Boosting Open Set Recognition Performance through Modulated Representation Learning
Authors: Amit Kumar Kundu
Vaishnavi S Patil
Joseph JaJa
Venue: ICLR 2026 Poster (2026)
Keywords: Open set recognition
representation learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: This paper introduces novel temperature schedules for improved open set recognition without incurring any additional overhead.

Abstract: The open set recognition (OSR) problem aims to identify test samples from novel semantic classes that are not part of the training classes, a task that is crucial in many practical scenarios. However, the existing OSR methods use a constant scaling factor (the temperature) to the logits before applying a loss function, which hinders the model from exploring both ends of the spectrum in representation learning -- from instance-level to class-specific features. In this paper, we address this problem by enabling temperature-modulated representation learning using a set of proposed temperature schedules, including our novel negative cosine schedule. Our temperature schedules allow the model to form a coarse decision boundary at the beginning of training by focusing on fewer neighbors, and gradually prioritizing more neighbors to smooth out the rough edges. This gradual task switching leads to a richer and more generalizable representation space. While other OSR methods benefit by including regularization or auxiliary negative samples, such as with mix-up, thereby adding a significant computational overhead, our schedules can be folded into any existing OSR loss function with no overhead. We implement the novel schedule on top of a number of baselines, using cross-entropy, contrastive and the ARPL loss functions and find that it boosts both the OSR and the closed set performance in most cases, especially on the tougher semantic shift benchmarks.

Published as a conference paper at ICLR 2026
BOOSTING OPEN SET RECOGNITION PERFORMANCE THROUGH MODULATED REPRESENTATION LEARNING
Amit Kumar Kundu Vaishnavi S Patil & Joseph Jaja
Department of Electrical and Computer Engineering, 'Department of Computer Science,
è 'Institute for Health Computing
University of Maryland, College Park, MD 20742, USA {amit31 4, vspatil, joseph edu
ABSTRACT
The open set recognition (OSR) problem aims to identify test samples from novel semantic classes that not part of the training classes, task that is crucial in many practical scenarios. However, the existing OSR methods use a constant scaling factor (the temperature) to the logits before applying loss function, which hinders the model from exploring both ends of the spectrum in representation learning- from instance-level to class-specific features. In this paper, we address this problem by enabling lemperature-moduultee representation learning using a set of proposed temperature schedules, including our novel negative cosine schedule. Our temperature schedules allow the model to form coarse decision boundary at the beginning of training by focusing on fewer neighbors, and gradually prioritizing more neighbors to smooth out the rough edges. This gradual task switching leads to a richer and more generalizable representation space. While other OSR methods auxiliary negative samples, such with
benefit by including regularization mix-up, thereby adding a significant computational overhead, our schedules can be folded into any existing OSR loss function with overhead. We implement the novel schedule on top of a number of baselines, using cross-entropy, contrastive and the ARPL loss functions and find that boosts both the OSR and the closed set performance in most cases, especially on the tougher semantic shift benchmarks
INTRODUCTION
Deep learning models have shown impressive performance by learning useful representations particu- larly for tasks involving the classification of examples into categorics present the training dataset, also known the closed set. However during inference, in many practical scenarios, test samples may appear from unknown classes (termed as the open set), which were not part of the training set. Hence, more realistic task known as the open set recognition (OSR) (Scheirer et al. (2012); CCen ct al. (2020a)) aims to simultaneously flag the test samples from unknown classes while accurately classifying examples from the known classes, requiring strong generalization beyond the support of training data.
Most of the early research attempts either model the unknown classes as long-tailed distributions (Vignotto& & Engelke| 2018; Bendale & Bould (2016), generate synthetic samples using generative models (Ge et al. 2017 Neal et al.] 2018 Chen al. 2021 Moon al. 2022) or with mix-up (Chen et al. 2021 Xu et al. [223]] Li et a [024]]]02]]2n Zhou et al. (021] to represent novel classes, or train secondary model with a separate objective, such as VAEs that include reconstruction based objective (Oza & Patel (2019); Yoshihashi et al. (2019): Zhou et al. (024a)). The synthetic examples may not generalize well a variety of unknown classes, whereas training generative or secondary models with mix-up are computationally demanding and often require higher memory. Later methods add regularization (Zhou et al., [02T]] Chen et al.] 202T: 2020a) to explicitly bound the open space risks. In essence, these methods create more empty regions in the representation space by pushing the decision boundary tighter and hoping that unknown representations lie in those regions. Forcing the creation of empty spaces does not result in improved OSR as it does not address the inherent
'The project codes available at httphs///gthhhh.oo//aaaa hatpaeccoooomami11llldeeeoeeeea

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(a) T 0.5
(b)= 1.0
(c) 2.0
(d) CosSch
(g) NegCosSch when training
(c) NegCosSch at the start of (f) NegCosSch as training final period
finishes
progresses
Figure 1: UMAP projection of representation spaces for different temperature schedules on classes of the Caltech-UCSD-B Birds dataset. (a)- (c) show representations for constant temperatures (T). For lower r, the representations of unknown and known classes are distributed, leading to a sharp decision boundary. For higher 7, the representations of known classes are more compact, making the decision boundary smoother. However, unknown samples overlap with the clusters of known classes. Mid value of 7 achieves a trade-off but does not gain the benefits of both ends. (e)- (g) show representations of our temperature schedule NegCosSch as the training progresses. A lower 7 at the start leads to coarse decision and the model gradually makes the classes more compact and the unknown representations are pushed away. Finally, (d) show the representation space for a previous schedule CosSch, which is better than fixed temperatures but not as compact as NegCosSch. Clustering diagnosis appears in Appendix E. and the experiment details appear in Appendix C
semantic proximity of tougher unknown samples to the known classes, incurring significant similarity between them and reducing the effectiveness of such methods.
Vaze al. (2022) establish new OSR baselines by training models with optimal design choices and argue that a well-trained closed set classifier achieves an improved OSR performance, where the unknown samples exhibit lower max-logit scores. This essentially has motivated the generation of OSR methods to learn even better representations for improving performance through a better loss function, such the contrastive loss (Khosla et al. (2020); Chen et (2020b)) with sample mix-up (Xu et al. (2023); Verma et al. (2018) Zhang et al. (2017)) and by adding different regularization schemes (Zhou al. (2024a): Bahavan al. (2025 et al. (2025); Wang et al. (2025)).
Moreover, the regular OSR benchmarks commonly used are small in scale. In this regard, semantic shift benchmarks (SSBs) are proposed by Vaze et al. (2022) on fine-grained datasets, having more classes with varying levels of OSR difficulty. Therefore, the methods that demonstrate improvement on smaller datasets but involve either data generation, mix-up, or training secondary models are unsuitable for the larger benchmarks training well-performing base model on them requires significant compute and memory. Most of the latest research does not use these benchmarks. This necessitates the development of advanced representation learning scheme that impose minimal computational overhead.
To achieve this, need to explore the inner mechanisms of the losses that are the basis of most OSR methods, such as the cross-entropy (CE) and the contrastive loss. These loss functions compute probabilities by applying temperature scaling to the logits- the model's raw outputs- where the
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temperature coefficient adjusts the sharpness of resulting probability distributions. It is the key parameter to control the learned features for both losses. Prior works (Wang & Liu 2021| Zhang
et al. 2022 Kukleva et al. 2023 Zhang al.) 202T) demonstrate that lower temperature encourages instance-specific representations while a higher value encourages class-specific ones. However, a fixed temperature throughout the training prevents the model from exploring both ends of this learning spectrum. In this regard, Kukleva et al. (2023) study the benefits of learning both instance-level and class-specific features primarily in the closed-set scenarios using self-supervised contrastive learning for long-tailed datasets using a cosine temperature schedule (TS), but the impact of temperature scaling or TS remains largely unexamined for novel classes and for the context of different losses.
In OSR, learning a representation space that provides both instance-specifee and class-specific features also erucial to achieve improved open set and closed set performance. this research, we analyze the representation space for different temperature scaling factors on both losses in an open set scenario. Based on the analysis, we propose novel temperature schedules for temperature modulated representation learning. We find temperature modulation with the proposed schedules is beneficial to create more compact clusters for representing the closed set classes, while keeping open set examples more distant from these clusters, resulting in overall improved representations.
The main contributions of this paper are summarized as follows:
We analyze the effects of temperature scaling in open scenario, using number of TSs, including our novel negative cosine schedule (NegCosSch), to explore temperature modulated representation learning. We find that the proposed schedules, even simple linear schedules, demonstrate better open and closed set performance compared to the usual constant temperature baselines and possible other schedules.
Our schedules can be seamlessly integrated into any existing OSR loss, such the CE, the losses based on contrastive learning and the ARPL loss by Chen et al. (202T), without any computational overhead. We show significant performance improvements the TinylmageNet benchmark and the SSBs.
Our strategy demonstrates strong performance improvements for the tougher SSBs over the baselines for both the closed set and the open set problems. We show that our scheme achieves stronger improvements with an increased number of training classes when the task becomes more difficult for the baseline model.
The rest of the paper is organized as follows. In Section 2 we discuss the relevant background on different losses and in Section 3] we discuss the effect of temperature scaling on known and unknown classes. In Section ( we describe the proposed scheme. In Section 5 we discuss our results followed by related works in Section 6 and present the concluding remarks Section 7
BACKGROUND ON LOSSES
During training, the model is decomposed into two components: The first component an encoder function f(-) which maps the input æ to a representation 2 = f(x). The second component h(-) maps the representations to task specific outputs, which is either linear classification layer if we train with the CE loss or a projection layer if we use the contrastive training. The final outputs, also called the logits, 1 h22) (z)) are then given as model predictions to the loss functions. We assume for a specific problem, model is trained for predefined number of epochs E. We further discuss the CE and the supervised contrastive (SupCon) losses and the effects of the temperature parameter, which provide basis for our proposed scheme. The ARPL loss is discussed in Appendix D
2.1 CROSS-ENTER Loss
For a batch of training data B = {II,, ) the CE loss is calculated as
LCE
one hot(y,) log(pk)
(I)
B
(EB
where pk: = softmax(41./ one hot(yk) ) is the one hot encoded vector of y and (-) is the dot product. The parameter > O is called the temperature.
