# 5.2. Compress a model

## 5.2.1. Theory

The compression of the DP model uses three techniques, tabulated inference, operator merging, and precise neighbor indexing, to improve the performance of model training and inference when the model parameters are properly trained.

For better performance, the NN inference can be replaced by tabulated function evaluations if the input of the NN is of dimension one. The idea is to approximate the output of the NN by a piece-wise polynomial fitting. The input domain (a compact domain in $$\mathbb R$$) is divided into $$L_c$$ equally spaced intervals, in which we apply a fifth-order polynomial $$g^l_m(x)$$ approximation of the $$m$$-th output component of the NN function:

$g^l_m(x) = a^l_m x^5 + b^l_m x^4 + c^l_m x^3 + d^l_m x^2 + e^l_m x + f^l_m,\quad x \in [x_l, x_{l+1}),$

where $$l=1,2,\dots,L_c$$ is the index of the intervals, $$x_1, \dots, x_{L_c}, x_{L_c+1}$$ are the endpoints of the intervals, and $$a^l_m$$, $$b^l_m$$, $$c^l_m$$, $$d^l_m$$, $$e^l_m$$, and $$f^l_m$$ are the fitting parameters. The fitting parameters can be computed by the equations below:

$a^l_m = \frac{1}{2\Delta x_l^5}[12h_{m,l}-6(y'_{m,l+1}+y'_{m,l})\Delta x_l + (y''_{m,l+1}-y''_{m,l})\Delta x_l^2],$
$b^l_m = \frac{1}{2\Delta x_l^4}[-30h_{m,l} +(14y'_{m,l+1}+16y'_{m,l})\Delta x_l + (-2y''_{m,l+1}+3y''_{m,l})\Delta x_l^2],$
$c^l_m = \frac{1}{2\Delta x_l^3}[20h_{m,l}-(8y'_{m,l+1}+12y'_{m,l})\Delta x_l + (y''_{m,l+1}-3y''_{m,l})\Delta x_l^2],$
$d^l_m = \frac{1}{2}y''_{m,l},$
$e^l_m = y_{m,l}',$
$f^l_m = y_{m,l},$

where $$\Delta x_l=x_{l+1}-x_l$$ denotes the size of the interval. $$h_{m,l}=y_{m,l+1}-y_{m,l}$$. $$y_{m,l} = y_m(x_l)$$, $$y'_{m,l} = y'_m(x_l)$$ and $$y''_{m,l} = y''_m(x_l)$$ are the value, the first-order derivative, and the second-order derivative of the $$m$$-th component of the target NN function at the interval point $$x_l$$, respectively. The first and second-order derivatives are easily calculated by the back-propagation of the NN functions.

In the standard DP model inference, taking the two-body embedding descriptor as an example, the matrix product $$(\mathcal G^i)^T \mathcal R$$ requires the transfer of the tensor $$\mathcal G^i$$ between the register and the host/device memories, which usually becomes the bottle-neck of the computation due to the relatively small memory bandwidth of the GPUs. The compressed DP model merges the matrix multiplication $$(\mathcal G^i)^T \mathcal R$$ with the tabulated inference step. More specifically, once one column of the $$(\mathcal G^i)^T$$ is evaluated, it is immediately multiplied with one row of the environment matrix in the register, and the outer product is deposited to the result of $$(\mathcal G^i)^T \mathcal R$$. By the operator merging technique, the allocation of $$\mathcal G^i$$ and the memory movement between register and host/device memories is avoided. The operator merging of the three-body embedding can be derived analogously.

The first dimension, $$N_c$$, of the environment ($$\mathcal R^i$$) and embedding ($$\mathcal G^i$$) matrices is the expected maximum number of neighbors. If the number of neighbors of an atom is smaller than $$N_c$$, the corresponding positions of the matrices are pad with zeros. In practice, if the real number of neighbors is significantly smaller than $$N_c$$, a notable operation is spent on the multiplication of padding zeros. In the compressed DP model, the number of neighbors is precisely indexed at the tabulated inference stage, further saving computational costs.1

## 5.2.2. Instructions

Once the frozen model is obtained from DeePMD-kit, we can get the neural network structure and its parameters (weights, biases, etc.) from the trained model, and compress it in the following way:

dp compress -i graph.pb -o graph-compress.pb

where -i gives the original frozen model, -o gives the compressed model. Several other command line options can be passed to dp compress, which can be checked with

