Image classification method based on online continuous learning

Through parameter importance balance and double-layer reinitialization replication weight algorithm, the problems of prediction deviation and resource consumption in online continuous learning are solved, and the model is efficiently adapted and stable on dynamic non-stationary tasks are achieved.

CN119723156AActive Publication Date: 2025-03-28TONGJI UNIV
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Patent Information

Application Number
CN202411688556.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-25
Publication Date
2025-03-28
Estimated Expiration
2044-11-25

AI Technical Summary

Technical Problem

The existing online continuous learning method based on empirical playback has the problem of significant model prediction deviation after training in dynamic non-stationary tasks, and the parameter isolation method increases storage consumption when the task changes, making it not suitable for online continuous learning.

Method used

A parameter importance balance (PIB) method is proposed to evaluate parameter importance by monitoring parameter changes, using Manhattan distance and minimum-maximum normalization techniques, and dynamically adjust the gradient descent coefficient. At the same time, a double-layer reinitialization replication weight algorithm was introduced to simulate human memory systems, effectively utilize knowledge through short-term and long-term memory pools to prevent catastrophic forgetting.

Benefits of technology

The prediction deviation of the model during task transfer is effectively corrected, the model's adaptability and stability between different tasks is improved, resource consumption is reduced, and real-time training and optimization are achieved.

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Abstract

The invention relates to an image classification method based on online continuous learning, and the method comprises the following steps: training a deep neural network for each task, evaluating the parameter importance in the network after the training of each task is completed, and determining an importance coefficient; performing real-time gradient modification in continuous network training according to the importance coefficient; initializing the weight of the deep neural network during the training of the next task by using a double-layer reinitialization copy weight algorithm; repeating the above steps for continuous online learning until deep neural network training of all tasks is completed; and inputting different types of images needing to be verified into the trained deep neural network, and carrying out single-head image classification to obtain an image classification result. Compared with the prior art, the method has the advantages that the stability and accuracy of the network can be kept during task transfer, and the training is efficient.
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Description

Technical Field

[0001] The present invention relates to the technical field of image classification, and in particular to an image classification method based on online continuous learning. Background Art

[0002] Image classification is a key computer vision task that is widely used in fields such as face recognition, medical image analysis, and automatic label generation. With the rapid development of deep learning technology, neural network-based models have shown superior performance in processing complex data sets. These models can effectively extract features from large-scale data and accurately classify them. However, traditional models often need to be retrained when faced with new categories, which leads to inefficiency and waste of resources. To solve this problem, image classification models based on continuous learning have emerged, which can maintain effective memory of existing knowledge while continuously receiving new data. This progress enables image classification tasks to adapt more flexibly to dynamically changing environments, promoting further development in the field of computer vision.

[0003] Deep neural networks (DNNs) are widely used in the field of artificial intelligence due to their excellent learning ability. However, when processing non-stationary sequence data, a phenomenon commonly known as catastrophic forgetting is found, that is, the model forgets previously learned knowledge after acquiring new experience. This phenomenon is essentially the stability-plasticity dilemma faced by DNNs. In order to alleviate the stability-plasticity dilemma and obtain human-like learning ability, continuous learning methods have been widely studied. Especially in more realistic online environments, sequence training data is presented as a dynamic one-time data stream. In this case, the model not only needs to face the stability-plasticity dilemma caused by catastrophic forgetting, but also needs to deal with the accuracy-efficiency dilemma. Existing effective methods mainly adopt the strategy of replaying past samples or representations. These methods are generally referred to as experience replay-based online continuous learning methods (ER-based OCL). In recent years, research on methods is considered to be crucial to enable DNNs to continuously acquire new knowledge in dynamic and non-stationary sequence tasks. However, existing ER-based OCL methods still face the problem of significant prediction bias of post-training models.

