation.
Under ideal conditions. for a given feature fod that does not belong any known category, the task model can be simplified to distinguishing whether it belongs to a seen or an unseen class. We argue that the feature distribution of known classes can serve as a reasonable background prior for modeling unseen classes. To theoretically support this intuition, we present the following results.
Lemma 1 shows that, after whitening. features from semantically related unseen classes C are geo- metrically closer to the training classes A than to unrelated seen-but-target classes B.
Lemma 1. Assume that the feature vectors of all classes follsw multivariate Gaussian distribution with a shared covariance matrix After applying a whitening transformation such that Σ I, the Mahalanobis distance reduces to the Euclidean distance. Let J LB PC denote the class-wise mean features of groups A, B, and C, respectively. Define the squared distances:
da = -| - -All?, da = =I -141|2
Then, under the following assumptions: 1). The encoder is trained solely on group and learns to capture its semantic structure. 2). The features of group C' align more strongly with the semantic subspace spanned by group A than by group B. i.e EHE > [..EEgg). 3). The distribution of means in group A is at least as dispersed as that in group B: Ellpal? El
follows that the expected distance satisfies E[dA] < E[dg], i.e., the expected distance between group C and the known training group A is smaller than that between C and the unrelated group B.
Building on this, Proposition further demonstrates that when the Gaussian distribution of training classes A is adopted as background model for "non-B" samples, and if the distribution of unseen class C' is closer to A, the model can more accurately classify C' samples as "non-B" in a binary decision setting (i.e., B vs. non non-B), B), thereby providing theoretical support for new class discovery.
Proposition 1. Assume that samples from classes A, B, and C in the feature space follow multi- variate Gaussian distributions with class means A, pn, and PeC, and a shared covariance matrix Σ. The label spaces of A, B, and C are disjoint. Suppose that class A is used as negative (non-B)

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Published as a conference paper at ICLR 2026
background model for open-set recognition, and samples classified as A (i.e., not B) if
(x - (A)) E- (A)= < (x 1 -BB).
Then, the Mahalanobis distance between μcc and μ.d. is smaller than that between pec and pB: (Nc - (AA) T - HA) < (nc - pB) T pB), a sample drawn from class C is more likely to be classified as A (non-B) than as B under this rule.
Under the whitening assumption of the covariance matrix, the Mahalanobis distance reduces to the Euclidean distance. Proposition provides an intuitive rationale for the OCD task, suggesting that the distribution of known classes can serve as a reasonable prior for modeling unknown classes. In practice, AGE initializes new categories using the global prior Exil and applies smoothing, which in turn approximately preserves the shared covariance assumption.
For an outlier sample fod, its probability density is computed as:
P (2T) 1 exp (-h ua) Ex 'fod -us))
(12)
In high-dimensional settings, raw PDF values can be extremely small, causing underflow errors. Using the logarithm transforms these tiny values into sums, preventing precision issues. Thus, convert the PDF to its log form:
log = (d)o)(2x) + log Dxl + (fos Ex (fod mm))
(13)
For each sample detected as an outlier, AGE first evaluates its likelihood under the multivariate Gaussian distributions of all known classes. If the sample is unlikely to belong to any known class, is treated as potential new category. Its feature is then incorporated into the set of discovered classes, with the initial covariance based the global background covariance and the class mean initialized accordingly.
To avoid numerical instability during PDF computation, we apply Principal Component Analysis (PCA) dimensionality reduction to the features during inference.
EXPERIMENTS
The proposed AGE was evaluated on several benchmark datasetss for image recognition tasks. These include the CIFAR-100 (Krizhevsky et al., 2009) dataset, the ImageNet- 100 dataset (Krizhevsky et al., 2012)), and the recently introduced Semantic Shift Benchmark datasets (Vaze et al., 2022b) which consist of the CUB-200 (Reed et al., 2016), and Stanford-Car (Krause et al., 2013). Addi- tionally, the more challenging Herbarium 2019 fine-grained classification dataset (Tan et al., 2019) was also used for evaluation. To enable more comprehensive comparison, similar to PHE, also evaluated on Pets (Parkhi et al., 2012) and iNaturalist (Van Horn et al., 2018), which includes the categories Fungi, Arachnida, Animalia, and Mollusca.
4.1 IMPLEMENTATION DETAILS
The backbone used in our experiments was ViT-B/16 (Dosovitskiy et al., 2021), pre-trained on the ImageNet dataset using the DINO self-supervised learning framework (Caron al., 2021). We used consistent training and testing settings across all datasets, with a batch size of 128, learning rate of 0.005, and a weight decay of 5e-5. The model was trained for 100 epochs. In the covariance smoothing prior, the soft parameter was set to 2, represented the relative importance of the prior covariance in the subsequent estimation of class-specific covariances. While threshold smoothing, was set to 0.5. The feature dimensionality is reduced to 42 using PCA. For validation, 20% of the training data was reserved. The sliding- window size used for covariance estimation is set to 20. We discuss the effects of these hyperparameters model performance in the ablation study and Appendix.
