A method and system for pushing goods in a digital mall

Abstract

The application discloses a kind of push method and system of commodity in digital mall.The decision front anchoring state is formed according to server arrival time and response residual, the current selected commodity prefix order coding is generated, the baseline trajectory of the end selection after reservation prefix and the additional trajectory of the end selection after adding a commodity are generated, and the two trajectories are coupled by the difference of zero input and zero output differential update.In the same observation window of lock, fact response is obtained by terminal action sampling, candidate increment is trained by double correction target of frozen prediction, fact innovation is settled once according to decision unique identification, and response residual orthogonal basis is updated.The system transmits data with decision unique identification by terminal event receiving interface, model calculation node, terminal sample storage, feedback settlement processor and push gateway adapter, selects commodity position by position, and submits final commodity sequence within byte and wake-up budget.

Description

Technical Field

[0001] This invention relates to the fields of terminal event processing, deep learning, and network message push technology, specifically to a method and system for pushing products in a digital mall. Background Technology

[0002] The product push server selects products based on the terminal's historical events and sends them through the message gateway. Users may also actively interact with products even without push notifications, so responses after sending cannot be entirely attributed to push notifications. Messages are also subject to constraints such as encoded byte count, notification permissions, and network status.

[0003] In multi-product messages, adding other products after selecting one product will change the final response. Treating the final response directly as simply appending the training label of the first product will cause inconsistencies between the training and prediction actions. Filtering only delivery records further alters the sample composition. It is necessary to ensure consistency between the prediction branch, the actual sampling action, and the gateway execution, and to control the issue of historical feedback repeatedly entering the online state. Summary of the Invention

[0004] This invention uses the currently selected product prefix as a condition, compares whether the selection ends after retaining the prefix or after adding a product, obtains the corresponding fact label through termination action sampling, and generates a product sequence that can be executed by the message gateway through structured zero-difference trajectory, same-window supervision and one-time feedback settlement.

[0005] The currently selected product prefix is ​​a list of products selected sequentially during message construction; the location anchoring state is a vector fused with the pre-decision encoding and the sequential encoding of this list; the baseline trajectory represents the predicted state sequence after submitting the current prefix and ending the selection process, with an empty prefix corresponding to no message being sent; the append trajectory represents the predicted state sequence after submitting the complete list with an appended candidate. Here, the average response to the submission action is predicted, including non-delivery consequences caused by the gateway or network, not just the response under successful delivery conditions.

[0006] Termination action is the action that ends the selection immediately after maintaining the prefix or adding a candidate; candidate incremental response vector is the difference between the predicted response of the appended trajectory and the baseline trajectory in the same window; fact innovation is the error between the actual response and the actual action prediction; response residue is the sum of historical fact innovations maintained and decayed according to the decision identifier, and the response residue orthogonal basis is the set of orthogonal normalized column vectors spanned by these vectors.

[0007] Step S1: At the time of product push decision, collect terminal behavior events, historical push events, terminal network context and response residues that have been received by the server, form a causal mask according to the time of server arrival, set an attention threshold with non-negative parameters to the historical push events through the response residues, and encode the pre-decision anchoring state.

[0008] Step S2: The pre-decision anchoring state and the sequential encoding of the currently selected product prefix are merged into a position anchoring state. The baseline trajectory for the selection ends after submitting the currently selected product prefix is ​​recursively submitted from the position anchoring state. A differential trajectory for the selection ends after adding candidate products is generated through encoding difference initialization and zero-input zero-output differential update. The baseline trajectory and the differential trajectory are added together to obtain the additional trajectory.

[0009] Step S3: At the decision moment, the response observation duration and the observation window that prohibits further push are predetermined. The commodity-level predicted responses of the baseline trajectory and the additional trajectory are aggregated according to the same observation window and the same time weight. The candidate incremental response vector of the additional trajectory relative to the baseline trajectory is calculated.

[0010] Step S4: Record the input before decision-making, the prefix of the currently selected product, the set of remaining candidate products and the probability of action allocation at the selected product selection position. Extract the termination action to retain the prefix of the currently selected product or add a candidate product. After the termination action is executed, it is prohibited to add more products. Record the complete observation window response, including the non-delivery record, to form a termination action training sample.

[0011] Step S5: Use the actual response of the training sample of the termination action to supervise the trajectory corresponding to the actual action, construct a dual correction target based on the frozen trajectory prediction value and the action allocation probability, train the candidate incremental response vector within the common support range of the action, and add amplitude constraints to the differential trajectory.

[0012] Step S6: For the decision of the completed observation window, calculate the fact innovation between the actual response and the trajectory prediction value corresponding to the actual action, write the fact innovation into the response residue once according to the unique identifier of the decision, and perform threshold orthogonalization based on the historical fact innovation after time decay to obtain the response residue orthogonal basis;

[0013] Step S7: Calculate the candidate incremental response vector of the remaining candidate products and its new direction outside the response residual orthogonal basis under the currently selected product prefix. Select candidate products according to the ratio of task weighted increment and new direction. After each addition, re-execute steps S2 and S3 until the stop action is selected or the single message product quantity limit is reached.

[0014] Step S8: Pre-encode each candidate product to be added using the push gateway's formal encoding rules, determine the set of actionable actions within the single message byte limit, the current period's remaining sending byte budget, and the remaining wake-up budget, submit the final product sequence as a single product message, record the actual sending and delivery results, execute the observation window, and submit the complete feedback to step S6 to update the response residue for the next decision.

[0015] This invention also provides a product push system for a digital marketplace. The system includes a terminal event receiving interface, a model computing node, a termination sample storage, a feedback settlement processor, and a push gateway adapter. The terminal event receiving interface transmits terminal behavior events, historical push events, and terminal network context to the model computing node at the server arrival time. The model computing node reads the response residue and response residue orthogonal basis maintained by the feedback settlement processor, and performs dual-trajectory prediction, candidate incremental calculation, and position-by-position selection. The push gateway adapter constrains actionable actions with the gateway's formal encoding results and returns the actual sending and delivery results. The termination sample storage associates the pre-decision input, action allocation probability, final product sequence, and complete observation window response with a unique decision identifier. The feedback settlement processor updates the response residue and response residue orthogonal basis only once after the complete settlement of the observation window and transmits the updated result back to the model computing node. Each component transmits data records with unique decision identifiers through the business server's internal data bus or an authenticated service interface.