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2.2 SUPERVISED CONTRASTIVE Loss
For given batch B, the SupCon training utilizes a multi-viewed batch by taking two augmented
samples of the same original sample. The multi-viewed batch B' { 7. ū.)) where ズ25 and
T2k-1 are two random augmentations of 2& (1 S k S B), and 1/2k-1 122 yk- Below we refer
to as the anchor index from 1 = (1,.., 2B). The SupCon loss (Khosla et al. 2020 defined by:
(xp(sim((;,4p//r)
Cnn
Σ PEP(()
log
(2)
iE! [P())
LREA()) exp(sim (sim((, La)/))
Here, sim(44, is the cosine similarity between I, and I and A(t) I' {i} is the set of all samples in B' except i. P(i) {p + y = }p} is the set of indices in B' having the same label as y; and distinct from i. Contrastive loss, by construction, gains its strength by pushing away the representations of the negative samples (samples of other classes) and by producing compact clusters of representations for the (positive) samples of the same class.
3 EFFECT OF TEMPERATURE ON KNOWN AND UNKNOWN SAMPLES
The SupCon loss applies hard negative mining from penalizing the harder negative samples more through the exponential function (Khosla et al.] (2020)) The measure of hardness of sample with respect to an anchor is determined by the scaled similarity. Therefore as a scaling factor, the temperature plays critical role controlling the trade-off between uniformity and semantic structure in the representation space shown in Wang & Liu (202T): Kukleva et al. (2023) for the self-supervised loss (Chen et al. (2020b)) This effect mostly translates to the supervised case except for the fact that the definition of positive and negative samples are now different.
For any given anchor index i, the gradient of LsupCon with respect to a negative logit I, can be computed as shown in the following equation.
ÖL SupConn OLsupCon X 3sim(1,,,)
Osim(l;,4g 1 [softmax (a0 x Øl,
Osim(l,,4)
Øl
For smaller values of temperature т, as the differences in scaled similarity get amplified, the nearest negative samples receive the highest gradient (Wang & Liu (202I)) and the model minimizes similarity to them with respect to anchor i. The model aggressively pushes the nearest negative samples away, leading features that are appropriate for instance-level discrimination and distributing the embeddings over the representation space. However, the positive samples do not cluster tightly because, like the negative samples, fewer positive neighbors get priority in the loss function (Figure Tal. The resulting decision boundary is sharper. The open set representations do not get closer to the known classes due the heavy penalty of having slight dissimilarity.
With larger т, the differences in scaled similarity diminish and the repulsive force gets distributed more negative neighbors. The model can decrease the loss by learning the class-specific features rather than the instance discriminating features to push away easy negatives, inducing semantic structures. Due to compact clusters of within-class representations, the resulting decision boundary smoother. However, as the model is now less aggressive in removing the negatives, lot of open set examples get close to the known classes (Figure Ich.
Similarly in CE loss, lower values of temperature (T < 1) leads to a sharper output probability distribution over the training classes (Guo et al. (2017)), while the higher values of T > I makes the output probability distribution smoother.
The value of T is usually kept constant throughout the entire training for both losses, which is set either to predefined value or chosen with hyperparameter tuning.
PROPOSED METHOD
In this section, we formally introduce our problem, describe our proposed temperature modulation and explain how schedules lead to learning representations useful for OSR.
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4.1 PROBLEM DEFINITION
We are given a labeled training dataset Dtr = {(z,, vil} C X' x V. where xi is the training sample with label yt- X' is the input space and the labels of Dr, come from a closed label space D. i.c. Ys E V. Vi. The total number of classes in the closed set is C 1 The test dataset Drest C X VUO consists of samples whose label space YUO is different than y. and Ony 0. O is the set of unknown classes defined as the open set. The objective of OSR is to classify test sample among the closed set classes or to flag as belonging to an unknown class. We assume that information about the nature of unknown classes or any auxiliary samples are unavailable during training.
4.2 RATIONALE FOR TEMPERATURE SCHEDULING
For temperature dependent loss function, is usually kept constant throughout the training process. We denote constant TS by TCoas. de- fined as
Temperature Scheduling 0..7 -.I. 200
Touult - 0.25)
Towett (1r)
Tousia
0.1
TCons((e () = T, Ve
Where e the epoch number.
As discussed in Section lower temperature encourages the instance-specific representation learning, while a higher value pushes towards the class-specific features. For OSR, if the test representation from a novel class becomes too class specific, the model easily finds its similarity to one of the known classes. On the other hand, if the feature is too instance-specific the model known class. Therefore to avoid these pitfalls,
160
300
500
Figure 2: Different temperature schedules.
is under-confident in assigning any sample model needs to capture a delicate combination of both the desirable properties- good class-specific representations while having room for instance-level discriminating power within the class. Moreover, Familiarity Hyporhesis by Dietterich & Guyer (2022) states that most existing OSR methods flag semantic novelty from the absence of learned class-specific features and it recommends extract features for interesting content beyond the class-specific features for detecting novelty. If the model finds similarity between a novel sample and a known class because of the class-specific features, the mnstance-speciff features should maintain the separation between them. A constant temperature throughout the training restricts the opportunity to traverse through this trade-off and fails to achieve the benefits of both extremes, limiting the quality of final representations. Utilizing the effects observed in Section and to facilitate the traversal through the spectrum, we propose to gradually switch between the two objectives using generalized cosine schedule, which describe next.
4.3 PROPOSED TEMPERATURE SCHEDULES
Instead of a constant value, we propose schedule the temperature (replacing by T(e)) from range [T +T] ] as the training progresses using a generalized cosine schedule, which is defined as
TeCosson(E,T' -T, ,,K,
T r
( 71 + cos( 2ne kT)), if TESE- &P 2
(5)
elsewhere
where value kT represents the delay of cosine wave with respect to the starting epoch, P is the period of the wave (Figure 2) and & can be from [0, 1). k reduces Eq. (5) to the regular cosine schedule (CosSch), proposed by Kukleva et al. (2023) for the self-supervised tasks on the long-tailed datasets. With CosSch, the model starts training with a higher temperature + and goes to a lower temperature
(6) Proposed Negative Cosine Schedule. We find that rather than using Eq. (6). it is beneficial for the task switching if we start with lower temperature -- and move towards higher value +
Temnstch (e; - P)) = TTcusaaleTtt,r,PPPP
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Starting with lower temperature, the model provides priority to fewer neighbors, learning the coarse structure of representation space, resulting in a sharper decision boundary. The open set samples remain distributed and distant from any cluster of known classes (due to heavy penalization of slight dissimilarity for the lower r ). As temperature increases, the model prioritizes more neighhors and gradually pulls the positive samples its own cluster, refining on the coarse representation space. This makes within-class representations more compact and the decision boundary smoother while the core separation learned earlier is maintained. The open set samples are not pulled tightly because their features are unknown to the model, maintaining the separation. This leads to richer and potentially more generalized representation space for both open set and closed set performance.
The second half cycle (decreasing from higher to a lower temperature) facilitates the exploration by refining the model again for the instance-specific features and a smooth transition for the restart of next periodic cycle. The periodic restart can help the model to refine its first solution and find better one nearby to generalize more effectively, when tackling the challenging feature spaces. The model settles down better if the final few epochs maintain a higher temperature rather than follow the wave (epochs 500-600 in Figure 2). Figure Iillustrates the concept with UMAP projection of representation spaces for different TSs.
For = in Eq. 5), the temperature starts with a lower value and goes to higher one, looking like negative cosine wave, hence the name negative cosine schedule (NegCosSch).
,T, TNegCossane;=7.. ,T_, P) = P
Our experiments demonstrate that NegCosSch surpasses both CosSch and GCosSch (with other values of * 1) OSR performance. Although initially aimed for OSR, NegCosSch also improves closed set classification, while being applicable any model architecture and loss function, such as CE. SupCon and ARPL (Chen et al., (222)) and incurring no additional computational burden, as only includes an epoch-dependent temperature in loss function.
Choice of and Other Proposed Monotonic Schedules. We find that a single monotonic increase with the first half cycle of NegCosSch (termed as Seaottonc-NeeCosSee or M M-NegCosSch), where P = 2E, is a sufficiently competitive TS, removing the need to tune for P.
TM-NeCCoschhEiTT. (T") = + +.5((+ - - (1-co((eTT cos(co/E))):))))
(8)
Even a linear or an exponential temperature increase performs better than the baseline constant temperature. The exact formulations of these appear in Appendix [ Otherwise, P in Eq. (7) can be chosen by dividing E by the number of cycles. We denote periodic NegCosSch as P- NegCosSch. From ablation studies, we observe that varying P' or the number of cycles does not impact the performance significantly. P needs to be within functional range that allows for sufficient exploration for example, P 200 performs consistently well across the benchmarks.
Choice of (T+,T") ).). Based on our ablation studies across the datasets (Appendix E.5). we derive that for any good value of constant temperature (which can be chosen from hyperparameter tuning), using NegCosSch is more effective by setting ++ = r + A, T = T - A (or alternatively, 7+ + 7 = 7) in the SupCon loss with the increment A RJ 0.1 or 0.2. The heuristic is also structurally informed: the placement of T at the center ensures that the temperature is being varied around good operating point. A reasonable value of A is crucial because a large A may collapse the semantic structure in the representation space: the excessively low r may disrupt the initial formation of semantic structure, while the higher + may remove the necessary instance-level discrimination. For example, hyperparameter tuning on TinyImageNet provides us a high OSR performance for Tcomst with 7 = 0.2. Leveraging this, we derive that TNegConScth ( 0.4, r = 0.1) or TNogCosSch = 0.3, T 0.2) are better choices than (Cons(T = 0.2), TCossch ( 0.4, r 0.1) and TCosseh(T+ = 0.3, r = 0.2). For the CE loss, we find - = 2T, T = r/2 as a good choice because here, the temperature scales the logits instead of similarities. The derived relations allow us to bypass the necessity of explicitly tuning for both 7 and -+.
Inference. For CE loss, we the model is for inference. However for SupCon loss, we remove the projection layer and a linear classifier is trained for evaluation. We use the maximum logit based scoring rule for OSR score.

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5 RESULTS AND DISCUSSION
In this Section, we describe the benchmarks used for evaluating our method, the experiment settings followed by results and discussion.
Benchmarks. Here, we present the performance with different TSs on the TinyImageNa and the SSBs. The SSBs are defined on three fine- aree-graied datasets: the Settech-UCSD-BEEE itt al. () FGVC-Aircrafi (Krause et al. 2013) and Stanford Cars (SCars) Maji et al. (013)). For SSBs, the open set classes are divided into 'Easy' and 'Hard' splits by computing the semantic similarity (based on the labeled visual attributes) of each pair of classes, the details of which can be found in Vaze et al. (2022). The different difficulty levels along with more training classes make these datasets harder OSR benchmarks than the other ones. Most of the OSR research does not report results on the SSBs. Moreover, we report the performance of our NegCosSch on the CIFAR benchmarks- CIFARIO, CIFAR+10 and CIFAR+50- from literature with their details in the Appendix.