We compared approach with state-of-the-arr methods such DifIGRE (Liu al., 2025), PHE (Zheng et al., 2024), SMILE (Du et al., 2023), as well as adaptive approaches including SLC (Har- tigan, 1975), MLDG (Li al., 2018), RankStat (Han al., 2020), and WTA (Jia al., 2021).

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Published as a conference paper at ICLR 2026
Table 2: Comparison with the State of the Art methods. The best results are marked in bold.
CIFAR-BE 100
ImageNet-100
CUB-200
Scars
Herbarium19
Method
Old
Old
New
Old
All
Old
Old
SLC
44.4
59.0
32,9
86.6
28.6
44.0
14.0
23.0
14,9
27.4
MLDG
50.6
61.0
29.8
30.6
72.3
9.7
29.5
48.4
20.1
24.0
41,6
15.4
20.8
36.7
12.3
RankStat
35.0
44.0
17.0
31.1
73.3
9.8
21.2
26,9
18.4
14.8
19.9
12.3
13.8
20.6
10.2
52.9
30.8
72.9
21.9
26,9
24.4
14.6
21.2
SMILE
51.6
61.6
31.7
33.8
74.2
13.5
32.2
50.9
22.9
26.2
46.7
16.3
22.9
39.3
14.1
PHE
55,9
70.0
27.7
34.1
80.6
10.8
36.4
55.8
27.0
31.3
61.9
16.8
22.5
38.5
14.0
DiIGGR
54.4
36.5
27.7
48.1
AGE (Ours)
60.8
75.8
48.2
87.1
59.8
34.8
62.7
30.9
54.7
Table 3: Comparison with the State of the Art methods. The best results are marked in bold.
Fungi
Arachnida
Animalia
Mollusca
Pets
Food101
Method
All
Old
New
All
Old
New
All
Old
New
All
Old
New
All
Old
New
All
Old
New
27.7
RankStat
23.8
50..5
12.0
26.6
51.0
10.0
31.4
54.9
21.6
29.1
55.2
15.5
35.2
42.3
28.4
22.3
50.7
7.8
WTA
27.5
65.6
12.0
28.1
55.5
10.9
33.4
59.8
22.4
30.3
55.4
17.0
35.2
46.3
29.3
18.2
40.3
5.1
8.4
PHE
31.1
67.9
15.2
37.0
75.7
12.6
40.3
55.7
31.8
39.9
65.0
26.5
48.3
53.8
45.4
29.1
64.7
11.1
DITGRE
47.7
76.6
29.4
43.5
63.2
35.3
42.6
62.0
32.3
49.6
50.1
49.3
(Ours)
40.0
66.1
28.5
42.7
73.7
23,3
44.1
34.2
43,0
70.0
28.7
61.5
66.5
58.8
30.5
70.0
10.4
Specifically, SLC is an incremental clustering algorithm that sequentially processes data, assigning samples to existing clusters or creating new ones based distance threshold. RankStat deter- mines class by ranking features and using the top-3 ranked features to define class descriptors. WTA divides the feature embeddings into three groups and generates predictions based the index of the maximum activation within each group. All experiments were conducted using an NVIDIA GeForce RTX 4090 GPU.
4.2 EVALUATION PROTOCOLS
Following prior work such as PHE and OCD, we adopted only the Strct-HHungrraa protocol as the evaluation metric (Vaze et al., 2022a), which can formulated as:
Dgl
ACC
max PEP()))
1
Σ
I(y, p((,))
(14)
[QQ
where P()2) defines the optimal matching between predicted and ground-trutt truth labels for the test samples. This matching is obtained using the Hungarian algorithm, which finds the permutation that minimizes the total mismatch between predictions and true labels.
4.3 RESULTS
Here we present comprehensive comparison various methods across different datasets, high- lighting the performance of our proposed approach. As shown in Table 2, on two representative coarse-grained datasets, CIFAR-I00 and ImageNet-100, our method achieves an average improve- ment of 9.5% in overall accuracy compared to PHE (Zheng et al., 2024), demonstrating its strong advantage in general category discrimination. For fine- fine-grained datasets commonly used in GCD tasks, including CUB-200, Scars, Herbarium 19, and Pets, our method achieves an average improve- ment of 8.8% overall accuracy compared with PHE, further validating in fine-graine grained scenarios. Notably, compared to DifiGRE (Liu et al., 2025), which leverages multi- modal and generative approaches, AGE still achieves performance that is nearly comparable.
generalization ability
Importantly, these performance gains are primarily attributed to the superior ability of our method to recognize novel categories. Across the six datasets mentioned above, our method improves the accuracy novel categories by average of 16.7%. Result highlights the effectiveness of open-set detection mechanism in identifying emerging classes and demonstrates the ability the proposed AGE module leverage information from known classes accurately discover novel ones.
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Table 5: Comparison between different dimen- sionality reduction methods.
Table 4: Effects of each component.