[0004] Some existing continuous learning methods related to parameter isolation show that different parts of the neural network have different importance in correcting prediction biases for different tasks. In these parameter isolation methods, masks are usually used to fix or adjust parameters that are closely related to the previous learning task. These methods are effective in improving the overall accuracy of the model. However, they require different model parameters to be assigned to each task, which will continuously increase storage consumption as the tasks change, and are therefore not suitable for dynamic non-stationary sequence tasks faced by online continuous learning. Online continuous learning methods based on experience replay are believed to be able to correct prediction biases while keeping resource consumption relatively low. Researchers have made various improvements to ER-based OCL, such as sample selection methods and loss function correction methods. However, few studies on ER-based OCL focus on the impact of independent parameter changes in different parts of the model during training, which may further reduce prediction biases on dynamic non-stationary tasks. Summary of the invention

[0005] The purpose of the present invention is to provide an image classification method based on online continuous learning to optimize the prediction deviation of deep neural networks on dynamic non-stationary tasks.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] The present invention first proposes a parameter importance balancing (PIB) method, which updates all model parameters and output layer parameters at different stages, thereby correcting the prediction biases of all neurons and output layer neurons respectively. First, in order to evaluate the importance of each independent parameter in retaining the previous task knowledge, the present invention monitors the changes of parameters in each online continuous learning (OCL) task. The correlation between parameters and tasks is quantified by using Manhattan distance measurement before and after task transfer, supplemented by the minimum-maximum normalization technique. In order to reduce time and space overhead, only the maximum value of each parameter's real-time importance update is retained during the entire training process.

[0008] Using this importance measure, the present invention designs a unique gradient descent coefficient for each parameter and combines it with asymmetric cross entropy. This method forces the network to retain parameters that are more important to the previous task during back propagation, while quickly updating parameters with less impact, thereby correcting the prediction bias caused by individual parameter updates during task transfer.

[0009] The present invention draws on the idea of ​​the human memory system and proposes a new method, called a double-layer reinitialization copy weight algorithm, to solve the problem of catastrophic forgetting caused by the rapid update of the output classifier: In the human memory system, there are three different storage mechanisms: sensory memory, short-term memory, and long-term memory. These forms of memory interact with each other to overcome forgetting and consolidate knowledge. In the double-layer reinitialization copy weight algorithm, the parameters obtained by gradient descent are regarded as sensory memory, and the first layer of consolidation transfers knowledge to the short-term memory pool. Then, the knowledge is further consolidated into the long-term memory pool according to the defined probability. Finally, the knowledge stored in the long-term memory pool is used for prediction. This double-layer consolidation strategy can correct the prediction bias caused by the output classifier.

[0010] The online continuous learning method proposed in this invention needs to achieve the following points:

[0011] (1) Parameter Importance Evaluation Algorithm: This algorithm is responsible for monitoring and evaluating the importance of each parameter in different tasks. It uses Manhattan distance to calculate parameter changes and performs minimum-maximum normalization to quantify the relevance of the parameter to the task.

[0012] (2) Real-time gradient modification algorithm: This algorithm dynamically adjusts the gradient descent coefficient according to the evaluated parameter importance to ensure that the network retains important parameters during backpropagation, while allowing minor parameters to be updated quickly to reduce prediction bias.

[0013] (3) Double-layer reinitialization copy weight algorithm: This algorithm simulates the storage mechanism of human memory, regards the parameters obtained by gradient descent as sensory memory, and transfers knowledge to the short-term and long-term memory pools through the first layer of consolidation and defined probability, thereby effectively utilizing the knowledge stored in the long-term memory during prediction and preventing catastrophic forgetting.

[0014] In summary, the present invention provides an image classification method based on online continuous learning, comprising the following steps:

[0015] Step S1: train a deep neural network for each task, evaluate the importance of parameters in the network after each task training is completed, and determine the importance coefficient;

[0016] Step S2: performing real-time gradient modification in continuous network training according to the importance coefficient;

[0017] Step S3: Initialize the weights of the deep neural network for the next task training using a double-layer reinitialization copy weight algorithm;

[0018] Step S4: Repeat steps S1 to S3 for continuous online learning until the deep neural network training of all tasks is completed;

[0019] Step S5: Input the different categories of images that need to be verified into the trained deep neural network, perform single-head image classification, and obtain image classification results.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) This paper improves the traditional continuous learning method and proposes a parameter importance evaluation mechanism. By monitoring the changes of parameters in different tasks, the update strategy of parameters can be dynamically adjusted. This innovation can effectively correct the prediction bias and improve the adaptability of the model between different tasks.

