A general commodity sequence representation learning method in a recommendation system
By using pre-trained language models and contrastive learning tasks, the transferability and cold start problems of product sequence representation in recommendation systems were solved, achieving efficient adaptation and new product recommendation in different recommendation scenarios.
Patent Information
- Application Number
- CN202211109840.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2022-05-10
- Filing Date
- 2022-09-13
- Publication Date
- 2026-02-03
- Estimated Expiration
- 2042-09-13
AI Technical Summary
Existing methods for representing product sequences in recommendation systems rely on explicit product labels, which leads to poor transferability and cold start problems, making it difficult to reuse and effectively recommend new products in different recommendation scenarios.
We employ a pre-trained language model to encode product text, learn general product representations through a parametric whitening network and a hybrid expert-enhanced adapter module, and enhance the fusion of data representations from different domains through sequence-product comparison and sequence-sequence comparison tasks. We also design fine-tuning strategies for induction and transduction to adapt to new scenarios.
It enables the learning of general representations across multiple domains, which can be efficiently transferred to new domain recommendation scenarios, effectively recommending new products without requiring a large amount of interaction data, thus improving the transferability and cold start performance of the recommendation model.
Smart Images
Figure CN115408988B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of recommender systems, and in particular to a general method for learning product sequence representations in recommender systems. Background Technology
[0002] In modern recommender system research, sequence recommendation aims to recommend suitable products to users based on their historical product interaction sequences. Early research often relied on matrix factorization, while recent studies primarily view it as a product sequence representation learning task. This involves assigning a unique label (ID) to each product and using neural network methods such as recurrent neural networks (RNNs) and Transformers to encode the product sequence into a representation, and then making product recommendations based on this representation.
[0003] However, existing methods for representing product sequences in recommender systems rely on explicit product labels, which leads to two main problems:
[0004] 1. Portability: Even if different recommendation scenarios use the same data format, the product sequence representation model learned based on product labels is difficult to transfer to new recommendation scenarios due to the lack of shared product labels, thus limiting the reusability of the recommendation model. When faced with a new recommendation scenario, this invention often requires retraining the product sequence representation model, resulting in significant resource consumption.
[0005] 2. Cold Start: For new products in recommendation scenarios, interaction records related to the new products are very scarce. Product label representation requires a large amount of relevant interaction data for training. Therefore, in such product cold start scenarios, this invention cannot obtain well-trained product label representations, and thus often fails to achieve good recommendation results.
[0006] The information disclosed in this background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention
[0007] The purpose of this invention is to provide a general product sequence representation learning method in a recommender system. This invention takes a general product sequence as input and learns a general product sequence representation model through pre-training. To learn a representation that can be transferred between recommender scenarios, two key problems need to be solved: (1) learning a general product representation; and (2) learning a general sequence representation. To learn a general product representation, this invention designs an adapter module based on a parameter whitening network and hybrid expert enhancement to achieve inter-domain fusion and adaptation. To learn a general sequence representation, this invention designs two contrastive learning tasks, called sequence-product contrastive task and sequence-sequence contrastive task, and samples negative examples from multiple domains. Based on the above methods, this invention can be transferred inductively or transductively to new recommender scenarios in a parameter-efficient manner.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] This invention provides a general product sequence representation learning method in a recommender system, comprising the following steps:
[0010] S1: General text-based product representation: Encode the associated text of products using a pre-trained language model to learn transferable product representations; First, use a pre-trained language model to learn initial text representations. Since text representations in different recommendation scenarios may constitute different semantic spaces, the semantics of the text are transformed into a unified semantic space suitable for recommendation tasks through a parameter whitening network and a hybrid expert-enhanced adapter network.
[0011] S2: General Commodity Sequence Representation: Further enhances the integration and adaptation of data representations across different domains through sequence-commodity comparison tasks and sequence-sequence comparison tasks;
[0012] S3: Parameter fine-tuning: Two fine-tuning settings are considered based on whether the product label in the target field is suitable for use, namely induction and transduction.