CUB-200
ImageNet- 100
Compoment
CUB-200
ImageNet-
100
OSR
PDF
LW
Sc
All
Old
New
All
Old
New
Methods
All
Okd
New
All
Old
New
X
26.2
57.2
10.7
35.2
75.5
30.1
PCA
46.3
59.8
39.4
48.2
87.1
28.6
/
X
27.0
58.1
11.2
35.8
76.8
30.6
LDA
46.1
61.6
38.3
49.1
78.1
27.2
ICA
63.0
85.3
45.0
57.8
38.6
47.8
87.1
28.1
RP
40.1
61.9
29.2
52.2
87.1
34.7
38.8
28.6
43.7
20.9
0.1
31.1
PLS
45.4
67.9
34.2
45.0
87.1
23.9
46.3
59.8
39.4
48.2
87.1
28.6
NCA
45.2
62.8
36.4
48.7
89.0
0.6
0.3
0.7
204
0.4
62
355
6.
0.
011
Hyperro
Hyper
Figure 3: Performance with different 8,
Figure 4: Performance with different dimensions.
To further verify the robustness of our framework in complex real-world settings, conducted ex- periments on the more challenging iNaturalist dataset, with results presented Table Compared with PHE, our method achieves average improvement of 5.3% in overall accuracy, with partic- ularly strong performance on the Fungi dataset where the gain reaches 8.6%. These results further confirm the generalization capability and stability of our approach across diverse and large-scale category spaces.
ABLATION STUDY
To investigate the impact of each component in the proposed AGE frame- work, conducted series of ablation studies systematically evaluate their contributions the novel category discovery task. As shown in Table 4, the Soft Covariance plays critical role. In the early stages of real-time inference, the number of samples per class insufficient, resulting in highly unstable covariance estimation. This instability adversely affects the computation of PDF, potentially causing model instability or numerical explosion. Fig. 3 presents our investigation and analysis of the impact of soft covariance model performance, showing that the model achieves op- timal performance when = The incorporation of Ledoit- Wolf variance estimation offers a more robust covariance estimate, enhancing the capability to discover novel categories. When the OSR component is removed, the performance degrades significantly, as the known classes are treated as background, preventing the accurate identification of previously classes. This indirectly vali- dates the effectiveness of leveraging known categories as background information to facilitate the discovery of novel classes.
Effects of Components
Effects of Dimensionality Reduction Since high-dimensional density estimation is unstable due degraded covariance estimation, apply PCA to reduce feature dimensionality. Table 5 com- pares the performance of several dimensionality reduction methods, including Linear Discriminant Analysis (LDA), Independent Component Analysis (ICA), Random Projection (RP), Partial Least Squares (PLS), and Neighborhood Components Analysis (NCA). On ImageNet, RP better preserves global structure and inter-class distances due to coarse category granularity. On the fine- ane-grained CUB-200 200 dataset, however, RP may distort subtle local features, leading to poorer performance.
In Fig. investigate the impact feature dimensionality. Since numerical instability occurs in PDF computation when the dimensionality exceeds 128, we set the horizontal axis maximum to 64. As the dimensionality increases, the accuracy on ImageNet- steadily improves, whereas CUB- 200 shows rise-then-fall trend. This discrepancy mainly arises from the granularity differences between the two datasets: ImageNet-100 contains coarser categories, where higher dimensions help preserve informative features: in contrast, CUB-200, being fine- -inengaieed dataset, may suffer from increased noise or overfitting in high dimensions, leading to degraded performance.

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Published as a conference paper at ICLR 2026
Effects of Numerical Stabilization Term To evalu- ate the role of the numerical stabilization term eI in co- conducted a series of ablation studies by varying the value of & and analyzing its im- pact final performance (as shown in Table 6). Without this stabilization term, the computation of the PDF often suffers from numerical instability due to the singularity of the covariance matrix. A properly chosen stabilization term helps suppress singularity and enhances numerical stability, particularly when the sample size is small. How-
Table 6: Performance with different nu- merical stabilization term E.
variance estimation,
CUB-200
ImageNet- 100
All
Old
New
All
Old
New
1e-7
45.9
57.2
40.3
47.6
87.1
27.8
le-5
46.3
59.8
39.4
48.2
87.1
28.6
lc-4
45.8
62.6
37.4
47.1
87.1
27.0
le-3
43.4
61.7
34.2
45.3
87.1
24.2
le-2
30.9
58.8
17.0
32.7
85.3
6.2
ever, an excessively large & causes the covariance matrix to become overly diagonal-dominant, resulting in oversmoothing of the class-specific covariance structures and reducing inter-class discriminability. Consequently, the model fails to effectively cap- ture correlations among features. As increases, AGE gradually degenerates into SLC, which relies solely on feature distances for classification. When & = 1e-2, the performance closely approaches that of SLC.
Effects of Different OSR Methods We
Table 7: Performance with different OSR meth- ods.
adopt MSP combined with the proposed soft- thresholding strategy as our OSR approach. In Table 7, we report the Open Set Classification Accuracy (OSAcc) and Out-of-Distribution We further investi- gate additional OSR methods, including En- engy Score, MSP, and MSP+ for confidence estimation, and compare their AUROC and FPR TPR95. The results indicate that using FPR95 induce strong bias toward known classes, particularly on fine- fineggraied datasets. MSP+ un- der sharpened logits becomes even more challenging for distinguishing OOD samples. It is worth noting that conventional OSR evaluation metries are typically based on an optimal threshold, which ultimately requires selecting reasonable threshold. The soft-thresholding strategy proposed in this work represents an effective attempt to apply various OSR methods in practice.
