Learnware Specification via Dual Alignment
Authors: Wei Chen
Jun-Xiang Mao
Xiaozheng Wang
Min-Ling Zhang
Venue: ICML 2025 poster (2025)
Keywords: Learnware paradigm
learnware specification
model reuse
Primary area: general_machine_learning->transfer_multitask_and_metalearning
TL;DR: This paper proposes a learnware specification via dual alignment, demonstrating superior performance in the learnware paradigm.

Abstract: The learnware paradigm aims to establish a learnware dock system that contains numerous leanwares, each consisting of a well-trained model and a specification, enabling users to reuse high-performing models for their tasks instead of training from scratch. The specification, as a unique characterization of the model's specialties, dominates the effectiveness of model reuse. Existing specification methods mainly employ distribution alignment to generate specifications. However, this approach overlooks the model's discriminative performance, hindering an adequate specialty characterization. In this paper, we claim that it is beneficial to incorporate such discriminative performance for high-quality specification generation. Accordingly, a novel specification approach named Dali, i.e., Learnware Specification via Dual ALIgnment, is proposed. In Dali, the characterization of the model's discriminative performance is modeled as discriminative alignment, which is considered along with distribution alignment in the specification generation process. Theoretical and empirical analyses clearly demonstrate that the proposed approach is capable of facilitating model reuse in the learnware paradigm with high-quality specification generation.

Learnware Specification via Dual Alignment
Wei Chen 12
Jun-Xiang Mao 123
Xiaozheng Wang 3 Min-Ling Zhang 12
Abstract
source investment, and specialized development expertise. These factors pose substantial challenges for non-experts building high-performance models from scratch, while it is ideal if their tasks could be tackled by reusing existing well- trained models. However, issues such as data privacy, model inflexibility, and catastrophic forgetting further complicate the reuse and adaptation of models for users.
The learnware paradigm aims to establish learn- ware dock system that contains numerous lean- wares, each consisting of a well-trained model and a specification, enabling users to reuse high- performing models for their tasks instead of train- ing from scratch. The specification, as a unique characterization of the model's specialties, domi- nates the effectiveness of model reuse. Existing specification methods mainly employ distribution alignment to generate specifications. However, this approach overlooks the model's discrimina- tive performance, hindering an adequate specialty characterization. In this paper, we claim that it is beneficial incorporate such diseriminative performance for high-qualit specification gen- eration. Accordingly, a novel specification ap- proach named DALI, i.c., Learnware Specifica- tion via Dual gnmment,, is proposed. In DALI, the characterization of the model's 's discriminative performance modeled as discriminative align- ment, which considered along with distribution alignment in the specification generation process. Theoretical and empirical analyses clearly demon- strate that the proposed approach is capable of fa- cilitating model reuse in the learnware paradigm with high-quality specification generation.
The learnware paradigm (Zhou, 2016) provides a systematic approach that allows users to build new machine learning solutions by leveraging existing well-established models instead of developing models from scratch. A learnware is a well-trained machine learning model equipped with a small-scale specification that describes its capabilities and specialties. This specification, serving as the unique identi- fier for both the learnware and its associated model, enables the model to be effectively reused by new users without requiring access to the original training data. In the sub- mitting stage, developers worldwide can voluntarily submit their trained models to learnware dock system (Tan et al., 2024c), and the system helps developers generate specifi- cations corresponding to their models. In the deploying stage, when a user needs to address specific task, instead of starting from scratch, she can submit her requirement to the learnware dock system. The system identifies and recommends useful learnwares, allowing the user to achieve better performance than training a model from scratch using their own data. Recently, to advance research on the learn- ware paradigm, the learnware dock system, Beimingwu, has been developed and released (Tan et al., 2024c).
Introduction
Obviously, the design of the specifications is pivotal in the learnware paradigm (Zhou & Tan, 2024). Well-crafted spec- ifications that adequately characterize models' specialties can greatly improve the accuracy of learnware identification and the effectiveness of model reuse. Existing specifica- tion methods primarily rely on distribution alignment, i.e., ensuring that the specification's distribution similar to that of the model's training data. Although this approach partially describes the model's applicable scope from the perspective of its training data, it overlooks the model's inherent discriminative ability, resulting in an inadequate characterization of the model's 's specialties.
Currently, the machine learning paradigm of step-by-step model construction from seratch, tailored to specific tasks, has achieved remarkable success. However, this success is heavily dependent on several key factors: a large volume of high-quality labeled data, significant computational re-
'School of Computer Science and Engineering, Southcast University, Nanjing. China Key Lab. of Computer Network and Information Integration (Southeast University). MOE, China IInformation Technology and Data Management Department of China Mobile Communications Group Zhejiang Co., Ltd. Corre- spondence to: Min-Ling Zhang <zhangml @ scu.edu.en>.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 20255 by the author(s).
In light of the above observations, we postulate that more adequate characterization of the model's specialties can be

---

Learnware Specification via Dual Alignment
expected if the model's s discriminative performance can be appropriately considered within specification generation pro- cedure. Accordingly, a novel specification approach named DALI, i.e., Learnware Specification via Dual ALggueent is proposed. In DALI, the characterization of the model's discriminative performance is modeled as discriminative alignment, which is carefully incorporated along with dis- tribution alignment in the specification generation process. For discriminative alignment, our objective is to ensure that the discriminative performance of the generated specifica- tion closely approximates the model's 's inherent discrimi- native performance. For distribution alignment, we strive to guarantee that the distribution of specifications for the same class is as similar as possible to the distribution of the training data. Through this dual alignment mechanism, the DALI approach enables the generated specifications to simultaneously focus on the model from both discrimina- tive performance and training data distribution perspectives, thereby more adequately characterizing the model's 's capa- bilities and specialties. Theoretical and empirical analyses clearly demonstrate that the proposed DALI approach is ca- pable of facilitating model reuse in the learnware paradigm with high-quality specification generation.
original data or auxiliary data across feature spaces. To take the importance of label information into consideration, Tan et al. 2024a enhances the representation capacity of the RKME specifications by incorporating label information into the generation procedure, thereby enabling the hetero- geneous learnware paradigm. Meanwhile, Guo et al. 2023 encodes label information as a part of the RKME specifi- cation to address scenarios involving heterogeneous labels. Based the above research, the learnware dock system, Beimingwu, was recently released to systematically sim- plify the entire learnware paradigm and promote its research and practical applications (Tan et al., 2024c). Moreover, since the performance of the learnware paradigm based on RKME specifications heavily depends on the choice of ker- nel function, Chen et al. 2025 proposed replacing RKHS with neural embedding space to overcome this limitation, achieving specifications that align closely with class feature distributions of the training data.
Obviously, the aforementioned specification methods pri- marily rely on distribution alignment to generate spec- ifications, i.e., ensuring that the specification's 's distribu- tion is similar to that of the model's training data. How- ever, neglecting the model's intrinsic discriminative perfor- mance may lead to suboptimal specifications of low-quality, thereby compromising the effectiveness of model reuse. To address this limitation, this paper proposes a novel specifi- cation approach DALL, simultancously considering both the model's discriminative performance and the feature distribu- tion has mastered, in order to generate specifications that more adequately characterizations the model's ' specialties.
2 Related Work
The learnware paradigm (Zhou, 2016; Zhou & Tan, 2024) offers a systematic approach to managing well-cstablished models, enabling users to directly reuse existing models based on their specialties to address specific requirements, rather than constructing models from scratch. A learnware consists of well-trained model and a specification describ- ing its specialties, where the specification ensures privacy protection and unique identifiability (Lei et al., 2024; Shen & Li, 2025). As a core component of the learnware paradigm, the specification has garnered significant research attention in recent years, with substantial efforts focused on generat- ing specifications that effectively characterize model special- ties. Wu et al. 2023 proposed generating specifications with Reduced Kernel Mean Embedding (RKMF) technique, en- suring that reduced set is approximate to the task data dis- tribution in the Reproducing Kernel Hilbert Space (RKHS). Subsequently. Zhang et al. 2021 extended this RKME spec- ification method to handle user requirements with unseen job components. To date, RKME specification methods have achieved impressive success acToss various scenarios in the learnware paradigm. In the heterogeneous feature space scenarios, Tan et al. 2023 assumes access to the orig- inal training data and employs subspace learning to unify heterogencous features into a shared feature space, thereby generating RKME specifications. To relax the strong as- sumption of data accessibility, Tan et al. 2024b explored the correlation of heterogeneous feature tasks, enabling the generation of RKME specifications without accessing the
3 Preliminaries
The learnware paradigm consists of two distinct stages: a submitting stage and a deploying stage.
The Submitting Stage. In this stage, a developer can spon- taneously submit her well-trained model f to the learnware dock system. To better characterize the submitted model f. the system help the developer assign the model spec- ification R, which sketches its capabilities and specialties. Currently, the specification is primarily derived from the dataset D = [(x,, }=) used to train the model, serving as its unique identifier. Here, we assume that D comprises K classes, where X Rd (x E x)) denotes the feature space of D, and y 21. K} (v )) represents the label space of DD. The model f. along with its correspond- ing specification R, forms a learnware (f. R), which is then stored in the learnware dock system for future use.
.........
The Deploying Stage. In this stage, suppose a user has task requirement corresponding to the dataset D {(x,, ) Here, we assume that D comprises K classes, where X' = R2d (x E 2) denotes the feature space of D, and
2