(CUB) Wah
Training Details. We mostly follow the experiment settings and design choices from Vaze et al. (0022). For TinylmageNet, we use VGG32-like model and for SSBs, use ResNet50 model pretrained on the places365 datase We run each experiment with 5 random seeds and report the vision transformer model in Appendix E.4
average results. We also include results
We perform ablations on P from {100, 200, 1200} and temperatures from TupConn {0.025, 0.05, 0.1, 0.2, 0.3, 0.4, for the SupCon loss. For TinylmageNet, we tune both the Toonst baseline (r = 0.2) and our schedules ((r+,- = (0.4, 0.1)) on a validation set. For SSBs, we only tune т 0.2 to optimize the constant baseline and apply the derived relationship, (Tt.T)) (0.3, 0.1). as detailed in Section 4.3 which achieves strong improvements without extensive tuning. For CE loss, with the most utilized base temperature being 1.0, we set (r*, ,T) at (0.5, 2.0). We set P = 200 for all periodic TSs and P = 2E = 1200 for M-CosSch and M-NegCosSch for consistent comparison. The training details appear in the Appendix.
Metrics. We report the closed set performance as a C-class classification using accuracy (%), the open set performance as khown-unknows detection using AUROC (%), and the area under the open set classification rate curve (OSCR %). The OSCR curve measures the trade-off between Correct Classification Rate (CCR) for known samples and False Positive Rate (FPR) for unknowns (Dhamija al. (2018)). We also implement the OpenAUC metric by Wang et al. (2022) and find that its scores are very similar to OSCR. We report OpenAUC in Appendix E.3 Now, we discuss the results.
5.1 ABLATION STUDY ON T'EMPEATURE SCHEDULES
Here, we compare the closed set and open set performance among different TSs, such as a random schedule, a linear decrease and an increase, exponential and logarithmic monotonic increases, periodic and monotonic CosSch and NegCosSch on CE loss. We present the results in Table T For most cases, our proposed TSs, such as P P-NegCosSchh M- M-NegCosSch, linear and exponential increases perform better than the constant baseline, CosSchs and other listed schedules in terms of all metrics. While the simpler schedules, such as linear and exponential increases demonstrate competitive results, in terms of a single best result across a column, P-NegCosSch wins at a maximum number (8 out of 18) of cases and M-NegCosSch wins at 4 cases. Their collective gains prove that the proposed temperature modulation scheme is fundamentally better than the constant baseline and other schedules. The standard deviations of these results across the trials are presented in Table 4 in the Appendix.
5.2 PERFORMANCE OF OUR TEMPERATURE SCHEDULES ACROSS VARIOUS Loss FUNCTIONS
Here, we report the performance on different OSR loss functions and the recent BackMix method (Wang et al. 2025) by including and without our NegCosSch in Table 2 We implement the ARPI. loss, the CF baseline by Vaze et al. (2022) and the widely implemented SupCon loss in the recent OSR literature (Xu et al., 2023; Zhou et al. 2024a). As label smoothing (LS) has shown significant performance improvements in several cases as demonstrated by Vaze et al. (2022). we experiment both with and without uniform LS, considering them as separate baselines for the CE and SupCon
'n spite of our efforts, we could not find the same pretrained model mentioned in Vaze et al. (2022) online. Therefore, we use the pretrained model from Zhou al, (2017) trained on places365, which completely unrelated to the SSBs.
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Table I: Comparison of different TSs on CE loss. For SSBs, the OSR results are shown on 'Easy/ Hard' splits. We bold the top three results for each metric and underline the best case.
Accuracy (%)
AUROC
OSCR
Accuracy (58)
AUROC
OSCR
Schodule
CUB
Aireraft
Constant (Baseline)
84.43
83.55
/74998
70.49 726.33333
90.88
90.35 88148
82.05
74.25
Lincar decrease
79.86
58.59
90.58
89.53 79.7
72.41
Random
85.06
85.02 75..54
72.28 64.32
91
62.37 90.76
82.55 75.17
84.63
/62.93
74.51
M-CosSchh
81.77
79.55/714
64.96/ 58.35
90.62
88.63 80.92
80,35 73.57
Logarithmic increase
85.15
84.91
76.07
72.25
64.82
91.19
90.86 82.58
82.77
75.47
Exponential increase (ours)
86.12
86.65 78.05
74.64/ 67.35
90.88
90.92 82.93
82.54 75.54
Lincar increase (ours)
86.22
86.
78.01
74.58 67.32
90.97
91.11 83.25
82.87 76
P-NogCosSch (ours)
67.01
76.14
M. NesCh (ours)
86.12
86.79 78.08
74.7 67.3
91.15
91.15 83.23
82,99 766
SCars
Tiyy ImageNet
Constant (Baseline)
96.76
94.03 84.82
11.04// 82.
84.55
82.85
74.74
Lincar decrease
96.25
92.51 83:47
89. 80.50.
84.12
82.64
74.28
Random
94,31
91.58
P-CosSch
96.63
93.85 84,88
90.75 82.14
84.41
83.12
74.79
M-CosSch
96.27
92.21 82.7
$8.84/ 79.73
84.19
82.76
74.36
Logarithmic increase
97.07
94.92 85.42
92. 18.18//88 83.03
84.74
82.96
74.91
Exponential increase (ours)
97.27
95.08 86.03
92.5 83:75
84.98
83.05
75.15
Lincar
97.19
95.19 86.18
92.55 83.86
84.9
83.16
PoNehCosSchh (ours)
97.3
95.03 86.05
92.49/ 83.81
84.85
83.02
75
M-NocCosSchh (ours)
97.22
95.18 86.26
92.57
84.24
82.79
74.41
losses. We aim to investigate whether our proposed TSs offer orthogonal benefits irrespective of L.S Here, we do not optimize performance for the LS coefficient and temperatures but use fixed set of hyperparameters for consistency.
We observe that including the proposed schedules (P-NegCoSSch M-NegCosSch) in any OSR loss function improves performances both for the closed set and open set problems over the corresponding constant temperature baseline for all cases except for two, such as for Aircraft on SupCon loss including LS and P-NegCoSSch, and for Tiny Imnyeneeeeet on CE loss including LS and M-NegCosSch. Our NegCosSch provides performance boost for up 1.87% of accuracy, up 3.3%/3.1 % of open set AUROC in the 'Easy'/ /'Hard' splits and up to 4.4%/3.966% of OSCR. This amount of performance boost comes without any additional computational cost. Between our two schedules, the M-NegCosSch performs better in most cases than the periodic one, demonstrating that the primary benefit for most cases derived from monotonic negative cosine increase. However, P-NegCosSch outperforms in several cases such as for CUB and Aireraft benchmarks on CE and BackMix, and for the open set metrics on TinylmageNet with ARPL and BackMix, which confirms that refining with periodicity can help achieving improved representation space depending on the data characteristics.
Moreover, our method can be used together with LS to further boost the performance in few cases (for CUB- M-NegCosSch and TinylmageNet with CE loss). Even for cases where LS does not improve the constant baseline performance (for the Stanford cars 'Hardd split and Aircraft with CE loss), our NegCosSch outperforms the corresponding baseline. In these few cases, LS may drops in OSR metrics because it leads to max-logit suppression as shown in Xia et al. (2025), which degrades the ranking of scores by assigning relatively lower max-logit on the correct known samples and higher scores for unknowns compared to the without-LS case. In spite of this, our TSs boost OSR performance even where L.S alone failed. Overall for SSBs, the CE loss performs better than SupCon loss. We believe that our scheme, in principle, can improve other OSR methods, such as the method by Jia et al. (2024).
5.3 PROPOSED SCHEDULE IS MORE BENEFICIAL WITH MORE TRAINING CLASSES
To show the strength our NegCosSch with increased number of training classes, we train models on CE loss with {20%, 40%, 60%, 80%, 100%) of the randomly chosen training classes for the SSBs without changing the open set. In Figure 3 we plot the improvement sponding baseline. defined
metric m over the corre-
improvement m [[TNegCosschl (r+, r-] max,eTes {m[ T (7)]].
Here, TcE = (0.5, 1.0, 2.03. We observe an overall upward improvement trend with more training classes in most cases for both the 'Fasy" and 'Hard' OSR splits. The negative values in Figure 3c
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Table 2: Performance on different OSR loss functions, with and without the proposed schedules. Open set results are shown on 'Easy / Hard' splits. We highlight the cases where our TS produces better results than the baseline and underline the best result for each case.
Accuracy (%)
AUROC (58)
OSCR (%)
Accuracy (%)
AUROC (S)
OSCR (8)
Loss
Schedule
CUB
Aircraft
Constant
84.43
83.55 / 74.98
/0.49/63.34
90.88
90.35 88
82.05 74.22
CE (woo LS)
M. NegCoSSchh(ou)))
86.12
86.79 78.08
74.7/67..
91.15
91.15 83,23
82,99 /66
P-NegCosSchrours)
Constant
85.53
85.15 / 777.77
72.77 66.26
90.73
86.85 79.72
78.84 72.55
CE + LS Vaze
M-NegConSchh(ours)
86.21
87.66 77.066
75.53/ /8.23
91.34
88.25 81.19
80.62 74.36
P-NegCosSchrourrs)
86.12
78.03 86,43
/
91.1
87.25
80.03
79,55 73.17
Constant
83.43
86,94
73.95
72.42/ 66 66
90.71
88.78 81.79
80.51 74.37
SupCon
M-NogCosSchrours)
85.3
88.14/ 75.81
75.09
64.72
90.45 82.49
82.57 75..51
LS)
P-NegCosSchtours)
84.12
87.5 74.95
73.54 63.13
90.61
89.27 81.97
80.96 / 74.55
Constant
83.72
86.43 /
6
90.05
88.97 81
80.11 73.88
SupCon + LS
M-NegCosSSchrouss)
85.28
88.05 75.78
74,97 64.63
90.55
89.47 81.85
80.95 74.28
P-NegCosSchrours)
84.38
75.16
73.5 63.39
90.43
81.78
80.2 74.08
ARPI al.