[0022] (2) The present invention introduces a real-time gradient modification algorithm that dynamically adjusts the gradient descent coefficient according to the importance of the parameters, ensuring that the parameters important to the previous task are better retained during the back-propagation process while quickly updating the secondary parameters, thereby maintaining the stability and accuracy of the model when facing task transfer.

[0023] (3) The present invention proposes a two-layer reinitialization copy weight algorithm that simulates the human memory system and adopts a two-layer consolidation strategy to effectively solve the catastrophic forgetting problem of the output classifier by transferring knowledge from sensory memory to short-term and long-term memory pools, thereby improving the overall performance of the model.

[0024] (4) The present invention supports online training and optimization, simplifies the training process of the entire continuous learning process, saves the required time, realizes real-time training verification, and the model is practical and efficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of the method of the present invention;

[0026] Figure 2 It is a schematic diagram of the image classification process of the present invention;

[0027] Figure 3 Schematic diagram of parameter importance evaluation and real-time gradient modification method;

[0028] Figure 4 Schematic diagram of the process of reinitializing the copy weight algorithm for the two layers. DETAILED DESCRIPTION

[0029] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0030] like Figure 1As shown, this embodiment provides an image classification method based on online continuous learning, which mainly includes a parameter importance evaluation method, a real-time gradient modification method, and a double-layer reinitialization copy weight method. The three together constitute a continuous learning deep neural network training process, which can be applied to image classification, such as Figure 2 Specifically, the method comprises the following steps:

[0031] Step S1: Train a deep neural network for each task, evaluate the importance of parameters in the network after each task training is completed, and determine the importance coefficient.

[0032] Specifically, the Manhattan distance of parameter per task change is used to represent the importance of the parameter to the task, and two normalizations are performed to retain the relative change of the parameter and limit the range of change of the parameter importance, including the following steps:

[0033] Step S11: After each task k (k>1) is trained, the optimized network parameters θ are recorded by capturing the state of the deep neural network when the sample of task k+1 first appears. k The network parameters include network weights {w {1,k} ,…,w {m,k} ,…,w {M,k}}, where M represents the total number of parameters.

[0034] Step S12: In order to measure the change of a specific weight, the Manhattan distance between the network weight parameter after the current task training is completed and the network weight parameter after the previous task training is completed is calculated:

[0035] δ {m,k} =|w {m,k} -w {m,k-1} |,

[0036] Among them, δ {m,k} represents the weight w between tasks k and k-1 {m,k} Manhattan distance.

[0037] Step S13: performing mean-based normalization and minimum-maximum normalization processing on the Manhattan distance to obtain an importance measure of each parameter on the current task k.

[0038] Due to the change of network model, δ {m,k} The magnitudes of δ may be significantly different. To address this problem, we can {m,k} Normalize to reduce the influence of their original scale and keep only relative changes:

[0039]

[0040] Among them, δ ′m,k Denotes δ m,k This normalization ensures that the impact of each parameter change is proportional to its relative importance, rather than being directly affected by its absolute scale. In this way, the present invention effectively mitigates the variability introduced by different network architectures, thereby achieving a more consistent assessment of parameter importance across tasks.

[0041] The changes between neurons can show large differences. For example, if one neuron has a change of 10 and another neuron has a change of 1×10 -6 , the former may vary by several orders of magnitude more than the latter. This difference does not mean that the first neuron is more important than the second neuron in task k. To solve this problem, the present invention applies min-max normalization to limit the importance of each neuron to a standardized range. k ={δ { ′ 1,k} ,…,δ { ′ M,k}} represents the set of Manhattan distances after mean-based normalization, i.e., the set of parameter changes. Then, the importance measure of each parameter associated with task k is given by the following min-max normalization:

[0042]

[0043] Among them, I m,k represents the importance measure of parameter m related to task k, and α and β are hyperparameters that define the importance range of task-related parameters. m,k is normalized to the range [α,β]. Usually, I m,k The default setting is 1, which means that when I m,k =1, the importance of parameter m in task k is considered to be average. Therefore, the value of the interval [α, β] also determines the criterion for measuring the importance of parameters. When α>1, it is assumed that all parameters are considered important for any task and should be retained to some extent. On the contrary, when β<1, it is assumed that all parameters are considered unimportant for any task, which indicates that these parameters should be encouraged to update faster, which is obviously unrealistic. Therefore, when choosing the values ​​of α and β, α<1, β>1 are usually set.