CUB-200
Pets
FPR TPR95
AUROC
FPRØ TPR95 TPR8
AUROC
Accuracy (OODAcc).
76.9
63.9
82.3
Energy Score MSP:
77,7
77.9
61.5
84.3
76.1
78.4
73,3
80.0
OSAcc
OODAce
OSAcc
OODACE
MSP4Soot
75.4
74.8
70.1
60.9
Effects of Noises To evaluate the potential impact of old-class noise on Gaussian estimation and the subse- quent new-class discovery process, we include addi- tional ablation study focusing on noise injection. Specif- ically, we compare new-class prediction performance un- der three settings: (1) completely masking all old-class samples, (2) keeping the original dataset distribution un- changed, and (3) injecting simulated old-class noise into the estimation procedure. The noise samples are synthe- sized using the old-class mean and an amplified version of the global variance to intentionally increase their pertur- bation strength. As shown in Table 8, the accuracy differences across the three settings are minimal, indicating that AGE is highly robust to old-class noise and does not suffer noticeable degradation even when small amount of misrouted samples is introduced.
Table 8: Performance with different
Noises. New: Accuracy on New Classes, Est.: Estimated Number of Classes
CUB-200
Pets
Scars
New
Est.
New
Est.
New
Est.
(1)
43.5
329
64.6
93
25.2
429
(2)
43.9
401
64.2
147
25.1
634
(3)
43,2
452
78.0
169
73.3
697
CONCLUSION
In this paper, we propose novel framework called Adaptive Gaussian Expansion to address key limitations of existing On-the-fly Category Discovery methods. By decomposing the OCD task into a combination of sub-tasks and incorporating dynamic probabilistic model, AGE enables robust and real-time adaptation to emerging categories. Unlike previous approaches, the proposed frame- work allows the model to directly predict old classes their corresponding ground-truth labels, offering a more practical solution. Extensive experiments on diverse datasets demonstrate that AGE consistently outperforms prior methods, particularly in identifying novel categories.
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ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under the Grants No. 62371235 and No. U25A20444, in part by the Key Research and Development Plan of Jiangsu Province under Grant No. BE2023008-2.
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A APPENDIX
A.1 DETAILS OF DATASETS
For the experimental evaluation, the datasets were partitioned into labeled and unlabeled subsets. Specifically, for the CIFAR-100 100 dataset, 80% of the data was allocated to the labeled set Ds, while for the remaining datasets, this ratio was set 50%. The labeled data was sampled from the labeled classes, and the unlabeled data Do was formed by merging the remaining instances. As mentioned earlier, we further split 20% of the training samples as validation set to assist with anomaly detec- tion. Details of the datasets are provided in Table 9 and Table 10.
Table 9: Statistical comparison of data partitions.
CIFAR-100
ImageNet-100 100
CUB-200
Stanford-Cars
Herbarium
Ys
80
50
100
98
341
Ds
16k
25.5k
1.2k
1.6k
1.6k
Labeled
VV
80
100
341
Dv
4k
6.4k
0.3k
0.4k
7.2k
DQ
100
100
200
196
683
Unlabeled
DQ
30k
95.3k
4.5k
6. lk
25.4k
Table 10: Statistical comparison of data partitions.
Fungi
Arachnida
Animalia
Mollusea
Pets
Food101
Ds
61
28
39
47
341
51
Ds
1.5k
1.3k
1.2k
1.6k
1.9k
15.3k
Labeled
Dy
61
61
39
47
341
51
Dv
0.3k
0.3k
0.3k
0.4k
0.5k
3.8k
D/l
121
56
77
93
683
101
Unlabeled
DQl
5.8k
4.3k
5.1k
6.1k
7.0k
56.6k
A.2 EFFECTS OF VALIDATION SET PROPORTION
Regarding the proportion of validation samples, larger validation set helps estimate a more accurate covariance matrix, while larger training set is beneficial for learning better features. In Table 11, we compare the impact of different validation set proportions on performance. For the fine-graid fine-grained CUB-200 dataset, insufficient training samples lead drop in accuracy due to its limited sample size. contrast, since the Pets dataset has fewer categories, the validation split has a smaller effect on performance.
Table 11: Performance with different validation set proportion.
CUB-200
Pets
All
Old
New
All
Old
New
20%
46.3
59.8
39.4
61.5
66.5
58.8
30%
45.6
57.6
39.5
59.0
66.8
54,8
40%
43.9
56.6
37.5
61.2
67.6
57.8
50%
42.6
55.9
35,9
62.3
67.6
59.6
60%
42.2
54.1
36.2
61.1
72.2
55.3
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A.3 PROOF OF LEMMA AND PROPOSITION
Proof of Lemma 1. Since the feature space is whitened, we have Σ - I and thus the Mahalanobis distance becomes the squared Euclidean distance. Expanding the squared distance between the means in the whitened space yields:
ICc 2 = || + || - HCMA
|Cc |Bll || 2 + ||| 2 PCUB.
