1. Introduction
 Aiming at the shortcomings of traditional RNN and LSTM demand forecasting models that cannot handle the problem of multiple feature sequences, we propose a demand forecasting model based on ConvLSTM. It can extend the onedimensional input LSTM to a multidimensional input model. Through the expansion of FCLSTM, a convolution structure is added during state transition, such that the network can capture the spatial characteristics of the data while dealing with timing issues.
 According to the problem of centralized machine learning modeling, regarding the inability to directly share and exchange demand forecastrelated data between ecommerce enterprises, we introduce the framework of Federated Learning, such that ecommerce companies of the same type can indirectly achieve the goal of demand information sharing modeling through Horizontal Federated Learning, under the premise that private data is not available locally, thus avoiding the leakage of private data.
 Experimental results on a large number of real data sets show that, compared with benchmark experiments, our proposed method improves the accuracy of the ecommerce enterprise demand prediction model while avoiding the leakage of private data, and the bullwhip effect value is even greater—close to the target value of 1—effectively alleviating the bullwhip effect of the entire supply chain system on demand forecasting.
2. Literature Review
2.1. Federated Learning
2.2. Ecommerce Enterprise Demand Forecasting
2.3. LSTM
3. Method and Results
3.1. Preliminary Knowledge and Definition
3.1.1. Typical Horizontal Federated Learning
3.1.2. Neural Network Based on TimeSeries
3.2. Design of ECommerce Enterprise Demand Forecasting Method Based on HFConvLSTM
3.2.1. ECommerce Enterprise Demand Forecasting Model Based on ConvLSTM
3.2.2. ECommerce Enterprise Demand Forecasting Model Based on HFConvLSTM
Algorithm 1 BackPropagation of ConvLSTM based on Federated Averaging. 

3.3. Experimental Design and Analysis
3.3.1. Data Set
3.3.2. Data PreProcessing and Data Set Segmentation
3.3.3. Comparison of Algorithms
3.3.4. Evaluation Index
3.3.5. Experimental Setup
3.3.6. Display and Analysis of Experimental Results
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Symbol  Meaning 

k  Participant Index 
${D}_{k}$  Data set owned by participants 
${M}_{k}^{t}$  Participant k’s local model in round t 
${M}^{t}$  Global model for round t 
${M}^{t+1}$  Global model for round t+1 
${\Delta}_{k}^{t}$  The gradient change of participant k in round t 
${\Delta}^{t}$  The gradient change of the global model in the t round 
${h}^{l(r,c)}$  The neuron of the ${c}^{\mathrm{th}}$ dimension in the ${r}^{\mathrm{th}}$ time step for the ${l}^{\mathrm{th}}$ layer 
${u}^{l(r,c)}$  The state of the ${c}^{\mathrm{th}}$ dimension in the ${r}^{\mathrm{th}}$ time step for the ${l}^{\mathrm{th}}$ layer 
F;I;G;O  Forget gate; Input gate; quasiunit state; Output gate 
${w}_{hx}$  Weight coefficient along the direction of the network layer 
${w}_{hh}$  Weight coefficient along the time step 
⊗  Multiply by element 
⊕  Add by element 
$\sigma $  Sigmoid activation function 
tanh  Hyperbolic tangent activation function 
Symbol  Meaning 

$Colum{n}_{name}$  Description 
$ite{m}_{skuid}$  SKU unique identification code 
$ite{m}_{firstcateid}$  Firstlevel category 
$ite{m}_{secondcateid}$  Secondlevel category 
$ite{m}_{thirdcateid}$  Threelevel category 
$bran{d}_{code}$  Brand code 
$Att{r}_{cd}$  Attribute code 
$Att{r}_{valuecd}$  Attribute value 
$D{c}_{id}$  Warehouse code 
Date  Date 
$quantity$  Sales 
$vendibility$  Inventory status at the end of the day 
$Origina{l}_{price}$  Price of the day (0–1) 
$discount$  Sales discount (0–10) 
$Promotio{n}_{type}$  Promotion form code 
$\mathit{i}\mathit{t}\mathit{e}{\mathit{m}}_{\mathit{s}\mathit{k}\mathit{u}\phantom{\rule{3.33333pt}{0ex}}\mathit{i}\mathit{d}}$  $\mathit{D}{\mathit{c}}_{\mathit{i}\mathit{d}}$  Date  vendibility  $\mathit{O}\mathit{r}\mathit{i}\mathit{g}\mathit{i}\mathit{n}\mathit{a}{\mathit{l}}_{\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}}$  discount  $\mathit{A}\mathit{t}\mathit{t}{\mathit{r}}_{\mathit{c}\mathit{d}}$  $\mathit{A}\mathit{t}\mathit{t}{\mathit{r}}_{\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\phantom{\rule{3.33333pt}{0ex}}\mathit{c}\mathit{d}}$ 
Participants (k)  1  2  3  4  5  6 