[0016] Termination action sampling ensures that fact labels correspond to a clear final message list, avoiding the need to supervise single append branches with responses from subsequent appends. Prefix order encoding makes candidate responses change with the selected items and their order. Zero-input, zero-output differential updates ensure that the two trajectories are strictly consistent under stopping conditions.

[0017] At the decision-making moment, historical inputs are frozen, and window locking ensures that training and online prediction use the same response range. The contribution table is updated by unique identifiers to prevent duplicate accumulation caused by multiple backhauls from the same window; gateway precoding excludes actions that cannot be sent in advance. The above is a mechanism analysis and does not represent actual measured improvements. Attached Figure Description

[0018] Figure 1 This is a flowchart of the overall product push method of the present invention. Detailed Implementation

[0019] Example 1 is executed by the e-commerce business server, model inference server, push gateway, and terminal event collection service. Before training, the sampling and observation lock in step S4 is deployed to collect complete window data. During training, steps S1 to S3 and step S5 are executed, and step S6 only reads the historical contributions that have been settled at that time. After going live, the model parameters are fixed, and selection and sending are performed according to steps S1 to S3, S7, and S8. Step S6 is executed after the window ends. The step number indicates the function correspondence, and training data collection does not require a pre-trained model.

[0020] In the system implementation, the terminal event receiving interface is deployed between the terminal event acquisition service and the e-commerce business server. After completing the unique event identifier verification, server arrival time writing, and field integrity check, it transmits the event record to the model computing node. The model computing node can be implemented by a model inference server with a processor and memory. The memory stores model parameters, response residues, and response residue orthogonal bases. The processor executes steps S1 to S3 and step S7. The push gateway adapter is deployed between the e-commerce business server and the push gateway. It calls the same serialization encoder as the formal sender to execute step S8 and writes the sending receipt along with the decision unique identifier to the termination sample memory. The termination sample memory uses a record table with the decision unique identifier as the primary key, ensuring that the input, allocation probability, final sequence, receipt, and window response of a decision can only form one replaceable record. The feedback settlement processor listens for the window completion identifier, executes step S6, updates the fact innovation corresponding to the decision by overwriting, and then transmits the aggregated response residues and the reconstructed response residue orthogonal bases to the model computing node. Thus, model computation, message execution, and feedback settlement form a traceable data loop through a unique decision identifier, rather than a loose collection of modules corresponding to names.

[0021] All times and durations below are in seconds, byte budgets are in bytes, and model vectors are dimensionless real vectors. `t` represents the decision timestamp, `l` and `q` represent historical event positions, `m` represents the current selected position, `i` represents the candidate item, and `k` represents the prediction time slice. Square brackets are only used for grouping or constructing vectors; semicolons or the symbol `∥` indicate concatenation by coordinates; commas separate function parameters. The transpose symbol `T` indicates row and column interchange; adjacent matrices indicate matrix multiplication; adjacent scalars and vectors indicate coordinate-wise scaling; `⊙` indicates element-wise multiplication of vectors of the same dimension. Addition and subtraction are operations of the same dimension; division by a scalar is coordinate-wise division; scalar functions are calculated coordinate-wise when applied to vectors.

[0022] Step S1: Establish Pre-Decision Anchoring State. This step establishes a shared pre-decision input for all candidates to prevent late events from being written back. Data is sorted by server arrival time and deduplicated; the historical event window length is determined by the deployment configuration. Context c includes terminal foreground / background identifiers, notification permission identifiers, network reachability identifiers, round-trip latency, remaining bytes, and wake-up budget; numerical fields are normalized using a fixed scale based on the training set, and missing fields are padded with zeros and marked with a missing identifier. The dimension of c is denoted as... .

[0023] Specifically, in step S1, the vector mapping the historical push event q to the response space is denoted as... ,Will The squared projection of the second norm onto the residual orthogonal basis Q is denoted as . ,Will The squared norm of the positive smoothness Recorded as The coincidence ratio of the response directions is determined by the following formula. Gated input and residual threshold :

[0024]

[0025]

[0026]

[0027] The slash indicates that the numerator is divided by the denominator. To prevent positive numbers with a denominator of zero, e is the natural constant. It means that the base is e and the expression is... This refers to the power operation of the exponent. and Adjacent signs indicate scalar multiplication, while the minus sign indicates scalar subtraction. Identify historical push events. To The value obtained by executing the logic gate function. and Adjacent elements represent scalar multiplication. and For training parameters, the subscript q represents the sequence number of the historical push event, and the subscript g indicates that the parameter is used for residual gating. The variables on the left are determined by the calculation results on the right.

[0028]

[0029] Where σ is the logic gate function, exp is the natural exponential function, and x is any real number; the output is strictly between zero and one, and is subsequently used for gating and response probability. The natural logarithm is denoted as ln, and its domain is positive.

[0030]

[0031] Where v is dimensional vector, Let L be the dimension of the input vector, which is a 2-norm. Coordinate indices used only for L2 norm operations. For the vector v, the first Σ represents a coordinate, where Σ indicates the coordinates. From 1 to Summation, where √ denotes the non-negative square root, and N(v) denotes the L2 norm of vector v; (v) represents the norm of the sum of the absolute values ​​of the coordinates of vector v.

[0032]

[0033] Where Norm is the layer normalization calculated based on individual vector coordinates. The arithmetic mean of all coordinates. The squared value is the average of the squared deviations of the coordinates relative to the mean; the mean is broadcast to all coordinates during subtraction. g and b are trainable scaling and bias in the same dimension, with independent parameters for each Norm call; To keep the number a constant positive, this embodiment uses one part per million to prevent division with zero variance.

[0034]

[0035] in, One-dimensional time encoding, For time difference used only for time encoding, To maintain a fixed positive time scale, this embodiment uses one second, with the maximum value being the larger one. When a terminal clock malfunction causes a negative time difference, the threshold is set to zero, and an error flag is appended to the event object input.

[0036]

[0037] in, The time when the event occurred. The server arrival time; Embedded for event types, For event object embedding and exception identifiers, respectively have and The category embeddings are a trainable table read from the category index; unknown categories use a dedicated index. for OK, add Add a matrix with two columns. for dimensional event vector, This is for hiding dimensions. All projection matrices and biases are learned during training.