[0044] By applying the above approach, a task-dependent importance measure can be derived for each parameter of the network over all observed tasks k.

[0045] Step S14: Determine the importance coefficient based on the principle that the deep neural network maintains the maximum task-related importance measure of each parameter throughout the continuous training process.

[0046] In order to ensure that the parameter importance measure can consistently reflect its relevance and reduce computational and storage overhead, the present invention maintains the maximum task-related importance of each parameter throughout the training process and obtains the importance coefficient:

[0047]

[0048] Among them, I m represents the importance coefficient of parameter m in all previous tasks and can be calculated in real time during training. t Indicates the current task.

[0049] Step S2: performing real-time gradient modification in continuous network training according to the importance coefficient.

[0050] This embodiment adopts a method of directly modifying the neuron gradients in the neural network training, and incorporates the parameter importance information into the training process to alleviate catastrophic forgetting and retain the knowledge of previous tasks.

[0051] The core idea of ​​parameter importance is to prioritize parameters that are critical to the learned task. To this end, after performing stochastic gradient descent (SGD) at each training time step t, the gradient of the parameter is adjusted according to the parameter's importance coefficient. Specifically, for each parameter m, its gradient is denoted by g m,t , and the parameter importance coefficient I m As a correction factor, the gradient is corrected using the correction factor:

[0052]

[0053] Among them, g ′ m,t represents the gradient of the parameter m at time step t after adjustment, taking into account the importance of the parameter. This modification ensures that the parameters with higher importance are updated more cautiously, thereby preserving their contribution to the previous task.

[0054] Deep neural networks use the corrected gradient {g ′ 1,t ,…,g ′ M,t}, which effectively incorporates parameter importance information into the training process. This approach helps manage the trade-off between learning new tasks and retaining knowledge of old tasks, ultimately improving the model's ability to adapt to new tasks without forgetting.

[0055] Step S3: Use the double-layer reinitialization copy weight algorithm to initialize the deep neural network weights for the next task training to solve the problem of too fast update of output classifier parameters.

[0056] The two-layer reinitialization copy weight algorithm is applied to the deep neural network after each training task in the learning process. It consists of two layers, where the first layer simulates the transformation of sensory memory into short-term memory. The weights assigned to the first layer are positively correlated with the strength of the memory stimulus, which is measured by the proportion of such samples in the current memory and the proportion of such samples in the past memory; during this process, the human brain naturally undergoes forgetting, a mechanism designed to prioritize the retention of more important knowledge. The second layer simulates the transformation of short-term memory into long-term memory. The weights assigned to the second process are weakly positively correlated with the strength of the memory stimulus, so the square root function is used for modeling.

[0057] Specifically, the two-layer reinitialization replication weight algorithm performs the following steps:

[0058] S31: First, the sensory memory comes from the knowledge acquired during the training process, that is, the model parameters obtained by gradient descent. The mean shift technique can simply normalize the model parameters of the output classification layer to keep its scale within a certain range and highlight the characteristics of a single class. Therefore, this technique is called a simulation of sensory memory. The sensory memory of the output classifier is defined as the parameter weight defined for each class after each round of training minus the mean of the weights of all classes that appeared in this round, that is:

[0059]

[0060] in, represents the network's sensory memory for class j at time step t, ω j,t represents the jth parameter of the output classification layer at time step t, S t Represents the set of sample labels input to the network at time step t. It is worth noting that the mapping of the output layer parameters to each category is determined by the nature of the softmax activation function. The softmax function connected to the last linear layer converts the output layer parameters into the classification probability of each category.