---

Learnware Specification via Dual Alignment
K3 (6 E Y) represents the label space of D. To address this task, the system will help the user generate specification It tailored to their requirements. The user then submit R to the learnware dock system, which will match and return potentially useful learnwares to the user based on the submitted specification ft. Subsequently, the user can solve the task by reusing these learnware models.
pseudo-labels convey the model's inherent discriminative performance, while the true-labels provide the class feature distribution that the model has mastered. Therefore, our goal is to ensure that the specification captures both of these types of information, thereby comprehensively characteriz- ing the model's capabilities and specialties.
Discriminative alignment. According to the learnware specification mechanism, both the training data and the specification lie within a hypothesis set H C { : X - )), where & is the predictor (e.g., neural network). Moreover, the training data distribution in the pseudo-label space, i.c., effectively reflects the model's 's discrim- inative performance. By aligning the specification with this distribution through encoding, we can characterize the model's inherent discriminative performance. In theory, any distance metric in the distribution space be employed to measure the difference between distributions, facilitating the corresponding approximations. However, most of these (e.g., the Kullback-Leibler divergence) are independent of the learning process of the model, making it hard to estimate from finite data and overly strict (Konstantinov & Lampert, 2019). Intuitively, a well-trained model should demonstrate performance consistent with its performance on the training data when applied to distributions that are similar to the characteristic distribution of the training data. Specifically, if a network performs well on training data distribution in the pscudo-label space but poorly on the specification, the performance discrepancy between them is significant. Con- versely, if all functions in H. exhibit similar performance both, they are considered to be identical. From this, we can use H--iscrepanncy (Konstantinov & Lampert, 2019) to measure this performance discrepancy, ensuring that the distribution of the training dataset D = [(x,, B.) in the pseudo-label space is aligned to that of the specification R, thus achieving discriminative alignment. The specific formula is as follows:
RKME Specification. The specification is the central part of the learwware paradigm, functioning both characteri- zation of the model's capabilities and as its unique identifier. Currently, specifications primarily characterize the distribu- tions mastered by the model while ensuring privacy protec- tion. The RKME specification method (Tan et al., 2024c) learns the data distribution in the RKHS Hy through the Kernel Mean Embedding (KME) technique (Muandet al., 2017). This approach safeguards data privacy by employing reduced set to approximate the empirical KME. Specifi- cally, the RKME specification is generated by optimizing the following objective:
D = (x, )=))
min 3.Z
k (xi,
Σ 5=1
8yk(zz)))
-)
(1)
He
Here, the m-sized tuple R- = {(3,, 2,),,, acts as the specification, where m < n. Z = { is the reduced set, and [ = {3,)7= are non-negative weight coefficients. k(..)) is predefined kernel function, and H4 is the RKHS associated with this kernel. It is evident that a major draw- back of the RKME specification method is that its per- formance heavily relies on the predefined kernel function, which limits its applicability in different scenarios.
4 Methodology
In practice. the class distributions of the training data under true-labels are often entangled in the feature space. How- ever, the corresponding well-trained model possesses dis- criminative ability, enabling disentanglement in the output space. If the generated specification focuses solely on the feature distribution to describe the model's capabilities, it often fails to characterize its discriminative performance, resulting in an inadequate specialty characterization. There- fore, the proposed approach considers both the model's dis- criminative performance and the feature distribution of the training data, providing a comprehensive characterization of the model's capabilities and specialties.
Ldis sup ((((vo(x)))) - ((voo=). vz),, (2)
VoEHH
where E is the cross-entrope loss function, g(z) vz² +a is the smooth approximation of the absolute value opera- tor, and a is a small constant. Here, the specification is denoted as R = {(2,, N2;) ) where Km & n with the initialization of the specification involving random sam- pling of m data points from each class in the training data D {(x, b.) In addition, to avoid the inter-class dependent discriminative disparities' introduced by the net-
4.1 The Proposed of DALI Approach
'Assume there are 3 classes of data: (a, b, c). If the model is trained on the set {a, b), the resulting parameters will characterize the discriminative information between a and b, while training on {b, c} will characterize the discriminative information between b and c. This leads to significant variations in the model parameters related to class b, resulting in discrepancies in the synthesized representation of b generated from different parameter sets.
Let (ūe) be the pseudo-labels generated by the model trained on the dataset D = {xx, })) where {ær P represents the true-labels. Generally, these two groups of labels are not identical, which leads to different latent infor- mation between the pseudo-labels and the true-labels. The
3

---

Learnware Specification via Dual Alignment
work parameter O. the H is denoted as numerous random initialized neural networks under the distribution Po. Due to the strong representational capability of random neural networks (Saxe et al., 2011; I; Cao et al., 2018; Amid et al., 2022; Lee et al., 2023), which ensure the preservation of both intra-class and inter-class information when mapping data to the embedding space (Giryes et al., 2016), can be regarded as providing a partial interpretation of the in- puts. Meanwhile, combination of numerous random neu- ral networks offers a comprehensive interpretation. Thus, numerous random neural networks can effectively encode the discriminative performance in the pscudo-label space and, through 7L-discrepancy, align the specification with for discriminative alignment, thereby characterizing the well-trained model's discriminative performance.
achieving an adequate characterization of the model's capa- bilities and specialties. The overall procedure of the DALI approach is outlined in Algorithm I of Appendix A.
The following detailed propositions provide a theoretical analysis of the expected loss bound of the proposed DALI approach, as well as its privacy protection. For simplicity, we consider only one class and omit the label vectors, while also providing some assumptions.
Assumption 4.1. Let the random neural network vh R - Rd be considered nonlinear, where On represents the weight parameter of the 1-th layer and the corresponding activation function is denoted as pt. Except for the final layer, which is a linear classification layer, the other layers of the network dhe Rd - R are similar to those of vho.
Distribution alignment. While characterizing the model's discriminative performance, we also desire the specification to capture the feature distribution provided by the true-label space. This provides a more comprehensive characterization of the model's 's capabilities. To achieve this, in numerous random neural embedding spaces, we use the Maximum Mean Discrepancy (MMD) compute the unbiased es- timate of the class expectation between the training data D {(x, 31) in the true-label space and the specifi- cation R. ensuring that their class feature distributions are aligned. The formula is expressed as:
Assumption 4.2. We assume here least one specification R" = (-), ... (((R) that minimizes (4.
For further simplification in analysis, we separately perform the upper bound analysis for Lais and LMMD. The details of upper bound analysis are as follows:
Proposition 4.3 (Upper bound for Lais). According the theorem I of (Mohri & Muftoz Medina, 2012). we assume that the loss function E is bounded by M, where M lies between O and 1. Let a hypothesis set H C { : X + + y/-- For any ô >> O, with probability at least - 8 over the data, the following holds for th:
LMMD = EawPa
Σ (x)
Ldis = (x(1bo(x), 77 (((00(=),)=)
Dil (x.
1=1
(3)
log 1
(5)
$29M ((()) + (D, + M
1
2
(2)
R&
(Z.
where
where D& and R& represent the subsets of the training data and the specification corresponding to the k-th class, respec- tively. the Rd + Rd is the embedding neural network, where d' < d and 0- ~ Pa represents the randomly initial- ized parameters under the distribution Pe of the embedding network parameter.
BR()) = E,r sup ol(vbox)).)) BoED
and a are independent Rademacher random variables. In addition, the the is the random initialized neural network under distribution Po. and E is the E, loss function.
Proposition 4.4 (Upper bound for LMSDD) Let x E
Overall. During the overall specification generation pro- cess, by integrating discriminative alignment and distribu- tion aligmment, the objective function of the proposed DALI approach can be expressed as:
{x, (X,, 34) E D} and z E {zil(zi, V2.) E R} be con- sidered Borel probability measures in the data topological space X. According (Golowich al., 2018), the empir- ical Rademacher complexity of à for dataset D is defined by:
min Lais + LMMD-
(4)
RD(1) < (lg) + 1)II Mr())
(6)
It is worth noting that the specification R {(z), Vz, v2,,) Km characterizes the well-trained model's discriminative perfor- mance and mastered feature distribution by simultancously aligning the discriminative performance in the pseudo-label space and the class feature distributions in the true-label space across numerous random neural networks, thereby
VID)
where eb is the embedding network of depth I over the topo- logical space X, and each layer network parameter matrix 1 has a Frobenius norm bounded by Mr(j). The acti- vation function a 1-Lipschitz and positive-homogeneou
4