\$ dp compress --help

An explanation will be provided

usage: dp compress [-h] [-v {DEBUG,3,INFO,2,WARNING,1,ERROR,0}] [-l LOG_PATH]
[-m {master,collect,workers}] [-i INPUT] [-o OUTPUT]
[-s STEP] [-e EXTRAPOLATE] [-f FREQUENCY]
[-c CHECKPOINT_FOLDER]

optional arguments:
-h, --help            show this help message and exit
-v {DEBUG,3,INFO,2,WARNING,1,ERROR,0}, --log-level {DEBUG,3,INFO,2,WARNING,1,ERROR,0}
set verbosity level by string or number, 0=ERROR,
1=WARNING, 2=INFO and 3=DEBUG (default: INFO)
-l LOG_PATH, --log-path LOG_PATH
set log file to log messages to disk, if not
specified, the logs will only be output to console
(default: None)
-m {master,collect,workers}, --mpi-log {master,collect,workers}
Set the manner of logging when running with MPI.
'master' logs only on main process, 'collect'
broadcasts logs from workers to master and 'workers'
means each process will output its own log (default:
master)
-i INPUT, --input INPUT
The original frozen model, which will be compressed by
the code (default: frozen_model.pb)
-o OUTPUT, --output OUTPUT
The compressed model (default:
frozen_model_compressed.pb)
-s STEP, --step STEP  Model compression uses fifth-order polynomials to
interpolate the embedding-net. It introduces two
tables with different step size to store the
parameters of the polynomials. The first table covers
the range of the training data, while the second table
is an extrapolation of the training data. The domain
of each table is uniformly divided by a given step
size. And the step(parameter) denotes the step size of
the first table and the second table will use 10 *
step as it's step size to save the memory. Usually the
value ranges from 0.1 to 0.001. Smaller step means
higher accuracy and bigger model size (default: 0.01)
-e EXTRAPOLATE, --extrapolate EXTRAPOLATE
The domain range of the first table is automatically
detected by the code: [d_low, d_up]. While the second
table ranges from the first table's upper
boundary(d_up) to the extrapolate(parameter) * d_up:
[d_up, extrapolate * d_up] (default: 5)
-f FREQUENCY, --frequency FREQUENCY
The frequency of tabulation overflow check(Whether the
input environment matrix overflow the first or second
table range). By default do not check the overflow
(default: -1)
-c CHECKPOINT_FOLDER, --checkpoint-folder CHECKPOINT_FOLDER
path to checkpoint folder (default: .)
-t TRAINING_SCRIPT, --training-script TRAINING_SCRIPT
The training script of the input frozen model
(default: None)

Parameter explanation

Model compression, which includes tabulating the embedding net. The table is composed of fifth-order polynomial coefficients and is assembled from two sub-tables. For model descriptor with se_e2_a type, the first sub-table takes the stride(parameter) as its uniform stride, while the second sub-table takes 10 * stride as its uniform stride; For model descriptor with se_e3 type, the first sub-table takes 10 * stride as it’s uniform stride, while the second sub-table takes 100 * stride as it’s uniform stride. The range of the first table is automatically detected by DeePMD-kit, while the second table ranges from the first table’s upper boundary(upper) to the extrapolate(parameter) * upper. Finally, we added a check frequency parameter. It indicates how often the program checks for overflow(if the input environment matrix overflows the first or second table range) during the MD inference.

Justification of model compression

Model compression, with little loss of accuracy, can greatly speed up MD inference time. According to different simulation systems and training parameters, the speedup can reach more than 10 times at both CPU and GPU devices. At the same time, model compression can greatly change memory usage, reducing as much as 20 times under the same hardware conditions.

Acceptable original model version

The model compression interface requires the version of DeePMD-kit used in the original model generation should be 2.0.0-alpha.0 or above. If one has a frozen 1.2 or 1.3 model, one can upgrade it through the dp convert-from interface. (eg: dp convert-from 1.2/1.3 -i old_frozen_model.pb -o new_frozen_model.pb)

Acceptable descriptor type

Descriptors with se_e2_a, se_e3, se_e2_r and se_atten_v2 types are supported by the model compression feature. Hybrid mixed with the above descriptors is also supported.

Available activation functions for descriptor:

• tanh

• gelu

• relu

• relu6

• softplus

• sigmoid

1

This section is built upon Jinzhe Zeng, Duo Zhang, Denghui Lu, Pinghui Mo, Zeyu Li, Yixiao Chen, Marián Rynik, Li’ang Huang, Ziyao Li, Shaochen Shi, Yingze Wang, Haotian Ye, Ping Tuo, Jiabin Yang, Ye Ding, Yifan Li, Davide Tisi, Qiyu Zeng, Han Bao, Yu Xia, Jiameng Huang, Koki Muraoka, Yibo Wang, Junhan Chang, Fengbo Yuan, Sigbjørn Løland Bore, Chun Cai, Yinnian Lin, Bo Wang, Jiayan Xu, Jia-Xin Zhu, Chenxing Luo, Yuzhi Zhang, Rhys E. A. Goodall, Wenshuo Liang, Anurag Kumar Singh, Sikai Yao, Jingchao Zhang, Renata Wentzcovitch, Jiequn Han, Jie Liu, Weile Jia, Darrin M. York, Weinan E, Roberto Car, Linfeng Zhang, Han Wang, J. Chem. Phys. 159, 054801 (2023) licensed under a Creative Commons Attribution (CC BY) license.