[0061] S32: In the complementary memory system, the hippocampus is responsible for converting sensory memory into short-term memory by selectively processing certain information. The first layer of the two-layer reinitialization copy weight algorithm simulates this process of the hippocampus. When a sensory memory is received, the two-layer reinitialization copy weight algorithm randomly selects one of the following two actions to perform:

[0062] 1) Merge current sensory memory with existing short-term memory;

[0063] 2) retaining previous short-term memories and not processing current sensory memories;

[0064] The short-term memory of the network for class j at time step t is calculated as follows

[0065]

[0066] Among them, ∈ is a random variable uniformly distributed in the interval [0,1], p is a hyperparameter, which represents the probability that the network converts sensory memory into short-term memory, represents the short-term memory retention coefficient of category j at time step t, which is calculated as:

[0067]

[0068] Among them, P j,t represents the number of times category j appears at time step t during network training, U j,t Represents the number of occurrences of category j in the label set.

[0069] S33: The neocortex is responsible for converting short-term memories into long-term memories, and the more frequently a class is reviewed, the more its memory is consolidated. The second layer of the two-layer reinitialization copy weights algorithm simulates this process of the neocortex by fusing short-term memories with existing long-term memories according to a specified retention ratio.

[0070] The long-term memory of the network for class j at time step t is calculated as follows

[0071]

[0072] in, represents the long-term memory retention coefficient of category j at time step t, which is calculated as:

[0073]

[0074] Step S4: Repeat steps S1 to S3 for continuous online learning until the deep neural network training of all tasks is completed.

[0075] Through the first three steps and combined with the asymmetric cross entropy loss function, the loss function of the deep neural network in continuous training is constructed as follows:

[0076]

[0077] in, represents the cross entropy loss function, and denote the cross entropy loss of the data stream and the data obtained from the memory buffer, respectively. and represents the subset of training samples at time step t, represents the categories encountered so far, Refers to the current training category.

[0078] Step S5: Input the different categories of images that need to be verified into the trained deep neural network, perform single-head image classification, and obtain image classification results.

[0079] According to experimental results, the present invention can still maintain a certain image classification accuracy in the class incremental continuous learning scenario with the emergence of new categories.

[0080] This example applies the method to the CIFAR-10 dataset and compares it with some classic methods in online continuous learning (ER, iCaRL, MIR, DER++, ER-ACE, AR1*). The results are shown in Table 1 below (M represents the number of samples in the replay memory pool, ACC represents the accuracy of the method (the larger the better), and FR represents the forgetting rate of the method (the smaller the better).

[0081] Table 1 Comparison of experimental results

[0082]

[0083]

[0084] In the experiment on CIFAR-10 in the standard OCL scenario, different memory buffer sizes have a significant impact on the performance indicators. The iid method reveals the upper limit of the learning accuracy of the network model on this dataset (in the absence of the forgetting problem). In the scenarios of M=20, M=100 and M=500, the present invention shows a significant accuracy advantage over other baseline methods, and the average accuracy is improved by 39.2% compared with the ER method. In addition, the present invention can further reduce the FR index based on ER-ACE and AR1*, and has the lowest FR index in the M=20 and M=100 settings, which proves that the present invention has better performance in effectively consolidating the memory of past knowledge.

[0085] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. An image classification method based on online continuous learning, characterized in that: The following steps are involved: Step S1: train a deep neural network for each task, evaluate the importance of parameters in the network after each task training is completed, and determine the importance coefficient; Step S2: performing real-time gradient modification in continuous network training according to the importance coefficient; Step S3: Initialize the weights of the deep neural network for the next task training using a double-layer reinitialization copy weight algorithm; Step S4: Repeat steps S1 to S3 for continuous online learning until the deep neural network training of all tasks is completed; Step S5: Input the different categories of images that need to be verified into the trained deep neural network, perform single-head image classification, and obtain image classification results.

2. The image classification method based on online continuous learning according to claim 1, characterized in that: The step S1 comprises the following steps: Step S11: After each task k (k>1) is trained, the optimized network parameters θ are recorded by capturing the state of the deep neural network when the sample of task k+1 first appears. k The network parameters include network weights {w {1,k} ,…,w {m,k} ,…,w {M,k} }, where M represents the total number of parameters; Step S12: Calculate the Manhattan distance between the network weight parameters after the current task training is completed and the network weight parameters after the previous task training is completed; Step S13: performing mean-based normalization processing and minimum-maximum normalization processing on the Manhattan distance to obtain an importance measure of each parameter on the current task k; Step S14: Determine the importance coefficient based on the principle that the deep neural network maintains the maximum task-related importance measure of each parameter throughout the continuous training process.