[0013] As a further technical solution, the step S1 of using a pre-trained language model to learn the initial text representation specifically involves:
[0014] First, the BERT model is used to learn the initial text representation; given product i and its corresponding text t. i First, a special identifier [CLS] and words from the product text are concatenated in sequence and then input into the BERT model, i.e.:
[0015] x i =BERT([[CLS];w i ,…,w c])
[0016] Where x i This is the latent vector corresponding to the [CLS] symbol in the last layer of the BERT model, which is the initial text representation of the product encoded. c represents the total number of words in the product text, and w i w represents the i-th word in the product text c It represents the last word in the product description.
[0017] As a further technical solution, the semantic conversion achieved through the parameter whitening network in step S1 is specifically as follows:
[0018] A linear transformation is used to convert the initial text representation into an isotropic semantic space. Unlike traditional whitening methods based on preset mean / variance, the parametric whitening network introduces learnable parameters to better adapt to unknown recommendation scenarios. The formula is as follows:
[0019]
[0020] Where b and W1 are learnable parameters. It is the converted product text representation.
[0021] As a further technical solution, the domain fusion and adaptation achieved in step S1 through the hybrid expert-enhanced adapter specifically involves:
[0022] To bridge and adapt semantic gaps across domains, for a single product, multiple parameter-whitened representations are learned simultaneously, and these representations are adaptively fused to generate a general product representation. Specifically, G parameter-whitening network modules are introduced as experts, and a hybrid expert-enhanced adapter is constructed based on a parameterized gated routing module.
[0023]
[0024] in It is the output of the whitening network with the kth parameter, g k These are the corresponding fusion weights learned by the gated routing module, specifically defined as:
[0025] g = Softmax(x) i ·W2+δ)
[0026] δ=Norm()·Softplus(x i ·W3)
[0027] Here we use the initial representation x from the BERT output. iAs input to the routing module; further, parameter matrices W2 and W3 are introduced to adaptively generate the weights corresponding to each expert module; in order to balance the load of each expert module, the Norm() function is used to generate random Gaussian noise controlled by W2; g is the fusion weight vector learned by the gated routing module, and δ is the learned noise vector.
[0028] As a further technical solution, the sequence-item comparison task in step S2 specifically includes:
[0029] The sequence-item comparison task aims to capture the intrinsic relationship between sequence semantics and the potential next item. Unlike previous item prediction tasks, for a given sequence, items from various domains are used as negative examples to enhance semantic fusion and adaptation between domains and help learn a general sequence representation.
[0030] Consider a batch of B training examples, where each training example contains a sequence of items and the next item; first, they are encoded into a representation {<s1,v1> ,…, B ,v B >}, where s represents the normalized sequence representation, and v represents the normalized representation of the item at the next time step; the loss function for contrastive learning can be formally expressed as:
[0031]
[0032] Here, products from the same training batch are treated as negative samples, and τ is the temperature parameter; since the batch is randomly constructed, negative samples {v} from the same batch are considered as negative samples. j′ This will include products from multiple sectors. s represents the sequence-item contrast loss. j This represents the normalized representation of the j-th sequence in the batch, v. j This represents the normalized representation of the j-th item in the batch at the next time step, where j and j′ are labels identifying the sequence and the item at the next time step in the batch.
[0033] As a further technical solution, the sequence-sequence comparison task in step S2 is specifically as follows: by constructing a comparison between product sequences from multiple domains, a sequence-level pre-training task is proposed; the task objective is to identify data-enhanced product sequences from sequences from multiple domains; two data augmentation strategies are considered: (1) product discarding means randomly deleting a fixed proportion of products from the original product sequence; (2) word discarding means randomly deleting words from the product text; given a target sequence s j Data augmentation sequences Sequences are considered positive samples, while other sequences in the same batch are considered negative samples; the sequence-sequence contrast learning loss function can be formally expressed as:
[0034]
[0035] Since the batches are randomly constructed, the negative examples in the same batch naturally contain sequences from multiple domains; in the implementation, the product text representations after word-dropping data augmentation are preprocessed, making pre-training more efficient. Here The sequence-to-sequence contrast loss is represented by s. j′ This represents the normalized representation of the j′-th sequence in the batch.