[0038] Let J represent the identity matrix with rows and columns of d; the indicator function is denoted separately as J, taking the value 1 if the condition is true and 0 otherwise, and it does not share the same sign as the identity matrix. Let L be the number of visible events in the history window, and the mask... exist The value is zero when it is earlier than t and q is not greater than l, and negative infinity is taken otherwise. In the implementation, invisible key positions are deleted first and then normalized, without actually calculating the logarithm of zero. A dedicated empty event is used for inserting empty history, so L is at least one.

[0039]

[0040] Where Q is an orthogonal basis of the responses settled before the decision, having three rows and at most three columns; For three lines The event projection matrix of the column. The response direction coincidence ratio is between zero and one; Q is the spacetime numerator set to zero. The superscript T only indicates transpose, and the square acts on the L2 norm result.

[0041]

[0042] in, Determined according to the aforementioned gating input formula This is a binary identifier for historical push events; non-push events are represented by zero. and It is a trainable scalar. e The exponentiation ensures that the overlap coefficient is positive, and the push event threshold does not increase when the overlap increases; the non-push event threshold is always one. It is a scalar, unlike the internal vector parameter g of Norm.

[0043]

[0044] in, Attention score, without positional double subscripts. It still indicates the arrival time; and All An L2 matrix, mapping lookup and key, the transpose of which multiplies the inner product scalar. The threshold must be strictly positive to compute ln; invisible positions are directly excluded.

[0045]

[0046] in, To normalize attention weights, This index is used only for summing historically visible positions; the summation only includes visible positions, and the maximum valid score is subtracted first during the actual calculation to prevent exponent overflow. The weights are non-negative and sum to one.

[0047]

[0048] in, for Order-value mapping matrix, for The historical dimension indicates that the sum of the residuals represents two terms of the same dimension.

[0049]

[0050] in, The three-dimensional response residue at decision time t; for OK, add Add a three-column matrix, for A three-row matrix Let z be a third-order identity matrix. Pre-decision anchoring state: the first term integrates history and context, the second term projects directions not covered by history; both are... Dimension, output and proceed to step S2.

[0051] Step S2: Generate prefix-conditional dual trajectories. The effect of a candidate depends on the already selected items and their order; therefore, the actual prefix is ​​explicitly encoded, instead of simply accumulating candidate increments to replace the item list. The t index for the same decision is omitted below. P represents the ordered prefix, C represents the frozen set of candidate items, and the candidate encoding... for The dimension is obtained by linearly mapping product identifiers, category embeddings, and price and inventory features normalized according to a fixed training scale, with missing values ​​masked; silent encoding. It is fixed as the zero vector. It refers to the configured product coding dimension.

[0052] Specifically, in step S2, the product code of candidate product i is... Through mapping matrix Transformed and Appended Action Vectors Add them together and multiply by the candidate product identifier function. The initial candidate action difference state is obtained. The stop action corresponds to The value is zero; the difference-preserving gate for the k-th prediction time slice is denoted as... Repair the door Determined to be 1 minus And update the candidate action difference state as follows:

[0053]

[0054] Where ζ is the time decay vector, The difference between the outputs of the differential update network under candidate code difference input and zero code difference input is represented by the superscript `upd`, which indicates the differential update result. The symbol `⊙` represents element-wise multiplication of vectors of the same dimension, and the plus sign represents coordinate-wise addition of two vectors of the same dimension. The subscript `k - 1` represents the previous prediction time slice. The output difference is obtained by subtracting the output corresponding to the zero code difference input from the output corresponding to the candidate code difference input coordinate-wise. The subscript `i` represents the candidate item, the subscript `0` represents the initial state, and the subscript `k` represents the current prediction time slice. The subscript 'e' in the matrix indicates that the matrix is ​​used for product code mapping. The subscript 'a' in the text indicates an additional action. The subscript i in the code indicates that the indicator value is taken for candidate product i, and the difference state on the left is updated by the calculation result on the right.

[0055]

[0056] in, This is a position index used only for prefix order recursion, with values ​​ranging from one to the prefix length. The first in the prefix One product, for Dimensional order state; for 1-th order matrix, for OK Column matrix for Dimensional bias. tanh is the hyperbolic tangent, mapping the input to -1 to 1 coordinate by coordinate; This is an empty prefix state.

[0057]

[0058] Where |P| represents the length of the list. for Double the line Column matrix This indicates the anchoring status. If the prefixes are the same, the same baseline recursion is shared; if the prefixes change, the calculation is recalculated.

[0059]

[0060] in, As the baseline initial state, These are candidate difference initial states; for OK Column matrix for An action vector is added to the dimension, while the stopping action vector is fixed at zero. A candidate identifier i of zero represents stopping. Both initial states are... The difference is strictly zero when the time stops.

[0061]

[0062] Where G is the baseline drift unit and ψ is the two-dimensional time code. for OK, add Add a two-column matrix, for 1-th order matrix, and for Dimensional bias. s is Dimensional input status.

[0063]

[0064] Where k ranges from 1 to K, and K is the total number of preset time slices. Take the ratio of the time slice number to K and the slice length to... The length of the two-dimensional vector composed of the ratio of the two vectors is denoted as Δ. This is the baseline state.

[0065]

[0066] Where Diff is the differential update unit; , and for 1-th order matrix, for OK Column matrix for OK Column matrix for Dimensional bias. Both computations share all matrices; when When both e and 'e' are zero, the output is strictly zero, without relying on additional penalties to approximate the value.

[0067]

[0068] in, for 3D difference preservation gate, for line, double add Add a two-column matrix, for Dimensional bias.

[0069]

[0070] in, for The dimensional trainable decay parameter, ζ, is A dimensional decay vector; the exponent is calculated coordinate by coordinate, with each coordinate between zero and one. ζ is shared by all time slices when the slice length is fixed.

[0071]

[0072] in, for In the dimensional difference update result, upd is the update label, not the exponentiation.

[0073]

[0074] in, Subtract 1 from each coordinate The resulting gate complement vector. All multiplication and addition results are... Dimension. With the stop encoding at zero and the initial difference at zero, it can be inferred that the difference for all time slices is strictly zero.

[0075]

[0076] in, This represents the state where the selection ends immediately after adding item i. The baseline branch represents submission P, and the append branch represents the list after submission P with item i appended; both include the average result of the natural delivery mechanism, without multiplying the delivery probability again into the output. The parameter set is collectively referred to as θ, including all encoding, gating, and output parameters in this embodiment; This refers to calculating all steps in S1. This step involves recursion throughout, without setting up any unexpanded black-box networks.