---

Learnware Specification via Dual Alignment
activation function (such as the L,) and the input sat- isfies ||x|| B. If R, then, with probability at least
The relevant proof can be seen in Appendix D. Evidently, in the DALI approach, the discrepancy between the initial specification and the pseudo-barycenter of the training data decreases as the specification size increases. Conversely, the discrepancy becomes more pronounced when the speci- fication size is smaller. This offers a compelling rationale for why a larger specification size could lead to data leak- age. However, in the learnware paradigm, the specification size remains significantly smaller than the training data size, thereby ensuring the privacy protection of DALI approach.
1 - 6, and for any arbitrary small 8 > 0, the empirical MMD with neural embedding is bounded by:
LMMD(D,R)
(ID) + RR) log 1 2|
<2ND 2Rx + RRRRY
The detailed relevant proof can he found in Appendix B. By combining the upper bound analysis of Proposition 4.3 and 4.4, in the DALI approach, we bound the gap between the empirical loss of the training data in neural networks and the expected loss of the specification. This bound is influenced by performance discrepancy, network parameter norms, and network depth. However. by leveraging numerous random neural networks, we can mitigate the impact of these factors on the discrepancy, enabling the specification to comprehen- sively characterize the model's discriminative performance and mastered feature distribution.
4.2 The Submitting Stage
In this stage, developer spontaneously submits her task and well-trained model to the learnware dock system to generate a specification. This specification, combined with the model, constitutes the learnware, which is subsequently stored within the system. Suppose the developer can vol- untarily submit their well-trained model f X + y along with a local private training dataset D = {(x, y)) Since the DALI approach requires additional discriminative performance from the well-traine' model, the outputs of the model on the training data are used as pseudo-labels. This is specifically represented as follows:
Based on Assumption 4.1 and 4.2, we can further prove the minimization of the proposed DALI approach's 's objective function loss, while ensuring privacy protection.
Proposition 4.5 (Minimizer of (4.).). In the DALI ap- proach, the specification R is initialized by randomly se- lecting R samples from D, i.e., Vz E {zil(zi, Uz.) E R), x. Then, the specificution
y = fx;), i= 1,2, n. DEY
(10)
3x E (xi((x:)1) Vk) E D), Rs is optimized using (4) to ensure that the model per- formance of R and D are consistent under the hypothesis set H. and that the burycenters of R' coincides with the barycenters D. Specifically, it can be expressed as:
This label setup ensures that the generated pseudo-labels encapsulate the discriminative performance of the will- trained model. Then, the system processes the dataset {(x, yt, 8.))= which includes both true-labels and the pseudo-labels, using Eq.(4) to generate a specification R = ((z), Uz,, Km that completely characterizes the model's specialties. This specification R is subsequently combined with the well-trained model f to form the learnware {f, Rt). which is stored within the system. The detailed procedure is provided in Algorithm 2 of Appendix A.
[(0141(PI 1.ppp---.- -- (0) xx))) 0)-
((0 .. (p1(0) z²))), +z)++
D
pr (0) xx))))
[D]
R
4.3 The Deploying Stage
1
pi(O ... (p1(01 =)m + O.
R
At this stage, users search for useful learnwares in the leam- ware dock system based on their requirements, reusing either a single well-established model or a combination of mod- els to fulfill their requirements. According to the DALI ap- proach in (4), the requirement dataset D [(x,, g.) ( submitted by the user is first processed to generate speci- fication î = {(2,, y2,,) f representing the requirement. In this process, pseudo-labels are replaced with truellabels, ensuring that the specification generated under discrimi- native alignment and distribution alignment maintains fea- ture distribution similarity while preserving discriminability among class distributions. Here, the learnware dock sys- tem contains c learnwares. Then, the system searches for matching existing learwware specifications through the re- quirement specification, identifying useful learnwares to
The relevant proof can be found in Appendix C. This indi- cates that the proposed DALI method can optimize the dis- criminative alignment and distribution alignment between the specification and the training dataset.
Proposition 4.6 (Private protection). Based on to Proposi- tion 4.5, Assumption 4.2 and the specification R. is initial- ized by randomly selecting [R] samples from DD ize.Vzz E az (zi, V2.) E R), 3x E {x,1(x,, v.) &D,, x, we can derive the conclusion:
2 =X; + (())(())))) - ((v0(z).
+ D
1
Σ vo(x,)
(z(z)
(9)
R&
JEDz
JERL
5

---

Learnware Specification via Dual Alignment
meet the user requirement. This process is expressed as:
5.1 Experimental Setup
Dataset. We evaluate the learnware paradigm by extracting and reconstructing datasets from DomainNet (Peng et al., 2019) and NICO (He et al., 2021). These two image datasets are commonly used to assess the effectiveness of model reuse. Specifically, both datasets contain domains with over- lapping classes. In the NICO dataset, we selected 6 different domains: [autumn, dim, grass, outdoor, rock, water]. The DomainNet dataset includes domains: [clipart, infograph, painting, quickdraw, real]. Such hierarchical structures are well-suited for the learnware paradigm. Here, we extract 4 label spaces from the overlapping classes of 11 domains across the two datasets, which facilitate the subsequent ex- perimental design of developer tasks and user requirements according to different scenarios in the learnware paradigm. The specific label spaces are as follows:
K W
1 [
min
2
Rig
ER
(11) Here, Ra represents the j-th class specification in the i-th learwware. The relationship between the existing learnware specifications and requirement specification is denoted by W [01,1,--.. Wr, K.] where Σi=1 Σド= Wiy 1, K.
and -=1 Wi, represents the usefulness of the i-th learn- ware in addressing the user requirement. W can be obtained by optimizing the quadratic programming problem shown in (11) using any off-the- the-hee--hef solvers.
After this process, we can obtain d' candidate useful learn- K; Waj (ranked from largest to smallest), where = K. Then, due to the potential heterogeneity of label spaces, to enhance learnware model reuse, we uti- lize Cosine similarity to quantify the differences between the classes in the requirement specification and those in the candidate learnware specifications. This similarity estab- lishes the relationship between the learnware models and the requirement class data, and is expressed as:
wares by مككك
Label space A: ["flower", "horse", "cow", "rabbit", "tiger", "bird", "bus", "sailboat", "train", "helicopter")
Label space B: ["butterfly", "owl", "bird", "giraffe", "frog", "squirell, "train", "tent", "truck", "umbrella"]
Label space C: ["flower", "horse", "cow", "rabbit", "tiger"]
Label space D: ["bird", "giraffe", "frog", "squirell" "tiger"]
Similarity Cosine
z)
[Rg
R
(E.
(12)
Implementation details. In this experiment, we use RKME, RKME-W (Guo et al., 2023), and LANE specification meth- ods as baselines, with parameters set to their optimal choices. To ensure the fairness of the comparative experiments, the global feature extractor and the well-established models included in the learnware dock system are derived from DenseNet201 (Huang al., 2017) and ResNet18 (He et al., 2016). The random neural network de in the DALI approach is set to ConvNe:BN (Rawat & Wang, 2017). The detailed implementation can be found in Appendix E.
where i E [R), E E [e'] and j E [K,]. Subsequently, a
bipartite graph is constructed based on the Cosine similarity between the classes of the requirement specification and the classes of the candidate learnware specifications, where the edge weights represent the similarity. The two node sets cor- respond to the classes of the requirement specification and the learnware specifications. respectively. Through the Hun- garian algorithm (Kuhn, 1955), we can obtain the maximum matching for each bipartite graph. This enables the system to identify the most similar learnware based on the maxi- mum class similarity, thereby allowing the corresponding requirement class data to reuse the associated learnware's well-established model f. The procedure of this stage is detailed in Algorithm 3 of Appendix A.
5.2 Different Label Space Settings
The proposed DALI approach incorporates label informa- tion, while in the learnware paradigm. both homogeneous and heterogencous label space scenarios exist between the specification label space and the user requirement label space. Therefore, we use different label space settings to validate the proposed approach. In the homogeneous label space setting, we have 11 domains 2 label spaces (A and B) = 22 developer tasks. Each model trained these tasks is treated as a learnware's 's well-trained model, and the cor- responding specifications are used together to construct the learnware dock system. Moreover, the data not included in the 22 tasks is treated as the 22 user requirements. For each user requirement, the system contains 22 candidate
5 Experiments
To demonstrate the superior specification quality of the proposed DALI approach in the learnware paradigm, we conduct comparative experiments under different (homoge- neous or heterogeneous) label space settings and mixed task settings. Furthermore, we perform additional tests to verify the privacy protection and provide a visualization of the specification. Additionally, an ablation study is carried out to analyze each alignment component of the DALI approach.
6

---

Learnware Specification via Dual Alignment
Table The result of Pretak (%) metric in useful learnwares identification under different label space settings.
Table 2. The result of superclass accuracy (%) and quality (%) the mixed task setting of learwnare paradigm. Noting that Label refers to the real label of the specification.
LABEL SETTING
METHODS
SIzE
PRE@1
PRE@2
20
50.00
77.27
METHODS
SIZF
ACC
QUALITY
LABEL?
RKME
100
40.91
63.64
63.64
RKME
RKME-W W
20
100.00
100.00
100
90.91
X
HOMOGENEOUS LABEL SPACE
100
100.00
100.00
20
100.00
RKME-W
xx5
90.91
100.00
100
100.00
LANE
Kx 10
95.94
100.00
Kx5
95.94
53.19
V
LANE
Kx5
100.00
100.00
Kx10
100.00
90.23
DALI
Kx10
100.00
100.00
K
100.00
75.68
DALI
100.00
94.05
20
45.46
54.55
RKME
100
59.10
63.63
(A and B) 22 developer tasks as superclasses, i.e., 22 su- perclasses; and label space A U B x 11 domains = 11 user requirement tasks. Thus, each requirement task contains two superclasses, i.e., each requirement task requires two corresponding learnware to be solved. This ensures that no single learwware model in the system can solve the require- ment independently, but rather, combination of models required to address the requirement. Furthermore, in order to evaluate the performance of the learnware dock system constructed by each specification method, it is implemented here by evaluating the accuracy of the system in identifying useful learnware, i.e., the superclass accuracy. Meanwhile, our proposed method is to generate class specification. In order to verify the inter-class discriminability of the class specification, it is evaluated here by accessing the class accuracy of the corresponding specifications through the de- veloper's pre-trained model test, i.e., quality. Table 2 shows that the proposed approach outperforms or matches other methods both metrics under the mixed task setting. More- over, the DALI approach outperforms the LANE method in quality metrics, indicating that the DALI provides a superior specification quality compared to methods that only capture the mastered feature distribution of the model. Note that the specifications of the related RKME methods do not have labels, so the quality assessment cannot be performed.
20
63.64
68.18
RKME-W W
HETEROGENEOUS
100
63.64
68.18
LABEL SPACE
Kx5
63.64
68.18
LANE
Kx10
63.64
63.64
Kx5
68.18
72.73
DALI
Kx10
63.64
63.64
Iearnwares. the heterogeneous label space setting, we treat data from the 11 domains and label spaces C/D as the user requirements, and the data from the 11 domains and label spaces A/B as the developer tasks. In this setting, learnware in the system shares the same label space as the user requirement. Here, we use Pre@k (Guo et al., 2023) as the evaluation metric for this experiment to assess the performance of the learnware dock systems, constructed with different methods under two label space settings, in identifying useful learnwares based on user requirements. The Pre@k metric is defined as:
1 T
Preak - DITTfmee < k),
(13)
where x/ is ranked from smallest to largest based on the similarity measure between the learnware specifications and the requirement specification, while also considering the performance of each learnware model f on requirement (ranked from largest to smallest). T represents the num- ber of requirements. The specific experimental results are shown in Table 1. The results show that the proposed DALI approach achieves precise identification of useful learnwares in homogeneous label space and maintains high identifica- tion accuracy even in the more challenging heterogeneous environment. Furthermore, under two different specification sizes, the proposed approach outperforms or matches other methods in both label space scenarios.
5.4 Further Analysis
Privacy protection analysis. Privacy protection in the spec- ification has always been a key concern in the learnware paradigm. Here, we assess the privacy protection perfor- mance of the proposed approach using the Binary Classifier based Membership Inference Attack (MIA) in the White- Box Setting method (Hu et al., 2022). In this method, the Table 3. The prediction correctness (%) result of the Membership Inference Attack in the White-Box Setting method.
5.3 Mixed Task Setting
METHODS
ACCURACY
ROC
PRECISION
One important purpose of learnware paradigm is to enable well-trained models in the learnware dock system to be used "beyond the capabilities of any single model". Therefore, we use the mixed task setting to validate the proposed ap- proach. In this setting, we have 11 domains x label spaces
RANDOM RKME
90.55-10.16
90.55+0.116
84.48-L0.30
66.13+0.81
66.1310.81
60.32+0.44
LANE
64.00:0.522
64.00=0.52
58.55+0.27
DALI
64.57+0.49
64.57+0.49
58.9240.24
7