$D{c}_{id}$  0  1  2  3  4  5 
The amount of data  433,315  424,875  423,169  416,310  279,957  149,859 
Number of types of $Sk{u}_{id}$  1000  998  996  996  994  989 
Participant  LSTM  BiLSTM  ConvLSTM 

1  2425.65  2088.26  2028.26 
2  3213.35  2476.14  2022.91 
3  3147.89  3063.81  3021.43 
4  3088.95  2721.45  2519.63 
5  3256.61  2880.67  2647.27 
6  3101.05  2905.18  2853.63 
Participant  LSTM  BiLSTM  ConvLSTM 

1  0.2886  0.2173  0.2076 
2  0.2879  0.2767  0.2476 
3  0.2793  0.2749  0.2634 
4  0.2682  0.2368  0.2363 
5  0.1381  0.1348  0.1026 
6  0.0923  0.0737  0.0558 
Participant  LSTM  BiLSTM  ConvLSTM 

1  1.1391  0.8667  0.8819 
2  0.7206  1.2149  0.8096 
3  0.8725  1.1185  0.9058 
4  0.9047  1.0947  1.0847 
5  0.8672  0.8847  1.1153 
6  1.1557  0.8479  1.1327 
Participant  HFLSTM  HFBiLSTM  HFConvLSTM 

(1,2)  2264.96  2084.55  1979.45 
(1,3)  2300.45  1933.24  1836.43 
(1,4)  2088.05  1643.76  1271.07 
(1,5)  2134.68  1766.73  1677.92 
(1,6)  2127.88  1715.98  1519.06 
(2,3)  3013.89  2685.15  2448.72 
(2,4)  3046.40  2868.42  2613.40 
(2,5)  3101.35  2369.03  1797.95 
(2,6)  3087.15  2601.80  2110.68 
(3,4)  3070.60  2429.39  2355.04 
(3,5)  3013.65  2635.99  2382.52 
(3,6)  2981.24  2520.39  2312.14 
(4,5)  3038.78  2638.10  2628.71 
(4,6)  3012.31  2626.32  2432.85 
(5,6)  3088.55  2771.18  2554.51 
(1,2,3,4,5,6)  2307.93  2176.45  1890.68 
Participant  HFLSTM  HFBiLSTM  HFConvLSTM 

(1,2)  0.2166  0.1992  0.1597 
(1,3)  0.2708  0.2541  0.2172 
(1,4)  0.2235  0.1715  0.1658 
(1,5)  0.1062  0.1037  0.0833 
(1,6)  0.0847  0.0788  0.0706 
(2,3)  0.2784  0.2545  0.2296 
(2,4)  0.2594  0.2280  0.2072 
(2,5)  0.1373  0.1288  0.1062 
(2,6)  0.0758  0.0720  0.0659 
(3,4)  0.2489  0.1996  0.1561 
(3,5)  0.1198  0.1072  0.0939 
(3,6)  0.0809  0.0616  0.0472 
(4,5)  0.1171  0.0963  0.0884 
(4,6)  0.0876  0.0779  0.0618 
(5,6)  0.0824  0.0750  0.0664 
(1,2,3,4,5,6)  0.0807  0.0686  0.0655 
Participant  HFLSTM  HFBiLSTM  HFConvLSTM 

(1,2)  1.1199  0.8801  0.8938 
(1,3)  0.8967  1.0949  0.9071 
(1,4)  0.9176  0.9176  1.0623 
(1,5)  1.1095  1.0866  0.9335 
(1,6)  1.1174  1.0881  0.9202 
(2,3)  1.0957  1.0921  0.9133 
(2,4)  0.9173  0.9208  1.0630 
(2,5)  1.1135  0.8888  0.8983 
(2,6)  0.8520  0.8872  0.9039 
(3,4)  0.9226  0.9305  1.0691 
(3,5)  0.8944  1.1007  1.0957 
(3,6)  0.8904  0.9134  1.0663 
(4,5)  1.0810  0.9335  0.9482 
(4,6)  1.0836  1.0722  0.9395 
(5,6)  1.1057  0.8993  1.0907 
(1,2,3,4,5,6)  0.9117  0.9336  0.9439 
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