[0077] Step S3: Aggregate candidate responses within the same window. The observation duration H is fixed before action selection, and KΔ is used. The scheduling lock prevents further product pushes to the terminal from t to t+H. The window start includes t, and the end does not include t+H. Events fall into a unique time slice based on the server arrival time. Both training and prediction use these K time slices, and delivery delay is part of the submitted action response. When an observation lock violation occurs, the entire sample is not used for model training, the online rollback stops, and shorter labels are not fitted to the full window prediction.

[0078] Specifically, in step S3, the baseline aggregation response at the end of the selection process after retaining the currently selected product prefix P is determined by the following formula. Additional aggregation response when ending the selection after adding candidate item i and candidate incremental response vector :

[0079]

[0080]

[0081]

[0082] Where P represents the currently selected product prefix, i represents the candidate product, k represents the prediction time slice, K represents the total number of prediction time slices, 0 indicates the baseline branch where the selection ends after retaining the currently selected product prefix, and 1 indicates the append branch where the selection ends after adding candidate products. The baseline trajectory outputs the product-level response for candidate product i in the k-th prediction time slice. To append the product-level response of the trajectory output for candidate product i in the k-th prediction time slice, Σ represents the summation over each prediction time slice with index k from 1 to K. The non-negative normalized time weights for the k-th prediction time slice. Adjacent to the corresponding product-level response indicates that the response vector is weighted coordinate by coordinate using a scalar. The minus sign indicates that the aggregated response vector is subtracted coordinate by coordinate from the baseline aggregated response vector. The variable on the left is determined by the weighted sum or vector difference on the right.

[0083]

[0084] Where R is the three-dimensional response output head, and the three coordinates are the predicted probabilities of browsing, adding to cart, and purchasing at least once within the time slice; for OK, add Column matrix For three lines Column matrix for Dimensional bias, This is a 3D offset. Both branches query the same product code.

[0085]

[0086] Wherein, β is the non-negative time discount configuration, selected through the validation set; The non-negative normalized time weights sum to one. This is an index used only for predicting time-slice normalized summation.

[0087]

[0088] in, Indicates the baseline status of the response output header R. and candidate product codes The subsequent output of the 3D product-level response, To preserve the 3D aggregate response prediction of product i at time P, the number zero is the baseline branch label instead of the power.

[0089]

[0090] in, This indicates that the response output header R has received an append status. and candidate product codes The subsequent output of the 3D product-level response, To end the selection of the three-dimensional aggregated response prediction after adding product i, the number one is to add the branch label, not the successful delivery condition.

[0091]

[0092] in, The output is a three-dimensional candidate incremental response, with coordinates ranging from -1 to 1. It measures the marginal change in the response of item i itself and does not claim to represent the total revenue of the entire marketplace or the full spillover effect of other items. The output is used for training and scoring in step S7.

[0093] Step S4: Construct training samples for termination actions. Within the controlled sampling traffic that meets the conditions of frequency control, notification permissions, and gateway budget, a prefix is ​​first generated, and a sampling position is selected before action extraction. This decision generates only one termination sample at that position. The prefix can be generated by the current policy; a complete ordered list and candidate set are recorded. Random actions are only extracted from the set of actionable actions verified in step S8, while stop actions are always retained. The final list is submitted immediately after appending, and no further selection of another item is performed.

[0094] Specifically, in step S4, the pre-decision history, terminal network context, currently selected product prefix, remaining candidate product set, and budget composition conditions are recorded as X. The stop action and the candidate actions confirmed as feasible by the gateway pre-coding are combined into a set of feasible actions A, and the probability of terminating the action allocation is recorded according to the following formula:

[0095]

[0096]

[0097] Where Pr represents conditional probability operation, and the vertical line indicates that Z is the actual extraction action when the condition record X is given. The probability of drawing action 'a' is not less than the lower bound of the positive probability. The symbol ∈ indicates that action a belongs to the set of possible actions A, Σ indicates that the probability distribution of all actions in A is summed and the summation result is 1. The product selection ends immediately after the termination action of adding candidate products is extracted. The subscript a represents the action in the set of possible actions, and the subscript min represents the positive lower bound of the action probability. The value on the left is determined by the conditional probability or the summation result on the right.

[0098]

[0099] Where X represents the complete record of pre-decision history, context, prefixes, candidate sets, and budget; A represents the set of actionable actions, including zero-stopping actions; and Z represents the actual termination actions. The probability is directly recorded by the sampler; Pr represents the conditional probability; the vertical bar indicates a given condition; and ∈ indicates belonging to a set. (Restrictions) At least a positive lower bound Furthermore, the number of actions multiplied by this lower bound does not exceed one. Different prefixes do not need to come from the same user, but they must be within the supported range of the target deployment prefix distribution.

[0100]

[0101] in, This is a three-dimensional binary fact vector, where each coordinate represents whether product i has been viewed, added to cart, or purchased in the k-th segment. Labels are aggregated with equal weights. Associations are completed based on terminal, product identifier, event unique identifier, and server time. Zero is only assigned when the entire window for collecting service heartbeats and server-side order reconciliation confirmation is complete; missing data cannot be used as a zero label. The repeated mapping function Ψ is no longer used here; labels and predictions are in the same three-dimensional space from the beginning.

[0102] A stop with an empty prefix indicates no transmission; a stop with a non-empty prefix indicates prefix submission. Both groups save transmission failures and undelivered results. D is only used as a binary execution log, without filtering out undelivered samples or as a processing probability multiplier. This predicts the overall effect of the submission action. Old logs with only successful transmission records cannot be directly used as this training set; if there are no probability records or missing stop comparisons, samples are used to fill in the gaps. Users are grouped for training and validation, and the same user cannot cross folds; historical state replay only reads the settlement feedback at that time.

[0103] Missing samples are not labeled. If the missing rate differs significantly between actions, the missing samples should be repaired before training; having only complete samples does not automatically guarantee the absence of missing sample bias. Causal explanations are limited to the following conditions: controlled action randomization, effective observation locks, complete logs, and consistent training and deployment execution mechanisms. Regions that do not meet these conditions are only allowed to conservatively stop.

[0104] Step S5: Train with fact-based supervision and cross-fitting. First, pre-train the response network using labels corresponding to actual actions. Stopped samples supervise the baseline of all remaining candidates, while appended samples only supervise the appended branches of the appended candidates.