---

Learnware Specification via Dual Alignment
aiiing data autumnnc
Training date: autumnnc Spectficston autumn-C Training date: ciiprrt Speci clpprtes
Specificaioo: C
Trsining date: clpart-
Specification: cliparted
Twiring data: autumn-
specification: autummnn
Trairing data: cipart
Specification: dipart
(a)DALI
(b)LANE
(c) RKME
Figure 1. Visualization of the training data and specification from the task perspective.
Table 4. Ablation study results of DALI approach for identifying useful learwwares by Pre@k metric under different label space settings.
Speciiccaio Clasc flraer
SpeciPiation Casc flow Specifiction oger
Spati Clasic
LABEL SETTING
Cass
LMMD
PRE@]
@RE@2
59.09
90.91
HOMOGENEOUS
90.91
100.00
LABEL SPACE
100.00
100.00
59.09
63.64
HETEROGENEOUS LABEL SPACE
(A)DALI
LALA
63.64
68.18
68.18
72.73
Figure 2. Visualization of the training data and specification from the task class perspective.
Analysis of the ablation study. The objective function of the proposed DALI approach consists of two components: one that is discriminative alignment, denoted as Ldiss and another that is distribution alignment, denoted as LMMD- Here, we validate and analyze the effectiveness these two alignment components through an ablation study. Table presents the ablation study results of the Preãk evaluation for identifying useful learnwares under different label space settings. The results show that the specification generated by each individual component achieves good accuracy in identifying useful learnwares, while the combination of both components yields the greatest performance improvement.
target model is obtained using the training data mem- ber data, and the feature representations of non-member specification and member data are recorded in the target model. Then, a binary classification attack model is trained using the recorded feature representations. Finally, the at- tack model predicts whether the specification corresponds member or non-member, and the evaluation is performed using three classification metries: Accuracy, ROC and Pre- cision. Note that in this experiment, the specification size is set to 100, and the random method involves randomly select- ing 100 samples from the training data no- no-member data. Table shows that, except for the random method, other specification methods exhibit privacy protection capability.
6 Conclusion
Visualization analysis. To further highlight the superior the
specification quality of the DALI approach, SNE method to visually represent the training data from different domains and the corresponding specifications un- der various methods. Figure 1 shows that all three methods effectively enable the specifications to capture the feature distributions of the tasks that the model is proficient in. Moreover, we provide a visualization of the class data and class specifications from the task, shown in Figure 2. It is apparent that the DALI approach's class specification is more discriminative than the class specification of the LANE method. This indicates that the specification, by cap- turing both the model's discriminative performance and the mastered feature distribution, achieves an adequate charac- terization of the model's 's capabilities and specialties.
In summary, this paper introduces the DALI approach, which achieves more adequate characterization of model's capabil- ities and specialties through discriminative alignment and distribution alignment. Discriminative aligmment is accom- plished by modeling the model's intrinsic discriminative performance to ensure that the generated specification's dis- criminative performance aligns with its. Simultaneously. distribution alignment is realized by ensuring the specifi- cation's 's class feature distribution closely resembles that of the training data. This enables the constructed learnware dock system to handle various label space scenarios be- yond mixed tasks. Theoretical and experimental analyses demonstrate that the proposed approach achieves superior specification quality in the learnware paradigm.
8

---

Learnware Specification via Dual Alignment
Impact Statement
Guo, L.-Z., Zhou, Z., Li, Y--,, and Zhou, Z.-H. Identi- fying useful learnwares for heterogeneous label spaces. In Proceedings of the 40th International Conference on Machine Learning, pp. 12122-12111 Honolulu, Hawaii, 2023.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
He, K., Zhang, X., Ren, S., and Sun, J. Deep residual learn- ing for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778 Las Vegas, USA, 2016.
Acknowlegement
The authors wish to thank the anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Science Foundation of China (62225602), the Postgraduate Research & Practice Innova- tion Program of Jiangsu Province (KYCX25_0455 _0484, and the Big Data Computing Center of Southeast University.
He, Y., Shen, Z., and Cui, P. Towards non-iid image clas- sification: A dataset and baselines. Pattern Recognition, 110:107383, 2021.
Hu, H., Salcic, Z., Sun, L., Dobbie, G., Yu, P. S., and Zhang, X. Membership inference attacks machine learning: survey. ACM Computing Surveys, 54(115):33:1122333)) 2022.
References
Amid, E., Anil, R., Kottowski, W., and Warmuth, M. K. Learning from randomly initialized neural network fea- tures. arXiv preprint arX.v:2202.064: 2022.
Huang, G., Liu, Z., Van Der Maaten, L., and Weinberger, K. Q. Densely connected convolutional networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4700-4708, Honolulu, USA, 2017.
Cao, W., Wang, X., Ming. Z., and Gao, J. A review on neural networks with random weights. Neurocomputing 275:278-288 287,882287222 2018.
Konstantinov, N. and Lampert, C. Robust learning from untrusted sources. In Proceedings of the 36th Interna- tional Conference on Machine Learning, volume 97, pp. 3488-3495 California, USA, 2019.
Chen, W., Mao, J.-X., and Zhang, M.-L. Learnware specifi- cation via label-aware neural embedding. In Proceedings of the 39th AAAI Conference on Artificial Intelligence, Philadelphia, Pennsylvani, 2025.
Kuhn, H. W. The hungarian method for the assignment problem. Naval research logistics quarterly, 2(1-2)):3- 97, 1955.
Dong, T., Zhao, B., and Lyu, L. Privacy for free: How does dataset condensation help privacy? In Proceedings of the 33rd International Conference on Machine Learning, volume 162. pp. 5378-5396, Baltimore, USA, 2022.
Lee, J., Kim, J.-H., and Lee, J.-S. Demystifying randomly initialized networks for evaluating generative models. In Proceedings of the 37th AAAI Conference on Artificial Intelligence, volume 37, pp. 8482-8490, Washington, DC, 2023.
Garriga-Alonso, A., Rasmussen, C. E., and Aitchison, L. Deep convolutional networks as shallow gaussian pro- cesses. In Proceedings of the 7th International Confer- ence on Learning Representations, New Orleans, LA, 2019.
Lei, H.-Y., Tan, Z.-.., and Zhou, Z.-H. On the ability of developers' training data preservation of learnware. In Advances Neural Information Processing Systems 37, Vancouver, Canada, 2024.
Giryes, R., Sapiro, G., and Bronstein, A. M. Deep neural networks with random gaussian weights: A universal classification strategy? IEEE Transactions on Signal Processing, 64(13):3444-345 2016.
McDiarmid, C. On the method of bounded differences. Surveys in combinatorics, 141(1):148-14)) 188, 1989.
Golowich, N., Rakhlin, A., and Shamir, O. Size-indepeenden sample complexity of neural networks. In Conference On Learning Theory, pp. 297-299, Stockholm, Sweden, 2018.
Mohri, M. and Muñoz Medina, A. New analysis and al- gorithm for learning with drifting distributions. In Algo- rithmic Learning Theory: 23rd International Conference ALT, volume 7568 of Lecture Notes in Computer Science, pp. 124-138, Lyon, France, 2012.
Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., and Smola, A. A kernel method for the two sample- problem. In Advances in Neural Information Processing Systems 19, volume 13, pp. 513-520, Vancouver, Canada, 2006.
Muandet, K., Fukumizu, K., Sriperumbudur, B., Schölkopf, B., et al. Kernel mean embedding of distributions: A review and beyond. Foundations and Trends@ in Machine Learning, 10(1-2):1 1-41, 2017.