Taking expectations over class means in groups A and B respectively:
E E[dA]
| 2| + E uA 112 2
E| Ejdg]
||e|l* B 1|2 1u B(Bl
Subtracting the two gives:
Ejda] E[da] = (El|æøl1 Ellual??) 2 ue (B[us] Elual))
Under the stated assumptions:
me (E|na) BluB)) 0, Bll E PB 12 2 0,
which implies that
E E[dgl - E[dA] > O.
and thus
E[dA] < E[dø].
Proof of Proposition I. Let X ~ (uc, Σ) be sample from class C. The log-likelihoods under Gaussian distributions with means a and μ& (and shared covariance E) are:
log PA = - (X MA)
T (X- - MA) + const,
2
1
log Pn X) =
2 (X μB) M (X pB) + const.
Hence, the classification rule reduces comparing Mahalanobis distances:
d (X -1A)) > 1A),
dB = (X -BB) T pB).
Let Y = 1-1/2(X - mc), so that Y ~ ~N(0,) I). Define:
E 1/2 1/2 (pc MA), b= b= 1/2
( (Mc pB).
Then we can rewrite:
da I| + all?
dB Y b1p.
Thus, the condition dA < dg becomes:
Y + all Y b1l
2(b-a) Y ||a|| ||b||
Since Y ~ NO, T). the projection (b- a) TY is scalar Gaussian random variable with zero mean
and symmetric distribution. If ||a||2 < ||b||, then the threshold on the right-hand side is negative, and we have:
P(da < d = (b (b-on T 5 (Iaal - -1b1)) > 0.5.
This implies that sample from class C' is more likely be classified A (non-B) than B under the Mahalanobis distance-based decision rule.
Therefore, when MC is closer to μad than to μs in the Mahalanobis sense, using class as a non- B background model leads to a correct classification (as non-B) with probability greater than 0.5, making it a justified and effective open-set prior.
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A.4 VISUALIZATION
To better illustrate the superiority of AGE and its practical benefits, we provide t-SNE visualizations of both known and novel classes from the CUB-200 dataset. Fig. 7 depicts the feature distribution of known classes, where translucent gray points represent samples from both ground-truth novel classes and predicted novel classes. Samples with the same color correspond to the same predicted class, It is clear that our method not only accurately recognizes known classes but also yields reliable predictions. Fig- 6 presents the feature distribution of novel classes, with translucent gray points again indicating novel class samples. AGE demonstrates pronounced advantage in clustering novel samples: instances from the same predicted class form compact clusters in the feature space while maintaining clear separations from other classes. These results highlight ability to effectively dis- tinguish and structure novel class features without any prior category information, providing strong evidence of its effectiveness in novel class identification and modeling under the open-set recogni- tion setting.
(a) Ground Truth
(b) Prediction
Figure 5: The t-SNE visualization of known classes the CUB- dataset.
(a) Ground Truth
(b) Prediction
Figure 6: The t-SNE visualization of novel classes on the CUB-200 dataset.
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For intuitive visualization of how categories emerge throughout the dynamic discovery process, we plot a series of t-SNE maps on the Pets dataset continual-leariing style. (a) shows only the old classes; (b-d) illustrate the progressive emergence of new classes; (e) presents the final predictions for all newly discovered classes; (f) provides the corresponding ground truth.
(a)
(c)
(
Figure 7: The t-SNE visualization the Pets.
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A.5 EFFETCS OF B
In our experiments, we observed that using either a global threshold or per-class threshold can lead to significant bias. A global threshold may overlook certain low-confidence classes, while per- class thresholds can be excessively noisy when the validation set is small. In Fig.8, we visualized the confidence distributions for several classes CUB-200 along with thresholds under different values. The results show that the ooft-hhresholding strategy effectively mitigates such bias.
KDE of Positive vs Negative Samples
KDE Positive Negative Samples
500
Pesitive
Negative
Beta 1.0
3000
Negathve
Beta 0.5
2500
Beta 3.0
Dendity
2000
200
100
0
0.008
0.030
0.012
0.014
0.006
0.018
0.020
0.022
Value
Volue
(a) Black footed Albatross
Sooty Albatross
Positive Negative Samples
Negative Semples
Pos tive
500
Positive
600
Ncaatty
500
500
Sata 0.0
400
Densit
Dansby
500
200
100
0.008
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.008
0.010
0.002
0.014
0.016
0.018
0.020
0.022
Volue
Value
(c) Rusty Blackbird
(d) Pelagic Cormorant
Figure 8: Confidence distributions of selected classes on CUB-200
In Fig. 9, we summarize the impact different values of the fusion coefficient / on the performance of anomaly detection. The evaluation metric is the accuracy of OOD) detection, defined as the proportion of samples correctly identified as either in-distribution or
0.78
CUB-200
Scars
0.74
Herbarium 19
Accuracy
0.70
0.68
0.66
0.64
0.0
0.2
0.4
0.5
0.8
8
Figure Performance with different
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A.6 PSEUDO-CODE
To improve clarity and ensure reproducibility, we provide the pseudocode of the proposed Adaptive Gaussian Expansion (AGE) inference procedure in Algorithm 1. This offers concise summary of the key steps involved, particularly in the streaming setting where real-time category discovery is required.