[0105] Specifically, in step S5, the additional probability correction residual is determined by the following formula. Stopping probability correction residual and dual correction target :

[0106]

[0107]

[0108]

[0109] in, and These are the actual values ​​for extracting additional candidate item i and the indication value for stopping the action, respectively. The curly braces specify that the coordinate-by-coordinate subtraction of the two response vectors should be performed first. and The curly brace indicates that the resulting vector is scaled coordinate-by-coordinate using the indicator value, and the slash indicates that the resulting vector is divided coordinate-by-coordinate by the corresponding action assignment probability. or , For actual product-level response, and The auxiliary response model is separated from the target sample by user and frozen. The plus and minus signs in the dual calibration target both indicate the coordinate operation of the same-dimensional response vector. The subscript i indicates the candidate product, the subscript 0 indicates the stop action, the superscript 1 indicates the append branch, the superscript 0 indicates the baseline branch, the superscript ref indicates that it comes from the frozen auxiliary response model, and the superscript dr indicates the dual calibration result. The left-hand variable is determined by the calibration operation result on the right.

[0110]

[0111] in, The mean square error is three dimensions. The predicted response is given by the input loss function. The factual response to the input loss function is divided by the average of the three coordinates.

[0112]

[0113] in, In order to stop the actual loss, Remove the candidate set after the stop action from the set of possible actions. It is the number of its elements. Records with a value of zero will not be included in model training; training will stop immediately.

[0114]

[0115] in, In order to claim additional actual losses, for and The sum of both labels includes the actual consequences of non-delivery, without additional multiplication by D.

[0116] For the actual final non-empty list S, perform the same baseline recursion with S as a prefix, using the product index. Query each item in S and aggregate them in the same window, denoted as . The computation predicts the responses that submit the complete list for use in step S6; it also requires direct factual supervision and cannot rely solely on training on the remaining candidates.

[0117]

[0118] in, For the full list of response losses, This is a product index used only for iterating through the final list S. and All responses are in three dimensions within the same window. When S is empty, this item is defined as zero and division is skipped.

[0119] Divide the training users into at least two disjoint folds. For each target fold, pre-train and freeze the auxiliary response model using the other folds, and compute baseline predictions at the target fold. Additional forecasts "Freeze" means that gradients are not backpropagated when calculating correction labels, while "ref" only indicates that the prediction comes from the frozen auxiliary model.

[0120]

[0121] in, To add probability correction residuals, they are only non-zero when i is actually chosen; To record the probability, at least There is no division by zero.

[0122]

[0123] in, To correct residuals for stopping probabilities. No fact label needs to be created for an action if no corresponding action is selected.

[0124]

[0125] in, The goal is a dual correction for freezing. Under controlled randomization and with correct probabilities, the probability-weighted residuals in the conditional expectation compensate for auxiliary prediction errors; a single correction label can extend beyond the negative one to one interval without being mistakenly treated as probability clipping. Statistical correction does not equate to recovering the unexpected future for each user.

[0126]

[0127] in, The candidate incremental supervision loss uses the same H and ω as the target. This is calculated only for samples where both the stop and the candidate have common support and complete data.

[0128]

[0129] in, It represents the average difference magnitude for each candidate, each time slice, and each hidden coordinate. It controls for excessive latent offsets and does not claim to guarantee that the latent state is uniquely identifiable.

[0130]

[0131] in, This is a sample index used only for the training batch. This refers to the number of samples within a batch. and The non-negative loss weight is determined using the user isolation validation set. To achieve the batch average total loss, the target network θ is updated via backpropagation, while the auxiliary ref prediction remains fixed. This is used during the pre-training of the auxiliary model. and The differential amplitude term does not use calibration labels that have not yet been constructed. The original constant-zero constraint and repeated baseline loss are no longer listed separately. Since the random assignment probability is known, the bias network, which is not necessary, is no longer used for training.

[0132] Step S6: Settle factual innovations based on unique identifiers. Historical prediction biases provide feedback for the next round regarding aspects not yet explained by the model. For the final sequence S, calculate the baseline prediction after submitting the complete S using the prefix encoding from step S2 upon transmission, and for each item in S, query the output header using the same complete sequence status query, freezing it as... This avoids comparing the prediction with the complete sequence feedback when the prefix is ​​shorter. Empty messages do not contribute to the push.

[0133] Specifically, in step S6, the decision unique identifier n and its final product sequence are considered. Determine factual innovation according to the following formula and current response residue :

[0134]

[0135]

[0136] Among them, the vertical lines enclose This represents the number of items in the final item sequence. The superscript -1 indicates taking the reciprocal of the item quantity, and Σ indicates taking the reciprocal of the item quantity. All goods in Sum of all settled decisions in the process. For the final product sequence of decision n, the actual response of product i within the complete observation window is represented by the minus sign within the curly braces, indicating that the aggregated response vector is subtracted from the actual response vector coordinate by coordinate. This is the aggregated response output for product i after submitting the complete final product sequence. This is the set of unique identifiers for decisions that have been settled before the current time. The time decay coefficient is determined based on the current time, the end time of the window, and the positive decay time scale. and The adjacent representation scales the fact innovation vector coordinate-wise using the time decay coefficient, where the subscript n represents the unique identifier of the decision, the subscript i represents the product in the final product sequence, and the subscript t represents the current decision time. The two subscripts represent the current decision time and the settled decision identifier, respectively, and the left vector is determined by the average or weighted summation result of the right vector.

[0137]

[0138] Where n is a unique identifier for the non-empty final message decision. This is the product sequence for this message. Innovation for three-dimensional average facts; The full observation window for this decision is used. It is only generated during complete settlement; even if the delivery is not completed, the prediction error is calculated based on the original action. This indicates that after submitting the complete list, the baseline aggregate prediction for product i is retrieved.

[0139]

[0140] in, The time decay coefficient used for factual innovation in decision n at the current decision time t. Let n be the end time of the observation window for decision n. The positive decay timescale is determined by the validation set.

[0141]

[0142] in, This is the set of decision identifiers that have been settled up to the current decision time t and are still within the retention period. Each decision identifier has only one row; late events within the same window are recalculated and replaced after deduplication. No additional line is added. As a residual of the three-dimensional historical response, the unsettled window does not inject the complete predicted increment in advance.