---

Learnware Specification via Dual Alignment
Peng, X., Bai, Q. Xia, X., Huang, Z.., Saenko, K., and Wang, B. Moment matching for multi-source domain adaptation. In Proceedings of the IEEE International Conference Computer Vision, pp. 1406-1415, Seoul, South Korea, 2019.
Rawat, W. and Wang. Z. Deep convolutional neural net- works for image classification: A comprehensive review. Neural Computation, 29(9):33522244 2449, 2017.
Saxe, A. M., Koh, P. W. Chen, Z., Bhand, M., Suresh, B., and Ng, A. Y. On random weights and unsupervised feature learning. In Proceedings of the 28th International Conference Machine Learning, pp. 1089-1096, Wash- ington, USA, 2011.
Shen, Z.-Y. and Li, M. Identifying useful learnwares via learnable specification. Frontiers of Computer Science, 199944199344, 2025.
Tan, P., Tan, Z.-H., Jiang, Y., and Zhou, Z.-H. Handling learwwares developed from heterogeneous feature spaces without auxiliary data. In Proceedings of the 32nd Inter- national Joint Conference Artificial Intelligence, pp. 4235-4243, Macao, China, 2023.
Tan, P., H.-T., Tan, Z.H.,, and Zhou, Z.-H. Handling learn- wares from heterogeneous feature spaces with explicit label exploitation. In Advances in Neural Information Processing Systems 37, Vancouver, Canada, 2024a.
Tan, P., Tan, Z.H Jiang, Y., and Zhou, Z.-H. Towards en- abling learnware to handle heterogeneous feature spaces. Machine Learning, 1 113(3):1399-186) 2024b.
Tan, Z.-H., Liu, J.-D., Bi, X.-D., Tan, P., Zheng, Q.-C., Liu, H.-T., Xie, Y., Zou, X-C.., Yu, Y., and Zhou, Z.-H. Beimingwu: A learnware dock system. In Proceedings of the 30th ACM SIGKDD Conference Knowledge Discovery and Data Mining, pp. 9773-5782, Barcelona, Spain, 2024c.
Wu, X.-Z., Xu, W., Liu, S., and Zhou, Z.HH. Model reuse with reduced kernel mean embedding specification. IEEE Transactions on Knowledge and Data Engineering, 35 (1):699-710, 2023.
Zhang, Y.J., Yan, Y.-H., Zhao, and Zhou, Z.-H. Towards enabling learnware to handle unseen jobs. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, pp. 10964-10972, Virtual Event, 2021.
Zhou, Z.-H. Learwarr: on the future of machine learning. Frontiers of Computer Science, (0(4):589-590 2016.
Zhou, Z.HH. and Tan, Z.H. Learnware: Small models big. Science China Information Sciences, 67(1):112103 2024.
10

---

Learnware Specification via Dual Alignment
A
Algorithm details
The detailed procedure the proposed DALI approach is presented in Algorithm 1. First of all, the specification is initialized through random sampling from the developer dataset (Step 1). Then, among numerous random neural networks, the model's discriminative performance and the feature distributions training dataset are encoded, allowing the specification align both discriminatively and distributively during the optimization process (Step 2-7). Finally, the generated specification is combined with the well-established model to create the learnware.
The proposed approach, as an integral part of the learnware paradigm, will be applied in this framework. The learnware paradigm is primarily divided into two stages: the submitting stage and the deploying stage. The detailed procedures for the submitting and deploying stages based on the DALI approach are outlined Algorithm and Algorithm 3.
Algorithm The DALI approach
Input: Dataset D = {xx, B)] with pesudo-lables (ū
Parameter: Neural network the parameterized with 0, random probability distribution over parameters Pe. neural em- bedding network vh parameterized with 9, random probability distribution over parameters Pa, iteration T, learning rate 7/
1: Randomly initialize the specification I from D, with each class having size of m, and the specification class label y/+ is consistent with the true label of the sampled data class;
2: for = 1 to T do
Po: 4: Sample ~ Pa:
3: Sample
Compute the objective function DALI approach Eq.(4);
6: Update by the Adam optimizer;
7: end for
Output: Specifiction A {(z,, Uz, )
Algorithm 2 The Submitting stage
Input:
Developer training dataset D
X1. well-trained model and learnware dock sys-
tem.
1: Obtain the pseudo-labels { i by (10);
2: Obtain specification R by Alg.1; Learnware {ff, R) is stored in the learnware dock system.
Algorithm 3 The Deploying stage
Input: User requirement dataset D = ((x, f and learnware dock system.
1: Load the learnware dock system;
2: Obtain the specification R. by Alg.1, where the pseudo-labels are substituted with true labels;
3: Compute W by (11);
4: Select c' candidate learnware by W;
5: Compute the similarity between each class in the specification ft and each class in the c' candidate learnware specification
by (12) to construct a bipartite graph;
6: Run the Hungarian algorithm to find the maximum matching for each specification Å class;
7: Reuse the corresponding learnware model f for the corresponding requirement Đ class by maximum matching.
B Proof of the upper bound of DALI specification.
For further simplification in analysis, we transform the upper bound analysis of the DALI approach into separate upper bound analyses for Lais and LMMDs D. where the formulas of Ldis and LMMD are given Eq.(2) and Eq.(3).

---

Learnware Specification via Dual Alignment
B.1 The upper bound of Ldis
According to the theorem I of (Mohri & Muñoz Medina, 2012), let Φ be the function defined over any sample D and R in the (X x 3) by
4 (
sup ((x,))))((((( (x), Ø) (((ve()))) voE
(14)
where H C {ab: : - + -)). In addition, she is denoted as numerous random initialized neural networks under the distribution Pg. Now, we assume that (z, yx) E and (z', 1/2) E are two sample sets differing by one labeled point. We have:
( (R)) & sup [e(vo(=), U=) ((vo(=') ).1( s M, veEV
((R)
(15)
where M is a constant and M Thus, by the McDiarmid's inequality theorem (McDiarmid, 1989), the following holds:
2c
Pr (R) - BR-D ( > S exp( R-D
(16)
M
Then, the bound of (R-D[9(At) is given as:
BR-D| [+))
-BR-D
sup B(x,))-/((((b(xx).0) m) HoEV
((( {((v)o()))=))
=B sup ( - Uz)l + Bla.aa)n((((bb())..)))))))))"))) -(()))()))
NoEw
<B
sup Bxx,))==(((()0(x)..oo))))))))))) Bcs.,))a((((bb(()))).))) + E NoEw
sup ((x.:))=n(((0o(()))...... (((1/((()))))))))))))))))))))))) yz)
<R
sup (F(x.))-(((<b0(>> (())))))))) + sup (B(x.)))=<(((Vol( ((V)))))))))) NoEV
voEw
<discn (D. R) + sup (( [[) (((vo(((())))))))))))))))))))))) V
<discn (D, R) (bb kg)
(17)
where R(y. Eg) is the empirical Rademacher complexity of the loss function by and bg is the by loss for some 2 1, Eiva( (x, 7)) = l 3/ for T' E V. It can be expressed as the upper bound of the hypothesis set H C (v: X + }}. From the (Mohri & Muñoz Medina, 2012), the Rademacher complexity R(b, ey) I ((()), where R(b) is given as:
R(
Esr sup ol(vo(x).v) NoEV
(18)
Therefore, by combining (16), (17) and (18), the upper bound of Lais can be expressed as:
((vo(z).vz) ((wo(x))))))) 5 29 R(b) disco + M1 log 1
(19)
B.2
The upper bound LMMD
First, we perform the upper bound analysis for LMMD. Based on Definition of (Mohri Muñoz Medina, 2012), we can obtain the Rademacher complexity of the network embedding function th with respect to [DI-sample. The specific expression is
D
RD = E.
sup VoEw
1
Σ
(20)
D
+=1
12

---

Learnware Specification via Dual Alignment
where ,..... ; with of independent uniform random variables taking values in {-1, 1). According (Golowich al., 2018), let be the embedding network of depth I over the topological X, where each network parameter matrix 0j has Frobenius norm at most Mf) and the activation function be 1-Lipschitz and positve-homogeneeu activation function (such as the ReLU). Then,
B( B(y2log(2)) + 1) M=(i)
RD( S
(21)
V D
where assuming the input ||x|| S B. Let x and be random variables defined on a topological space X, with respective
Borel probability measures and q. Given observations := (X1...... X.. and R := {=1..... 2m independently and identically distributed (i.i.d) for p and q. respectively. Moreover, we use the shorthand notation Ex (v)(()) == Ex (V (x)) and Ex [vo(()] (=)] :- Ex~glVe [=)] ] denote expectations with respect p and 9, respectively, where ~ p denotes has distribution p. The & : R + Edd, where IR is the toplogical space X. < d' and the function parameter. Based on the above definition, the Maximum Mean Discrepancy (MMD) can be expressed as:
MMD 0. p.g] == sup (Ex(vo())) (x(ro(())
(22)
A biased empirical estimate of the MMD (Gretton et al., 2006) is
D
1
MMD. D, = sup d'
tha (x;)
tha (z())
(23)
DD
R
Furthermore, according to (Garriga-Alonso et al., 2019), the output of a neural network vhe (CNN) can be viewed as Gaussian process under the constraints of an infinite number of (convolutional) filters. Assume the and are different, the upper bound on the absolute difference between MM D(b, P. g] and MD(V, D, R] is expressed as:
IMD peppp,p.. 4) MMD D, RJ
D
I
1
= sup (Ep() (y(o))) - sup UsED
(x())
Σ
v
(z(z))
D
R
iml
jm1
(24)
R
< sup the E1
(Ep(vo) - (xbo)
(x:)
+
D
R
A,p.1.DRR)
Next, we provide upper bound on the difference between Ap,, q, D, R) and its expectation. Changing either of x or in (pp, q. D, R) results in changes in magnitude of at most (v)) or 2 R| respectively. We apply the McDiarmid's inequality theorem (McDiarmid, 1989) to obtain
D
Pr (A(p, D, R) 2EE (p. D. R)] > S exp(
(25)
2Rp
( (R])
13