Algorithm 1 Adaptive Gaussian Expansion
Input: Validation set Dv. query stream Do, encoder E, projection head H, classifier C Parameter: Threshold smoothing 3, soft prior s, stability
Output: Predicted labels Yę
1: Extract features f; = E(;;) for all x; Dv
2: Apply PCA to reduce feature dimensionality to
3: Compute class wise confidence means μ4 and stds Σg on Dv
4: Compute thresholds: т 14%: Σs. global To YY 2x
5: Final threshold: of
Tk + (1 (1- .T
6: Estimate μıx. covariance Σg for each class using Ledoit-Wol. shrinkage
7: for each query sample I; Do do
8: Extract and project feature fi PCA(E(2:)) Compute prediction p; Softmax(C(((f)))
9:
10:
if max(pi) > aarg max(p;; then
11:
Assign label arg max(p:)
12: else
Compute log-PDF's log Ps using Eq. 13 for all novel clusters if predicted as known then Create new cluster with mean f.. covariance Epricr else
14:
16:
Assign cluster k- arg max log P;: Update f4- and Σς- with Ledoit-Woll Wolf 19: end
18:
20:
end if
21:
end for
22:
return predicted labels YQ
19

---

Published as a conference paper at ICLR 2026
A.7 STABILITY ANALYSIS OF AGE
To evaluate the stability of AGE, we conducted five independent runs and reported the mean and standard deviation of the results, shown in Table 12. The results demonstrate that AGE consis- tently exhibits low variance across multiple datasets, indicating strong stability and robustness under different random initializations. AGE not only achieves higher average performance most sce- narios but also significantly reduces performance fluctuations, further validating its reliability and robustness in practical applications.
Table 12: Stability evaluation of AGE across five runs. Results are reported as mean standard deviation.
Dataset
All
Old
New
CIFAR-100
60.24::0.17
75.63+0.46
29.46:10.85
ImageNet-100
48.16:0..5
87.08+0.03
28.59:00.33
CUB-200
46.20=0.52
61.57=0.40
38.51=0.67
Scars
35.01
63.05+0.51
21.47:0.48
Pets
61.78
66.60+0.01
58.944:2.71
Herbarium 19
30.93++0.25
54.57+0008
18.20-+0.40
Fungi
39.3910.73
64.9014.44
28.08+2.60
Arachnida
43.11=0.60
73.7810.15
23,8210097
Animalia
44.33:10.44
66.78+0.18
35.03++0.58
Mollusca
43.23++0.0
69.95=10.44
29.01+0.62
Food101
30.16:10.12
69.95
9.87
A.8 COMPARISON WITH K-MEANS CLUSTERING
We further conducted comparative experiments with the classical clustering method K-means. Specifically, we directly performed clustering on all samples in the query set DQ during the infer- ence stage. Since K-means relies on the global distribution have certain advantages in specific scenarios. We report the classification performance across mul- tiple datasets and provide a comprehensive comparison with our proposed AGE method, as shown in Table 13.
all samples during inference, it may
As shown the table, K-means achieves slightly better novel class recognition performance than AGE some datasets, such as CIFAR-100 and ImageNet-100.. However, this advantage mainly stems from its dependence on global distribution information, making less suitable for online or incremental category discovery tasks. In contrast, AGE demonstrates stronger known-class reten- tion and more stable novel-class discovery performance on certain datasets, particularly exhibiting significant advantages fine-grained datasets such Herbarium 19 and Scars. This validates that AGE can achieve robust and generalizable category discovery without access to the global sample distribution.
Table 13: Comparison with the inductive K-means.
CIFAR-100 100
Image Net
CUB-200
Scars
Herbarium19
Method
All
Old
New
All
Old
New
All
Old
New
All
Old
New
All
Old
New
K-means
65.9
77.8
42,3
66.6
71.6
50
53.0
52.8
53.1
33.7
36.6
31.6
26.5
33.8
22.6
AGE
60.8
75.8
30.7
48.2
87.1
28.6
46.3
59.8
39.4
34.8
62.7
21.3
30.9
54.7
Fungi
Aruchnida
Animalia
Mollusca Old
Pets
Method
All
Old
New
All
Old
New
All
Old
New
All
New
All
Old
New
K-means
40.0
55.9
33.0
45.3
65.5
32.6
44.9
53.8
41.2
44.7
68.3
32.2
69.0
52.8
77.6
AGE (Ours)
40.0
66.1
28.5
42.7
73.7
23.3
44.1
68.3
34.2
43.0
70.0
28.7
61.5
66.5
58.8
20

---

Published as a conference paper at ICLR 2026
A.9 TIME EFFICIENCY
To compare the time complexity of AGE with that of existing methods, we measured the inference time across multiple datasets, where the reported cost for AGE includes the threshold estimation on the validation set. As shown in Table 14, AGE incurs slightly higher time cost than SMILE and PHE. yet achieves a substantial improvement in accuracy. is worth noting that AGE does not require training on the validation set during the training phase, leading to slightly reduced overall training time compared with prior methods.
Table 14: Time efficiency (seconds) of different methods.