Chen
Constant
M-NegCosSchitours)
86.47
85.8
87.6 80.53
86.93 79.7
79.65 74.41
78.64 73.36
91.26
90.88
91.55 82.01
90.75 81.77
86.65 / 78.39
85.98 78.26
E-NegCosSchrours)
86.51
80.12 87.57
79.61 74.05
90.98
91.52/ 82.02
86.55 78.38
BackMix
Constant
82.12
82,39
72.99
67 67.94 60.32
90.53
92.41 82.44
83,75 03.75//0 75.09
Wang et
M-NegCoSch (ours)
82.84
83,97 74.66
69.71/ 62.1
91.37
84.43
84.19 77.36
2025
P-NegCoSch (ours)
83,98
84.54 74.13
71,23 62.66
91.49
92.3 83.68
84.35 / 76.72
SCars
Tiny ImageNet
Constant
84.82
91.04/82. 19
81,95
CE (w/o LS)
M-NegCosSch(ouns)
97.22
95.18 / 16.266
92.57 /83.95
81.98
79.21
69.84
P-NegCoSSch(ours)
97.3
95.03 86.05
92.49 83.81
82.23
79.05
69.91
Constant
97.05
94.67 / 84.35
91.95 82.02
84.55
82.85
74.74
M-NegCosSch(ours))
92.42
82.79
P-NegCosSchruurs)
97.23
94.82 / 84,54
92.24/ 82.31
84.85
83.02
75
SupCon (wlo
Constant
96.58
92.99 / 82.8
89.92. 80.12
85.37
82.87
70.61
M-NegCosSch(ours)
96.79
93.57 / 82,76
90.66
80.26
85.4
83.21
70.98
LS))
P-NegCosSchrours)
90.31 80.53
83.09
70.71
Constant
96.6
93.03 83.32
89.95
80.800 63
85,18
70.31
SupCon LS
M-NegCosSchrours))
96.84
93,58 / 83.15
90.69/ 80.62
85,57
83.11
71.04
P-NegCoSSchiourr)
96.69
83.29 93.45
90.43 80.66
85.23
83.05
70.72
Constant
97.37
95.22 85.89
93.46 84.7
85.02
83
74.89
M-NegCosSchtrurss)
86.03 95.25 85.71
84.82
83.07
75.03
P-NegCosSchrours)
97.21
93.47 84.52
85
83.12
75.07
Constant
96.81
93.23 84.39
90.33 /
82.32
81 233
67.1
BackMix
M-NegCoSch (ours)
97.52
94.86 / 86.48
92.56/ 84.48
82.6
81.62
67.37
P-NecCoSSch (ours)
86.04
92.31 83.89
82.5
1.5
Im prppooous vermentttt 196
improvement
Im provemeent
0.5
Accurio Bay
80
0.0
19
training classes
number training classes
number training classes
(a) CUB
(b) SCars
FGVC-Aircraft
Figure 3: Effect on performance improvement for our proposed schedule over the baselines with varying number of training classes, Increasing the number of training classes tends to yield greater improvements in OSCR across all datasets, along with significant improvements in AUROC and accuracy, with the effect being most pronounced for CUB and least for FGVC-Aircraft, Error bars represent the standard deviations across trials with random training classes
due to the fact that measure improvement the maximum of three baselines. With more training classes, the task becomes harder for the base model, which is observed by the performance decline. Nonetheless, our schedule gains higher improvement with more training classes.

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We observe that the benefits of our schedules may reduce when the number of training classes is relatively small, which also occur in the CIFAR benchmarks (discussed in Appendix E.8) The baseline performance the CIFAR benchmarks are already substantial, whereas the tougher SSBs require significant improvement, where the benefits of our proposed schedules are realized most. We leave extending temperature modulation these smaller benchmarks future work.
6 RELATED WORKS
Open Set Recognition. Since the introduction of OSR problem, it has received significant interest in the research community. Most of the research attempts can summarized into several common categories, some of which are discussed in Section I Besides the use of generative models, input mani-fold mix-up, other works add auxiliary samples with different strong augmentations for training
models (Wang al., [025 Jiang al. [2033] Jia et al. 2024) Xu & Keuper). Another huge group of research depends on training an additional model with a secondary objective function (Oza &
Patel (2019); Sun al. (2020); Perera al. (2020); Yoshihashi et al. (2019); Zhang et al. 2020);
Jia et al. (2024), Zhou et al. (0024a). However, training a generative model or a secondary VAE model is a cumbersome task on the real-life larger benchmarks it requires sigmificant computation overhead and therefore. is not practical. Moreover mix-up based methods, such as manifold mix-up can increase the amount of computation during backpropagation as the interpolation of samples occurs in hidden layer, changing the standard forward-backwer pass procedure Verma et al. 2019).
2020a Wang et al. (2022)) or add regularization to bound the open set risks (Zhou et al. (2021): Lu et al. (2022);
Another set of methods either construct different loss function (Chen al. (2021)
Yang et al. (2024a)). For example, the method by Zhou et al. (2021) learns additional place-holders for the novel classes. Methods by Chen et al. (2021: 2020a) learn the reciprocal points of known classes representing the 'otherness' corresponding to each class. These methods try to create additional empty regions in the representation space hoping that open set representations lie in those regions. The new baseline by Vaze et al. (2022) with well-trained closed set classifiers has triggered the OSR research for better representation learning schemes. For example, methods by Xu et al. (2023) ; Xu (2024);[Li [ et al. )2024); [Bahavan et al. (2025): et al. (2025) train models using the contrastive loss with regularization and heavy augmentations (Wang et al. (2025); y; [Tiang et al. (2023); ; Jia et al. (2024))
The method by Wang et al. (2024) trains multiple experts for extracting diverse representations. and Yang et al. (2024b) proposes an open set self-learning framework, which adapts the model according to the test data assuming that it is available. Furthermore, several prior works have focused on developing fine-grained OSR methods (Lang et al., 2024 Bao et al. 2023 Sun et al. 2023).
Temperature Scaling. Temperature scaling in the CE loss plays crucial role in knowledge distillation (Hinton et al.] (2015)), model calibration (Guo et al. (2017)) and so on. Since the contrastive loss has become popular for many tasks (Chen et (2020b)) Khosla et al. (2020), studies have aimed to understand its behavior. Recently, methods by Jeong et al. (2024) Qqu et al. (2024) utilize temperature cool-down in language models.
7 CONCLUSION
We develop novel temperature schedules, which can be folded into any existing OSR loss function, such as cross-entropy, contrastive or ARPL without any computational overhead. We find that starting with a lower temperature and moving towards a higher temperature results in making tighter representation clusters for the closed set classes, while the representations of the open set examples remain more distant. This process is more effective than using fixed temperature or the opposite schedule. Our proposed schedules demonstrate strong performance improvements on the regular and the tougher semantic shift benchmarks for both closed set and open set problems for some of the well-known OSR loss functions, even on top of label smoothing. The benefit of our scheme can be better realized with larger number of training classes.
ETHICS STATEMENT
Open set recognition is crucial for enhancing safety and reliability in machine learning systems operating in changing environments by detecting novel patterns. For instance, all categories of interest
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may not be represented in the training set due their rarity categories may emerge due to dynamic nature. The capability of a deep model knowing what it doesn't it know enhances trust across various critical applications.
The solution for the OSR problem yet to be improved, especially for larger datasets. Their performance depends on the semantic closeness between the known and unknown classes. Hence, the methods cannot be solely relied upon in deployment. For example, an over-sensitive OSR system can lead to a high false alarm rate.
ACKNOWLEDGMENTS
The authors would like to acknowledge the partial support provided for this work by the University of Maryland Institute for Health Computing (UM-IHC) and the University of Maryland Institute for Advanced Computer Studies (UMIACS).
REPRODUCIBILITY STATEMENT
Our implementation adheres rigorously the benchmarks, i.e., the set of known- unknown splits de- fined in the standard OSR literature, such as in Vaze et al.] (2022). For consistent comparison, we use the same experiment settings and design choices in model architecture and hyperparameters, the de- tails of which can be found in Appendix[[ Detailed information on the hardware and software utilized provided Appendix G Project codes are available at: http:///hhbbcccmm///a1111///////
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Supplementary Materials
A MONOTONIC TEMPERATURE SCHEDULES
Different monotonic TSs- such the linear, exponential, and logarithmic increases, as well as the linear decrease, over the range , r |- are listed below. Similar to our negative cosine TS, the linear and exponential schedules also start with lower value of and gradually switches the task with higher value. For random TS, we pick a random temperature from [T_,7" .++] at each epoch.
Timear T T T +
(9)
E
Texponential (e5 (eT (7 - x
)o/B
(10)
log(c)
Togurithmiic (c; T T (r* + イ x
(11)
log E
denear-decreaee (e:
x- -+ e (rt )
(12)
E
B GRADIENTS OF Loss FUNCTIONS
B.1 GRADIENT OF SUPCON Loss
For any sample E I, the gradient of LsupC'oa in Eq.
with respect to negative logit L/
b LsspOon
0
Σ
sim(l,,
4p) + log
Σ
exp(sim(1,, 1.)/T))
Øly
(1,4(),,,,)
P())
T
PEP(I)
aE/((i)
Isim(li,4)
Øl, (4))
0sim(li,4)
Zagh(ii exp(sim(l,, la)T) x Øl,
P(()
PE P()
1sim(l,,1,)
[sottmax (sim(h;;aa/mi) x
Øli
We already discussed this in Section Similarly, the gradient of Lsuppcon with respect to positive logit l
0 LL 01,
Osim(li,4g)
7[P(1)) (P(()) (at
Ö1,
To push the gradient towards O, value the softmax function should approach towards [P(]] For large value of r, this is possible when all negatives are far away than the positives, to have minimum effects in the denominator of softmax function. Moreover, the differences of scaled similarities between anchor and the positives diminish, inducing the class-specific features.
B.2 GRADIENT OF CE LOss
The gradient of LCE with respect to the logit of output node corresponding to the true label of sample k.
OLCE ④ log 04.
exp(lk.j/7)
Ø4g E. cxp(14,/7) (40/)a -
For small the differences of scaled logits will be amplified, and the softmax will approach towards an indicator function. The same softmax value in this gradient term computes the probability for the output node of the true class which will approach towards 1.0. Therefore. the resulting probability distribution is sharper. For large r, the differences of scaled logits will diminish, and the softmax will approach towards 1 1/C, making the resulting probability distribution smoother.