[0143] When constructing Q, read the decayed fact innovation vector of decision n in order of contribution time from newest to oldest. Q starts as a three-row, zero-column empty matrix. For each Perform projection elimination twice consecutively; the first pass orthogonally transforms the working vector. Pick The second input is the result of the first input.

[0144]

[0145] The left arrow indicates that the result on the right is assigned to... The columns of Q are normalized; the two passes are used to reduce floating-point errors. The projection is zero when Q is empty.

[0146]

[0147] Square brackets indicate appending column-wise. Only in N( Exceeding a fixed positive threshold And the number of columns is less than the configuration limit. Execute at the time. The integer is between one and three, determined by the validation set. The denominator is not incremented. Thresholds are used to prevent division by zero. Q is reconstructed after contribution expires, without retaining failed directions; an online verification is performed to ensure that the transpose of Q multiplied by Q approaches the corresponding identity matrix. If the new direction space is saturated, step S7 still retains the basic score.

[0148] Step S7: Position-by-position scoring. In each round, the trajectory is regenerated from the true ordered prefix. The order of the prefix is ​​recursively encoded into the candidate value, and an interference value already included in the current prediction is no longer repeatedly deducted.

[0149] Specifically, in step S7, the candidate incremental response vector is... The new direction is obtained by projecting it onto the residual orthogonal basis Q of the response. The proportion of the new direction is determined by the following formula. Direction adjustment factor and the position selection value of candidate product i :

[0150]

[0151]

[0152]

[0153] in, For new directions The 2-norm, for L2 norm plus positive smoothing , slashes indicate Divide by , and Adjacent represents scalar multiplication, w is a non-negative task weight vector, and the superscript T indicates that w is transposed. The transposed w is then multiplied by... Adjacent means the inner product of two vectors of the same dimension, and the resulting inner product is... Adjacent elements represent scalar multiplication. The non-negative adjustment coefficient is the value used to select the position of the stop action. The value is zero, where the subscript P represents the currently selected product prefix, and the subscript i represents the candidate product. The subscript d in the formula indicates that the denominator is composed of the candidate incremental response vector. Confirmed, the subscript ν indicates that the parameter is used for adding direction adjustment, the subscript 0 indicates that the action is stopped, and the variable on the left is determined by the ratio on the right, scalar addition, or inner product multiplication.

[0154]

[0155] in, The proportion of newly added candidate directions other than the historical error directions, which is between zero and one; The scale is zero when the vector is zero. When Q is empty, it is treated as an empty projection. This scale measures the directional difference relative to the history of model error and is not claimed to be a direct measurement of user repeating interest.

[0156]

[0157] Where w is the three-dimensional non-negative task weight, with the coordinates summed to one, corresponding to browsing, adding to cart, and purchasing, and is fixed before deployment; The non-negative adjustment coefficient is selected through the validation set. For candidate scores, To stop scoring. Multiplication maintains the sign of the increment to prevent negative increment items from being rewarded as positive simply because of directional novelty.

[0158] Select the action with the highest score from the feasible set. If there is a tie, stop the selection process and then determine the tie order among candidates based on the product identifier. After appending, recalculate using the true new prefix, without writing feedback that has not yet occurred into r or Q. The process ends when the maximum number of messages per message is reached, there are no positive score candidates, or there is a lack of training support. This method is a position-wise greedy method and does not claim to be globally optimal. The final overall prefix prediction is used in step S6.

[0159] Step S8: Pre-encoding, transmission, and feedback. In this embodiment, at most one message is sent at a time to ensure that the final execution list matches the training of the termination action. Each proposed additional action is first pre-encoded into a complete list, with a byte budget including the title, identifier, product field, and protocol encapsulation, before proceeding to the S7 contention; a consistency check is then performed during transmission.

[0160] Specifically, in step S8, the actual number of encoded bytes of the currently selected product prefix P is determined by the following formula. And the conditions for sending:

[0161]

[0162]

[0163]

[0164]

[0165] in, This indicates that the push gateway performs byte counting after encoding the complete message to be sent according to the formal serialization encoding rules. `min` represents the number of bytes counted from the beginning of the message. and The smaller value is selected from the two values. The sign ≤ indicates that the value on the left is not greater than the value on the right. The vertical bar enclosing P indicates the number of products in the currently selected product prefix. The sign ≥ indicates that the value on the left is not less than the value on the right. Maximum number of bytes per message. Budget for remaining bytes to send in the current period. This is the maximum number of items that can be purchased in a single message. For the remaining wake-up budget, the subscript P represents the currently selected product prefix, the subscript msg represents a single message, the subscript rem represents the remaining amount in the current period, and the subscript max represents the configuration limit. This indicates that formal encoding will be performed on the currently selected product prefix, and the value on the left is determined by the byte count result on the right.

[0166]

[0167] in, This indicates that the push gateway encodes the complete message to be sent, formed by the prefix P of the currently selected product, according to the formal serialization encoding rules. This represents the byte count of the encoded result. This represents the actual number of encoded bytes for a non-empty message; an empty prefix corresponds to no transmission, the execution cost is defined as zero, and an empty message is not submitted.

[0168]

[0169] in, This refers to the maximum number of bytes allowed per message from the gateway. Budget for the remaining bytes in the current frequency control cycle. This is the maximum number of items that can be purchased in a single message. For the remaining wake-up budget, Indicates from and The smaller value is taken. The budget comes from the service execution and is atomically deducted upon sending. Each message is accounted for as one wake-up budget, without a guarantee of the actual number of wake-ups by the operating system. Network retries are included in the byte budget; no retries are made if the budget is exceeded.

[0170] If changes to gateway parameters cause the final list validation to fail, a feasible set is regenerated and recalculated without bypassing the budget. Submissions or network failures retain actual actions and failure records, execute observation locks, and collect natural responses. After observation, settlement is based on the unique decision identifier; notifications are only logged and cannot be copied to individual product responses.

[0171] Taking candidate coffee beans, filter paper, and thermos as an example: First, compare sending nothing versus sending only one item. After selecting coffee beans, re-compare sending only coffee beans versus sending coffee beans with added filter paper, or adding a thermos. If adding filter paper is sampled at a certain position during training sampling, only coffee beans and filter paper are ultimately submitted, without adding a thermos; only then does this fact window correspond to the corresponding termination branch. Before sending, check the total number of bytes in the complete message; after the window ends, recalculate and settle the prediction error for the complete list. This example only illustrates the process and does not represent experimental results.