CUB-200
Scars
Pets
ImageNet-100
Herbarium9
Fungi
SMILE
34
29
745
330
78
PHE
34
60
29
747
331
78
AGE (Ours)
37
68
32
794
368
85
A.10
EFFECTS OF TEST SAMPLE ORDERING
Since the model needs to retain information from previously observed test samples during inference, which inherently depends on their content, we compare the performance of AGE under different scenarios. In previous studies, test datasets are typically presented in an unshuffled order to better simulate real-world conditions, where novel classes often appear succession observation aligned with the locality principle in computer memory access. Table 15 presents the impact of shuffling test samples on performance, showing that AGE exhibits low sensitivity to the temporal order of data, thereby highlighting its robustness.
Table 15: Performance with different ordering.
CUB-200
Pets
All
Old
New
All
Old
New
Order
46.3
59.8
39.4
61.5
66.5
58.8
Shuffle
46.4
62.8
38.1
62.1
66.6
59.8
A.11 EFFECTS OF SLIDING- WIIDINGWWNNOWW SIZE
To examine the influence of sliding window size on model performance, we evaluate two datasets where the effect is particularly evident. As shown in Table 16, accuracy improves steadily with increasing window size, suggesting that larger window yields a more stable and reliable covariance estimation.
Aldingg-wnndow
Table 16: Performance with different window size.
CUB-200
Fungi
New
New
2
32.7
63.2
18.0
37.3
67.4
23.9
4
34.6
63.7
20.6
38.1)
66.6
25.4
8
35.2
63.1
21.7
38.6
67.3
25.6
16
35.2
62.7
21.9
39.5
67.3
27.3
32
35.3
63.1
21.9
39.9
67.3
27.9
A.12 FURTHER DISCUSSION
Compared to existing methods, the advantages of AGE are not limited to its superior performance; more importantly, it demonstrates greater practicality in real-world applications. In approaches such SMILE and PHE, identifying previously seen classes requires retrieving representative hash codes from the old class samples. However, due to the inherently sensitive nature of hash codes, these methods often suffer from low classification accuracy.
21

---

Published as a conference paper at ICLR 2026
The proposed method effectively addresses the long-standing issue of suboptimal performance in feature-level clustering approaches. By using features as unique identifiers for samples during train- ing, AGE eliminates the need for additional parameters loss terms, thereby introducing extra training computational overhead.
A.13 FUTURE WORK
The current outlier detection module in AGE adopts a relatively simple thresholding strategy and does not leverage recent advances in the Open Set Recognition domain. Future research could explore deeper integration with state-of-the-art Open Set Recognition techniques enhance outlier detection capabilities.
Moreover, under the constraint streaming data, AGE has demonstrated even higher performance than K-means on certain datasets. This suggests the potential of integrating AGE into tasks such as Novel Category Discovery and Generalized Category Discovery.
Finally, believe that incorporating language models to guide OCD can effectively alleviate the bias caused by the inherent invisibility of novel classes. Future work may consider exploring multi- modal approaches to further improve performance.
22


Reviews:
[{"review_id": "mwQigEukhr", "reviewer": "Reviewer_hjpN", "summary": "This paper analyzes OCD’s practical limits and establish a formal performance lower bound, motivating a reformulation into two sub-tasks: Open-Set Recognition and Fully Novel OCD. It introduces soft class thresholding to directly detect known classes, improving deployability, and propose Adaptive Gaussian Expansion (AGE), which models class PDFs to dynamically discover novel categories on the fly. Across multiple datasets, the proposed approach achieves state-of-the-art results.", "questions": "See weaknesses", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The problem reframing is clear. Separating known-class retention (OSR) from novel class discovery is pragmatic and improves deployability.\n2. The paper is clearly written and easy to follow.\n3. The proposed method achieves strong empirical results.", "weaknesses": "1. The lemma 1 assumes shared covariance and whitening, which may be restrictive. The link from these assumptions to the actual AGE decision process (with smoothed per-class covariances and priors) could be tightened.\n2. The soft class-wise threshold is somewhat heuristic. There is limited analysis of calibration, class imbalance, or alternative OSR baselines (e.g., energy score, MSP+temperature) for the thresholding module.\n3. The paper describes deciding “falls within existing cluster” by maximum posterior but does not specify a principled threshold or DP concentration parameter mapping for new cluster instantiation; the “CRP-like” notion is qualitative rather than a formal nonparametric Bayesian update.\n4. There're quite a lot of hyperparameters and the proposed method seems to be sensitive to hyperparameters. While some ablations are provided, key hyperparameters materially impact performance. Guidance or automatic selection strategies are limited.", "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": "", "extra_scores": {}}, {"review_id": "Rsul0Yp7jC", "reviewer": "Reviewer_NpEm", "summary": "The paper presents a novel framework called Adaptive Gaussian Expansion (AGE) for On-the-fly Category Discovery (OCD). The paper identify a performance lower bound for existing OCD methods and reformulate the task into two sub-problems: open-set recognition and fully novel OCD setting. AGE uses a probabilistic approach based on Gaussian distributions to model known and novel classes, enabling real-time classification and clustering without prior knowledge of class numbers. The method shows significant improvements over prior work across multiple benchmarks.", "questions": "1.Does the superior predictive performance on emerging categories contribute to the prediction of old categories?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. This paper establishes a theoretical lower bound for OCD, exposing the structural flaw of existing hashing methods that fail to fully exploit known-class information, and provides a rigorous benchmark for future work.  \n2. The task is decomposed into open-set recognition and novel class discovery: a threshold first filters known samples, then Gaussian clustering handles anomalies, cutting off most easy decisions early and reducing noise for the later stage.  \n3. AGE estimates per-class mean and covariance and explicitly computes membership probabilities via the multivariate Gaussian PDF, capturing intra-class shape and scatter and yielding finer uncertainty estimates along decision boundaries.", "weaknesses": "1.All samples falling below the confidence threshold are forwarded to AGE as novel candidates, yet the paper offers no mechanism to identify those that are merely low-confident members of known classes. Consequently, old-class noise is injected into the subsequent Gaussian estimation, biasing the covariance estimates and spawning spurious clusters.\n2.Key parameters in the equations are reported only as bare values without physical interpretation or selection criteria, raising the barrier to comprehension. It is recommended that all parameters appearing in the formulas be thoroughly explained.\n3.The paper lacks sufficient references to relevant research from the past three years. This undermines the persuasiveness of its argument regarding timeliness and innovation. It is recommended to supplement the study with comparative experiments and discussions involving SOTA methods published in recent years.", "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": "", "extra_scores": {}}, {"review_id": "VF6IJKXy8A", "reviewer": "Reviewer_MoeU", "summary": "This paper focuses on the On-the-Fly Category Discovery (OCD) task. The authors point out that existing OCD methods rely on hash-based encodings (e.g., PHE, SMILE), which lead to a serious overestimation of the number of categories and poor adaptability to downstream tasks. To address these issues, the authors propose: Establishing a theoretical lower bound, revealing that a closed-set classifier alone can achieve a certain level of performance; Reformulating the OCD task into two subtasks — Known Category Recognition (Open-Set Recognition, OSR) and Real-time Novel Category Discovery; Introducing the Adaptive Gaussian Expansion (AGE) framework, which enables adaptive expansion of class distributions through dynamic Gaussian modeling; Achieving significant performance improvements on multiple benchmark datasets.", "questions": "Please see the weakness.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1.\tThe paper is clearly written, well-structured, and effectively supported with figures and tables.\n2.\tThe ablation study is relatively comprehensive, verifying the effects of factors such as soft covariance, threshold β, and PCA dimensionality on the model’s performance.", "weaknesses": "1.\tThe core characteristics of OCD lie in real-time streaming input and no requirement for global access to historical data. Although the AGE method claims to be “on-the-fly,” it actually depends on a pre-trained encoder, a validation set for estimating class-specific thresholds, and the need to update means and covariance matrices whenever a new sample arrives. Does such a design—requiring continual updates of historical statistics—truly satisfy the assumption of “real-time streaming discovery”? In a continuous data stream scenario, how can its time and memory complexity remain feasible as data grows linearly?\n2.\tDoes AGE merely transfer the thresholding mechanism from the hash space to the Gaussian density space? Is there any theoretical or empirical evidence that it can control the number of discovered categories more accurately? If the threshold is chosen improperly, could it also lead to category fragmentation or under-segmentation?\n3.\tThe paper claims to distinguish known and novel samples through soft-thresholding, yet this decision relies on fixed β-based confidence statistics. If the class distribution of the validation set differs significantly from that of the test set, can the threshold remain reliable? Does this mechanism truly embody the dynamic adaptivity required by OCD, or does it only work under static distributions?\n4.\tThe paper lacks intuitive experimental visualizations to demonstrate how categories dynamically emerge during the on-the-fly discovery process.\n5.\tThe literature review is incomplete, missing several recently published related works.", "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": "", "extra_scores": {}}, {"review_id": "UU5B7BoHhE", "reviewer": "Reviewer_BgKL", "summary": "This paper studies the novel task of On-the-Fly Category Discovery (OCD), in which the model needs to perform real-time classification of potential future categories using prior knowledge. Previous methods suffer from severe overestimation of the number of categories. This paper first formally identifies a performance lower bound for the task, then decomposes OCD into two sub-tasks, i.e., Open-Set Recognition and a Fully Novel OCD setting. Specifically, this work proposes soft class thresholding and Adaptive Gaussian Expansion (AGE) for two tasks, respectively. Extensive experiments show the proposed AGE achieves remarkable performance.", "questions": "See weakness. How to guarantee the estimated threshold could generalize to test-time samples?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. This paper is well-motivated and easy to follow.\n2. Some theoretical analyses are provided to validate the proposed insights.\n3. The proposed method outperforms previous SOTA by a large margin on various datasets.\n4. Detailed ablations are conducted to validate the validity of each component.", "weaknesses": "1. How to guarantee the estimated threshold using the validation set is precise and applicable to detect outliers/new classes in test samples? The authors should provide some explanations and experimental results of the first task, i.e., open-set recognition.\n2. The writing and logic in Section 3.4 should be improved. For example, the lemma and proposition should be rearranged and interspersed with the viewpoint statement, rather than putting them all together at the end of Section 3.4.\n3. According to my understanding, the novelty of AGE mainly lies in the inference time. I was wondering whether the method consumes more computations, so the comparison of inference time between the proposed method and previous works should be provided.", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)