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C TRAINING DETAILS
Benchmarks. There are known-unknown random splits defined in the regular OSR benchmarks. We consider 4 regular benchmarks, such as the CIFARIO, CIFAR+10. CIFAR+50 and the TinylmageNet benchmarks. The CIFARIO benchmark has closed set classes and 4 open set classes, whereas CIFAR+10 10 and CIFAR+50 have 4 closed set classes from the CIFARIO dataset and 10 and 50 open set classes from CIFARI 10 dataset respectively. TinylmageNet has 20 training classes and 180 closed set classes. The SSBs are defined with 50% of the classes in training and rest 50% classes are divided into 'Easy", 'Medium' and 'Hard' splits. Similar to Vaze et al. (2022), we combine the 'Medium' and 'Hard' splits to report as the 'Hard' split in our paper. For each split, different random seeds and we report average results.
each experiment with 5
Model Architecture. We follow experimental settings similar to the existing literature, such in Vaze et al. (022)). For the regular benchmarks, we train VGG32-like models from seratch and for the SSBs, train ResNet50 models pretrained the places365 dataset for supervised task. The feature dimensions are 128 and 2048 for the regular benchmarks and the SSBs respectively. The linear projection layer for SupCon training has the same number of input and output nodes as the feature dimension.
Hyperparameters. We train all models for 600 epochs with the SGD optimizer with a momentum of 0.9 and a weight decay of 10-4 - We use cosine learning rate scheduler with warm-ups and 2 restarts the 200-th and 400-th epoch. The initial learning rate set to 0.1 for the CIFAR benchmarks and 0.001 for the SSBs. For TinylmageNet,, it is set to 0.01 for the CE loss and we tune it to 0.05 for the SupCon loss. Rand-Augment is used for data augmentations in all cases. While tuning, we select the hyperparameters by maximizing the closed-set performance on a validation set. The validation set is constructed by holding out 20% random training data from one known-unknown split. Batch size is set to 128 for the regular benchmarks. For the SSBs, the batch size is set to 12 as only this amount can be accommodated in our single GPU for each experiment in the SupCon training. The images are resized to 32 32, 64 x 64, and 448 x 448 respectively for the CIFAR, the TinyImageNet benchmarks and the SSBs.
Label Smoothing. For Tinylmage and the SSB datasets, report results both including and without uniform LS as LS has shown improvements for these datasets. For the CE loss, we choose the I.S coefficients from Vaze et al. (2022). For LS in SupCon loss, we implement the following function instead of
LSC.L= =
1
Σ
Σ
1 (1-a)]] x + + Ho Ni(a)
Maaalll
log Σ Eae/M exp(sim 24, 2 //T
exp(sim Zi, 2;)/T)
[2|
SET JEN()
(13)
a)1 w= + عー 1 vull where is the smoothing coefficient and 1 is the indicator function. For contrastive loss, tune from {0.1, 0.2, 0.3); however, a = 0.2 in Table 2 for consistent comparison.
with ((a))=Eel))
We randomly choose 10 training classes from the defined closed set of the CUB benchmark and keep the open set as it is. We train models with constant temperatures of 0.5, 1.0, 2.0, TCossch (r+ = 2.0, -- 0.5) and our TNegCosSch(7" and without LS. To show the training progress in our method, we plot the features at the beginning. the middle and the end of the last scheduling period starting at epoch 400. We standardize the features by subtracting the mean and scaling them to unit variance before applying UMAP transformation. For clear visualization, we plot features of all the closed set samples and 10% random open set samples.
Details for the UMAPs in Figure 1.
2.0, -- 0.5) with CE loss
D DISCUSSIONS ON THE ADVERSARIAL RECIPROCAL POINT LEARNING
The adversarial reciprocal point learning (ARPL) method (Chen et al. 2021) defines a reciprocal point for each category c, denoted by Ter which is regarded as the latent representation of the 'otherness' corresponding to each class. The reciprocal points CC are learnable parameters. Given a logit 4 f(x;) and reciprocal point r., their distance d(1,, r') calculated by combining the Euclidean
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distance and the dot product as the following:
delli, re) 1114. rell2, dal4,re) =4 ra d(li, = doll. rell)
D is the number of feature dimension in l. The final classification probability is calculated as: exp(d((;,
plu = c/a (re)m-1)
_ exp(d((;,Tmm/T)
The total loss calculated as
LRRPL -log ply; c/2,, (reler)) + f:
(
(14)
We observe that the distance is also scaled with the temperature parameter (r) in this loss. X is to adjust the trade-off between the two loss terms and set to 0.1 and, I the learnable margin parameter.
E ADDITIONAL RESULTS
Here, we discuss the performance variability of the proposed TSs, ablation studies on (T",T") and k; some results on a vision transformer model, and performance on the CIFAR benchmarks.
Table Representation space geometry analysis. Metrics measure cluster quality (intra-class and inter-class scatter) and average distance from the unknown samples to the nearest prototype of known classes. NegCosSch achieves competitive inter-class separability and the highest average distance from unknown samples nearest prototype, demonstrating that our proposed schedule learns improved representation space geometry for both the tasks.
CUB
SCars
Schedule
intra-class scatter (L)
inter-class margin (f)
unknowas' dis- lance to nearest
intra-class scatter (J)
inter-class margin (1)
unknowns' dis- lance to nearest
protetype (f)
prototype (1)
Const. (r 0.5)
0.1463
0.5503
0.4172
0,0819
0.6587
0.3869
Const. 2.0)
0,1252
0.7805
0.3974
0.0609
0.9129
0.3797
Const. (r 1.0)
0.1349
0.6586
0.41
0.0754
0.7923
0.3814
P-CosSch
0.1287
0.6832
0,4037
0.072
0.8127
0,3826
P.NegCosSch
0.1318
0.7741
0.423
0.068
0.3951
0.4002
E. REPRESENTATION SPACE ANALYSIS WITH GEOMETRIC PROPERTIES
To strengthen our claim that the proposed schedules improve the overall representation learning, conduct a quantitative diagnosis to analyze the learned space with the following geometric properties- intra and inter-class scatter, and the average distance from unknown samples to the nearest prototype of known classes, which are defined as
intra-class scatter
Σ
||
Pell2
7p
(z.EZ. (y:=)
inter-class margin
lle - -yll
j=1,ت
distance of unknowns to nearest prototype
Σ
|| - -Pol Isecc
min
Zu
2 EZ
Where, Zy and Z, is the set known and unknown representations respectively and Pe is the prototype for class The metries reported in Table We observe that lower temperature achieves a higher intra-class scatter and a lower inter-class margin (as encouraged by the instance- specific learning), indicating poor separation. It also achieves higher average distance from
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Table Performance standard deviation of different TSs on CE loss across various seeds.
Accuracy (%)
AUROC (%)
OSCR (%)
Accuracy (%)
AUROC (%)
OSCR (%)
TS
CUB
Aireraft
Const. (Baseline)
0.2
0.26/0.26
0.41/0.3 0.37
0.39
0.77 /0.52
0,42/0.47
Lincar decrease
0.78
0.35/ 1.02
0.76/ 1.03
0,29
0.42 /..53
0.46 0.46/0.58 70.56
Random
P.CosSch
0.42
0.59
0.6 0.7
0.31
0,74/0.27
0,85 00.3
0.63
0.32
0.85
Logarithmic increase
0.12
0.39/ 0.48
0.39/0.44 0.46
0.32
0,34 /0.49
0,53 /0.45
Exponential increase (ours)
0.2
0.28 0.18
0.15
0.27
0.26 0.26/0.54
0.12/0,54
Lincar increase (ours)
0.19
0.25
0.29
0.12/0.56
0.23 /0.73
PoNecCosSch (ours)
0.47
0.38 0.23
0.34 0.4
0,34
0.25 /0.43
0.26 0.26/0.5
MosNeCCoSchh (ours)
SCars
TiyyImageNet
Const. (Baselinc)
0.1
0.52 0..49
0.51 0.51/0.55 0.55
0,25
0.24
0.21
Linear decrease
0.76
0.9/0.88
Random
0.1
0,5 0.79
/
0.19
1.23
1.1
0.55/ 0.96
M-CosSch
0.13
0.66
0.61 0..59
0.1
0,32
0,28
Logarithmic increase
0.15
0.56
0.41 00.67
0.28
0.33
Exponential increase (ours)
0.1
0.55
0.6/
0.12
0.2
0,22
Lincar increase (ours)
0.1
0.23/0.53
0.27/ 0.58
0.24
0.32
0.37
PoNegCosSch (ours)
M. NeseShh (ours)
0.09
0.22/0.51
0.26/ 0.55
0.15
0.22
0.19
unknown samples the nearest class prototype, which desirable property for better OSR. higher temperature achieves the opposite, resulting from the class-specific learning, indicating a better closed set separation. mid value achieves a trade-off in terms these geometric properties, while our proposed schedule (P-NeCCoSSch) successfully achieves necessary combination from both the extremes - lower intra-class seatter, higher inter-class margin and a higher average distance from unknowns to prototypes. This structural superiority confirms that our schedule better utilizes the entire representation space.
E.2 PERFORMANCE VARIABILITY
Here, present the standard deviations of performance metries across trials with 5 different seeds. Tables f and present the standard deviations for the performance results reported in Tables and 2. respectively. The proposed TSs demonstrate either better similar standard deviation compared to the baseline and the other TSs (presented Table 4) and for all losses (presented in Table considering the significant performance boost achieved by our proposed ones.
Statistical Significance Test. We perform one-sided non-parametric Wilcoxon rank tests to evaluate the statistical significance of improvements for CE and SupCon losses in Table 2 We test the hypothesis that our proposed schedules achieve higher performance than the corresponding constant temperature baseline. The resulting p-values are presented in the table In the majority of cases, our schedules achieve the minimum possible p-value (p 0.03125), indicating a consistent improvement across all trials. Even cases with slightly higher p-values, our schedule surpasses the baseline in the majority of trials. We underline the only two instances where our schedule does not outperform baseline and a higher p-value expected.
E.3 IMPACT OF DIFFERENT INFERENCE SCORING RULES
To test the robustness. we evaluate our schedules across multiple other OSR scoring rules, such as the energy score (Liu al. 2020), ODIN (Liang af., 2017). Cosine-margel margin (Deng al., (019). max-logit, confidence (or max- nax-probabillity) and OpenAUC LUCCWan (Wang et al. 2022) scores. While the OSCR curve measures the trade-off between CCR and FPR across all thresholds, the OpenAUC is simplified threshold-free ranking score that can be expressed as the sum of pair-wise loss terms and
removes the need to calculate the numerical integral with histograms. The results presented in Table
7 confirm that TSs outperform the baseline in the majority of cases, irrespective of the scoring rule used. The improved representations learned through our schedules confirm that the performance benefits are transferable across different scoring rules.
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Table Performance standard deviation of constant baseline and our NegCosSch on different losses across various seeds.