[0036] As a further technical solution, the induction in step S3 is specifically set as follows:
[0037] In the first setting, the new domain is not suitable for a product label-based recommendation system; since it does not rely on product labels, a general text representation can be learned for new products; given a product sequence and candidate products in the target domain, they are first encoded into a general representation s and Then, predictions are made based on the following probabilities:
[0038]
[0039] Here, a softmax operation is performed on the candidate set of the target domain. Where i t+1 P represents the candidate product label at time t+1. I (i t+1 |s) represents a given general representation s in the inductive scenario, which is related to item i at time t+1. t+1 The probability of interaction.
[0040] As a further technical solution, the transduction in step S3 is specifically set as follows:
[0041] In the second setting, assuming all product labels have already appeared in the training set, a representation of the product labels can also be learned; in this setting, text representations are incorporated. and label representation As a representation of a commodity; therefore, the following predicted probabilities exist:
[0042]
[0043] here This represents the enhanced generic sequence representation of the product label; note that the parameters of the product sequence encoder remain fixed in this setting.
[0044] In each setup, the parameters of the hybrid expert-enhanced adapter are fine-tuned using the cross-entropy loss function; after fine-tuning, predictions can be made based on the probabilities described above. T (i t+1|s) represents a given general representation s in the transduction scenario, which is related to item i at time t+1. t+1 The probability of interaction.
[0045] By adopting the above technical solution, the present invention has the following beneficial effects:
[0046] 1. Transferability. The product sequence representation learning method proposed in this invention can simultaneously learn general representations on sequence data from multiple domains and efficiently transfer them to new recommendation scenarios such as new domains, new markets, and new platforms, without needing to share users or products.
[0047] 2. Cold Start. The general product text representation method proposed in this invention can effectively recommend new products on the platform without requiring a large amount of interaction data for training. Attached Figure Description
[0048] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0049] Figure 1 This is a diagram illustrating the overall architecture of the general commodity sequence representation learning method of this invention. Detailed Implementation
[0050] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0051] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0052] Combination Figure 1 As shown in the figure, this embodiment provides a general product sequence representation learning method in a recommendation system, including the following steps:
[0053] General text-based product representation:
[0054] To achieve general product sequence representation learning, products from different recommendation scenarios (different domains / markets / platforms) need to be encoded into a unified semantic space. To this end, this invention learns transferable product representations by encoding the text of the products. This invention first uses a pre-trained language model to learn initial text representations. Since text representations in different recommendation scenarios may constitute different semantic spaces, this invention proposes a parametric whitening network and a hybrid expert-enhanced adapter network to transform the semantics of the text into a unified semantic space suitable for recommendation tasks.
[0055] Product text encoding based on pre-trained language models:
[0056] This invention first uses the BERT model to learn initial text representations. Given product i and its corresponding text t... i This invention first uses (1) a special identifier [CLS]; and (2) words from the product text concatenated in sequence and inputs them into the BERT model.
[0057] x i =BERT([[CLS];w i ,…,w c ]),
[0058] Where x i This is the latent vector corresponding to the [CLS] symbol in the last layer of the BERT model, which is the initial text representation of the product encoded. c represents the total number of words in the product text, and w... i w represents the i-th word in the product text c It represents the last word in the product description.
[0059] Semantic transformation is achieved through a parametric whitening network:
[0060] Although this invention can obtain semantic representations of product text from the BERT model, these representations are not yet suitable for direct application to recommendation tasks. Existing research has found that BERT's representation space is a non-smooth, anisotropic semantic space, a problem particularly pronounced when encoding product text from various recommendation scenarios with significant semantic gaps. Therefore, this invention employs a simple linear transformation to convert the initial text representation into an isotropic semantic space. Unlike traditional whitening methods based on preset mean / variance, this invention designs a parametric whitening network, introducing learnable parameters to better adapt to unknown recommendation scenarios.