---

Learnware Specification via Dual Alignment
where is the every arbitrary small and >> In addition, exploit symmetrization upper bound the expectation of (p, q, D, R). have
(D, q, D, R)]
D
1
=DD, sup VoEV
(v(s))
v (x)) - (1b0) +
v/
(z))
D
R
i=
[2]|
R
=Ep,a sup d EV
ED
Σ
s (x,)
-Ero +
()))))
(D]
R
D
[2]
RR
1
< EDD,R,' sup (4)
(x
(x,)
vha (z3)) +
vo (z1)
[D]
|
(26)
1=1
j=1
D
IR
E sup
( [x(xx))) +
()((o(z))) - v0(21)))
[D]
|
NoEV
j=1
ED. sup PoES
3s (vx((() vxx())))
+ ERR sup VoEW
Σ
- - +b((2)))
D
R
22 W. + Rn 4))
where (a) uses Jensen's 's inequality, (b) uses the triangle inequality, (c) substitutes Definition 20. By combining (2. and (2,( we derive the final upper bound result, specifically given by:
R
Pr (A(p.,, D. - 2(R p) + Rn(v, q)] > e) S exp( (R RR))
(27)
Therefore, the bound of LMMD is expressed as:
(ID) + [R]) log
LMMD (D, R) < 2Rp + 2Rn + RoRRY
(28)
2|
where the definition of R(H,p) p) is similar to R((b by giving in (21))
C Proof of Proposition 4.5.
Based on the Assumption 4.1, assume that the random neural network the Rdd - RR. to be the 2-layer network with Binary Cross-Entropp Loss and the random neural embedding network tha Rd -> Rdd to be the 2-layer network for the sake of inference and analysis. The activation function in both networks is set to ReLU, denoted as Thus, from a specific class, the objective function the DALI approach, represented by (4, can be rewritten as:
D
R
P
R
1
lo (p-1(p(0x).)) v.)
Lo (p(0 2;),
p
x:)
p(O
2i),
(29)
R
D
R
daia
dyrMD
where
to (x, Ti) = J. log (xx,) + (1 - ū:) log(1 0x;))
(30)
and Oxx) = exx(xx) is the sigmoid activate function for binary classification.
Since each element 0g,i of the i-th layer network parameter O, exists as 0,,j i.dd A( 1), for a given input vector x [zylısied Rdd the operation of this network layer without activation function is given as (Dong et al., 2022):
h x 0 = [Milssisa E ERA
(31)
14

---

Learnware Specification via Dual Alignment
1.idd where hy ~ (0, Eラ= 27). Then, since activation function p(x) := max(0, p(h) = [max((, ho)le e R. Define Y max(0, X), where the random variable X ~ (0, o²). Moreover, H is following the same distribution of |, where B ~ Bernoulli()) indenpent of X and Ex [H] Es [] Fx[[X]] As result, for each input of activation function, we have the corresponding ouput is given as
ply) p(0x) B [0x),
(32)
where @ is clement-wie wise multiplication and B [B By substituting the above formula into Eq,(2 obtain further rewriting of ddis and MMMD, which are expressed as:
[2| to- 80-1 (0B)sgn(0zz))) Uz;)
dais
(0_(
(33)
D
R
1=1
and
D
|8
1
MMDD 8
sg 9x,
Bj sgn 0z (zz))z
(34)
[
In the above (36) and (37), sxn(x) denote the sign of x that |x sxn(x)x. Since this focuses on a specific class, the vector Bernoulli random variable B, reduces to the single random variable By
To simplify the derivation, auxiliary variable ip introduced, defined as:
Pe.x: sfggg(():)..
(35)
The dais and dMMD can rewritten as:
P
R
ddis
Lo-1
to (p0,2 0zz, Ux,)
D
|
1DD
1
(U log
(1 y4) log(1 - 0x;)))
(36)
[D]
v=
(Uz, log ((.o,.2,0,) + (1 Væ, log(1 ((po,,,,
R
j=1
and
D
1 R R
dMMD= =
1
Pa.x X;
Σ 20
(37)
D
For each specification data point 2,, the derivatives Ldis and LMMD are given as:
aLdis
d
ad
EE
(38)
0z,
d2 + Oz.
and
0LMMD
(dMMD))
adMMD
Egg
Eo 2(
)dMMD
(39)
0z,
0z,
Oz.
where
Od
(J/z,
(1.0,
(40)
Oz,
R
and
ddMMD
1
[R]] Po,x, θT.
(41)
Oz.
15

---

Learnware Specification via Dual Alignment
Therefore, the gradient of Lais and LMDD Zg are given
dLdis
ddis (- |R] (Vz, - (l
Eo
Oz.
d +
(42)
ddis
Ee
/dtss + ( [R]] (Uze.
and
MLMDD
Oz.
Eg
2(
20,,,
1
JAMMD
Rt]
[R|
2
1
(43)
Eg
(
00.x, 90,x X;
20 90,,
R
D
[2
i=1
1=1
[2]
Eg
2
(
1
Σ
B (0z.) B. sgn (x, (x,)x;
1
Bg (2, Bfggn B3j (0)))))
R
D
R
According to (Dong et al., 2022), we know that E. Ea(sgn( (0))n))))g (0)) 0 Rdddd and
||x||||=||| [(TT 2))cos(0) + 2sin(o)), (44)
TEg (z)) 0] = Eg (sgn(((g0)) sgn (zz((0z))00)
where x = 2, Eo |sgu (xx)sgn(())))))) (0x)))n()2))) t 0| = La. while Eg [sgn[ (xx)sg()((nn 02) 0] = -Ia if = =2 fact, this formula can be seen as a matrix depending on the angle ø between x and z.
In summary, in the DALI appoach, the initialization of is randomly selected from D, ensuring that 2, R and sharing corresponding labels. Based on Eq.(42) and Eq.(43), it can be concluded that even though and x undergo transformations through two layers of non-linear neural network, their classification performance and mean values can still be preserved. During optimization, the aforementioned equations also indicate that each z is updated in the direction that minimizes the task performance discrepancy and the pseudo-barycenter distance between datasets. Therefore, the specification not only aligns the class feature distributions but also aligns the discriminative ability during the optimization process, ensuring that the specification can more comprehensively skecth the model's capability.
The above reasoning is based on the assumption of two-layer non-linear network. Extending this analysis to multi-layer
The average loss of objective function
Class mean discrepancy
0.0200
1400
0.0175
0.0150
1000
Value
0.0125
value
800
0.0100
600
0.0075
0.0050
400
0.0025
1000
1000
Number iterratonn
Number iterations
Figure 3. During the optimization iterations, the average loss value the objective function for the DALI approach (left) and the class mean discrepancy between the optimized specification and the training data (right).
16

---

Learnware Specification via Dual Alignment
non-linear network still holds. If E (z.1(z E R). 3x E ((x,;)) E D), == x and y, Ur H, we have
C(0) (pr ... (0) x))) 0) (p .. (pi x²))), 8))
1 [D]
D
1
R
(45)
Pi ...
(.. (p: xx)))
pi(Or (pi(0) =m))) 0.
|R
Additionally, we provide auxiliary proof through experiments. In this case, data from label space A in the autumn domain of the NICO dataset is selected as the task training data to generate specification. The training dataset comprises 10 classes, and the specification size is set to 10 x 5. Throughout this process, we continuously record the average loss value of the objective function for the DALT approach at each optimization iteration and the class mean discrepancy between the optimized specification and the training dataset. Details are illustrated in the Figure 3. The experimental results show that the DALI approach's objective function reaches optimal performance after approximately 1000 iterations, while the class mean discrepancy between the specification and the training data remains in the most similar state. This further confirms the class pseudo- barycenter relationship between the specification and the training dataset, while also supporting the privacy protection analysis of the DALI approach.
D Proof of Proposition 4.6
Suppose the number of training dataset D classes is one. Since the size of the specification R. denoted as Km, is significantly smaller than the size of training dataset D, denoted n, and based on Assumption 4.2 and Proposition 4.5, in the objective function's 's optimization process of the DALI specification approach, we can obtain:
P
2 = xx + ((vo(x)), 0) ((vo(z)) Un) +
vx(x))
vo(z,)
(46)
D
R 1=1
where the specification R is initialized with first [R] samples of D, i.e, Vz {zil(zi, Vz,) R), 3x E {(x,, y.) D). x. Evidently, in the DALI approach, the discrepancy between the initial specification and the bseudo-barycent of the training data decreases as the specification size increases. Conversely, the discrepancy becomes more pronounced when the specification size is smaller. This offers a compelling rationale for why a larger specification size could lead to data leakage. In practice, due to differences in data size, the mean and classification performance of randomly sampled specification and the training data are different. Consequently, the optimized z still exhibits certain differences discriminative alignment and distribution alignment. This ensures the ability of privacy protection.
E Implementation details
To validate that the proposed DALI approach can generate high-quality specification in the learnware paradigm, we use RKME, RKME-W W, and LANE specification methods as baselines. Detailed descriptions of these methods are provided as follows:
RKME (Wu et al., 2023): Using Kernel Mean Embedding (KME), a reduced set is generated in the Reproducing Kernel Hilbert Space (RKHS) via Maximum Mean Discrepancy (MMD) as the specification.
RKME-W (Guo et al., 2023): Building upon RKME, class-specific reduced model parameters incorporated into the reduced set to form the specification.
LANE (Chen et al., 2025): In the random neural embedding space, specification is generated by aligning with the inter-class feature distribution of the training data.
In the comparative experiments, the kernel functions of RKME and RKME-W W are Gaussian kernels with a bandwidth parameter of 2.0, and the reduced model of RKME-W achieves optimal parameters through RexNet-18 (He et al., 2016). Furthermore, the parameters involved the LANE method and the proposed DALI approach are identical, including a batch size set to 64, ConvNe:BN (Rawat & Wang, 2017) network architecture, an activation function ReLU, and normalization layer set to GroupNorm.
17