Accuracy (%)
OSCR
Accuracy
AUROC
OSCR
Loss
Schedule
Aircraft
Constant
0.2
0.26/0.26
0.41 70.37
0.39
0.77 /0.52
0,2/0..0
LS)
M-NegCosSchrrours)
0.44/0.22 /0228
0.670.45
0.31
0.15/ 1.547
0.26/0.3
P. )-NeeCosSchtours)
0.47
0.38 / 0.23
0.34/0.4
0.34
0.25 00.3
0..5/0.5
Constant
0.14
0.58/ /034
0,2/
0.16
0.27 /0.54
0.19
M-NegConsSchtours)
0.34
0.59/ / 0.36
0.59 0.38
0.26
0.58 0.29
0.54/ 0.18
P-NogCosSchroous))
0.22
0.77 /0.31
0.44
0.25
0.77 0.22
SupCon (wlo
Constant
0:23
0.35/0.23
1.79 /0.53
M-NegCosSchiours)
0.28
0.18/ 0.38
0.34/
0.28
0.38 / 0.24
0.39 0.34
(-NegCosSchhtours)
0.21
0.13 0.31
0,26 0.35
1.08
1.37 0.55
2,07 1.18
Constant
0.2
0,24/0,32
0.44/0.38
0.69
1.03 00.55
1.35 / 0.85
SupCon
M-NegCosSSchrours))
/.117
P. NeggCosSchioours
0.32
0.62 0.62 0.4
0.78 0.57
0.53
1.77 /044
1.82 / 0.51
Constant
0.17
0.55 0.56
0.37 0.47
0.46
0.47 0.56
0.41 0.58
hen
M NegCosSchitours)
0.19
0.85 /0.42
0.54 0.26
0.42
0.559
0.67 0.51
al. 2021
P-NooCosSchroous)
0.87/0.45
0.4
0.47
0.63
0.62
SCars
TinyImageNet
Constant
0.1
0.52/ / 0.49
0.51 /0.52
0.2
0.21
0.23
LS)
M-NecConSch(ours) P-NecCosSchrouns)
0.09
0:22 /0511
0.25/0.55
0.27
0.27
0.32
0.1
0.29 0.66
0,21 0.59
0.38
0.32
0.4
Constant
0.1
0.26/ 0.22
0.25 /.22
0.25
0.24
0.21
+
M-NegCosSchrours)
0.33/0.29 0.33
0.15
0.19
ScNhoorsSchtoour)
0.14
0.26/0..
0.34/0.31
0.29
0.37
0.36
Constant
0.12/0.45
0.25/0.39
0.18
0.17
LS)
SupCon
(wlp
M: M-NecCCssSch(ours))
0.15
0,18 0011
0,18/
0.2
0.04
0.15
NegCosSchhtours)
0.2/
0.2/0.32
Constant
0.06
0..3
0.19
0.25
0.16
0.27
SupCon LS
M-NegCosSchrours)
0.1
0.2/0.38
0.23/0.33
0.16
0.09
P-NegCosSChiourr))
0.05
0.19/0.25
0.19/0.25
0.15
0.12
0.14
Constant
0.47
0.08 0.992
0.27 0,79
0.1
0.13
0.12
ARPL
M-Neg(ooSSchrours)
0.34
0.1
0.07 /037
0.37
0.29
0.24
S.NhoursS)hiourr)
0.19
0.12/0.67
0.18/0.7
0.17
0.25
0.17
Table 6: p-values from one-sided Wilcoxon rank tests comparing the proposed schedules to the baseline over random trials. A p-value of 0.031 indicates the proposed schedule outperforms the baseline in all 5 trials. We underline the only two instances where our schedule does not outperform the baseline and higher p- v-value expected.
Accuracy (%)
AUROC(%)
OSCR (%)
Accuracy (%)
AUROC (%)
OSCR (%)
Loss
comparing schedule
CUB
Aireraft
CF
M-NegCosSch P-NegCosSch
0.03
0.03 /0.03
0,03/0.00
0.09
0.03 0.03
0.03
0.03
0.03 /0.00
0.03 /0.03
0.03
0.03 / 0.03
0.03/0.03
SupCon
M. M-NeyCosSch
0.03
0.03 0.03/0.00
/0.03
0..03
0.03
0.06 / 0.06
0.06/0.06
P-NegCosSch
0.03
0.03/0
0.03
0.19
0.15/0.15
0.31/
Sears
Tiny ImageNet
CE
M- M-NegCosSch
0.03
0.03 / 0.03
/
0.15
0.15
0.03
NegeCoshh
0.03
SupCon
M-NegCosSch
0.09
0.03 0.59
0.03 0.21
0.15
0.03
P-NegCosSch
0.31
0.06/0 0.15
0.94
0.03
0.31
E.4 PERFORMANCE ON VISION TRANSFORMER
We evaluate our proposed NegCosSch on SSBs using tiny vision transformer (ViT) Ww et al. 2022) to demonstrate the robustness and general applicability of our schedules across the contemporary ViT architectures, with the results are presented in Table & The improvements observed in this table confirm the benefits of temperature modulation when integrated into transformer backbone. The
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Table 7: Evaluation of robustness to different open-set scoring rules. Our proposed schedules maintain a performance improvement across all tested scoring rules for the majority of the cases.
AUROC Energy
OpenAUC Max-Iogit
scoring nule
Max-logie
Max Max-proh. proh.
ODIN
cosine head
Loss
schedule
CUB
CE
Constant
$3.55/74.98
83.81 78.05
83.11 / 74.19
83.17
85.33 76.26
63.5
M- MoNeeChuSch (ours)
86.79 78.08
86.43 / 80
87.21 78,18
87.6/77.6 77.38
88.05 78.86
74.71 77.31/67.31
P.NeyCoSch (ours)
86
86.91
87.04/ 76.71
78.47
74.9 67.01
SupCon
Constant
86.94/ 73,95
86.48 76.35
86.05 (72.57
86.75 73.2
86.57
76.24
72.42/ 61.67
M-NegCoSehh (ours)
88.14/75.M
87.82/ 77.27
87.56 74.35
88.21 / 74.81
88.66
78.34
75.1 / 64.73
P-NegCoSch (ours)
87.5 74,95
87.3/76.78
87.05 73:75
18.69 / 74.33
87.9 77.69
73.55 / 63.14
Aircraft
CF
Constant
90.35 81.48
84.96 81.53
87.63 /81 .55
87.3/ 79.64
85.05 80
82,05 / 74,26
M-NegCooSch (ours)
91.15/ 83.23
88,34/80 82.18
92.19 84.67
92.64 84,5
89,26 83.42
83/ 76,01
P-NchCoSchh (ours)
83.15
85.24/
86.56 81.12
83.44/ 76.15
SupCon
Constant
81.79
84,59/ 80.66
85 85.96/
84 80.5
84.1 1808 79
80,52/ 74,39
M-NegCooShh (ours)
90.45 82,49
90.55 82.3
90.84/ 82244
91.14/ / 82.37
91.33 81.93
82.57 / 75.52
P-NegCuSch (surs)
89.27 81.97
86.29 / 81.27
87.11 /8144
87.43 80.97
85.48 181.55
80.97 74.56
SCars
CE
Constant
94.03 84,82
93.82/ 84,99
93.04 / 84,2
92.89/ 83,93
93.49 84, 16
91,05 82.2
M. NeNeSShh (ours)
95.18 86.26
94.84/ 83.58
95.14 84.86
95.15 84.8
94.78
84.41
92.57 83.96
P-NegCoSch (ours)
95.03/ 86.05
94.59 85.68
94.55 86.18
94,49 86.
94.28 $5.4
92.5 / 83.82
SupCon
Constant
92.41
82.85
/3.57
89,93 80,13
M-NegCooch (ours)
93.57 82,76
94.34 83,1
93.39 / 82.26
93.88 / 82.56
95.1 /83.55
90.67 80.27
P-NegCoSch (ours)
93.32/ 83.16
93.73 / 83.39
92.72. 82.56
93.23 82,9
94.13 82.84
90.32/ 80.54
TinyImageNet
CE
Constant
78.6
79.59
80.95
78.39
80.
69.23
M-NegCooch (ours)
79.21
78.11
81.19
78.09
80.44
P-NogCoSch (ours)
79.05
77.65
81,09
78.08
80,37
69.92
SupCon
Constant
82.87
83.05
82.93
80.
81.
70.63
M. NegCoSch (ours)
83.21
82.99
83.11
80.2
81.49
70.9
PoNecCoSch (ours)
83.09
82.9
83.05
$1.42
results in the table, along with previous results from VGG and ResNet-based architectures, confirm the applicability our proposed TSs across a diverse range model architectures.
Table 8: Performance on SSBs with tiny ViT architecture.
CUB
Aircraft
SCars
method
Acc. (%) AUROC
OSCR (S) Acc. (%)
AUROC (S)
OSCR
Acc. (%)
AUROC (3)
OSCR (%)
Const. (basetine)
77.82 08
95.62
92.5 83.67
88.54/
M. NegCosSch (ouns)
91.07 92.06/ / 80.67 83.79 /3.51
88.51
89/78.78
79.12/70.41
95.8
93.1/83
89, 89.28/79661
P-NegCosSch (nurs)
91.2 / /7303
88.65/79.68
79.12/71.46
96.03
93.08/83.08
89.47/79.9
E.5 ABLATIONS ON (Tt,T
Figure presents the OSR performance of our NegCosSch along with the regular cosine TS and constant temperatures in SupCon loss on the regular benchmarks, We vary (7+, TT from T SupCoon and compare TNegCussch(T* ,P) with Tct P), Te (T nearest 1 17 +
and
Teons(( r-), ). The objective of the quadruplet wise comparisons is determine our proposed TS outperforms a regular cosine TS, a constant temperature set to the midpoint of (r+ ",, or set to
T- with various pairs of (7+, ; -)) We observe that for the CIFARIO. CIFAR+10 and TinyImageNet benchmarks, our proposed TS yields better open set AUROC than CosSch and constant temperatures for most of the quadruplet comparisons. We find the improvements or degradations to insignificant
for the CIFAR+50 benchmark with the highest AUROC found for Tcosseh (0.3, 0.1). By observing the
best performances of our NegCosSch, we formulate the strategy mention in Section for choosing (T))
'By 'nearest', we mean nearest temperature is chosen from TupCoon
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83,00
AUROC (%)
82.75
AUROC (%)
95.0
82.25
Conntfr f(f
Loratf
77
Nestosclls
Coddehir
93.8
Contl/
Conal-
Cos
82.00
(0.2. 0.055
(03. (02, 0.3)
(033 (..
(04, 0.)
(04. 0.3)
(04, 0.2)
0.)
(05, 0.3)
(0.1. 0.00555)
10 0.)
(0 025)
(0.2. 0.055
(02. 0.))
(.13.0.)