[0172] The implementation parameters can be set to 64 hidden dimensions, 32 product coding dimensions, or 12 time slices; these are only configurable implementation examples and not optimal values ​​based on actual testing. The observation duration, training sample size, and minimum action coverage requirements should be determined in conjunction with the frequency control window allowed by business requirements and the validation set error. Without sufficient termination sampling data, this model cannot claim to have incremental recognition capabilities.

Claims

1. A method for pushing products in a digital marketplace, characterized in that, include: Step S1: At the time of product push decision, collect terminal behavior events, historical push events, terminal network context and response residues that have been received by the server, form a causal mask according to the time of server arrival, set an attention threshold with non-negative parameters to the historical push events through the response residues, and encode the pre-decision anchoring state. Step S2: The pre-decision anchoring state and the sequential encoding of the currently selected product prefix are merged into a position anchoring state. The baseline trajectory for the selection ends after submitting the currently selected product prefix is ​​recursively submitted from the position anchoring state. A differential trajectory for the selection ends after adding candidate products is generated through encoding difference initialization and zero-input zero-output differential update. The baseline trajectory and the differential trajectory are added together to obtain the additional trajectory. Step S3: At the decision moment, the response observation duration and the observation window that prohibits further push are predetermined. The commodity-level predicted responses of the baseline trajectory and the additional trajectory are aggregated according to the same observation window and the same time weight. The candidate incremental response vector of the additional trajectory relative to the baseline trajectory is calculated. Step S4: Record the input before decision-making, the prefix of the currently selected product, the set of remaining candidate products and the probability of action allocation at the selected product selection position. Extract the termination action to retain the prefix of the currently selected product or add a candidate product. After the termination action is executed, it is prohibited to add more products. Record the complete observation window response, including the non-delivery record, to form a termination action training sample. Step S5: Use the actual response of the training sample of the termination action to supervise the trajectory corresponding to the actual action, construct a dual correction target based on the frozen trajectory prediction value and the action allocation probability, train the candidate incremental response vector within the common support range of the action, and add amplitude constraints to the differential trajectory. Step S6: For the decision of the completed observation window, calculate the fact innovation between the actual response and the trajectory prediction value corresponding to the actual action, write the fact innovation into the response residue once according to the unique identifier of the decision, and perform threshold orthogonalization based on the historical fact innovation after time decay to obtain the response residue orthogonal basis; Step S7: Calculate the candidate incremental response vector of the remaining candidate products and its new direction outside the response residual orthogonal basis under the currently selected product prefix. Select candidate products according to the ratio of task weighted increment and new direction. After each addition, re-execute steps S2 and S3 until the stop action is selected or the single message product quantity limit is reached. Step S8: Pre-encode each candidate product to be added using the push gateway's formal encoding rules, determine the set of actionable actions within the single message byte limit, the current period's remaining sending byte budget, and the remaining wake-up budget, submit the final product sequence as a single product message, record the actual sending and delivery results, execute the observation window, and submit the complete feedback to step S6 to update the response residue for the next decision.

2. The method for pushing products in a digital mall according to claim 1, characterized in that, In step S1, the vector that maps the historical push event q to the response space is denoted as... ,Will The squared projection of the second norm onto the residual orthogonal basis Q is denoted as . ,Will L2 norm squared plus positive smoothness Recorded as The coincidence ratio of the response directions is determined by the following formula. Gated input and residual threshold : ； ； ； The slash indicates that the numerator is divided by the denominator. To prevent positive numbers with a denominator of zero, e is the natural constant. It means that the base is e and the expression is... This refers to the power operation of the exponent. and Adjacent signs indicate scalar multiplication, while the minus sign indicates scalar subtraction. Identify historical push events. To The value obtained by executing the logic gate function. and Adjacent elements represent scalar multiplication. and For training parameters, the subscript q represents the sequence number of the historical push event, and the subscript g indicates that the parameter is used for residual gating. The variables on the left are determined by the calculation results on the right.

3. The method for pushing products in a digital mall according to claim 2, characterized in that, In step S2, the product code of candidate product i is... Through mapping matrix Transformed and Appended Action Vectors Add them together and multiply by the candidate product identifier function. The initial candidate action difference state is obtained. The stop action corresponds to The value is zero; the difference-preserving gate for the k-th prediction time slice is denoted as... Repair the door Determined to be 1 minus And update the candidate action difference state as follows: ； Where ζ is the time decay vector, The difference between the outputs of the differential update network under candidate code difference input and zero code difference input is represented by the superscript `upd`, which indicates the differential update result. The symbol `⊙` represents element-wise multiplication of vectors of the same dimension, and the plus sign represents coordinate-wise addition of two vectors of the same dimension. The subscript `k - 1` represents the previous prediction time slice. The output difference is obtained by subtracting the output corresponding to the zero code difference input from the output corresponding to the candidate code difference input coordinate-wise. The subscript `i` represents the candidate item, the subscript `0` represents the initial state, and the subscript `k` represents the current prediction time slice. The subscript 'e' in the matrix indicates that the matrix is ​​used for product code mapping. The subscript 'a' in the text indicates an additional action. The subscript i in the code indicates that the indicator value is taken for candidate product i, and the difference state on the left is updated by the calculation result on the right.

4. The method for pushing products in a digital mall according to claim 3, characterized in that, In step S3, the baseline aggregation response at the end of the selection process after retaining the currently selected product prefix P is determined by the following formula: Additional aggregation response when ending the selection after adding candidate item i and candidate incremental response vector : ； ； ； Where P represents the currently selected product prefix, i represents the candidate product, k represents the prediction time slice, K represents the total number of prediction time slices, 0 indicates the baseline branch where the selection ends after retaining the currently selected product prefix, and 1 indicates the append branch where the selection ends after adding candidate products. The baseline trajectory outputs the product-level response for candidate product i in the k-th prediction time slice. To append the product-level response of the trajectory output for candidate product i in the k-th prediction time slice, Σ represents the summation over each prediction time slice with index k from 1 to K. The non-negative normalized time weight for the k-th prediction time slice. Adjacent to the corresponding product-level response indicates that the response vector is weighted coordinate by coordinate using a scalar. The minus sign indicates that the aggregated response vector is subtracted coordinate by coordinate from the baseline aggregated response vector. The variable on the left is determined by the weighted sum or vector difference on the right.