Reviews:
[{"review_id": "tT8K3GVxYj", "reviewer": "Reviewer_PFro", "summary": "The paper shows that existing specification methods primarily rely on distribution alignment to generate specifications and introduces DALI, which incorporates both discriminative and distribution alignments in the process. Theoretical and empirical results demonstrate that DALI improves specification quality, thereby facilitating model reuse in the learnware system.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your detailed feedback, and we hope our responses will address your concerns.\n\nQ1: The theoretical analysis is unrelated to the subsequent model search and reuse.\n\nAns: Our theoretical analysis is closely related to subsequent model search and reuse. Notably, the quality of the generated specification is crucial in the learnware paradigm (please refer to “Introduction” section), as it directly influences the accuracy of subsequent model search and reuse to a certain extent. From the perspectives of loss upper bound (Propositions 4.3 and 4.4), optimization (Proposition 4.5), and privacy protection (Proposition 4.6), our theoretical analysis demonstrates that the proposed \\textsc{Dali} method can generate superior specifications, thereby indirectly providing theoretical support for subsequent model search and reuse to some extent.\n\nQ2: The model search process still relies on a feature distribution-based matching approach.\n\nAns: In the model search process, we perform class feature distribution-based matching  approach on the generated specifications (Eq.(11)). Notably, the specifications are optimized by Eq.(4), and their generation process has fully considered the distribution properties and discriminative performance of the model. Therefore, the matching approach in Eq.(11) does not overlook these characteristics of the model.\n\nQ3: Questions on the efficiency of model search.\n\nAns: The model search process of our \\textsc{Dali} method is comparable in time complexity to existing methods such as RKME, RKME-W, and LANE, all of which require solving a quadratic programming problem similar to Eq.(11) with a complexity of at least $\\mathcal{O}(c^{3})$. This is because the submitted requirement task may not find a single specification in the learnware dock system that can fully solve the task but may need to combine multiple specifications to accomplish it. To the best of our knowledge, efficiently conducting model search remains an open problem in learnware research, requiring further in-depth exploration in the future. \n\nQ4: Small improvement compared to RKME-W.\n\nAns: RKME-W is an extension of the RKME method, incorporating knowledge distillation to retain network parameters as part of the specification. As a result, this method has a significantly larger resource overhead. In contrast, our proposed method outperforms RKME-W while maintaining a lower resource overhead, which we consider a significant improvement. We will emphasize this point in the revised version.\n\nQ5: Comparison of specification generation efficiency with RKME.\n\nAns: We empirically evaluated the specification generation time of the \\textsc{Dali} and RKME methods on datasets under the homogeneous label space setting. The average runtime of \\textsc{Dali} was 22.51s, while RKME required 14.05s. Since our approach incorporates random neural embedding mappings, its generation time is indeed slightly longer than RKME’s kernel mapping in this scenario. However, the difference remains within an acceptable range. Notably, \\textsc{Dali} achieves a significant performance improvement over RKME at a lower computational cost, a point we will emphasize in the revised version. \n\nQ6: The benefits of obtaining $c'$ candidate useful learnwares.\n\nAns: One important purpose of learnware paradigm is to enable well-trained models in the dock system to be used \"beyond the capabilities of any single model\". That is to say, in the learnware dock system, the user can get more than one learnware to solve the user's requirement. For example, the dock system contains learnware related to cucumber, tomato, orange, apple, cabbages, and the user's requirement task is fruit. Then the useful learnwares (candidate useful learnwares) for the requirement may be orange, tomato, and apple. Then, we don't know which part of the task corresponds to orange or apple. At this point, we need further obtain the relationship between the task and the useful learnwares (candidate useful learnwares) to enable model reuse.", "claims_and_evidence": "The claims made in the submission are supported by evidence.", "methods_and_evaluation_criteria": "Yes, the proposed method and the evaluation criteria make sense for the problem at hand.", "theoretical_claims": "I have generally checked the proofs, but some details have not been thoroughly verified.", "experimental_designs_or_analyses": "I have generally checked the experimental design and analysis, and they appear sound.", "relation_to_broader_scientific_literature": "The paper contributes to the field of the learnware paradigm by introducing a new learnware specification.", "essential_references_not_discussed": "No, essential prior works are appropriately cited and discussed.", "other_strengths_and_weaknesses": "Strengths:\n1. This paper proposes a new specification that incorporates the model's discriminative performance.\n2. The experiments compare the precision of model search and analyze the privacy protection of the new specification.\n\nWeaknesses:\n1. The theoretical analysis (Propositions 4.3-4.6) in this paper is unrelated to the subsequent model search and reuse, and it does not theoretically explain how this specification helps with model search and reuse.\n2. DALI improves the consistency of model performance over $R$ and $\\mathcal{D}$ by optimizing $\\mathcal{L}_{dis}$ during specification generation (which is one of the main contributions of the paper). However, the model search process does not explicitly leverage this characteristic and still primarily relies on a feature distribution-based matching approach.\n3. Assuming the number of existing models in the system is $c$, the complexity of solving Eq. (11) should be at least $O(c^2)$. This implies that the proposed model search algorithm has a time complexity that scales at least quadratically with the number of models, whereas existing model search algorithms have a linear time complexity, indicating that the proposed algorithm is more computationally expensive.\n4. In the experiments, the performance of DALI shows only a small improvement compared to the contrast method, RKME-W.", "other_comments_or_suggestions": "I have no other suggestions.", "questions_for_authors": "1. How does DALI compare to RKME in terms of specification generation efficiency?\n2. What are the benefits of obtaining $c'$ candidate useful learnwares during the model search process?", "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": "Ticj7kAJ0X", "reviewer": "Reviewer_jxaa", "summary": "This paper introduces a approach (DALI) to generating high-quality model specifications in the learnware paradigm. Unlike existing methods that rely solely on distribution alignment, DALI incorporates discriminative alignment, which captures the model's intrinsic discriminative performance. By jointly considering both alignments, DALI enhances specification quality, enabling more effective model reuse in a learnware dock system. Theoretical and empirical results demonstrate DALI's superiority in characterizing model capabilities and handling diverse label space scenarios.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the insightful feedback and the interest in our work! We hope our responses can address your concerns.\n\nQ1: Questions on differences with similar works.\n\nAns: The method proposed by [Tan et al. 2024a] adds conditional distributions from the pre-trained model's output labels to the marginal distribution of the data, enhancing the discriminativeness of the generated specification distributions. This idea is similar to the \\textsc{Dali} method, but their differences still exist in the following two aspects:\n\n(1) [Tan et al. 2024a] is an RKME-based method, and the quality of the generated specification heavily depends on the chosen kernel function. In contrast, our proposed \\textsc{Dali} method replaces the kernel function with neural embedding, making it more adaptable to complex scenarios.\n\n(2) \\textsc{Dali} collaboratively utilizes pseudo labels and true labels to characterize the model’s properties, whereas [Tan et al. 2024a] only leverages pseudo labels to enhance the discriminability of the class specification.\n\nAs for the potential advantage of considering the true labels of the task data, existing work [Chen et al. 2025] has demonstrated the effectiveness of using true labels to characterize feature distributions. This paper can be seen as building on that work by additionally considering model discriminative performance through pseudo-labeling, thereby achieving superior specification generation.\n\nQ2: Concerns about conflict of objectives.\n\nAns: In the learnware paradigm, the dock system stipulates that the performance of all pre-trained models submitted by developers will not be very poor. Therefore, the \\textsc{Dali} method we proposed does not face the issue of objective conflict in most scenarios. On the contrary, simultaneously considering pseudo labels and real labels allows the generated specification to more fully characterize the model, thus promoting model search and reuse. Our experimental results clearly verify this. However, if we consider scenarios where the performance of submitted pre-trained models is not restricted, which goes beyond the scope of this paper, personally, I believe that your idea of separately modeling real labels and model outputs is a promising concept for future research, but it needs to be empirically verified in more open environments.\n\nQ3: Questions about the tabular tasks.\n\nAns: This work is specifically designed for image-based scenarios and is not readily applicable to tabular data. Tabular data exhibits significant differences from image data in terms of feature sparsity, distribution skewness, and feature engineering nuances [Ye et al. 2024]. Handling tabular data may require additional customized modeling designs, which go beyond the scope of this paper. However, exploring the potential of the \\textsc{Dali} method for more diverse modalities is an interesting direction for future research.\n\nQ4: Questions about the modeling of discriminative alignment and random feature mapping.\n\nAns: In the discriminative alignment, inspired by [Konstantinov and Lampert 2019], [Mohri and Munoz 2012], and [Dong et al. 2022], we adopt the $\\mathcal{H}$-discrepancy method to measure distribution differences under limited data. The results of the ablation experiments (Table 4) clearly validate the effectiveness of this modeling approach. Furthermore, [Zhao and Bilen. 2022] well demonstrated that random feature mapping can be used as an interpretation of the input data, preserving the data information in a low-dimensional embedding space. Meanwhile,  Appendix C Proof of Proposition 4.5 provides a theoretical demonstration of why discriminant alignment can be as effective as distribution alignment.\n\n[Chen et al. 2025] Chen, W., Mao, J.-X., and Zhang, M.-L. Learnware specification via label-aware neural embedding. In Proceedings of the 39th AAAI Conference on Artificial Intelligence, Philadelphia, Pennsylvania, 2025.\n\n[Ye et al. 2024] Ye, H. J., Liu, S. Y., Cai, H. R., Zhou, Q. L., Zhan, D. C. A closer look at deep learning on tabular data. arXiv preprint arXiv:2407.00956, 2024.