0.1)
(0.3.02)
(0.3 0.2)
(04.0.1)
(04. 0.1)
(04.
105.
Temperature
Temparature range
(a) TinyImageNet
(b) CIFARIO
08.30
97.1
AUROC (%)
AUROC (%)
08.20
96.9
98.15
Coeatr
++
Cosmitt
Conal-
30
Coeatf
Conaf
08.05
(0.2. (0.2.0.08) 0.05)
(0.3, 0.1)
(04.0.1) 0.1)
(04, 0.1)
(04, (04.02)
(05, (05.0.1)
(05, 0.3)
(06, 0.4)
(0.6 0.)
98.7
(0.2. 0.05)
(03. (03.01)
(04, (04,
(04, (04,03)
(0.5. 0.1)
(0.5, (05.0.3) 0.3)
0.4)
(0.6, 05)
(00.
Temperature range
Temperature range
(c) CIFAR+10
(d) CIFAR+50
Figure 4: Open Set AUROC of different TSs for the SupCon loss on the regular OSR benchmarks.
E.6 ABLATIONS ON P AND i IN TecosScu
We perform an ablation study on P TNegCosSch using TinyImageNet with the SupCon loss for different pairs of (r+, (-) and the open set AUROC are presented in Table 9 We observe that different choices of produce similar OSR performance.
We also compare the open set AUROC TinylmageNet among different values of in ToCosSch- The temperatures are set to: 7* = 0.4 and - = 0.1. From Table 10 we observe that the open AUROC increases with the value of k; with the highest AUROC observed for NegCosSch.
Table 10: Open set AUROC on TinylmageNet for different values of k in TGCosSch-
Table 9: Open set AUROC (%) on TinyImageNet for different values of P in TNegCosSch-
Schedule
AUROC (%)
(r+,r7) P+
100
200
Tocusa Teusa
(0.3,0.2)
83.10
83.03
Tocossa (k 0.25)
82.93
(0.4.0.1)
82.91
83.09
Tocodias (k 0.50)
82.99
(0.4.0.2)
Tre 0.75)
83.03
Tacesaakk = 1) or Thestwshh
83.09
E.7 PERFORMANCE PROTOTYPICAL CONTRASTIVE LEARNING
We also show results with NegCosSch TinylmageNet and Aircraft using the prototypical contrastive (ProtoCon) learning in Table II The ProtoCon loss is recently used by Bahavan et al. (2025 Li al. (2025) for OSR. We observe improvements for all three metrics.
In ProtoCon, instead of contrasting an anchor representation with another sample, we contrast with the prototypes of known classes. We randomly initialize one prototype per known class {p]] The loss function forces all representations the same class to lie near its prototype and to move away from other prototypes, which is given
exp(sim(4, P/.)/T)
LprotoCon -
Σ log
(15)
ie! c=1 exp(sim(1:: (l.T))/TT)
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Published as a conference paper at ICLR 2026
We update the prototypes the fly at each iteration t. a is the learning rate for prototypes.
Ve-1 P2
K E 1: iJ c =0
(16)
| (1-o)1e RiElye-c
E
=o 4,
otherwise
Table 11: Performance using prototypical contrastive learning
TinyImageNet AUROC (%)
Aircraft AUROC (%)
TS
Accuracy (%)
OSCR (%)
Accuracy (%)
OSCR (%)
Const (baseline) NegCosSch
85.36
82.79
70.53
86.29
84.32/ 78.46 84.93 / 79.01
72.28/ /2.28/68.26
85.72
83.04
71.12
87.03
73.29 / 66.33
E.8 PERFORMANCE THE CIFAR BENCHMARKS
Here, we evaluate our periodic NegCosSch using the SupCon loss on the CIFAR benchmarks such as CIFARIO, CIFAR+10 and CIFAR+50 and the results are presented Table [2] The values of T for TConst are chosen as 0.05, 0.5, and 0.4 respectively with hyperparameter tuning for the CIFARIO, CI and CIFAR+50 benchmarks and the values of (r+,T") in our TS are (0.2, 0.05), (0.4,0.1) 0.1), and (0.5, 0.3) respectively. We observe that the closed set accuracy is similar to the baseline methods when we include our TS on these benchmarks, whereas we gain slight improvements in the open performance. The open set performance depends on the nature of the unknown classes and their semantic similarity with the known classes. We suspect that the benefits of our TS reduce when the number of training classes is relatively small, which occur in the CIFAR benchmarks. For example, there are only 6 training classes in CIFAR10 10 and 4 training classes in the CIFAR+10 and CIFAR+50 benchmarks. Moreover, the OSR AUROC on the CIFAR+10 10 and CIFAR+50 benchmarks are > 97% with tuned constant temperature baselines, leaving only a little scope for improvements. However, as mentioned before, we observe significant improvements both for the open set and closed set performance on the TinylmageNet and the SSBs, where they have larger number of training classes.
Table 12: Closed set accuracy, open set AUROC and OSCR (in %) for the SupCon baseline without and including the proposed NegCosSch on the CIFAR benchmarks.
CIFARIO
CIFAR+10
CIFAR+50
Mathods
Accurncy
AUROC
OSCR
Acouracy
AUROC
OSCR
Accurney
AUROC
OSCR
Consi, (Baseline)
94.04
96.32 96.33
95.21 97.03
NegCosSch (ours)
96.91
94,10
91.18
98.02
98.28
98.10
95.17
F RELATED WORKS (CONTINUED)
Here, we discuss the recent OSR methods in details. Wang et al. (0244) propose to extract diverse features from multiple experts with an attention diversity regularization ensure the attention maps are mutually different. Zhou et al. (2024a) propose a framework with contrastive training for classification and implement an additional VAE for reconstruction to compute an unknown score based on intermediate features. Yang et al. (2024b) propose a self-learning framework for test time adaptation.
Another line of work utilizes data augmentation. For example, Jia et al. (2024) propose asymmetric distillation to feed the teacher model with extra data through augmentation, filtering out the wrong prediction from the teacher model and assigning a revised label to them to train the student model. The method in Wang et al. (2025) augments the dataset by mixing the foreground of images with different backgrounds. Xu & Keuper propose new data augmentation with the help of visual explanation techniques, such as the LayerGAM to mask out the activated areas so that models can learn beyond the discriminative features.
The other methods are based on contrastive learning with different regularization. For example, Xu al. 2023); Li et al. 2024) train models with contrastive loss, sample mix up and label smoothing
22

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Published as a conference paper at ICLR 2026
for better representation learning. [Bahavan et al. (2025) also propose prototypical contrastive loss to pull all samples to its class prototype and push away the prototypes of other classes. Li et al. (2025) propose regularization inspired from the neural collapse perspective - the closed set classes are aligned with a simplex equiangular tight frame geometric structure. Recent works by /Zhou al. (2024b); Hua et al. (2025) introduce open world prompt tuning methods that improve vision language model's performance in an open-world scenario to make better predictions from a mix of known and unknown classes.
Although the recent methods aim for better representation learning, some of them achieve this through feeding more data the model with augmentation. On the other side, a few recent OSR methods do not use the same experiments settings maintained in most of works in the literature. For example, Wang al. 2025 2024); Jia al. (2024) use different backbone models for evaluation, which makes it harder to compare their methods with others.
G IMPLEMENTATION
Each model is trained on single NVIDIA-RTX2080T GPU requiring from 2 to 32 hours depending on the model and the dataset. Our implementation utilizes Python (v3.7) and PyTorch (v1.12), accelerated with CUDA (v11.3) and cuDNN (v8.2). Our codes are mostly built on top of the code- base by Vaze et al. 2022) and the implementation of SupCon loss taken from the official GitHub page by Khosla al. (2020). Our periodic NegCosSch schedule can be integrated into any existing loss with few lines of codes as the following:
import math class @GooineTemmrratueescchllllll
def _inii__isss____ t_p-2.0, t_m.0,, p-200, shift-1. 0, epochs 600)
self.t_p t_p self.t_m t_m
self.epochs epochs self.P =
self.s shift
self.e int (self. 0.5 * self.s self.P)
def get_temperature (self, epoch) if(t<self.e):
t = self.t_m + (self.t_p self.t_m) (1+ math. (2 maa.hh.p (epoch-self.s self.P/2) (Alf.P/2)/sef.Pm1 /self.P)) /2 else:
t self.t_p return
if (args. ( tttpetetttrraeecccccllllla #Sscoosssneteemeerttureeddddldd
()
for epoch in range (1,N_epochs+1)
if if heaggssttemerrturr_sceeeuuluu
criterioon.tmmeratuue
TS. TS.get_tentt De..ge_teemeraaure (epoch)
rest of the code
23


Reviews:
[{"review_id": "x2LXgjDq5C", "reviewer": "Reviewer_CfPf", "summary": "This paper investigates the open-set recognition (OSR) problem, aiming to enhance the model's ability to identify samples of novel semantic classes unseen during training when tested. The authors propose a modulated representation learning method that dynamically adjusts the temperature parameter in the loss function by introducing temperature scheduling, especially a novel negative cosine scheduling. This enables the model to focus on instance-level features to form rough decision boundaries in the early stages of training and gradually transition to semantic-level features to smooth the boundaries. Experiments demonstrate that the proposed method improves both OSR and closed-set performance across various loss functions and benchmark datasets without additional computational overhead.", "questions": "1. On Page 1 (near line 242), does \"group-wise features\" specifically refer to \"class-wise features\" (i.e., class-level features)? If so, it is recommended to uniformly use the standard terminology \"class-wise\" to avoid terminology confusion. If not, please explain the specific differences between \"group-wise features\" and \"class-wise features\" to help readers better understand the technical perspectives in the paper.\n2. The summation index a in Formula (2) is not defined. Does a iterate over the set A(i), representing all samples in the batch except the anchor i?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The idea of temperature scheduling is novel and insightful. In particular, the negative cosine scheduling achieves a smooth transition of task switching by reverse-adjusting the temperature, which is more effective than fixed temperature or traditional cosine scheduling. The method does not require introducing additional regularization or generating synthetic samples, reducing computational costs and providing a concise yet efficient solution to the OSR problem.", "weaknesses": "Although comparisons with baseline methods (e.g., ARPL, SupCon) have been conducted, some recent OSR methods based on augmentation or multi-expert models (e.g., Wang et al. 2024) are not included. It is recommended to incorporate a broader range of comparisons in the rebuttal or future work to fully demonstrate the superiority.\nThe performance improvement is limited on benchmarks with a small number of training classes (e.g., CIFAR), indicating that the method may be more suitable for scenarios with a rich number of classes. The authors should explicitly discuss this limitation and explore ways to extend it to small-scale data.\nThe selection of the temperature range (τ⁺, τ⁻) and period P relies on heuristic rules (e.g., τ⁺=τ+Δ). Despite parameter tuning, there is a lack of theoretical guidance. It is suggested that the authors analyze the boundaries of parameter sensitivity or provide adaptive adjustment strategies to enhance robustness.", "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": "imZyhf7gHs", "reviewer": "Reviewer_T1Y8", "summary": "The authors propose temperature schedules for reprsentation learning\nin open set recognition.  They use supervised contrastive loss for\nrepresentation learning.  For each sample in a batch, they create two\naugmentations. Positive pairs are from the same class.  