[0061]
[0062] Where b and W are learnable parameters. It is the converted product text representation.
[0063] Achieve domain fusion and adaptation through an adapter enhanced by hybrid experts:
[0064] To bridge and adapt semantic gaps across domains, this invention proposes learning multiple parameterized whitening representations simultaneously for a single product, and adaptably fusing these representations to generate a universal product representation. Specifically, this invention implements a hybrid expert architecture, introducing G parameterized whitening network modules as experts, and constructing a hybrid expert-enhanced adapter based on a parameterized gated routing module.
[0065]
[0066] in It is the output of the whitening network with the kth parameter, g k These are the corresponding fusion weights learned by the gated routing module, specifically defined as follows:
[0067] g = Softmax(x) i ·W2+δ),
[0068] δ=Norm()·Softplus(x i ·W3).
[0069] Here, the present invention uses the initial representation x output by BERT. i As input to the routing module, it contains domain-dependent biases. Furthermore, this invention introduces a parameter matrix W. . W3 adaptively generates the weights corresponding to each expert module. To balance the load of each expert module, this invention uses the Norm() function to generate the weights corresponding to each expert module. . The controlled random Gaussian noise. g is the fusion weight vector learned by the gated routing module, and δ is the learned noise vector.
[0070] General product sequence representation:
[0071] Since different domains typically correspond to user behavior sequences with different distributions, simply mixing product sequences from various domains for training may not be effective, and conflicts between behavior sequences from multiple domains may lead to a seesaw effect. Therefore, this invention designs two contrastive learning tasks to further enhance the integration and adaptation between different domains.
[0072] Self-attention sequence encoding:
[0073] Given a sequence of general product representations, this invention further uses a user behavior encoder to obtain sequence representations. This invention aims to learn the sequence features of general product representations, rather than based on product labels. Here, this invention uses a self-attention architecture, Transformers. Specifically, it comprises a stack of several multi-head attention layers (MHAttn(·)) and a feedforward neural network (FFN(·)). This invention first processes the learned general product representation v... i and the corresponding absolute position encoding representation p j The addition, input, and update process can be specifically represented as follows:
[0074]
[0075] F l+1 =FFN(MHAttn(F l )),
[0076] in This represents the concatenation of representations for each position in the l-th layer of the model. This invention uses the latent vector of the last position in the last layer of the model. As a sequence representation obtained through learning.
[0077] Multi-domain commodity sequence representation pre-training:
[0078] Given product sequences from multiple domains, this invention requires designing a suitable optimization objective to force the sequence encoder's output to reside in a unified representation space. By comparing sequences and products from multiple different domains, this invention aims to alleviate the seesaw effect and capture semantic connections between general product representations during the pre-training phase. To this end, this invention designs sequence-product comparison tasks and sequence-sequence comparison tasks.
[0079] Sequence-Product Comparison Task:
[0080] The sequence-item comparison task aims to capture the intrinsic relationship between sequence semantics and the potential next item. Unlike previous item prediction tasks, this invention uses items from various domains as negative examples for a given sequence, enhancing semantic fusion and adaptation between domains and helping to learn a general sequence representation.
[0081] This invention considers a batch of B training samples, where each training sample contains a sequence of items and the next item. This invention first encodes them into a representation {...}<s1,v1> ,…, B ,v B >}, where s represents the normalized sequence representation, and v represents the normalized representation of the item at the next time step. The loss function for contrastive learning can be formally expressed as,
[0082]
[0083] Here, products from the same training batch are treated as negative samples, and τ is the temperature parameter. Since the batch is randomly constructed, negative samples {v} from the same batch are considered as negative samples. j′ This will include products from multiple sectors. s represents the sequence-item contrast loss. j This represents the normalized representation of the j-th sequence in the batch, v. j This represents the normalized representation of the j-th item in the batch at the next time step, where j and j′ are labels identifying the sequence and the item at the next time step in the batch.