\n\n[Konstantinov and Lampert 2019] Konstantinov, N. and Lampert, C. Robust learning from untrusted sources. In Proceedings of the 36th International Conference on Machine Learning, volume 97, pp.3488–3498, 2019.\n\n[Mohri and Munoz 2012] Mohri, M. and Munoz Medina, A. New analysis and algorithm for learning with drifting distributions. In Algorithmic Learning Theory: 23rd International Conference ALT, volume 7568 of Lecture Notes in Computer Science, pp. 124–138,  2012.\n\n[Dong et al. 2022] Dong, T., Zhao, B., and Lyu, L. Privacy for free: How does dataset condensation help privacy? In \\textit{Proceedings of the 33rd International Conference on Machine Learning}, volume 162, pp. 5378–5396, 2022.\n\n[Zhao and Bilen. 2022] Zhao, B. and Bilen, H. Dataset condensation with distribution matching. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 6514-6523, 2023.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "Yes, I have checked the theoretical claims.", "experimental_designs_or_analyses": "Yes, I have checked the experimental designs and analyses.", "relation_to_broader_scientific_literature": "Simultaneously consider the true label distribution and the model output distribution to generate the learnware specification maybe helpful, but this should be more carefully discussed and verified by more experiments in different scenarios (like tabular tasks).", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "1. The learnware paradigm is useful when handling well-trained models, it is an interesting paradigm and the specification design is a quite important problem.\n2. This paper gives the theoretical analysis of the proposed learnware specification.", "other_comments_or_suggestions": "1. To verify the effectiveness of the proposed learnware specification, it is better to provide more experiments on the tabular tasks.\n2. More discussion of the learnware specification design can be provided, please see the questions for details.", "questions_for_authors": "1. Previous paper [Tan et al., 2024a] also encodes the marginal distribution of data and the conditional distribution of model, what is the difference between DALI and the previous work? In the [Zhou and Tan, 2024], specification is generated by the sketching the distribution of feature concatenated with the model output, what is the potential advantage of additionally considering the true labels of the task data, it there any experiments to verify the effectiveness of this design?\n2. When the developer's task is easy, the model outputs are more likely to be accurate, and the two objectives are more likely to align. However, when the task is challenging, the objectives can be conflict. Would it be beneficial to separately model the distribution of true labels and model outputs? In designing learnware recommendation rules, both the information of p(Y|X) from true labels and model outputs can be utilized with techniques like class-wise MMD.\n3. How does the newly proposed learnware specification perform in tabular tasks?\n4. In the discriminative alignment, how about using the embedding network and MMD distance like in the distribution alignment? It is there any experiment to verify the effectiveness of random feature mapping?", "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": "WxwovZMN0Z", "reviewer": "Reviewer_2dDo", "summary": "The learnware system is a model reuse system which is designed to choose the optimal model from a model repository based on rules derived from user datasets. The core of this system lies in the use of specifications for model selection. This paper introduces a novel specifications generation method called Dual Alignment, which consists of two components: discriminative alignment and distribution alignment. Compared to the traditional RKME-based specifications generation, Dual Alignment demonstrates performance improvements across various metrics.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the valuable feedback and appreciation of our work. We hope that our responses could mitigate your concerns.\n\nQ1: Question on the mixed task setting\n\nAns: In the experiments of this paper, we set up four label spaces. It is no difficult to find that the label space A(B) contains the label space C(D). In the mixed task setting, if the domains corresponding to all label spaces are set as developer tasks, this will lead to duplicate tasks in the dock system. The learngware paradigm for duplicate tasks will only keep the tasks with the best model performance, so here we do not use label space C and D in the mixed tasks setting. These two label spaces are still constructed mainly for heterogeneous label space setting.\n\nQ2: Question on the parameter K.\n\nAns: The parameter K is the number of dataset classes. If the number of the task dataset classes is 5, the specification size $K\\times 5 = 25$. In the latest version, we will further clarify this.\n\nQ3: Questions on the evaluation metrics.\n\nAns: In the Mixed Task Setting, both the superclass accuracy and quality metrics are actually classification accuracy metrics, just assessed differently. \n\nIn this setting, we have 11 domains $\\times$ 2 label spaces (A and B) $=$ 22 developer tasks as superclasses, i.e., 22 superclasses; and label space A$\\cup$B$\\times$11 domains $=$ 11 user requirement tasks. Thus, each requirement task contains two superclasses, i.e., each requirement task requires two corresponding learnware to be solved. This ensures that no single learnware model in the system can solve the requirement independently, but rather, a combination of models is required to address the requirement.\nFurthermore, in order to evaluate the performance of the learnware dock system constructed by each specification method, it is implemented here by evaluating the accuracy of the system in identifying useful learnware, i.e., the superclass accuracy. Meanwhile, our proposed method is to generate a class specification. In order to verify the inter-class discriminability of the class specification, it is evaluated here by accessing the class accuracy of the corresponding specifications through the developer's pre-trained model test, i.e., quality metric. In the latest version, we will further emphasize the description of the metrics.\n\nIn addition, since smaller specification size lose more information about the original data, this can lead to poorer  discriminability of the statutes, and thus poorer quality. However, since the deploying stage of the learnware paradigm based on neural embedding specification is identified useful learnware based on mean unbiased estimation, the discriminability of the specification do not greatly  affect the performance of the learnware paradigm (superclass accuracy metrics). This is why the experiments in this paper show the values of different quality metrics with 100% superclass accuracy metrics. \n\nQ4: Question on the label (check mark on label selection) in the Table 2.\n\nAns:  In Table 2, label (check mark on label selection) refers to the label of the specification, i.e., the real label.The specification generated by the \\textsc{Lane} method and the \\textsc{Dali} method are class specification with label. According to the previous answer, we know that the assessment of quality metric requires label to be obtained, so the RKME and RKME-W methods do not have label to obtain the quality assessment metric values, whereas the \\textsc{Lane} and the \\textsc{Dali} can obtain them.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "There is an issue with the selection of the evaluation dataset. In Section 5.1, it is mentioned that “we extract 4 label spaces from the overlapping classes of 11 domains across the two datasets.” However, in the later testing in Section 5.3, only label spaces A and B were used. Why were only these two chosen? And how were they selected?", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "In Table 1, the selection of size introduces a hyperparameter K, but its exact definition is unclear. What does K specifically refer to? Do K×5 and K×10 correspond to 20 and 100 in the RKME algorithm?\n\nIn Table 2, two metrics are introduced: superclass accuracy and quality. However, their explanations are somewhat abstract, especially superclass accuracy. How is superclass accuracy actually calculated? Also, why can different quality values exist when superclass accuracy is the 100%? This part is a bit confusing.\n\nAdditionally, compared to the RKME algorithm, the Dual Alignment method generates labels（check mark on label selection）. Do these labels refer to the pseudo-labels generated during the Submitting Stage?", "relation_to_broader_scientific_literature": "Yes, this paper makes a significant contribution to the learnware paradigm. Previous learnware systems did not distinguish between discriminative ability and feature distribution, but this paper introduces and analyzes them in detail. By bringing in a new perspective, it enhances the overall capability of the learnware system and could serve as valuable inspiration for future research.\n\nThe paper introduces a new classification dimension, helping users find the models they need more effectively. Additionally, the performance improvements from multiple analysis dimensions might complement each other which further boosting the system’s effectiveness.I’m curious if there will be any future work on combining this approach with the traditional RKME algorithm.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Pros:\n\nThis paper provides very detailed proofs. It gives upper bounds for both of the proposed loss functions and also includes an analysis of privacy issues in this scenario. From a theoretical perspective, it is a solid and comprehensive paper.\n\nCons:\n\nThe 5.1 Experimental Setup section does not clearly explain the metrics, which might make it difficult for readers who are not familiar with these metrics to fully understand the experiment results.", "other_comments_or_suggestions": "No", "questions_for_authors": "No question", "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:

Meta-review: ## Summary
This paper addresses the model specification problem in the learnware paradigm, where users select pre-trained models based on their specifications instead of training new models. The authors argue that existing specification methods based on distribution alignment do not fully reflect the model’s classification ability. To address this, they propose a method called Dali (Dual Alignment), which combines distribution alignment with a second component called discriminative alignment. The goal is to capture a model’s strengths for better reuse. The paper presents theoretical and empirical results showing that this method improves model selection performance.

## Evaluation and Decision

This paper introduces a new learnware paradigm that is useful when handling well-trained models. The reviewers have raised several important concerns and provided feedback to the authors. The authors have done a very good job addressing those concerns. Thus, with the interesting contributions of this paper, I recommend it for acceptance.  The proposed paradigm is interesting, and the specification design is quite an important problem. The paper also provides a theoretical analysis of the proposed specification. It proposes a new specification that incorporates the model's discriminative performance. It makes a significant contribution to the learnware paradigm. By bringing in a new perspective, it enhances the overall capability of the learnware system and could serve as valuable inspiration for future research. The experiments compare the precision of model search and analyze the privacy protection of the new specification.
Decision: Accept (poster)