They use\ntemperature in softmax to regulate the representation of intra-class\nsamples (relative to inter-class samples).  According to the\nFamiliarity Hypothesis (D&G, 2022), most OSR methods flag novelty\nbased on the absence of semantic features and recommends to extract\n\"interesting content features\" beyond the semantic features. The\nauthors propose varying the temperature to learn semantic features and\ninstance (\"content\") features.  Based on CosSch (starting with higher\ntemperature and going toward lower), they propose NegCosSch, which\nstarts from lower temperature and going higher.  Both follows a cosine\nfunction with a certain period.  During the first half of a cosine\ncycle, increasing temperature encourages semantic features.  During\nthe second half of a cosine cycle, decreasing temperature encourages\ninstance features.  Besides the periodic version (P-NegCosSch), they\npropose a monotonic version (M-NegCosSch) which only increases in\ntemperature.\n\nFor evaluation, they compare 6 existing methods over 4 datasets.  On\nmethods, they added exponential increase and linear increase as well\nin addition the two versions of NegCosSch.  The empirical results in\nTable 1 indicate their 4 methods generally outperform compared\nmethods.  However, among their four methods, a generally more\neffective methods is not apparent.  When used with different loss\nfunctions, P-NegCosSch and M-NegCosSch generally performs better than\nconstant temperature, while P-NegCosSch generally outperform the\nothers.  They also found that their method can benefit from more\nclasses.", "questions": "1.  Since P-NegCosSch does not seem to generally outperform\nM-NegCosSch, what are the main reasons?  Could the 2nd half of a cycle\n\"undo\" the 1st half of a cycle?\n\n2.  p6: \"Otherwise, P in Eq. (7) can be chosen by dividing E by the\nnumber of cycle?\"  How does one choose the number of cycles?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.  For open set recognition, Negative Cosine Schedule (NegCosSch) is\nproposed for temperature scheduling in softmax used in supervised\ncontrastive learning.\n\n2.  The proposed variations of P-NegCosSch and M-NegCosSch together\nwith exponential increase and linear increase generally outperforms\nthe other 6 existing methods over 4 datasets.\n\n3.  The paper is generally well written.", "weaknesses": "1.  The proposed method is a minor variation of the existing NegCosSch\nmethod for temperature scheduling.  Hence, the novelty level is not\nhigh.\n\n2.  The P-NegCosSch and M-NegCosSch do not seem to perform better than\nthe simpler exponential increase and linear increase.\n\n3.  The motivation for the periodic temperature schedule could be\nfurther discussed.  Also, it does not seem to outperform the monotonic\nincreasing version.\n\n4.  Part of the motivation is from semantic features vs\ninstance/content features, further analysis with NegCosSch would be\nsignificant.", "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": "bLdGCS2TjK", "reviewer": "Reviewer_u1CY", "summary": "This paper explores the influence of the temperature parameter in loss of OSR and introduces a novel temperature scheduling strategy NegCosSch. It varies the temperature during training, enabling the model to balance instance-level and semantic-level features in representation learning without additional computational cost. Extensive experiments on the CIFAR and SSB benchmarks demonstrate consistent performance improvements.", "questions": "My questions are mainly focused on the experimental section:\n\n+ Why is label smoothing introduced in Sec. 5.2? If it is only because “As label smoothing (LS) has shown performance improvements,” the purpose is not clearly justified.\n\n+ Why are the results of the Vision Transformer model on TinyImageNet presented? If this section is necessary, shouldn’t results on larger-scale datasets be shown?\n\n+ I would like to see the results about the metric OpenAUC [1]. \n\n+ The paper does not mention a validation set. How were the hyperparameters determined? Was the test set used for tuning, and are the final results reported based on that? I am mainly concerned.\n\nMinor point:\n\n+ Do some of the terms refer to the same concept (semantic-level, class-level, group-wise)? If so, please unify them.\n\n[1] Wang, Zitai, et al. \"Openauc: Towards auc-oriented open-set recognition.\" Advances in Neural Information Processing Systems 35 (2022): 25033-25045.\n\nIf authors address the Weaknesses and Questions, I will increase my score.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "+ This paper is well-written and easy to follow. I favor studies that derive methodological innovations from experimental observations.\n\n+ The details provided in the Appendix are clear and crucial, enhancing the paper’s overall logical flow and strengthening the credibility of some experiments.\n\n+ The empirical evaluation is extensive, covering multiple benchmarks and ablation studies.", "weaknesses": "+ The choice of $P$, $(\\tau ^{+}, \\tau ^{-})$ in the method is mainly heuristic. A more thorough theoretical analysis would improve the quality of the paper.\n\n+ Some of the authors’ statements lack experimental or theoretical support. For example, the discussion regarding empty regions in the representation space, the significant computational overhead in existing methods, and the statement *'Therefore, the methods that demonstrate improvement on smaller datasets…'*(lines 096–098).\n\n+ From my perspective, Sec. 4.2 constitutes one of the key sections for motivation. However, it remains unclear how the subsequent discussion is derived from Eq. (4), further clarification is needed.\n\n+ The figures (especially Fig.1 and Fig. 2) are not positioned near the relevant text, which hinders readability.\n\n+ Typos issue: line 135 *Section, 3*", "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": "2Gx3pCIZ6H", "reviewer": "Reviewer_TEAQ", "summary": "The paper addresses open-set recognition by replacing the fixed training temperature used in common OSR losses with epoch-wise temperature schedules that modulate representation learning from instance-level to semantic-level focus. \n\nIt proposes a generalized cosine framework and a new negative cosine schedule (NegCosSch) that starts at a low temperature to form coarse, separative boundaries and then increases to compact within-class clusters; linear and exponential increasing variants are also considered. The schedules plug into Cross-Entropy, Supervised Contrastive, and ARPL losses without extra computational cost. \n\nExperiments on TinyImageNet and the Semantic Shift Benchmarks (CUB, FGVC-Aircraft, Stanford Cars) demonstrate consistent gains over constant-temperature and prior cosine schedules in closed-set accuracy and open-set metrics (AUROC, OSCR), with improvements that tend to increase as the number of training classes increases. \n\nThe claimed contributions are (i) analysis of temperature effects for OSR, (ii) plug-and-play schedules, especially NegCosSch, applicable across losses, and (iii) empirical improvements on tougher benchmarks.", "questions": "1. Describe the dispersion and significance of improvements. Report mean±std over the five seeds you mention and include 95% CIs and paired tests for AUROC/OSCR/accuracy across all tables; currently tables list means only.\n\n2. Run factorial sweeps over (τ+, τ−) and period P for NegCosSch and monotonic variants, showing Pareto frontiers of closed- vs open-set metrics. Your choices (e.g., τ+∈{0.3–0.4}, τ−=0.1; “finish with high τ”) are presently heuristic. Quantify the robustness of performance to these settings.\n\n3. Justify why starting low-τ then increasing is fundamentally better for OSR.\n\n4. You use max-logit for unknown detection under SupCon/CE. Compare against energy score, ODIN-style perturbations, and cosine-margin heads, holding the backbone/schedule fixed. Does NegCosSch still win irrespective of the scoring rule?\n\n5. Breadth and strength of baselines\n   Reproduce stronger contemporary OSR baselines under your exact protocol/splits, not only constant-τ or CosSch: e.g., BackMix (TPAMI 2025), iCausalOSR (PR 2024a). This clarifies whether scheduling alone is competitive at today’s frontier.\n\n6. You claim plug-and-play for “any OSR loss”. Test at least one additional family—e.g., OpenAUC-style objectives or prototype-based methods—and report whether schedule benefits persist without retuning.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "The paper’s strengths span four fronts. On originality, it repurposes temperature scheduling, previously explored mostly for closed-set/self-supervised contrastive learning, into a unified, loss-agnostic mechanism for open-set recognition, with a negative cosine schedule that explicitly traverses instance→semantic regimes. This is a simple yet creative removal of the fixed-τ limitation that has constrained prior OSR training dynamics. \n\nIn terms of quality, the method is evaluated across multiple datasets of varying difficulty, multiple loss families (CE, SupCon, ARPL), and reports averages over five random seeds, showing consistent AUROC/OSCR and accuracy gains without requiring extra computation or architectural changes. \n\nThe paper clearly motivates the role of temperature, presents the proposed schedules using a generalized cosine formulation, and supplements intuition with gradient analyses and UMAP visualizations that illustrate how clusters evolve during training. \n\nIn terms of significance, the contribution is pragmatically valuable: it provides a drop-in schedule that improves both open- and closed-set metrics, scales favorably as the number of training classes increases, and can be integrated into existing OSR pipelines with negligible engineering overhead, thereby lowering the barrier to adoption on more challenging semantic-shift benchmarks.", "weaknesses": "The paper’s novelty is primarily curatorial, adapting known temperature-scheduling ideas (e.g., cosine schemes) to OSR, without a stronger theoretical account tying the proposed schedules to measurable properties of open-set boundaries; parameter choices such as (τ+, τ−), the period P, and the “finish high-τ” heuristic are fixed largely by heuristic guidance rather than principled sensitivity analyses. \n\nEmpirically, improvements are modest and reported without dispersion or significance testing; although the text states five seeds were used, tables report means only, so it is unclear whether +1–3% AUROC/OSCR gains exceed run-to-run noise. \n\nEvaluation breadth is limited: results focus on TinyImageNet and SSBs with a narrow architecture set (VGG-like, ResNet-50; ViT deferred to the appendix) and do not probe domain shift or cross-dataset OSR, leaving external validity uncertain. Comparisons emphasize constant-τ and cosine baselines; several competitive contemporary OSR methods in the related work are not reproduced under the same protocol, making relative advantage ambiguous. \n\nFinally, the “no computational overhead” claim overlooks the practical cost of tuning τ-ranges and schedule shapes, as well as the UMAP visualizations. While intuitive, these visualizations lack quantitative cluster diagnostics (e.g., intra/inter-class scatter, uniformity) to substantiate the representation-learning narrative.", "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)