[0084] Sequence-sequence comparison task:
[0085] By constructing comparisons between product sequences from multiple domains, this invention also proposes a sequence-level pre-training task. The task objective is to identify data-augmented product sequences from sequences from multiple domains. This invention considers two data augmentation strategies: (1) product discarding, which involves randomly deleting a fixed proportion of products from the original product sequence; and (2) word discarding, which involves randomly deleting words from the product text. Given a target sequence s j Data augmentation sequences Sequences are considered positive samples, while other sequences in the same batch are considered negative samples. The sequence-sequence contrast learning loss function can be formally expressed as:
[0086]
[0087] Since the batches are randomly constructed, negative examples within the same batch naturally contain sequences from multiple domains. In the implementation, this invention preprocesses the product text representations after word-dropping data augmentation, making pre-training more efficient. Here... The sequence-to-sequence contrast loss is represented by s. j′ This represents the normalized representation of the j′-th sequence in the batch.
[0088] Multi-task learning:
[0089] During the pre-training phase, this invention employs a multi-task learning strategy to jointly optimize the two proposed contrastive learning losses.
[0090]
[0091] Here, λ is a hyperparameter that controls the weights of the sequence-sequence comparison task. The pre-trained model can be fine-tuned to adapt to new domains.
[0092] Efficient parameter fine-tuning:
[0093] Because this invention can learn a general product sequence representation during the pre-training stage, it fixes the main parameters and only fine-tunes a small portion of the parameters of the hybrid expert-enhanced adapter for necessary adaptation. This invention finds that the proposed hybrid expert-enhanced adapter can be quickly adapted to new domains and can efficiently fuse features from the pre-trained model and the new domain. Specifically, this invention considers two fine-tuning settings—inductive and transductive—based on whether the product labels in the target domain are suitable for use.
[0094] Summary settings:
[0095] In the first setting, a product-label-based recommendation system is not applicable to the new domain. Since this invention does not rely on product labels, it can learn a general textual representation for new products. Given a sequence of products and candidate products in the target domain, this invention first encodes them into a general representation s and The present invention then makes predictions based on the following probabilities.
[0096]
[0097] Here, the present invention performs a Softmax operation on the candidate set of the target domain. Where i t+1 P represents the candidate product label at time t+1. I (i t+1 |s) represents a given general representation s in the inductive scenario, which is related to item i at time t+1. t+1 The probability of interaction.
[0098] Transduction settings:
[0099] In the second setting, this invention assumes that all product labels have appeared in the training set, and it can also learn the representation of product labels. In this setting, this invention incorporates text representations. and label representation As a product representation, this invention therefore has the following predicted probabilities:
[0100]
[0101] here This represents the enhanced generic sequence representation of the product identifier. Note that the parameters of the product sequence encoder remain fixed in this setting.
[0102] In each setup, this invention uses a cross-entropy loss function to fine-tune the parameters of the hybrid expert-enhanced adapter. After fine-tuning, this invention can predict based on the probabilities described above. T (i t+1 |s) represents a given general representation s in the transduction scenario, which is related to item i at time t+1.t+1 The probability of interaction.