5. The method for pushing products in a digital mall according to claim 4, characterized in that, In step S4, the pre-decision history, terminal network context, currently selected product prefix, remaining candidate product set, and budget composition conditions are recorded as X. The stop action and the candidate actions confirmed as feasible by gateway precoding are combined into a feasible action set A, and the termination action allocation probability is recorded according to the following formula: ； ； Where Pr represents conditional probability operation, and the vertical line indicates that Z is the actual extraction action when the condition record X is given. The probability of drawing action 'a' is not less than the lower bound of the positive probability. The symbol ∈ indicates that action a belongs to the set of possible actions A, Σ indicates that the probability distribution of all actions in A is summed and the summation result is 1. The product selection ends immediately after the termination action of adding candidate products is extracted. The subscript a represents the action in the set of possible actions, and the subscript min represents the positive lower bound of the action probability. The value on the left is determined by the conditional probability or the summation result on the right.

6. The method for pushing products in a digital mall according to claim 5, characterized in that, In step S5, the additional probability correction residual is determined according to the following formula. Stopping probability correction residual and dual correction target : ； ； ； in, and These are the actual values ​​for extracting additional candidate item i and the indication value for stopping the action, respectively. The curly braces specify that the coordinate-by-coordinate subtraction of the two response vectors should be performed first. and The curly brace indicates that the resulting vector is scaled coordinate-by-coordinate using the indicator value, and the slash indicates that the resulting vector is divided coordinate-by-coordinate by the corresponding action assignment probability. or , For actual product-level response, and The auxiliary response model is separated from the target sample by user and frozen. The plus and minus signs in the dual calibration target both indicate the coordinate operation of the same-dimensional response vector. The subscript i indicates the candidate product, the subscript 0 indicates the stop action, the superscript 1 indicates the append branch, the superscript 0 indicates the baseline branch, the superscript ref indicates that it comes from the frozen auxiliary response model, and the superscript dr indicates the dual calibration result. The left-hand variable is determined by the calibration operation result on the right.

7. The method for pushing products in a digital mall according to claim 6, characterized in that, In step S6, the decision unique identifier n and its final product sequence are considered. Determine factual innovation according to the formula below and current response residue : ； ； Among them, the vertical lines surround This represents the number of items in the final item sequence. The superscript -1 indicates taking the reciprocal of the item quantity, and Σ indicates taking the reciprocal of the item quantity. All goods in Sum of all settled decisions in the process. For the final product sequence of decision n, the actual response of product i within the complete observation window is represented by the minus sign within the curly braces, indicating that the aggregated response vector is subtracted from the actual response vector coordinate by coordinate. This is the aggregated response output for product i after submitting the complete final product sequence. This is the set of unique identifiers for decisions that have been settled before the current time. The time decay coefficient is determined based on the current time, the end time of the window, and the positive decay time scale. and The adjacent representation scales the fact innovation vector coordinate-wise using the time decay coefficient, where the subscript n represents the unique identifier of the decision, the subscript i represents the product in the final product sequence, and the subscript t represents the current decision time. The two subscripts represent the current decision time and the settled decision identifier, respectively, and the left vector is determined by the average or weighted summation result of the right vector.

8. The method for pushing products in a digital mall according to claim 7, characterized in that, In step S7, the candidate incremental response vector The new direction is obtained by projecting it onto the residual orthogonal basis Q of the response. The proportion of the new direction is determined by the following formula. Direction adjustment factor and the position selection value of candidate product i : ； ； ； in, For new directions The 2-norm, for L2 norm plus positive smoothing , slashes indicate Divide by , and Adjacent represents scalar multiplication, w is a non-negative task weight vector, and the superscript T indicates that w is transposed. The transposed w is then multiplied by... Adjacent means the inner product of two vectors of the same dimension, and the resulting inner product is... Adjacent elements represent scalar multiplication. The non-negative adjustment coefficient is the value used to select the position of the stop action. The value is zero, where the subscript P represents the currently selected product prefix, and the subscript i represents the candidate product. The subscript d in the formula indicates that the denominator is composed of the candidate incremental response vector. Confirmed, the subscript ν indicates that the parameter is used for adding direction adjustment, the subscript 0 indicates that the action is stopped, and the variable on the left is determined by the ratio on the right, scalar addition, or inner product multiplication.

9. The method for pushing products in a digital mall according to claim 8, characterized in that, In step S8, the actual number of encoded bytes of the currently selected product prefix P is determined by the following formula. And the conditions for sending: ； ≤ ； |P|≤ ； ≥1； in, This indicates that the push gateway performs byte counting after encoding the complete message to be sent according to the formal serialization encoding rules. `min` represents the number of bytes counted from the beginning of the message. and The smaller value is selected from the two values. The sign ≤ indicates that the value on the left is not greater than the value on the right. The vertical bar enclosing P indicates the number of products in the currently selected product prefix. The sign ≥ indicates that the value on the left is not less than the value on the right. Maximum number of bytes per message. Budget for remaining bytes to send in the current period. This is the maximum number of items that can be purchased in a single message. For the remaining wake-up budget, the subscript P represents the currently selected product prefix, the subscript msg represents a single message, the subscript rem represents the remaining amount in the current period, and the subscript max represents the configuration limit. This indicates that formal encoding will be performed on the currently selected product prefix, and the value on the left is determined by the byte count result on the right.

10. A product recommendation system for a digital marketplace, characterized in that, The system includes a terminal event receiving interface, a model computing node, a termination sample storage, a feedback settlement processor, and a push gateway adapter. The terminal event receiving interface receives terminal behavior events, historical push events, and terminal network context according to the server arrival time, and sends the receiving results to the model computing node. The model computing node reads the response residue and response residue orthogonal basis, forms the pre-decision anchoring state and the position anchoring state, recursively calculates the baseline trajectory and the append trajectory, calculates the candidate incremental response vector and the addition direction, and generates the proposed append candidate product for each position. The push gateway adapter performs formal encoding on the complete product sequence containing the proposed append candidate products, submits the final product sequence that meets the byte budget and wake-up budget to the push gateway, and writes the actual sending result and delivery result into the termination sample storage. The termination sample storage associates the pre-decision input, termination action probability allocation, final product sequence and complete observation window response with the decision unique identifier, and provides termination action training samples to the model computing node; The feedback settlement processor reads the complete observation window response and the trajectory prediction value output by the model calculation node for the actual action, updates the response residue and response residue orthogonal basis once according to the decision unique identifier, and transmits the update result to the model calculation node.

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