3. The image classification method based on online continuous learning according to claim 2 is characterized in that: The calculation method of the Manhattan distance is: δ {m,k} =|w {m,k} -w {m,k-1} | Among them, δ {m,k} represents the weight w between tasks k and k-1 {m,k} Manhattan distance.

4. The image classification method based on online continuous learning according to claim 3 is characterized in that: The mean-based normalization process is expressed as: Among them, δ′ m,k Denotes δ m,k The mean normalized value of .

5. The image classification method based on online continuous learning according to claim 4, characterized in that: The minimum-maximum normalization process is expressed as: Among them, I m,k represents the importance measure of parameter m related to task k, V k ={δ′ {1,k} ,…,δ′ {M,k} } represents the set of Manhattan distances after mean-based normalization, and α and β are hyperparameters that define the range of task-related parameter importance.

6. The image classification method based on online continuous learning according to claim 5, characterized in that: The importance coefficient is expressed as: Among them, I m represents the importance coefficient of parameter m in all previous tasks, k t Indicates the current task.

7. The image classification method based on online continuous learning according to claim 1, characterized in that: The step S2 is specifically as follows: for each parameter m, its gradient is recorded as g m,t , and the parameter importance coefficient I m As a correction factor, the gradient is corrected using the correction factor: Among them, g′ m,t represents the gradient after adjusting the parameter m at time step t; Deep neural networks use the corrected gradient {g′ 1,t ,…,g′ M,t } is updated, where M represents the total number of parameters.

8. The image classification method based on online continuous learning according to claim 1, characterized in that: The double-layer reinitialization replication weight algorithm includes two layers, wherein the first layer simulates the transformation of sensory memory into short-term memory, and the weight assigned to the first layer is positively correlated with the intensity of the memory stimulus, and the intensity of the memory stimulus is measured by the proportion of such samples appearing in the current memory and the proportion of such samples appearing in the past memory; the second layer simulates the transformation of short-term memory into long-term memory, and the weight assigned to the second process is weakly positively correlated with the intensity of the memory stimulus, and is modeled using a square root function.

9. The image classification method based on online continuous learning according to claim 8, characterized in that: The two-layer reinitialization replication weight algorithm performs the following steps: S31: The sensory memory of the output classifier is defined as the parameter weight defined for each class after each round of training minus the mean of the weights of all classes appearing in this round, that is: in, represents the network's sensory memory for class j at time step t, ω j,t represents the jth parameter of the output classification layer at time step t, S t Represents the set of sample labels input to the network at time step t; S32: The first layer of the two-layer reinitialization copy weight algorithm simulates the hippocampal process. When a sensory memory is received, the two-layer reinitialization copy weight algorithm randomly selects one of the following two actions to perform: 1) Merge current sensory memory with existing short-term memory; 2) retaining previous short-term memories and not processing current sensory memories; The short-term memory of the network for class j at time step t is calculated as follows Among them, ∈ is a random variable uniformly distributed in the interval [0,1], p is a hyperparameter, which represents the probability that the network converts sensory memory into short-term memory, represents the short-term memory retention coefficient of category j at time step t, which is calculated as: Among them, P j,t represents the number of times category j appears at time step t during network training, U j,t Represents the number of occurrences of category j in the label set; S33: the second layer of the two-layer reinitialization copy weight algorithm simulates the neocortical process by fusing the short-term memory with the existing long-term memory according to the specified retention ratio; The long-term memory of the network for class j at time step t is calculated as follows in, represents the long-term memory retention coefficient of category j at time step t, which is calculated as:

10. The image classification method based on online continuous learning according to claim 1, characterized in that: The loss function of the deep neural network in continuous training is expressed as: in, represents the cross entropy loss function, and denote the cross entropy loss of the data stream and the data obtained from the memory buffer, respectively. and represents the subset of training samples at time step t, represents the categories encountered so far, Refers to the current training category.

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