[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A general product sequence representation learning method in a recommender system, characterized in that, Includes the following steps: S1: Learning a general text-based product representation: Encoding the associated text of products using a pre-trained language model to learn a transferable product representation; First, the pre-trained language model is used to learn the initial text representation, and then the semantics of the text are transformed into a unified semantic space suitable for recommendation tasks through a parametric whitening network and a hybrid expert-enhanced adapter network. S2: Learning general product sequence representations: Further enhancing the integration and adaptation of data representations from different domains through sequence-product comparison tasks and sequence-sequence comparison tasks; S3: Parameter fine-tuning: Select the fine-tuning method based on whether the product label in the target field is suitable for use. When the product label in the target field is not suitable for use, inductive fine-tuning is used, and when the product label in the target field is suitable for use, transductive fine-tuning is used. The sequence-item comparison task mentioned in step S2 specifically includes: The sequence-item comparison task aims to capture the intrinsic relationship between sequence semantics and the potential next item. For a given sequence, items from various domains are used as negative samples. A batch consists of B training examples, each containing the item sequence and the item for the next time step. First, the training examples are encoded into representations. , This represents the normalized sequence representation. This represents the normalized representation of the item at the next time step; the loss function for contrastive learning can be expressed as: ； Products from the same training batch were treated as negative samples. It's a temperature parameter; negative samples from the same batch. Products encompassing multiple sectors; This represents the contrast loss between the sequence and the goods. Indicates the first in the batch The sequences are represented by normalization. Indicates the first in the batch The product at each time point is represented by a normalized method. and It is a label that identifies the sequence and next time item in a batch; The sequence-sequence alignment task described in step S2 specifically includes: A sequence-level pre-training task is proposed by constructing comparisons between product sequences from multiple domains. The goal of the sequence-level pre-training task is to identify data-augmented product sequences from sequences from multiple domains. Data augmentation is performed by randomly deleting words from product text. Given a target sequence Data augmentation sequences Sequences are considered positive samples, while other sequences in the same batch are considered negative samples; the sequence-sequence contrast learning loss function can be expressed as: ； The negative examples in the same batch contained sequences from multiple domains; This represents the sequence-to-sequence contrast loss. Indicates the first in the batch The sequences are represented by normalization.
2. The general product sequence representation learning method in the recommender system according to claim 1, characterized in that, Step S1, which involves using a pre-trained language model to learn the initial text representation, specifically involves: First, the BERT model is used to learn the initial text representation; given a product... and its corresponding text First, a special identifier [CLS] and words from the product text are concatenated in sequence and then input into the BERT model, i.e.: ； in It is the latent vector corresponding to the [CLS] symbol in the last layer of the BERT model, that is, the initial text representation of the product obtained by encoding. This represents the total number of words in the product text. The first in the product text One word, It represents the last word in the product description.
3. The general product sequence representation learning method in the recommender system according to claim 1, characterized in that, The semantic transformation achieved through the parameter whitening network in step S1 is specifically as follows: A linear transformation is used to convert the initial text representation to an isotropic semantic space; the parametric whitening network formula is as follows: ； in and These are learnable parameters. It is the converted product text representation.
4. The general product sequence representation learning method in the recommender system according to claim 1, characterized in that, The specific steps in step S1, which involve using a hybrid expert-enhanced adapter to achieve domain fusion and adaptation, are as follows: For a single product, multiple parameter-whitened representations are learned simultaneously, and these representations are adaptively fused to generate a general product representation. G parameter-whitening network modules are introduced as experts, and a hybrid expert-enhanced adapter is constructed based on a parameterized gated routing module. ； in It is the first The product learns the whitening representation of multiple parameters at each time step. It is the first The output of the parameter whitening network These are the corresponding fusion weights learned by the gated routing module, specifically defined as: ； ； Initial representation using BERT output As input to the routing module; further, a parameter matrix is introduced. and The weights for each expert module are generated adaptively. use Function to generate by Controlled random Gaussian noise; It is the fusion weight vector learned by the gated routing module. It is the learned noise vector.
5. The general product sequence representation learning method in the recommender system according to claim 1, characterized in that, The inductive fine-tuning in step S3 includes: Given a product sequence and candidate products in the target domain, the product sequence is first encoded into a general product representation. The candidate products are coded as follows Predictions are made based on the following probabilities. Then, predictions are made based on the following probabilities: ； Perform on the candidate set of the target domain Operations; among which express Candidate product number at any time This represents a given general product representation in an inductive scenario. ,exist Time and Goods The probability of interaction.
6. The general product sequence representation learning method in the recommender system according to claim 1, characterized in that, The transduction fine-tuning in step S3 includes: Fusion text representation and label representation As a representation of a commodity; predictions are based on the following probabilities: ； This represents the general sequence representation after product labeling enhancement; the parameters of the product sequence encoder are fixed; in each setting, the parameters of the hybrid expert enhancement adapter are fine-tuned using the cross-entropy loss function; after fine-tuning, predictions can be made based on the probabilities described above. This represents a given general product representation in a transduction scenario. ,exist Time and Goods The probability of interaction.